|MLA Citation:||Bloomfield, Louis A. "Complete Collection of Questions and Answers Home Page" How Everything Works 30 Jan 2015. 30 Jan 2015 <http://www.howeverythingworks.org/prints.php?topic=complete&page=0>.|
Falling rocks can be dangerous and, the farther they fall, the more dangerous they become. Falling raindrops, snowflakes, and leaves, however, are harmless no matter how far they fall. The distinction between those two possibilities has nothing to do with gravity, which causes all falling objects to accelerate downward at the same rate. The difference is entirely due to air resistance.
Air resistance—technically known as drag—is the downwind force an object experiences as air moves passed it. Whenever an object moves through the air, the two invariably push on one another and they exchange momentum. The object acts to drag the air along with it and the air acts to drag the object along with it, action and reaction. Those two aerodynamic forces affect the motions of the object and air, and are what distinguish falling snowflakes from falling rocks.
Two types of drag force affect falling objects: viscous drag and pressure drag. Viscous drag is the friction-like effect of having the air rub across the surface of the object. Though important to smoke and dust particles in the air, viscous drag is too weak to affect larger objects significantly.
In contrast, pressure drag is strongly affects most large objects moving through the air. It occurs when airflow traveling around the object breaks away from the object's surface before reaching the back of the object. That separated airflow leaves a turbulent wake behind the object—a pocket of air that the object is effectively dragging along with it. The wider this turbulent wake, the more air the object is dragging and the more severe the pressure drag force.
The airflow separation occurs as the airflow is attempting to travel from the sides of the object to the back of the object. At the sides, the pressure in the airflow is especially low due as it bends to arc around the sides. Bernoulli's equation is frequently invoked to help explain the low air pressure near the sides of the object. As this low-pressure air continues toward the back of the object, where the pressure is much greater, the airflow is moving into rising pressure and is pushed backward. It is decelerating.
Because of inertia, the airflow could be expected to reach the back of the object anyway. However, the air nearest the object's surface—boundary layer air—rubs on that surface and slows down. This boundary layer doesn't quite make it to the back of the object. Instead, it stops moving and consequently forms a wedge that shaves much of the airflow off of the back of the object. A turbulent wake forms and the object begins to drag that wake along with it. The airflow and object are then pushing on one another with the forces of pressure drag.
Those pressure drag forces depend on the amount of air in the wake and the speed at which the object is dragging the wake through the passing air. In general, the drag force on the object is proportional to the cross sectional area of its wake and the square of its speed through the air. The broader its wake and the faster it moves, the bigger the drag force it experiences.
We're ready to drop the penny. When we first release it at the top of the Empire State Building, it begins to accelerate downward at 9.8 meters-per-second2—the acceleration due to gravity—and starts to move downward. If no other force appeared, the penny would move according to the equations of motion for constant downward acceleration, taught in most introductory physics classes. It would continue to accelerate downward at 9.8 meters-per-second2, meaning that its downward velocity would increase steadily until the moment it hit sidewalk. At that point, it would be traveling downward at approximately 209 mph (336 km/h) and it would do some damage to the sidewalk.
That analysis, however, ignores pressure drag. Once the penny is moving downward through the air, it experiences an upward pressure drag force that affects its motion. Instead of accelerating downward in response to its weight alone, the penny now accelerates in response to the sum of two force: its downward weight and the upward drag force. The faster the penny descends through the air, the stronger the drag force becomes and the more that upward force cancels the penny's downward weight. At a certain downward velocity, the upward drag force on the penny exactly cancels the penny's weight and the penny no longer accelerates. Instead, it descends steadily at a constant velocity, its terminal velocity, no matter how much farther drops.
The penny's terminal velocity depends primarily on two things: its weight and the cross sectional area of its wake. A heavy object that leaves a narrow wake will have a large terminal velocity, while a light object that leaves a broad wake will have a small terminal velocity. Big rocks are in the first category; raindrops, snowflakes, and leaves are in the second. Where does a penny belong?
It turns out that a penny is more like a leaf than a rock. The penny tumbles as it falls and produces a broad turbulent wake. For its weight, it drags an awful lot of air behind it. As a result, it reaches terminal velocity at only about 25 mph (40 km/h). To prove that, I studied pennies fluttering about in a small vertical wind tunnel.
Whether the penny descends through stationary air or the penny hovers in rising air, the physics is the same. Of course, it's much more convenient in the laboratory to observe the hovering penny interacting with rising air. Using a fan and plastic pipe, I created a rising stream of air and inserted a penny into that airflow.
At low air speeds, the penny experiences too little upward drag force to cancel its weight. The penny therefore accelerated downward and dropped to the bottom of the wind tunnel. At high air speeds, the penny experienced such a strong upward drag force that it blew out of the wind tunnel. When the air speed was just right, the penny hovered in the wind tunnel. The air speed was then approximately 25 mph (40 km/h). That is the terminal velocity of a penny.
The penny tumbles in the rising air. It is aerodynamically unstable, meaning that it cannot maintain a fixed orientation in the passing airstream. Because the aerodynamic forces act mostly on the upstream side of the penny, they tend to twist that side of the penny downstream. Whichever side of the penny is upstream at one moment soon becomes the downstream side, and the penny tumbles. As a result of this tumbling, the penny disturbs a wide swath of air and leaves a broad turbulent wake. It experiences severe pressure drag and has a low terminal velocity.
The penny is an example of an aerodynamically blunt object—one in which the low-pressure air arcing around its sides runs into the rapidly increasing pressure behind it and separates catastrophically to form a vast wake. The opposite possibility is an aerodynamically streamlined object—one in which the increasing pressure beyond the object's sides is so gradual that the airflow never separates and no turbulent wake forms. A penny isn't streamlined, but a ballpoint pen could be.
Almost any ballpoint pen is less blunt than a penny and some pens are approximately streamlined. Moreover, pens weigh more than pennies and that fact alone favors a higher terminal velocity. With a larger downward force (weight) and a smaller upward force (drag), the pen accelerates to a much greater terminal velocity than the penny. If it is so streamlined that it leaves virtually no wake, like the aerofoil shapes typical of airplane components, it will have an extraordinarily large terminal velocity—perhaps several hundred miles per hour.
Some pens tumble, however, and that spoils their ability to slice through the air. To avoid tumbling, a pen must "weathervane"—it must experience most of its aerodynamic forces on its downstream side, behind its center of mass. Arrows and small rockets have fletching or fins to ensure that they travel point first through the air. A ballpoint pen can achieve that same point-first flight if its shape and center of mass are properly arranged.
Almost any ballpoint pen dropped into my wind tunnel plummeted to the bottom. I was unable to make the air rise fast enough to observe hovering behavior in those pens. Whether they would tend to tumble in the open air was difficult to determine because of the tunnel's narrowness. Nonetheless, it's clear that a heavy, streamlined, and properly weighted pen dropped from the Empire State Building would still be accelerating downward when it reached the sidewalk. Its speed would be close to 209 mph at that point and it would indeed damage the sidewalk.
As a final test of the penny's low terminal velocity, I built a radio-controlled penny dropper and floated it several hundred feet in the air with a helium-filled weather balloon. On command, the dropper released penny after penny and I tried to catch them as they fluttered to the ground. Alas, I never managed to catch one properly in my hands. It was a somewhat windy day and the ground at the local park was uneven, but that's hardly an excuse—I'm simply not good at catching things in my hands. Several of the pennies did bounce off my hands and one even bounced off my head. It was fun and I was more in danger of twisting my ankle than of getting pierced by a penny. The pennies descended so slowly that they didn't hurt at all. Tourist below the Empire State Building have nothing fear from falling pennies. Watch out, however, for some of the more streamlined objects that might make that descent.
The radiated power from all of these wireless communications devices is so small that we have yet to find mechanisms whereby they could cause significant or lasting injury to human tissue. If there is any such mechanism, the effects are so weak that the risk associated with it are dwarfed by much more significant risks of wireless communication: the damage to traditional community, the decline of ordinary human interaction, and the surge in distracted driving.
The uranium atom has the largest naturally occurring nucleus in nature. It contains 92 protons, each of which is positively charged, and those 92 like charges repel one another ferociously. Although the nuclear force acts to bind protons together when they touch, the repulsion of 92 protons alone would be too much for the nuclear force—the protons would fly apart in almost no time.
To dilute the electrostatic repulsion of those protons, each uranium nucleus contains a large number of uncharged neutrons. Like protons, neutrons experience the attractive nuclear force. But unlike protons, neutrons don't experience the repulsive electrostatic force. Two neutron-rich combinations of protons and neutrons form extremely long-lived uranium nuclei: uranium-235 (92 protons, 143 neutrons) and uranium-238 (92 protons, 146 neutrons). Each uranium nucleus attracts an entourage of 92 electrons to form a stable atom and, since the electrons are responsible for the chemistry of an atom, uranium-235 and uranium-238 are chemically indistinguishable.
When the thermal fission reactors of the Fukushima Daiichi plant were in operation, fission chain reactions were shattering the uranium-235 nuclei into fragments. Uranium-238 is more difficult to shatter and doesn't participate much in the reactor's operation. On occasion, however, a uranium-238 nucleus captures a neutron in the reactor and transforms sequentially into neptunium-239 and then plutonium-239. The presence of plutonium-239 in the used fuel rods is one of the problems following the accident.
The main problem, however, is that the shattered fission fragment nuclei in the used reactor fuel are overly neutron-rich, a feature inherited from the neutron-rich uranium-235 nuclei themselves. Midsize nuclei, such as iodine (with 53 protons), cesium (with 55 protons), and strontium (with 38 protons), don't need as many neutrons to dilute out the repulsions between their protons. While fission of uranium-235 can produce daughter nuclei with 53 protons, 55 protons, or 38 protons, those fission-fragment versions of iodine, cesium, and strontium nuclei have too many neutrons and are therefore unstable—they undergo radioactive decay. Their eventual decay has nothing to do with chain reactions and it cannot be prevented.
How quickly these radioactive fission fragment nuclei decay depends on exactly how many protons and neutrons they have. Three of the most common and dangerous nuclei present in the used fuel rods are iodine-131 (8 days half-life), cesium-137 (30 year half-life), and strontium-90 (29 year half-life). Plutonium-239 (24,200 year half-life) is also present in those rods. When these radioactive nuclei are absorbed into the body and then undergo spontaneous radioactive decay, they damage molecules and therefore pose a cancer risk. Our bodies can't distinguish the radioactive versions of these chemical elements from the nonradioactive ones, so all we can do to minimize our risk is to avoid exposure to them or to encourage our bodies to excrete them by saturating our bodies with stable versions.
What will really happen is a field emission discharge. The repulsion between like charges will eventually become so strong that those charges will push one another out of the metal and into the vacuum, so that charges will begin to stream outward from the metal sphere.
Another way to describe that growing repulsion between like charges involves fields. An electric charge is surrounded by a structure in space known as an electric field. An electric field exerts forces on electric charges, so one electric charge pushes on other electric charges by way of its electric field.
As more and more like charges accumulate on the sphere, their electric fields overlap and add so that the overall electric field around the sphere becomes stronger and stronger. The charges on the sphere feel that electric field, but they are bound to the metal sphere by chemical forces and it takes energy to pluck one of them away from the metal.
Eventually, the electric field becomes so strong that it can provide the energy needed to detach a charge from the metal surface. The work done by the field as it pushes the charge away from sphere supplies the necessary energy and the charge leaves the sphere and heads out into the vacuum. The actually detachment process involves a quantum physics phenomenon known as tunneling, but that's another story.
The amount of charge the sphere can store before field emission begins depends on the radius of the sphere and on whether the charge is positive or negative. The smaller that radius, the faster the electric field increases and the sooner field emission starts. It's also easier to field-emit negative charges (as electrons) than it is to field-emit positive charges (as ions), so a given sphere will be able to hold more positive charge than negative charge.
Instant reversals of direction, however, aren't physically possible (because of inertia) and aren't actually what your friend wants anyway. I'll say more about the distinction between torque reversals and direction reversals in a minute.
In general, a motor has a spinning component called the rotor that is surrounded by a stationary component called the stator. The simplest brushless DC motor has a rotor that contains permanent magnets and a stator that consists of electromagnets. The magnetic poles on the stator and rotor can attract or repel one another, depending on whether they like or opposite poles—like poles repel; opposite poles attract.
Since the electronics powering the stator's electromagnets can choose which of the stator's poles are north and which are south, those electronics determine the forces acting on the rotor's poles and therefore the direction of torque on the rotor. To twist the rotor forward, the electronics make sure that the stator's poles are always acting to pull or push the rotor's poles in the forward direction so that the rotor experiences forward torque. To twist the rotor backward, the electronics reverses all those forces.
Just because you reverse the direction of torque on the rotor doesn't mean that the rotor will instantly reverse its direction of rotation. The rotor (along with the rider of the scooter) has inertia and it takes time for the rotor to slow to a stop and then pick up speed in the opposite direction. More specifically, a torque causes angular acceleration; it doesn't cause angular velocity. During that reversal process, the rotor is turning in one direction while it is being twisted in the other direction. The rotor is slowing down and it is losing energy, so where is that energy going? It's actually going into the electronics which can use this electricity to recharge the batteries. The "motor" is acting as a "generator" during the slowing half of the reversal!
That brushless DC motors are actually motor/generators makes them fabulous for electric vehicles of all types. They consume electric power while they are making a vehicle speed up, but they generate electric power while they are slowing a vehicle down. That's the principle behind regenerative braking—the vehicle's kinetic energy is used to recharge the batteries during braking.
With suitable electronics, your friend's electric scooter can take advantage of the elegant interplay between electric power and mechanical power that brushless DC motors make possible. Those motors can handle torque reversals easily and they can even save energy in the process. There are limits, however, to the suddenness of some of the processes because huge flows of energy necessitate large voltages and powers in the motor/generators and their electronics. The peak power and voltage ratings of all the devices come into play during the most abrupt and strenuous changes in the motion of the scooter. If your friend wants to be able to go from 0 to 60 or from 60 to 0 in the blink of eye, the motor/generators and their electronics will have to handle big voltages and powers.
When those observers are in motion relative to one another, they'll certainly disagree about the time and distance separating two events (say, two firecrackers exploding at separate locations). For modest relative velocities, their disagreement will be too small to notice. But as their relative motion increases, that disagreement will become substantial. That is one of the key insights of Einstein's special theory of relativity.
But even when two observers are not moving relative to one another, gravity can cause them to disagree about the time and distance separating two events. When those observers are in different gravitational circumstances, they'll perceive space and time differently. That effect is one of the key insights of Einstein's general theory of relativity.
Here is a case in point: suppose two observers are in separate spacecraft, hovering motionless relative to the sun, and one observer is much closer to the sun than the other. The closer observer has a laser pointer that emits a green beam toward the farther observer. Both observers will see the light pass by and measure its speed. They'll agree that the light is traveling at "The Speed of Light". But they will not agree on the exact frequency of the light. The farther observer will see the light as slightly lower in frequency (redder) than the closer observer. Similarly, if the farther observer sends a laser pointer beam toward the closer observer, the closer observer will see the light as slightly higher in frequency (bluer) than the farther observer.
How can these two observers agree on the speed of the beams but disagree on their frequencies (and colors)? They perceive space and time differently! Time is actually passing more slowly for the closer observer than for the farther observer. If they look carefully at each others' watches, the farther observer will see the closer observer's watch running slow and the closer observer will see the farther observer's watch running fast. The closer observer is actually aging slightly more slowly than the farther observer.
These effects are usually very subtle and difficult to measure, but they're real. The global positioning system relies on ultra-precise clocks that are carried around the earth in satellites. Those satellites move very fast relative to us and they are farther from the earth's center and its gravity than we are. Both difference affect how time passes for those satellites and the engineers who designed and operate the global positioning system have to make corrections for the time-space effects of special and general relativity.
What you are actually seeing when raindrops land on warm surfaces is tiny water droplets in the air, a mist of condensation. Those droplets happen in a couple of steps. First, the surface warms a raindrop and speeds up its evaporation. Second, a small portion of warm, especially moist air rises upward from the evaporating raindrop. Third, that portion of warm moist air cools as it encounters air well above the warmed surface. The sudden drop in temperature causes the moist air to become supersaturated with moisture—it now contains more water vapor than it can retain at equilibrium. The excess moisture condenses to form tiny water droplets that you see as a mist.
This effect is particularly noticeable when it's raining because the humidity in the air is already very near 100%. The extra humidity added when the warmed raindrops evaporate is able to remain gaseous only in warmed air. Once that air cools back to the ambient temperature, the moisture must condense back out of it, producing the mist.
That lower-density objects float on water is a consequence of Archimedes' principle: when an object displaces a fluid, it experiences an upward buoyant force equal in amount to the weight of the displaced fluid. If you submerge a piece of ice completely in water, that piece of ice will experience an upward buoyant force that exceeds the ice's weight because the water it displaces weighs more than the ice itself. The ice then experiences two forces: its downward weight and the upward buoyant force from the water. Since the upward force is stronger than the downward force, the ice accelerates upward. It rises to the surface of the water, bobs up and down a couple of times, and then settles at equilibrium.
At that equilibrium, the ice is displacing a mixture of water and air. Amazingly enough, that mixture weighs exactly as much as the ice itself, so the ice now experiences zero net force. That's why its at equilibrium and why it can remain stationary. It has settled at just the right height to displace its weight in water and air.
As for why ice is less dense than water, that has to do with the crystal structure of solid ice and the more complicated structure of liquid water. Ice's crystal structure is unusually spacious and it gives the ice crystals their surprisingly low density. Water's structure is more compact and dense. This arrangement, with solid water less dense than liquid water, is almost unique in nature. Most solids are denser than their liquids, so that they sink in their liquids.
A transformer conveys electric power from one electric circuit to another. It performs this feat using several electromagnetic effects associated with changing electric currents—changes present in the alternating current of our power grid. In this case, the transformer is moving power from a high-voltage neighborhood circuit to a low-voltage household circuit.
For safety, household electric power uses relatively low voltages, typically 120 volt in the US. But to deliver significant amounts of power at such low voltages, you need large currents. It's analogous to delivering hydraulic power at low pressures; low pressures are nice and safe, but you need large amounts of hydraulic fluid to carry much power. There is a problem, however, with sending low voltage electric power long distances: it's inefficient because wires waste power as heat in proportion to the square of the electric current they carry. Using our analogy again, sending hydraulic power long distances as a large flow of hydraulic fluid at low pressure is wasteful; the fluid will rub against the pipes and waste power as heat.
To send electric power long distances, you do better to use high voltages and small currents (think high pressure and small flows of hydraulic fluid). That requires being careful with the wires because high voltages are dangerous, but it is exactly how electric power travels cross-country in the power grid: very high voltages on transmission lines that are safely out of reach.
Finally, to move power from the long-distance high-voltage transmission wires to the short-distance low-voltage household wires, they use transformers. The long-distance circuit that carries power to your neighborhood closes on one side of the transformer and the short-distance circuit that carries power to your lamp closes on the other side of the transformer. No electric charges pass between those two circuits; they are electrically insulated from one another inside the transformer. The electric charges that are flowing through your lamp go round and round that little local circuit, shuttling from the transformer to your lamp and back again.
The f-number is actually the ratio of the lens' focal length to its effective diameter (the diameter of the light beam it collects and uses for its image). Your zoom lens has a focal length that can vary from 70 to 300 mm and a minimum f-number of 5.6. That means the when it is acting as a 300 mm telephoto lens, its effective light gathering surface is about 53 mm in diameter (300 mm divided by 5.6 gives a diameter of 53 mm).
If you examine the lens, I think that you'll find that the front optical element is about 53 mm in diameter; the lens is using that entire surface to collect light when it is acting as a 300 mm lens at f-5.6. But when you zoom to lower focal lengths (less extreme telephoto), the lens uses less of the light entering its front surface. Similarly, when you dial a higher f-number, you are closing a mechanical diaphragm that is strategically located inside the lens and causing the lens to use less light. It's easy for the lens to increase its f-number by throwing away light arriving near the edges of its front optical element, but the lens can't decrease its f-number below 5.6; it can't create additional light gathering surface. Very low f-number lenses, particularly telephoto lenses with their long focal lengths, need very large diameter front optical elements. They tend to be big, expensive, and heavy.
Smaller f-numbers produce brighter images, but there is a cost to that brightness. With more light rays entering the lens and focusing onto the image sensor, the need for careful focusing becomes greater. The lower the f-number, the more different directions those rays travel and the harder it is to get them all to converge properly on the image sensor. At low f-numbers, only rays from a specific distance converge to sharp focus on the image sensor; rays from objects that are too close or too far from the lens don't form sharp images and appear blurry.
If you want to take a photograph in which everything, near and far, is essentially in perfect focus, you need to use a large f-number. The lens will form a dim image and you'll need to take a relatively long exposure, but you'll get a uniformly sharp picture. But if you're taking a portrait of a person and you want to blur the background so that it doesn't detract from the person's face, you'll want a small f-number. The preferred portrait lenses are moderately telephoto—they allow you to back up enough that the person's face doesn't bulge out at you in the photograph—and they have very low f-numbers—their large front optical elements gather lots of light and yield a very shallow depth of focus.
If a fork has particularly sharp tines, however, then you should be careful not to put in the microwave oven. Sharp metal objects can and do spark in the microwave oven. Those sparks are probably more of a fire hazard than a food safety hazard—they can ignite the food or its container and start a fire.
The packed powder will exert downward drag forces on the upward flow of oil and gas, slowing its progress and decreasing its pressure faster than gravity alone. With 3+ miles of hole to fill, the dense steel objects should impede the flow severely. As the flow rate diminishes, the diameters of the metal spheres can be reduced until they are eventually only inches or even centimeters in diameter. The oil and gas will then be forced to flow through fine channels in the "powder," allowing viscous drag and pressure drag to extract all of the pressure potential energy from the flow and convert that energy into thermal energy. The flow will, in effect, be attempting to lift thousands of pounds of metal particles and it will fail. It will ooze though the "packed powder" at an insignificant rate.
Another way to think about my technique is that it gradually increases the average density of the fluid in the well hole until that column of fluid is so heavy that the high pressure at the bottom of the hole is unable to lift it. The liquid starts out as a light mixture of oil and gas, but it gradually transforms into a dense mixture of oil, gas, and iron. Viscous forces and drag forces effectively couple the materials phases together to form a single fluid. Once that fluid is about 50% iron by volume, its average density will be so high (4 times the density of water) that it will stop flowing upward. If iron isn't dense enough (7.8 times water), you could use silver cannonballs (10.5 times water). Then you could say that "silver bullets" stopped the leak! The failed "top kill" concept also intended to fill the well hole with a dense fluid: heavy mud. But it required pushing the oil and gas down the well hole to make room for the mud. That displacement process proved to be impossible because it required unobtainable pressures and pumping power. My approach takes no pressurization or pumping at all because it doesn't actively displace the oil and gas.
Including deformable lead spheres in the mixture will further plug the upward flow. The lead will deform under the weight of metal overhead and will fill voids and narrow channels. Another refinement of this dense-fill concept would be to drop bead chains down the well hole. The first large ball in such a chain would be a "tug boat" that is capable of descending against the upward flow all by itself. It would be followed by progressively smaller balls that need to draft (travel in the wake of) the balls ahead of them in order to descend into the well. Held together by steel or Kevlar cord, those bead chains would accumulate at the bottom of the well and impede the flow more effectively than individual large balls. Especially streamlined (non-spherical) objects such as steel javelins, darts, rods, and rebar could also be dropped into the well at the start of the filling process. In fact, sturdy sacks filled with junk steel objects—nuts and bolts—might even work. Anything that descends into the well hole is good and smaller particles are better. The point is not to form a seal, since the enormous pressure that will develop beneath any seal will blow it upward. The point is always to form narrow channels through which the oil and gas will struggle to flow.
A video of this idea appears at: http://www.youtube.com/watch?v=8H29H_1vTHo and a manuscript detailing this idea appears on the Physics ArXiv: http://arxiv.org/abs/1006.0656. I'm trying to find a home for it in the scientific literature, but so far Applied Physics Letters, Physic Review E (which includes the physics of fluids), and PLoS (Public Library of Science) One have turned it down—they want articles with new physics in them, not articles applying old physics to new contexts, no matter how important those contexts. It's no wonder that the public views science as arcane and irrelevant.
One important difference between a candle flame and a natural gas flame: whereas the flame of a well-adjusted natural gas burner emits very little light (a dim blue glow), the flame of a candle is quite visible. That's because the wax vapor in a candle flame isn't mixed well with air before it begins to burn. Instead of burning quickly and completely, as natural gas does in a burner that premixes the gas with air, the wax vapor in a candle flame burns gradually as it continues to mix with air. The partially burned wax forms tiny carbon particles. Those carbon particles are so hot that they glow yellow-hot — they emit thermal radiation. In other words, they are "incandescent". It's those glowing carbon particles that produce the candle's yellowish light. Eventually the carbon particles burn away to carbon dioxide.
The color sensing cells in our eyes are known as cone cells and they can detect only three different bands of color. One type of cone cell is sensitive to light in the red portion of the spectrum, the second type is sensitive to the green portion of the spectrum, and the third type is sensitive to the blue portion of the spectrum.
Their sensitivities overlap somewhat, so light in the yellow and orange portions of the spectrum simultaneously affects both the red sensitive cone cells and the green sensitive ones. Our brains interpret color according to which of three cone cells are being stimulated and to what extent. When both our red sensors and our green sensors are being stimulated, we perceive yellow or orange.
That scheme for sensing color is simple and elegant, and it allows us to appreciate many of the subtle color variations in our world. But it means that we can't distinguish between certain groups of lights. For example, we can't distinguish between (1) true yellow light and (2) a carefully adjusted mixture of true red plus true green. Both stimulate our red and green sensors just enough to make us perceive yellow. Those groups of lights look exactly the same to us.
Similarly, we can't distinguish between (3) the full spectrum of sunlight and (4) a carefully adjusted mixture of true red, true green, and true blue. Those two groups stimulate all three types of cone cells and make us perceive white. They look identical to us.
That the primary colors of light are red, green, and blue is the result of our human physiology and the fact that our eyes divide the spectrum of light into those three color regions. If our eyes were different, the primary colors of light would be different, too.
Many things in our technological world exploit mixtures of those three primary colors to make us see every possible color. Computer monitors, televisions, photographs, and color printing all make us see what they want us to see without actually reproducing the full light spectrum of the original. For example, if you used a light spectrum analyzer to study a flower and a photograph of that flower, you'd discover that their light spectra are different. Those spectra stimulate our eyes the same way, but the details of the spectra are different. We can't tell them apart.
The two tubes within a pair operate in series: current flowing as a discharge through the gas in one tube also flows through the gas in the other tube. That's why they both go out simultaneously. Only one of them is actually dead, but since the dead one has lost its ability to sustain a discharge, it can't pass any current on to its partner. Replacing the dead tube is usually enough to get the pair working again, at least for while.
Leaving dead tubes in a fixture isn't the same as removing unnecessary tubes. Tubes often die slow, lingering deaths during which they sustain weak or flickering discharges that consume some energy without providing much light. Also, most fluorescent fixtures heat the electrodes at the ends of the tubes to start the discharge. During startup, the ballast runs an electric current through each electrode (hence the two metal contacts at each end of the tube) and the heated electrodes introduces electric charges into the gas so the discharge can start.
That heating current is only necessary during starting, but if the discharge never starts then the ballast may continue to heat the electrodes for days, weeks, or years. If you look at the ends of a tube that fails to start, you may see the electrodes glowing red hot. Because of that heater current, leaving a failed fluorescent tube in a fixture can be waste of energy and money. Be careful removing those tubes from the fixture—although they produce no light, they can still be hot at their ends.
Snap-together beads are a perfect model for many polymers. As individual beads, you can pour them like a liquid and move your hand through them easily. But once you begin snapping them together into long chains, they develop new properties that weren't present in the beads themselves. For example, they get tangled together and don't flow so easily any more.
That emergence of new properties is exactly what happens in many polymers. For example, ethylene is a simple gas molecule, but if you stick ethylene molecules together to form enormous chains, you get polyethylene (more specifically, high-density polyethylene, recycling number 2, milk-jug plastic). Ethylene molecules are called "monomers" and the giant chains that are made from them are called "polymers".
Polyethylene retains some of the chemical properties of its monomer units, namely that it doesn't react with most other chemicals and almost nothing sticks to it. But polyethylene also has properties that the monomer units didn't have: polyethylene is a sturdy, flexible solid. You can stretch it without breaking it. That happens because you can make its polymer molecules slide across one another, but you can't untangle the tangles.
To get an idea of what it's like to work with molecules that can slide through each other but may not be able to untangle themselves, shift over to cooked and drained spaghetti. If you dice the spaghetti up into tiny pieces, it's like the monomers—nothing to tangle. You can pour the tiny pieces like a liquid. But trying doing that with a bowl of long spaghetti noddles. They're so tangled up that they can't do much. In fact, if you let the water dry up to some extent, the stuff will become a sturdy, flexible solid, just like HDPE!
There is much more to say about polymers, for example, they're not all simple straight chains and some of them cross-link so that they can't untangle no matter what you do. But this should be a good start. Polymer molecules are everywhere, including in paper and hair. Paper is primarily cellulose, giant molecules built out of sugar molecules. Hair is protein polymer, giant molecules built out of protein monomer units. They're both sturdy, stretchy, flexible solids and they're both softened by water—which acts as a molecular lubricant for the polymer molecules. Not all polymers are sturdy, or stretchy, or flexible, but a good many are.
As for how your cell phone and the cell tower can communicate for miles despite all the intervening stuff, it's actually a challenge. The microwaves from your phone and the tower are partly absorbed and partly reflected each time they encounter something in your environment, so they end up bouncing their way through an urban landscape. That's why cell towers have multiple antennas and extraordinarily sophisticated transmitting and receiving equipment. They are working like crazy to direct their microwaves at your phone as effectively as possible and to receive the microwaves from your phone even though those waves are very weak and arrive in bits and pieces due to all the scattering events they experience during their passage. Indoor cell phone reception is typically pretty poor unless the building has its own internal repeaters or microcells.
There are times when you don't get any reception because the microwaves from the cell phone and tower are almost completely absorbed or reflected. For example, if you were to stand in a metalized box, the microwaves from your cell phone would be trapped in the box and would not reach the cell tower. Similarly, the microwaves from the cell tower would not reach you. Moreover, the box doesn't have to be fully metalized; a metal mesh or a transparent conductor is enough to reflect the microwaves. Transparent conductors are materials that conduct relatively low-frequency currents but don't conduct currents at the higher frequencies associated with visible light. They're used in electronic displays (e.g., computer monitors and digital watches) and in energy-conserving low-E windows. I haven't experimented with cell phone reception near low-E windows, but I'm eager to give it a try. I suspect that a room entirely walled by low-E windows will have lousy cell phone reception.
Light is a form of energy, so you can compare the visible light energy emitted by any lamp to the energy that lamp consumes. According to that comparison, an incandescent lightbulb is roughly 5% efficient—a 100-watt incandescent bulb emits about 5 watts of visible light. In contrast, a fluorescent lamp is typically about 20% energy efficient—a 25-watt fluorescent lamp emits about 5 watts of visible light.
Another way to compare incandescent and fluorescent lamps is via their lumens per watt. The lumen is a standard unit of usable illumination and it incorporates factors such as how sensitive our eyes are to various colors of light. If you divide a light source's light output in lumens by its power input in watts, you'll obtain its lumens per watt.
For the incandescent lightbulb appearing at the left of the photograph, that calculation yields 16.9 lumens/watt. For the "long life" bulb at the center of the photograph, it give only 15.3 lumens/watt. And for the color-improved bulb on the right of the photograph, the value is only 12.6 lumens/watt. Our grandchildren will look at this photograph of long forgotten incandescent bulbs and be amazed that we could squander so much energy on lighting.
The fluorescent lamp in the other photograph is far more efficient. It produces more useful illumination than any of the three incandescent bulbs, yet it consumes just over a quarter as much power. Dividing its light out in lumens by its power consumption in watts yields 64.6 lumens/watts. It is 4 times as energy efficient as the best of the incandescent lightbulbs. Some fluorescent lamps are even more efficient than that.
Another feature to compare is life expectancy. Even the so-called "long life" incandescent predicts a 1500 hour life, which is only 15% of the predicted life for the fluorescent lamp (10,000 hours). Although the fluorescent costs more, it quickly pays for itself in energy use and less frequent replacement. You should recycle a fluorescent lamp because it does contain a tiny amount of mercury, but overall it's a much more environmentally friendly light source.
First, the egg has its weight—it's being pulled downward by gravity. That weight force tends to make the egg sink. Second, the egg is being pushed upward by the water around it with a force known as "the buoyant force." The buoyant force tends to make the egg float. It's a battle between those two forces and the strongest one wins.
The buoyant force exists because the water that is now surrounding the egg used to be surrounding an egg-shaped blob of water and it was pushing up on that blob of water just hard enough to support the blob's weight. Now that the egg has replace the egg-shaped blob of water, the surrounding water is still pushing up the same amount as before and that upward force on the egg is the buoyant force.
Since the buoyant force on the egg is equal in amount to the weight of the water that used to be there, it can support the egg only if the egg weighs no more than the egg-shaped blob of water. If the egg is heavier than that blob of water, the buoyant force will be too weak to support it and the egg will sink.
It so happens that a hard-boiled egg weighs slightly more than an egg-shaped blob of pure water, so it sinks in pure water. But that egg weighs slightly less than an egg-shaped blob of very salty water. Adding salt to the water increases the water's weight significantly while having only a small effect on the water's volume. Salt water is heavier, cup for cup, than fresh water and it produces stronger buoyant forces.
In general, any object that weighs more than the fluid it displaces sinks in that fluid. And any object that weighs less than the fluid it displaces floats. You are another good example of this: you probably sink in fresh water, particularly after letting out all the air in your lungs. But you float nicely in extremely salty water. The woman in this photograph is floating like a cork in the ultra-salty water of the Dead Sea.
Below water's boiling temperature, bubbles of water vapor are unstable—they are quickly crushed by atmospheric pressure and vanish into the liquid. At or above water's boiling temperature, those water vapor bubbles are finally dense enough to withstand atmospheric pressure and they grow via evaporation, rise to the surface, and pop. At that point, I'd probably call the water vapor by its other name: steam. But where do those steam or water vapor bubbles come from in the first place?
Forming water vapor bubbles in the midst of liquid water, a process called nucleation, is surprisingly difficult and it typically happens at hot spots or non-wetted defects (places where the water doesn't completely coat the surface and there is trapped air). When you boil water in a metal pot on the stove, there are hot spots and defects galore and nucleating the bubbles is not a problem. When you boil water in a glass or glazed container using a microwave oven, however, there are no significant hot spots and few non-wetted defects. The water boils fitfully or not at all. The "not at all" possibility can lead to disaster.
Water that's being heated in a metal pot on the stove boils so vigorously that the stove is unable to heat it more than tiny bit above its boiling temperature. All the heat that's flowing into the water is consumed by the process of transforming liquid water into gaseous water, so the water temperature doesn't rise. Water that's being heated in a glass container in a microwave oven boils so fitfully that you can heat it above its boiling temperature. It's simply not able to use up all the thermal energy it receives via the microwaves and its temperature keeps rising. The water becomes superheated.
Most of the time, there are enough defects around to keep the water boiling a bit and it superheats only a small amount. When you remove the container of water from the microwave oven and toss in some coffee powder or a teabag, thus dragging air bubbles below the surface, the superheated water boils into those air bubbles. A stream of bubbles suddenly appears on the surface of the water. Most people would assume that those bubbles had something to do with the powder or teabag, not with the water itself. Make no mistake, however, the water was responsible and those bubbles are mostly steam, not air.
Occasionally, though, the water fails to boil at all or stops boiling after it manages to wet the last of the defects on the glass or glazed surface. I've made this happen deliberately many times and it's simply not that hard to do. It can easily happen by accident. With no bubbles to assist evaporation, the water's only way to get rid of heat is via evaporation from its top surface. If the microwave oven continues to add thermal energy to the water while it is having such difficulty getting rid of that energy, the water's temperature will skyrocket and it will superheat severely.
Highly superheated water is explosive. If something causes nucleation in that water, a significant fraction of the water will flash to steam in the blink of an eye and blast the remaining liquid water everywhere. That boiling-hot water and steam are a major burn hazard and the blast can break the container or blow it across the room. I've heard from a good number of people who have been seriously hurt by exploding superheated water produced accidentally in microwave ovens. It's a hazard people should take seriously.
After that long introduction, it's time to answer your question. Yes, I believe that the microwave makers are responsible for advising people of this hazard. Moreover, they know that they are responsible for doing it. If you look at any modern microwave oven user manual, you will find a discussion of superheating or overheating. Look at your manual, I'll bet it's in there.
But that discussion will almost certainly be buried in the middle of an long list of warnings. For example, in one manual, the discussion of overheated water appears as item 17 of 22, after such entries as "4. Install or locate this appliance only in accordance with the provided installation instructions" and "12. Do not immerse cord or plug in water". To be fair to the manufacturer, warning 17 is longest of the bunch and it suggests mostly reasonable precautions (although I'm not so happy with recommendation 17a: "Do not overheat the liquid."). No Duh.
I think the issue is this: most product warnings are provided not out of any sincere concern for the consumer, but out of fear of litigation. A manufacturer's goal when providing those warnings is therefore to be absolutely comprehensive so that they can point to a line in a user manual in court and claim to have fulfilled their responsibility. The number and order of the warnings makes no difference; they just have to be in there somewhere.
So all those warnings you ignore in product literature aren't really about consumer safety, they're about product liability. You ignore them because everything now comes with a thousand of them, ranging from the reasonable to the ridiculous. For my research, I ordered 99.999% pure sodium chloride (i.e., ultrapure table salt). It came with a 6-page Material Safety Data Sheet that identifies it as an "Xi Irritant", noting that it is "Irritating to eyes, respiratory system and skin" and recommending first aid measures that include:
"After inhalation: supply fresh air. If required, provide artificial respiration. Keep patient warm. Seek immediate medical advice.So much for swimming in the ocean...
After skin contact: Immediately wash with water and soap and rinse thoroughly. Seek immediate medical advice.
After eye contact: rinse opened eye for several minutes under running water. Then consult a doctor."
By design and by accident, our society has lost the ability to distinguish real risk from imaginary risk. We treat all risks as equal and spend way too much time worrying about the wrong ones. If you want to be safer around your cell phone, for example, you should worry more about driving with it in your hand than about the microwave radiation it emits. The current evidence is that your risk of injury or death due to a cell-phone related accident far outweighs your risk from cell-phone microwave exposure. Even if further research proves that cell phone microwave exposure is injurious, we should be acting according to our best current assessments of risk, not according to fears and beliefs.
That said, I'd like to see product literature rank their warnings according to risk and put the real risks in a separate place where they can't be overlooked or ignored. Put the real consumer safety stuff where the consumers will see it and put the product liability stuff somewhere else where the lawyers can find it. For a microwave oven, there are probably about half a dozen real risks that people should know about. Several of them are relatively obvious (e.g., don't heat sealed containers) and some are not obvious (e.g., liquids heated in the microwave can become superheated and explode).
Maybe we'll get a handle on risk someday. In the meantime, inform your friends and children that they should be careful about heating liquids in the microwave, particularly in glass or glazed containers. Just knowing that superheating is possible would probably halve the number of burns and other injuries that result from superheating accidents.
In all my years of experimenting with microwave ovens, I've only killed a magnetron once. But then again, I haven't run a microwave oven for more than a minute or two without anything inside it. If the oven works again after cooling down, then you're probably OK. The oven may have thermal interlocks in its microwave source to prevent that source from overheating and becoming a fire hazard. If the oven fails to work after an hour of cooling off, then you're probably out of luck. The magnetron and/or its power supply are likely to be fried and in need of replacement.
When a women stands on the floor, the floor must support her weight. Specifically, she isn't accelerating so the net force on her must equal zero. That implies that the floor must exert an upward force on her that exactly cancels her downward weight. She is motionless and stays motionless because there is no overall force on her.
Because the floor is pushing upward on her shoes, her shoes must be pushing downward on the floor. It's an example of the famous "action and reaction" principle known as Newton's third law: if you push on something, it pushes back equally hard in the opposite direction. Anyway, her shoes are pushing down hard on the floor.Now for the pressure part of the story. Because she is wearing flats, her shoes are pushing against a large area of the floor and the pressure—the force per area—she produces on the floor is relatively small. For example, if she weighs 130 pounds (580 newtons) and her shoes have a contact area of 10 square inches (65 square centimeters), then the pressure she exerts on the floor is about 13 pounds-per-square-inch (9 newtons-per-square-centimeter or 90,000 pascals). That's a gentle pressure that won't permanently dent most woods. It might dent cork or balsa, but that's about it.
But when she wears high heels, most of her weight is supported by a very small area of flooring. If the heels are narrow spikes with a contact area of 0.1 square inches (0.65 square centimeters) and she puts all of her weight briefly on one of the heels, she may exert a pressure of 1300 pounds-per-square-inch (9000 newtons-per-square-centimeter or 90 million pascals) on the floor. That's an enormous pressure that will permanently dent most wooden floors.
You can experiment with these ideas simply by supporting the weight of your right hand with the open palm of your left hand. If you lay your right fist on your left palm, you won't feel any discomfort in your left hand. The pressure on your left palm is very small. But if you instead point right index finger into your left palm and use that finger to support the entire weight of your right hand, it won't feel so comfortable. If you shift all of the weight to your fingernail, it'll start to hurt your left palm. What you're doing is reducing the area of your left palm that is supporting your right hand and as that area gets smaller, the pressure on your left palm increases. Beyond a certain pressure, it feels uncomfortable. Long before your palm dents permanently, you'll decide to stop the experimenting.
Each portion of cable responds to being pulled by accelerating, moving, and consequently pulling on the portion of cable adjacent to it. There will be a long series of actions—pulling, accelerating, moving, and pulling again—that propagates your influence along the cable. A wave will travel along the cable, a wave consisting of a local reduction in the cable's density. It's a stretching wave. In that respect, the wave is a type of sound wave—a density fluctuation that propagates through a medium.
How quickly the density wave travels along the cable depends on how stiff the cable is and on its average mass density. The stiffer the cable, the more strongly each portion can influence its neighboring portions and the faster the density wave will travel. The greater the cable's mass density, the more inertia it has and the slower it respond to pulls, so the density wave will travel slower.
A cable made from a stiff, low-density material carries sound faster than a soft, high-density material. A steel cable should carry your wave at about 6100 meters/second (3.8 miles/second). But a diamond cable would reach 12000 meters/second (7.5 miles/second) because of its extreme stiffness and a beryllium cable would approach 13000 meters/second (8.0 miles/second) because of its extremely low mass density.
Regardless of which material you choose, you're clearly not going to be able to send any signals faster than the speed of light. It would take a density wave more than 100,000 years to travel the 5-light year length of your cable. And sadly, friction-like dissipation effects in the cable would turn the density wave's energy into thermal energy in a matter of seconds, so it would barely get started on its journey before vanishing into randomness.
To begin with, plug-in power adapters are designed to keep their electromagnetic fields relatively well contained. They're engineered that way not because of safety concerns but because their overall energy efficiencies would diminish if they accidentally conveyed power to their surroundings. Keeping their fields inside keeps their energy inside, where it belongs. Moreover, any electric and magnetic fields emerging from an adapter probably don't propagate as waves and instead fall off exponentially with distance. As a result, it should be fairly difficult to detect electric or magnetic fields more than a few inches from the adapter.
Even if the adapter did project significant electric and magnetic fields all the way to where your dog sleeps, it's still unlikely that they would cause any harm. For years, researchers have been looking for a correlation between high-voltage electric power lines and a variety of human illnesses, notably childhood cancers such as leukemia. As far as I know, no such correlation has ever been demonstrated. In all likelihood, if there are any risks to being near 60-Hz electric or magnetic fields, those risks aren't large enough to be easily recognized.
In contrast to power adapters, cell phones deliberate emit electric and magnetic fields in order to communicate with distant receivers on cell phone towers. Those fields are woven together to form electromagnetic waves that propagate long distances and definitely don't vanish inches from a cell phone. Any electromagnetic hazard due to a power adapter pales in comparison to the same for cell phones.
Furthermore, cell phone operate at much higher frequencies than the alternating current power line. A typical cell phone frequency is approximately 1 GHz (1,000,000,000 Hz), while ordinary alternating current electric power operates at 60 Hz (50 Hz in Europe). Higher frequencies carry more energy per quanta or "photon" and are presumably more dangerous. But even though cell phones are held right against heads and radiate microwaves directly into brain tissue, they still doen't appear to be significantly dangerous. As unfond as I am of cell phones, I can't condemn them because of any proven radiation hazard. Their biggest danger appears to be driving with them; I don't understand why they haven't been banned from the hands of drivers.
Lastly, there are no obvious physical mechanisms whereby weak to moderate electric and magnetic fields at 60-Hz would cause damage to human or canine tissue. We're essentially non-magnetic, so magnetic fields have almost no effect on us. And electric fields just push charges around in us but that alone doesn't cause any obvious trouble. Research continues into the safety of electromagnetic fields at all frequencies, but this low-frequency stuff (power lines and cell phones) doesn't seem to be unsafe.
Actually, I could have registered this website as www.howeverythingworks.com, but I would have had to purchase that domain name from someone else. It is registered to a cybersquatter—someone who registers a domain name in hopes of selling it at a profit to someone else. Cybersquatting was hugely popular during the internet bubble, when companies were paying vast amounts of money for particular domain names. But these days, who wants to pay thousands of dollars for a name? I'm totally happy to be www.howeverythingworks.org and I'll let someone else pay the big bucks to purchase www.howeverythingworks.com. In the meantime, that domain is just a link to advertising and an offer to sell the domain name.
Even if the oven door has multiple layers of glass, those layers are there for your protection. If you touch the outside of the metal grid while the oven is on or get close enough to it through the last layer of glass, you'll be able to absorb some microwave power and it'll probably hurt. That's because while the holes in the grid are too small to allow the microwaves to propagate through them and truly escape from the oven, they do allow an "evanescent wave" to exist just outside each hole in the grid. That evanescent wave dies off exponentially with distance beyond the hole, so it won't travel around the room. But you don't want to put your finger in it.
For inexpensive microwave ovens, you're probably best off simply recycling the oven. I'm not happy about the modern everything-is-disposable state of appliances and equipment, but I can't say that it's cost effective to repair an oven that costs less than about $100. For more expensive microwave ovens, you can usually replace the window or the door. We have had a GE combination microwave and convection oven over our stove top for about 10 years and the door started to come apart about 18 months ago. I purchased a replacement microwave oven door over the web for $140 and installed it myself. It works beautifully. If you're not handy or are concerned about microwave leaks, you should probably have it replaced professionally. But you can look up the parts themselves online at a number of web sites and get an idea of what the cost will be.
In fact, turning off the power strip is likely to save energy as well. Many computer devices have two different "off" switches: one that stops them from doing their normal functions and one that actually cuts off all electrical power. Computers in particular don't really turn off until you reach around back and flip the real power switch on the computer's power supply. The same is true of television monitors and home theater equipment.
In general, any device that has a remote control or that can wake itself up to respond to a pretty button or to some other piece of equipment is never truly off until you shut off its electrical power. Our homes are now filled with electronic gadgets that are always on, waiting for instructions. Keeping them powered up even at a low level consumes a small amount of electrical power and it adds up. Last I heard, this always-on behavior of our gadgets consumes something on the order of 1% of our electrical power. Whatever it is, it's too much. So by turning off your power strip and completely stopping the flow of power to your computer, your speakers, your monitor, etc., you are saving energy. You lose the convenience of being able to turn everything on from your couch with a remote, but who cares. Energy is too precious to waste for such nonessential conveniences.
The idea of a wave that travels through space itself was a rather disorienting notion to scientists in the late 1800s. They were used to the idea that waves are disturbances in a tangible material or "medium": fluctuations in the density of air, ripples on the surface of water, vibrations of a taut string. Having observed that light and radio waves are electromagnetic waves, they set about looking for the medium that supported those waves. They were expecting to find this "luminiferous aether" but they failed. In fact, the absence of an aether led in part to Einstein's theory of special relativity.
The structure of a radio wave, or any electromagnetic wave, is quite simple. It consists only of a fluctuating electric field and a fluctuating magnetic field. An electric field is a structure in space that affects electric charge; it pushes on charge and causes that charge to accelerate. Similarly, a magnetic field is a structure that affects magnetic pole. Remarkably, changing electric fields produce magnetic fields and changing magnetic fields produce electric fields. That interrelatedness allows the wave's fluctuating electric field to produce its fluctuating magnetic field and vice verse. The wave's electric and magnetic fields endless recreate one another. Although electric charge or magnetic pole is needed to emit or receive a radio wave, that wave can travel perfectly well for billions of light years without involving any charge or pole. It travels through space itself.
An older oven would have used a heavy transformer, a capacitor, and a diode to convert ordinary household AC power to high-voltage DC power for its magnetron microwave tube. But since your oven was made recently, it probably uses a switching power supply to produce that high voltage. That supply contains a much more sophisticated electronic switching system to convert household AC power to high-voltage DC power. The new approach is cheaper and lighter, so it's taking over in microwave ovens. Just because it's more sophisticated, however, doesn't mean it's more reliable.
My guess is that the unit in your oven has a problem. If it has an intermittent contact in it or if there is a conducting path that is sparking somewhere in the power supply or in the unit as whole, they'll be randomly fluctuating currents present in the oven and those current fluctuations will produce radio waves. A sparking wire or carbonized patch on the power supply will start and stop the flow of current erratically and that can easily cause interference on the AM band. Ordinary AM radio is very susceptible to radio-frequency interference at around 1 MHz and sparking stuff tends to produce such radio waves. A car with a bad ignition system, a lawn mower, and a thunderstorm all interfere beautifully with AM reception. And I suspect that you've got a similar electrical problem in your oven. I doubt that your oven is a microwave hazard, but you should probably have a repair person to take a look at it. It shouldn't have anything sparking inside it.
Those YouTube videos were complete fakes; they didn't pop any popcorn while the camera was rolling. To make it appear that the cell phones were popping the corn, the people who produced the videos dropped already prepared popcorn into the frame and then photoshopped away the unpopped kernels. When you watch the video, it looks like the kernels are popping, but they're really just disappearing via video editing as precooked popcorn is sprinkle onto the set from above.
The reason they had to use video trickery is pretty clear: to pop popcorn with microwaves, those microwaves have to be extremely intense. Each kernel contains only a tiny amount of water and it's the water that heats up when the kernel is exposed to microwaves. If the microwaves aren't intense enough, the heat they deposit in the kernel's water will flow out to the rest of the kernel and into the environment too quickly for the kernel's water to superheat and then flash to steam.
Even when you put popcorn kernels in a closed microwave oven, it takes a minute or two for the kernels to accumulate enough thermal energy to pop. In that closed microwave oven, the microwaves bounce around inside the metal cooking chamber and their intensity increases dramatically. It's like sending the beam from a laser pointer into a totally mirrored room—the light energy in that room will build up until it is extremely bright in there. In the closed cooking chamber of the oven, the microwave energy also builds up until the microwave intensity is enough to pop the corn. How intense? Well, a typical microwave oven produces 700 watts of microwave power. Since the cooking chamber is nearly empty when you're popping popcorn, the cooking chamber accumulates a circulating power of very roughly 50,000 watts.
Although that power is spread out over the cross section of the oven, the microwaves are still seriously intense -- thousands of watts per square inch. To put that in perspective, a cell phone transmits a maximum of 2 watts and that power is spread out over at least 5 square inches so the intensity is less than 1 watt per square inch. When I saw those videos in Summer 2008, I realized that there was no way cell phones were ever going to pop popcorn. They certainly wouldn't do it while they are ringing, because that's when they are primarily receiving microwaves, not when they're transmitting them. It's when you're talking that your cell phone is regularly producing microwaves. It was all obviously just fun and games.
So what about your disassembled microwave oven? Since there is no metal box to trap the microwaves and accumulate energy, they'll only have one shot at popping the corn kernels. The microwaves will emerge from the magnetron's waveguide at high intensity, but they'll spread out quickly once there is nothing to guide them. You could probably pop kernel right at the mouth of the magnetron but not a few inches away. Unless you use microwave optics to focus those microwaves, they'll have spread too much by the time they get through the table and reach the kernels of popcorn and the kernels will probably never pop.
If that were the whole story, the worst that would happen with your experiment would be that it wouldn't cook popcorn. But there is a real hazard here. Sending about 700 watts of microwaves into the room isn't exactly safe. It's something like having a red hot coal emitting 700 watts of infrared light, except that you won't see anything with your eyes and this microwave "light" is coherent (i.e., laser-like) so it can focus really tightly. You'd hate to have some metal structure in the room or even inside the walls of the room focus the microwaves onto you. You absorb microwave much better than the corn kernels and you'll "pop" long before they do. Actually, your eyes are particularly sensitive to microwave heating and you might not notice the damage until too late. Without instruments to observe the pattern of microwaves in the room when the magnetron is on, I wouldn't want to be in the room.
When you cool a basketball, however, you reduce the pressure of its air. That's because the air molecules have less thermal energy at colder temperatures and thermal energy is responsible for air pressure. A basketball that was properly inflated at warm temperature becomes under-inflated when you cool it down. At the same time, the basketball's skin becomes less elastic and more leathery at cool temperatures. So the basketball suffers from under-inflation and from a leathery, not-very-bouncy skin.
If you cool a basketball to low enough temperature, its skin will freeze and become brittle. Just how low the temperature has to go depends on the material used in to make the basketball. I've never seen a basketball shatter on the court, even in pretty cold weather, so I doubt you can "freeze" one in a household freezer. But I'm sure that a dip in liquid nitrogen at -395 °F would do the trick. I often freeze rubber handballs in liquid nitrogen for my class and then shatter them on the floor.
If you look carefully at the string while it's vibrating in a mixture of several harmonics, you'll see that it has only one shape at any moment in time. It's just a jiggling string, after all. The parts of that shape, however, are evolving at different rates in time and those parts are actually the different harmonics going through their individual motions at their own frequencies.
But while the speed of light in vacuum is a constant, the speed of light in matter isn't. Light is an electromagnetic wave and consists of electric and magnetic fields. Electric fields push on electric charge and matter contains electric charges, so light and matter interact. That interaction normally slows light down; the light gets delayed by the process of shaking the electric charges. In air, this slowing effect is tiny, less than 1 part in a thousand. In glass, plastic, or water, light is slowed by about 30 or 40%. In diamond, the interaction is strong enough to slow light by 60%. In silicon solar cells, light is slowed by 70%. And so it goes.
To really slow light down, however, you need to choose a specific frequency of light and let it interact with a material that is resonant with that light. Because a resonant material responds extremely strongly to the light's electric field, it delays the light by an enormous amount. And by choosing just the right wavelength of light to match a particular collection of resonant atoms, Lene Hau and her colleagues managed to bring light essentially to a halt. The light lingers nearly forever with the atoms in their apparatus and it barely makes any headway.
To understand why light scatter depends on homogeneity, consider what happens when light pass through clear particles. Even though they are clear, light still interacts with them, as evidenced by rainbows, clouds, and even the blue sky. How best to think about that interaction depends on the size of the particles. If the particles are large, like smooth beads of glass or plastic, then they exhibit the familiar refraction and reflection effects of window panes and lenses. If the particles are small, like air molecules and tiny water droplets, then they exhibit a more antenna-like interaction with light. In effect, those tiny particles occasionally absorb and reemit the light waves, particularly at the short-wavelength (i.e., blue) end of the light spectrum.
Both types of interactions are quite familiar to us. Large particles scatter light about without any color bias and exhibit a white appearance. The more surface area a collection of particles has, the more light that collection scatters. For example, a large ice crystal is clear but crushed ice or snow is white. Similarly, a bowl of water is clear but a mist of water droplets is white. Lastly, a bowl of air is clear, but a froth of air bubbles in water is white. As you can see, the transparent particles don't have to be solids or liquids to scatter light, they can even be gases!
On the other hand, truly tiny particles scatter light about according to wavelength and color. In most cases, shorter-wavelength (blue) light scatters more than longer-wavelength (red) light. That effect, known as Rayleigh scattering, is responsible for the blue sky and the red sunset.
In a nutshell then, large transparent particles appear white and tiny transparent particles appear colored (typically bluish). And the more particles there are, the more light is scattered.
Returning to your question, a loose powder of transparent particles scatters light like crazy and appears white or possible colored, depending on particle size. As you pack the powder more and more tightly together, its surfaces join together and it starts to lose the ability to scatter light; it becomes less white and more translucent. When the consolidation is almost complete, the material acquires a slightly hazy look due to scattering by the occasional voids left inside the otherwise transparent material. Finally, when the material is fully consolidated and there is no internal surface left in the powder, it is homogeneous and clear. So sending light through a packed transparent powder and measuring the amount and color of the scattered light tells you a lot about how well consolidated that powder is.
A simple way to see why that's the case is to picture the gas as composed of many little bouncing balls inside the container. Those balls are perfectly elastic so they rebound from a stationary wall without changing their speeds at all. But the walls of the container aren't stationary, they move back and forth as you shake the container. Because of the moving walls, the balls change their speeds as they rebound. A ball that bounces off a wall that is moving toward it gains speed during its bounce, like a pitched ball rebounding from a swung bat. On the other hand, a ball that bounces off a wall that is moving away from it loses speed during its bounce, like a pitched ball rebounding from a bat during a bunt. If both types of bounces were equally common in every way then, on average, the balls (or actually the gas molecules) would neither gain nor lose speed as the result of bounces off the walls and the gas temperature would remain unchanged.
But the bounces aren't equally common. It's more likely that a moving ball will hit a wall that is moving toward it than that it will hit a wall that is moving away from it. It's a geometry problem; you get wet faster when you run toward a sprinkler than when you run away from the sprinkler. So, on average, the balls (or gas molecules) gain speed as the result of bounces off the walls and the gas temperature increases.
How large this effect is depends on the relative speeds of the gas molecules and the walls. The effect becomes enormous when the walls move as fast or faster than the gas molecules but is quite subtle when the gas molecules move faster than the walls. Since air molecules typically move at about 500 meters per second (more than 1000 mph) at room temperature, you'll have to shake the container pretty violently to see a substantial heating of the gas.
DC power also avoids the phase issues that make the AC power grid so complicated and fragile. It's not enough to ensure that all of the generators on the AC grid are producing the correct amounts of electrical power; those generators also have to be synchronized properly or power will flow between the generators instead of to the customers. Keeping the AC power grid running smoothly is a tour-de-force effort that keeps lots of people up at night worrying about the details. With DC power, there is no synchronization problem and each generating plant can concentrate on making sure that their generators are producing the correct amounts of power at the correct voltages.
Lastly, alternating currents tend to flow on the outsides of conductors due to a self-interaction between the alternating current and its own electromagnetic fields. For 60-cycle AC, this "skin effect" is about 1 cm for copper and aluminum wires. That means that as the radius of a transmission line increases beyond about 1 cm, its current capacity stops increasing in proportion to the cross section of the wire and begins increasing in proportion to the surface area of the wire. For very thick wires, the interior metal is wasted as far as power delivery is concerned. It's just added weight and cost. Since direct current has no skin effect, however, the entire conductor can be carry current and there is no wasted metal. That's a big plus for DC power distribution.
The great advantage of AC power transmission has always been that it can use transformers to convey power between electrical circuits. Transformers make it easy to move AC power from a medium-voltage generating circuit to an ultrahigh-voltage transmission line circuit to a medium-voltage city circuit to a low-voltage neighborhood circuit. DC power transmission can't use transformers directly because transformers need alternating currents to move power from circuit to circuit. But modern switching electronics has made it possible to convert electrical power from DC to AC and from AC to DC easily and efficiently. So it is now possible to move DC power between circuits by converting it temporarily into AC power, sending it through a transformer, and returning it to DC power. They can even use higher frequency AC currents and consequently smaller transformers to move that power between circuits. It's a big win on all ends. While I haven't followed the developments in this arena closely, I would not be surprised if DC power transmission started to take hold in the United State as we transition from fossil fuel power plants to renewable energy sources. Using those renewable sources effectively will require that we handle long distance transmission better than we do now and we'll have to develop lots of new transmission infrastructure. It might well be DC transmission.
The standard current limiter for fluorescent lamps and other discharge lamps that are powered from 60-cycle (or 50-cycle) alternating current has been an electromagnetic coil known as a ballast. When that coil is in series with the discharge, the coil's self-inductance limits how quickly the current flowing through the lamp can rise and therefore how much power the lamp can consume before the alternating current reverses direction. The discharge winks on and off with each current reversal and never draws more current than it can tolerate. Unfortunately, the lamp's light also winks on and off and some people can see that flicker, especially with their peripheral vision.
Actually, the ballast usually has another job to do in a traditional fluorescent lamp: it acts as a transformer to provide the current needed to heat the electrode filaments at the ends of the lamp. Heating those electrodes helps drive electrons out of the metal and into the lamp's gas so that the gas becomes electrically conducting. In total then, the ballast receives alternating current electric power from the power line and prepares it so that all the lamp filaments are heated properly and a limited current flows through the lamp from one electrode to the other.
In modern fluorescent lamps with heated electrodes, however, the role of the ballast has been usurped by a more sophisticated electronic power conditioning device. That device converts 60-cycle alternating current electric power into a series of electrical energy pulses, typically at about 40,000 pulses per second, and delivers them to the lamp. The lamp's flicker is almost undetectable because it is so fast and the limited energy in each pulse prevents the discharge from consuming too much power. It's a much better system. Compact fluorescent lamps use it exclusively.
So where might high voltage fit into this story? Well, there are some fluorescent lamps that don't heat their electrodes with filaments. They rely on the discharge itself to drive electrons out of the electrodes and into the gas to sustain the discharge. But that begs the question: "how does such a lamp start its discharge?" It uses high voltage. Because of cosmic rays and natural radioactivity, gases always have some electric charges in them: ions and electrons. When the voltage difference between the two ends of the lamp becomes very large, the electric field in the lamp propels those naturally occurring ions and electrons into the constituents of the lamp violently enough to start the lamp's discharge. The voltages needed to start these "cold cathode" lamps are typically in the low thousands of volts. For example, the cold cathode fluorescent lamps used in laptop computer displays start at about 2000 volts and then operate at much lower voltages.
But appearances can be deceiving. Since energy is a conserved quantity, the energy that you invest in the firewood can't disappear. It simply becomes difficult to find because it is dispersed in the burned gases that were once the wood.
To find that energy, imagine compressing the burned gases into a small container to make their weight more noticeable and reduces buoyant effects due to the atmosphere. You could then carry those burned gases, which include all of the firewood's atoms, back down the hill. As you descended, the container of burned gases would transfer its gravitational potential energy to you.
I've swept a number of details under the rug, such as the fact that many of the oxygen atoms in your container were originally part of the atmosphere rather than the log. But even when all those details are taken into account, the answer is the same: the firewood's gravitational energy doesn't disappear, it just gets more difficult to find.
Since eye safety requires limiting the amount of laser power that can enter a person's eye, you can make a laser more eye-safe by enlarging its beam. Even a powerful laser can be eye-safe if only a small fraction of the laser light can enter a person's iris and focus on their retina.
Although it's natural to think of a laser beam as a narrow pencil of light that stays narrow forever, that's not really the case. The diameter of a laser beam changes with distance from its source. The beams from typical lasers, including laser pointers, start relatively narrow and widen as gradually as the physics of light propagation will allow. But with the help lenses, you can change that widening process dramatically. For example, if you send a typical laser beam through a converging lens that has a focal length of 1 foot, the laser beam will converge to a very narrow "beam waist" 1 foot beyond the lens and will then spread relatively quickly with distance. It will return to its original diameter 1 foot beyond its waist and to 10 times its original diameter 10 feet beyond its waist. With its light spread out by a factor of 10 in both height and width, it will have only 1/100th the intensity (power per unit area) of the original beam. Because of its large size, only a fraction of the beam and its light power will now enter a person's iris and focus on their retina.
Using this scheme, you can have a beam that is extremely intense for the first 2 feet, including a super-intense waist at the 1-foot mark. But beyond that point, the beam spreads quickly and soon becomes so wide that it is no longer a eye hazard.
If the temperature of overly moist air is 32 F or below, planes preparing for takeoff can accumulate heavy burdens of ice. When water vapor condenses as ice directly onto the wings themselves, that condensation process is called deposition and is familiar to you as frost. Deposition is a relatively slow process, so most of the trouble for planes occurs when it is actually snowing or sleeting. Removing the ice then requires either heat or chemicals.
When the plane is flying at high altitudes, however, the air is extremely dry. Even though the air temperature is far below the freezing temperature of water, the fraction of water molecules in the air is nearly zero and the relative humidity is much less than 100%. That means that an ice cube suspended in that dry air would actually evaporate away to nothing. Technically, that "evaporation" of ice directly into water vapor is call sublimation and you've seen it before. Think of all the foods that have experienced freezer burn in your frost-free (i.e., extremely dry air) refrigerator or the snow that has mysteriously disappeared from the ground during a dry spell even though the temperature has never risen above freezing. Both are cases of sublimation — where water molecules left the ice to become moisture in the air.
The first approach, shifting the frequencies/wavelengths, is seriously difficult. There are optical techniques for adding and subtracting optical waves from one another and thereby shifting their frequencies/wavelengths, but those techniques work best with the intense waves available with lasers. For example, the green light produced by some laser pointers actually originated as invisible infrared light and was doubled in frequency via a non-linear optical process in a special crystal. The intensity and pure frequency of the original infrared laser beam makes this doubling process relatively efficient. Trying to double infrared light coming naturally from the objects around you would be extraordinarily inefficient. In general, trying to shift the frequencies/wavelengths of the various electromagnetic waves in your environment so that you can see them is pretty unlikely to ever work as a way of seeing the invisible portions of the electromagnetic spectrum.
The second approach, imaging invisible portions of the electromagnetic spectrum and then presenting a false-color reproduction to the viewer, is relatively straightforward. If it's possible to image the radiation and detect it, it's possible to present it as a false-color reproduction. I'm talking about a camera that images and detects invisible electromagnetic radiation and a computer that presents a false-color picture on a monitor. Imaging and detecting ultraviolet and x-ray radiation is quite possible, though materials issues sometimes makes the imaging tricky. Imaging and detecting infrared light is easy in some parts of the infrared spectrum, but detection becomes problematic at long wavelengths, where the detectors typically need to be cooled to extremely low temperatures. Also, the resolution becomes poor at long wavelengths.
Camera systems that image ultraviolet, x-ray, and infrared radiation exist and you can buy them from existing companies. They're typically expensive and bulky. There are exceptions such as near-infrared cameras — silicon imaging chips are quite sensitive to near infrared and ordinary digital cameras filter it out to avoid presenting odd-looking images. In other words, the camera would naturally see farther into the infrared than our eyes do and would thus present us with images that don't look normal.
In summary, techniques for visualizing many of the invisible portions of the electromagnetic spectrum exist, but making them small enough to wear as glasses... that's a challenge. That said, it's probably possible to make eyeglasses that image and detect infrared or ultraviolet light and present false-color views to you on miniature computer monitors. Such glasses may already exist, although they'd be expensive. As for making them small enough to wear as contact lenses... that's probably beyond what's possible, at least for the foreseeable future.
Part of the reason why it takes so long for the dissolved gases to come out of solution is that the gas can only leave through the exposed surface of the liquid. In an open bottle of carbonated beverage that may be only a few square inches or a few dozen square centimeters. The dissolved gas has to find its way to that exposed surface and break free of the liquid. That's a slow process. The same thing is happening in your wine: the dissolve carbon dioxide and oxygen gases must normally find their way to the top of the tank and then break free to enter the gaseous region at the top of the tank — another slow processes. To speed the escape of dissolved gases, you can enlarge the exposed surface of the liquid by bubbling an inert gas through the liquid. Here, inert gas is any gas that doesn't dissolve significantly in the liquid and that doesn't affect the liquid if it does dissolve. Nitrogen is great for wine because it doesn't interact chemically with the wine. As you let bubbles of nitrogen float upward through the wine, you provide exposed surface within the body of the liquid wine and allow carbon dioxide and oxygen to break free of the liquid and enter those bubbles.
The spherical interface between the gas bubble and the surrounding liquid is a busy, active place — gas molecules are moving between the gas and liquid in both directions. Because carbon dioxide is over-concentrated in the liquid, it is statistically more likely for a carbon dioxide molecule to leave the liquid and enter the bubble's gas than the other way around. It takes a little energy to break those carbon dioxide molecules free of the liquid and that need for energy affects the balance between dissolved carbon dioxide and gaseous carbon dioxide at equilibrium. The harder it is for the carbon dioxide molecules to obtain the energy they need to escape from the liquid, the greater the equilibrium concentration of dissolved carbon dioxide — the saturated concentration. But your wine is supersaturated, containing more than the equilibrium concentration of dissolved carbon dioxide, so carbon dioxide molecules go from liquid to gas more often than the other way around.
When the degree of supersaturation (excess gas concentration) is high, the transfer of gas molecules from liquid to gas bubble can be fast enough to make the bubbles grow in size significantly as they float up through the wine. You can see this type of rapid bubble growth in a glass of freshly poured soda, beer, or champagne. In beer, champagne, and your wine, however, the liquid surface of the bubble contains various natural chemicals that alter the interface with the gas and affect bubble growth. The "tiny bubbles" of good champagne reflect that influence.
Another way to provide the extra exposed surface in the wine and thereby allow the supersaturated dissolved gases to come out of solution would be to agitate the wine so violently that empty cavities open up within the wine. Although that approach would provide lots of extra surface, it would probably not be good for the wine. Bubbling gas through the wine is a much more gentle.
The exact choice of gas barely matters as long as it is chemically inert in the wine. Argon or helium would be just as effective, but they're more expensive (and in the case of helium, precious). The temperature of the gas doesn't matter significantly, but the temperature of the wine does. The cooler the wine, the higher the concentration of dissolved carbon dioxide and oxygen it will contain at equilibrium so you'll remove more of those gases if you do your bubbling while the wine is relatively warm.
Metals are good conductors of electricity and effectively "short out" any electric fields that are parallel to their surfaces. Microwaves reflect from the metal walls because those walls force the electric fields of the microwaves to cancel parallel to their surfaces and that necessitates a reflected wave to cancel the incident wave. Because of that cancellation at the conducting surfaces, the intensity of the microwaves at the walls is zero or very close to zero.
The ant survived by staying within a tiny fraction of the microwave wavelength (about 12.4 cm) of the metal surfaces, where there is almost zero microwave intensity. Had the ant ventured out onto your cup, it would have walked into real trouble. Once exposed to the full intensity of the microwaves, it would not have fared so well.
If you let the flames go on long enough and enough carbon develops, you'll probably start getting plasma balls in the oven (lots of fun, but not great for the oven... you can scorch its top surface because those plasma balls rise and skittle around the ceiling of the oven). Anyway, you can probably find the carbon areas if you look closely enough, but they're no worse than a little burnt toast.
By shrinking the volume of gas over the soda, your boyfriend reduces the number of CO2 molecules that must enter the gas phase in order to reestablish that equilibrium. BUT, when dense gas develops in the squeezed bottle, the high pressure of that gas will reinflate the bottle to its original size. The benefits of shrinking the gas volume will thus be lost.
To succeed in keeping more of the CO2 molecules in solution, you have to make sure that the squeezed bottle stays squeeze. That's hard to do. You're probably better off pouring the soda gently into a smaller bottle, one that just barely holds all of the liquid. That smaller bottle won't expand as a dense gas of CO2 forms above the liquid soda and the soda will reestablish its equilibrium without losing too many of its dissolved CO2 molecules.
When you watch a distant object move, you don't see it change angles quickly so you perceive it as moving relatively slowly. Take the moon for example: it is moving thousands of miles an hour yet you can't see it move at all. It's just so far away that you see no angular change. And when you look down from a high-flying jet, the distant ground is changing angles slowly and therefore looks like it's not moving fast.
In practice, however, most of the radiation involved in baking these desserts and letting them cool on a kitchen counter is in the infrared and it's hard to tell just what color a brownie or cake is in the infrared. It's likely that both are pretty dark when viewed in infrared light. Basically, even things that look white to your eye are often gray or black in the infrared. Thus I suspect that both the brownie and cake absorb most of the thermal radiation they receive while being baked and emit thermal radiation efficienty while they're cooling on the counter.
The fact that light waves can travel in vacuum, and don't need any material to carry them, was disturbing to the physicists who first studied light in detail. They expected to find a fluid-like aether, a substance that was the carrier of electromagnetic waves. Instead, they found that those waves travel through truly empty space. One thing led to another, and soon Einstein proposed that the speed of light was profoundly special and that space and time were interrelated by way of that speed of light.
That said, however, let me make two comments. First, the question quickly turns to computer interface issues, as though the chemical analysis part is trivial in comparison to computer presentation part. Physical science and computer science are truly different fields and not everything in the scientific domain can be reduced to a software package. Physics and chemistry haven't disappeared with the advent of computers and there will never be a firmware upgrade for your microwave oven that will turn it into a nutritional analysis laboratory. As a society, we've gone a bit too far in replacing science education with technology education, particularly computer software.
Second, while remote chemical analysis isn't easy, it can be done in certain cases with the clever use of physics and chemistry. One of my friends here at Virginia, Gaby Laufer, has developed an instrument that studies the infrared light transmitted by the air and can determine whether that air contains any of a broad variety of toxic or dangerous gases in a matter of seconds. Air's relative transparency makes it easier to analyze than an opaque casserole, but even when you can see through something it's not trivial to see what it contains. Gaby's instrument does a phenomenal job of fingerprinting the gas's absorption features and identifying trouble.
Note added: a reader informed me that there are now microwave ovens that can read bar codes and adjust their cooking to match the associated food. A scale in the base of the oven can determine the food's weight and cook it properly. Another reader suggested that a microwave oven might be able to measure the food's microwave absorption and weight in order to adjust cooking power and time. While that's also a good possibility, ovens that sense food temperature or the humidity inside the oven can achieve roughly the same result by turning themselves off at the appropriate time.
To clarify the term "net force," note that when an object is experiencing several separate forces, it doesn't accelerate in response to each one individually. Instead, it accelerates in response to the sum of all the forces acting on it: the net force. Remember that forces have directions associated with them (forces are vector quantities), so when you sum them you must consider their directions carefully. The proper force to consider in Newton's second law is actually the net force on the object. If you know both the net force on the object and the object's mass, you can predict the object's acceleration. And if the net force is zero, then the object doesn't accelerate at all — it coasts.
Despite the scary title "microwave radiation," a microwave oven is basically just another household electronic device. It is an extremely close relative of a convention cathode-ray-tube television set. If you're OK with putting CRT televisions and computer monitors in the landfill, you should have no problems with putting microwave ovens there, too. Even when the microwave oven is on, all it has inside it is microwave radiation and that's just not a big deal. The instant you turn it off, it doesn't even have those microwaves in it. It's just boring inert electronic parts and they'll sit in the landfill for generations, rusting and decaying like every other abandoned electronic gadget. I'd rather see it go to a recycling center and have its precious materials returned to the resource bin, but as landfill junk goes, it's not all that bad. Given that toxic chemicals are the primary concern with landfills, microwave ovens are probably rather innocuous. They have no radioactive contents and although the high-voltage capacitor might have oil in it, that oil can no longer be the toxic PCBs that were common a few decades ago. Even when that oil leaks into the environment, it's probably not going to do much.
So there you have it, microwave ovens go to their graves no more loudly or dangerously than old televisions or computers or cell phones.
In fact, I might start calling cell phones "microwave phones" because that's exactly what they are. They communicate with the base unit by way of microwave radiation. Given the number of people who have cell phones semi-permanently installed in their ears, concerns about microwave radiation should probably be redirect from microwave ovens to "microwave phones." Think about it next time your six-year-old talks for an hour with her best friend on that "microwave phone."
So far, so good. But if you make that straw longer, you'll need to suck harder. That's because as the column of water gets taller, it gets heavier. It needs a more severe pressure imbalance to push it upward and support it. By the time the straw and water column get to be about 40 feet tall, you'll need to suck every bit of air out from inside the straw because the pressure imbalance needed to support a 40-foot column of water is approximately one atmosphere of pressure. If the straw is taller than 40 feet, you're simply out of luck. Even if you remove all the air from within the straw, the atmospheric pressure of the water below the straw won't be able to push the water up the straw higher than about 40 feet.
To get the water to rise higher in the straw, you'll need to install a pump at the bottom. The pump increases the water pressure there to more than 1 atmosphere, so that there is a bigger pressure imbalance available and therefore the possibility of supporting a taller column of water.
OK, so returning to your question: once a well is more than about 40 feet deep, getting the water to the surface requires a pump at the bottom. That pump can boost the water pressure well above atmospheric and thereby push the water to the surface despite the great height and weight of the water column. Suction surface pumps are really only practical for water that's a few feet below the surface; after that, deep pressure pumps are a much better idea.
OK, so there is actually a multi-way tie for first place in the speed rankings. Your daughter's question is what comes next? The actual answer is that it's a many-way tie between everything else. With enough energy, you can get anything moving at just under the speed of light, at least in principle. For example, subatomic particles such as electrons, protons, and even atomic nuclei are routinely accelerated to just under the speed of light in sophisticated machines around the world. The universe itself has natural accelerators that whip subatomic particles up until they are traveling so close to the speed of light that it's hard to tell that they aren't quite at the speed of light. Nonetheless, I assure you that they're not. The speed of light is so special that nothing that has any mass at all can possibly travel at the speed of light. Only the ephemeral non-massive particles such as light particles (photons), gravity particles (gravitons), and strong force particles (gluons) can actually travel at the speed of light. In fact, once photons, gravitons, and gluons begin to interact with matter, they don't travel at the speed of light either. It's sort of a guilt-by-association: as soon as these massless particles leave the essential emptiness of the vacuum and begin to interact with matter, even they can't travel at the speed of light anymore.
That said, I can still offer the likely second place finisher on the speed list. I'm going to skip over light, gravity, and the strong force traveling in extremely dilute matter because that's sort of cheating — if you take something that naturally travels at the speed of light and slow it down the very, very slightest bit, of course it will come ridiculously close to the speed of light. In real second place are almost certainly cosmic ray particles. These cosmic rays are actually subatomic particles that are accelerated to fantastic energies by natural processes in the cosmos. How such accelerators work is still largely a mystery but some of the cosmic ray particles that reach our atmosphere have truly astonishing energies — once in a while a single cosmic ray particle that is smaller than an atom will carry enough energy with it that it is capable of moving small ordinary objects around. Even if it carries the energy of a fly, that's a stupendous amount of energy for an atomic fragment. Those cosmic ray particles are traveling so close to the speed of light that it would be a photo-finish with light itself.
Coming up with good ideas is hard work and if I had them, I'd have gotten hold of such a magnet myself. Although science is often taught as formulas and factoids, it's really about thinking and observing, and good ideas are nearly always more important than good equipment. Good ideas don't linger unstudied for long when commercial equipment is all it takes to pursue them.
The optical elements in your eye that are responsible for this image formation are the cornea and the lens. The cornea does most of the work of converging the light so that it focuses, while the lens provides the fine adjustment that allows that focus to occur on your retina.
If you're farsighted, the two optical elements aren't strong enough to form an image of nearby objects on your retina so you have trouble getting a clear view while reading. Your eye needs help, so you wear converging eyeglasses. Those eyeglasses boost the converging power of your eye itself and allow your eye to form sharp images of nearby objects on your retina.
If you're nearsighted, the two optical elements are too strong and need to be weakened in order to form sharp images of distant objects on your retina. That's why you wear diverging eyeglasses.
People are surprised when I tell them that they're nearsighted or farsighted. They wonder how I know. My trick is simple: I look through their eyeglasses at distant objects. If those objects appear enlarged, the eyeglasses are converging (like magnifying glasses) and the wearer must be farsighted. If those objects appear shrunken, the eyeglasses are diverging (like the security peepholes in doors) and the wearer is nearsighted. Try it, you'll find that it's easy to figure out how other people see by looking through their glasses as they wear them.
Because your finger and your body conduct electricity, the pad's electric charge is actually interacting with the electric charge on your entire body. In contrast, a straw is insulating, so the pad can only interact with charge at its tip, and while your car keys are conducting, they are too small to have the effect that your body has on that pad.
There are at least two ways for a pad and its electronics to sense your body and its electric charges. The first way is for the electronics to apply a rapidly alternating electric charge to the pad and to watch for the pad's charge to interact with charge outside the pad (i.e., on your body). When the pad is by itself, the electronics can easily reverse the pad's electric charge because that charge doesn't interact with anything. But when your hand is near the pad or touching it, it's much harder for the electronics to reverse the pad's electric charge. If you're touch the pad, the electronics has to reverse your charge, too, so the electronics sense a new sluggishness in the pad's response to charge changes. Even when you're not quite touching the pad, the electronics has some add difficulty reversing the pad's charge. That's because the pad's charge causes your finger and body to become electrically polarized: charges opposite to those on the pad are attracted onto your finger from your body so that your finger becomes electrically charged opposite to the charge of the pad. When the electronics then tries to withdraw the charge from the pad in order to reverse the pad's charge, your finger's charge acts to make that withdrawal difficult. The electronics finds that it must struggle to reverse the pad's charge even though you're not in direct contact with the pad. Overall, your finger complicates the charge reversals whenever it's near or touching the pad.
The second way for the pad's electronics to sense your presence is to let your body act as an antenna for electromagnetic influences in the environment. We are awash in electric and magnetic fields of all sorts and the electric charge on your body is in ceaseless motion as a result. You've probably noticed that touching certain input wires of a stereo amplifier produces lots of noise in the speakers; that's partly a result of the electromagnetic noise in our environment showing up as moving charge on your body. The little pad on the soda dispenser picks up a little of this electromagnetic noise all by itself. When you approach or touch the pad, however, you dramatically increase the amount of electromagnetic noise in the pad. The pad's electronics easily detect that new noise.
In short, soda dispenser pads are really detecting large electrically conducting objects. Their ability to sense your finger even before it makes contact is important because they need to work when people are wearing gloves. I first encountered electrical touch sensors in elevators when I was a child and I loved to experiment with them. Conveniently, they'd light up when they detected something and there was no need to clean up spilled soda. We'd try triggering them with elbows and noses, and a whole variety of inanimate objects. They were already pretty good, but modern electronics has made touch pads even better. The touch switches used by some lamps and other appliances function in essentially the same way.
The explanation is both simple and interesting: the rate at which water molecules leave the cloths doesn't depend on whether the window is open or closed, but the rate at which water molecules return to the cloths certainly does. That return rate depends on the air's moisture content and can range from zero in dry air to extremely fast in damp air. Air's moisture content is usually characterized by its relative humidity, with 100% relative humidity meaning that air's water molecules land on surfaces exactly as fast as water molecules in liquid water leave its surface. When you expose a glass of water to air at 100% relative humidity, the glass will neither lose nor gain water molecules because the rates at which water molecules leave the water and land on the water are equal. Below 100% relative humidity, the glass will gradually empty due to evaporation because leaving will outpace landing. Above 100% relative humidity, the glass will gradually fill due to condensation because landing will outpace leaving.
The same story holds true for wet clothes. The higher the air's relative humidity, the harder it becomes for water to evaporate from the cloths. Landing is just too frequent in the humid air. At 100% relative humidity the clothes won't dry at all, and above 100% relative humidity they'll actually become damper with time.
When you dry clothes in a room with the window open and the relative humidity of the outdoor air is less than 100%, water molecules will leave the clothes more often than they'll return, so the clothes will dry. But when the window is closed, the leaving water molecules will remain trapped in the room and will gradually increase the room air's relative humidity. The drying process will slow down as the water-molecule return rate increases. When the room air's relative humidity reaches 100%, drying will cease altogether.
When you ground an appliance, you're are making it possible for electric charge to equilibrate between that appliance and the earth. The earth is approximately neutral, so a grounded appliance can't retain large amounts of either positive or negative charge. That's a nice safety feature because it means that you won't get a shock when you touch the appliance, even if one of its power wires comes loose and touches the case. Any charge that the power wire tries to deposit on the case will quickly flow to the earth as the appliance and earth equilibrate.
But charge can't escape from the appliance through the grounding wire instantly. Light takes about 1 nanosecond to travel 1 foot and electricity takes a little longer than that. For charge to leave your appliance for the earth might well require 50 nanoseconds or more. That's not a problem for ordinary power distribution, so grounding is generally a great idea. Each cycle of the 60-Hz AC power in the U.S. takes 18 milliseconds to complete, so the appliance and earth have plenty of time to equilibrate with one another. But a cycle of the microwave power in the oven takes less about 0.4 nanoseconds to complete and there's just no time for the appliance and earth to equilibrate. At microwave frequencies, the electric current flowing through a long wire is wavelike, meaning that at one instant in time the wire has both positive and negative patches, spaced half a wavelength apart along its length. It's carrying an electromagnetic ripple.
The metal screen on the oven's door has to reflect the microwaves all by itself. It does this without a problem because the holes are so much smaller than 12.4 centimeters that currents easily flow around them during a cycle of the microwaves. Those currents are able to compensate for the holes in the screens and cause the microwaves to reflect perfectly.
The story wouldn't be the same if the bird made the mistake of spanning the gap from one wire to another. In that case, current could flow through the bird from one wire to the other and the bird would run the serious risk of becoming a flashbulb. Squirrels occasionally do this trick when they accidentally bridge a pair of wires. Some of the unexpected power flickers that occur in places where the power lines run overhead are caused by squirrels and occasionally birds vaporizing when they let current flow between power lines.
Most likely, one of you has been in contact with a insulating surface that has exchanged charge with you. For example, if you walked across wool carpeting in rubber-soled shoes, that carpeting has probably transferred some of its electrons to your shoes and your shoes have then spread those electrons out onto you. Rubber binds electrons more tightly than wool and so your shoes tend to steal a few of electrons from wool whenever it gets a chance. If you walk around a bit or scuff your feet, you'll typically end up with quite a large number of stolen electrons on your body. When you then go and kiss Uncle Al, about half of those electrons spread suddenly onto him and that current flow is shocking!
Anyone who claims to be able to extract useful energy through a process that starts with water and ends with water is a charlatan. Either they aren't producing any useful energy or it's coming from some other source. In these sorts of frauds, there is usually some electrical component that is supposedly needed to keep a minor part of the apparatus functioning. That component isn't insignificant at all; it's what actually keeps the entire apparatus functioning!
Hydrogen has such a mythical aura to it, but in the context of energy, it's just another fuel. Actually, it's more of any energy storage medium than a basic fuel. That's because hydrogen doesn't occur naturally on earth and can only be produced by consuming another form of energy. There is so much talk about "the hydrogen economy"Âť and the notion that hydrogen will rescue us from our dependence on petroleum. Sadly, politicians who promote hydrogen as the energy panacea neither understand science nor respect those who do. Since it takes just as much energy to produce hydrogen from water as is released when that hydrogen burns back into water, hydrogen alone won't save us.
As we grow progressively more desperate for useable energy, the amount of fraud and misinformation will only increase. There are only a few true sources for useable energy: solar energy (which includes wind power, hydropower, and biomass), fossil fuels (which include petroleum and coal), geothermal energy, and nuclear fuels. Hydrogen is not among them; it can be produced only at the expense of one of the others. Even ethanol, which is touted as an environmentally sound replacement for petroleum, has its problems; producing a gallon of ethanol can all too easily consume a gallon of petroleum.
Where energy is concerned, watch out for fraud, hype, PR, and politics. If we survive the coming energy and climate crises, it will be because we've learned to conserve energy and to obtain it primarily from solar and perhaps nuclear sources. It will also be because we've learned to set politics and self-interest aside long enough to make accurate analyses and sound decisions.
I'll begin to looking at how dust settles in calm air near the ground. That dust experiences its weight due to gravity, so it tends to descend. Each particle would fall like a rock except that it's so tiny that it experiences overwhelming air resistance. Instead of falling, it descends at an incredibly slow terminal velocity, typically only millimeters per second. It eventually lands on whatever is beneath it, so a room's floor gradually accumulates dust. But dust also accumulates on vertical walls and even on ceilings. That dust is held in place not by its weight but by electrostatic or chemical forces. When you go into an abandoned attic, most of the dust is on the floor, but there's a little on the walls and on the ceiling.
OK, now to the space shuttle. The shuttle is orbiting the earth, which means that although it has weight and is falling freely, it never actually reaches the earth because it's heading sideways so fast. Without gravity, its inertia would carry it horizontally out into space along a straight line path. Gravity, however, bends that straight line path into an elliptical arc that loops around the earth as an orbit.
So far no real surprises: dust near ground level settles in calm air and the shuttle orbits the earth. The surprise is that particles of space dust particles also orbit the earth! The shuttle orbits above the atmosphere, where there is virtual no air. Without air to produce air resistance, the dust particles also fall freely. Those with little horizontal speed simply drop into the atmosphere and are lost. But many dust particles have tremendous horizontal speeds and orbit the earth like tiny space shuttles or satellites.
Whether they are dropping toward atmosphere or orbiting the earth, these space dust particles are typically traveling at velocities that are quite different in speed or direction from the velocity of the space shuttle. The relative speed between a dust particle and the shuttle can easily exceed 10,000 mph. When such a fast-moving dust particle hits the space shuttle, it doesn't "settle."Âť Rather, it collides violently with the shuttle's surface. These dust-shuttle collisions erode the surfaces of the shuttle and necessitate occasional repairs or replacements of damaged windows and sensors. Astronauts on spacewalks also experience these fast collisions with space dust and rely on their suits to handle all the impacts.
Without any air to slow the relative speeds and cushion the impacts, its rare that a particle of space dust lands gracefully on the shuttle's surface. In any case, gravity won't hold a dust particle in place on the shuttle because both the shuttle and dust are falling freely and gravity doesn't press one against the other. But electrostatic and chemical attractions can hold some dust particles in place once they do land. So the shuttle probably does accumulate a very small amount of accumulated space dust during its travels.
The first scantron systems, however, were far less capable. They read the pencil marks by shining light through the paper and into Lucite light guides that conveyed the transmitted light to phototubes. Whenever something blocked the light, the scantron system recorded a mark. The marks therefore had to be opaque in the range of light wavelengths that the phototubes sensed, which is mostly blue. Pencil marks were the obvious choice because the graphite in pencil lead is highly opaque across the visible light spectrum. Graphite molecules are tiny carbon sheets that are electrically conducting along the sheets. When you write on paper with a pencil, you deposit these tiny conducting sheets in layers onto the paper and the paper develops a black sheen. It's shiny because the conducting graphite reflects some of the light waves from its surface and it's black because it absorbs whatever light waves do manage to enter it.
A thick layer of graphite on paper is not only shiny black to reflected light, it's also opaque to transmitted light. That's just what the early scantron systems needed. Blue inks don't absorb blue light (that's why they appear blue!), so those early scantron systems couldn't sense the presence of marks made with blue ink. Even black inks weren't necessarily opaque enough in the visible for the scantron system to be confident that it "saw" a mark.
In contrast, modern scantron systems used reflected light to "see" marks, a change that allows scantron forms to be double-sided. They generally do recognize marks made with black ink or black toner from copiers and laser printers. I've pre-printed scantron forms with a laser printer and it works beautifully. But modern scantron systems ignore marks made in the color of the scantron form itself so as not to confuse imperfections in the form with marks by the user. For example, a blue scantron form marked with blue ink probably won't be read properly by a scantron system.
As for why only #2 pencils, that's a mechanical issue. Harder pencil leads generally don't produce opaque marks unless you press very hard. Since the early scantron machines needed opacity, they missed too many marks made with #3 or #4 pencils. And softer pencils tend to smudge. A scantron sheet filled out using a #1 pencil on a hot, humid day under stressful circumstances will be covered with spurious blotches and the early scantron machines confused those extra blotches with real marks.
Modern scantron machines can easily recognize the faint marks made by #3 or #4 pencils and they can usually tell a deliberate mark from a #1 pencil smudge or even an imperfectly erased mark. They can also detect black ink and, when appropriate, blue ink. So the days of "be sure to use a #2 pencil" are pretty much over. The instruction lingers on nonetheless.
One final note: I had long suspected that the first scanning systems were electrical rather than optical, but I couldn't locate references. To my delight, Martin Brown informed me that there were scanning systems that identified pencil marks by looking for their electrical conductivity. Electrical feelers at each end of the markable area made contact with that area and could detect pencil via its ability to conduct electric current. To ensure enough conductivity, those forms had to be filled out with special pencils having high conductivity leads. Mr. Brown has such an IBM Electrographic pencil in his collection. This electrographic and mark sense technology was apparently developed in the 1930s and was in wide use through the 1960s.
At the risk of telling you more than you ever want to know, I'll point out that the filament behaves approximately according to Ohm's law: the current that flows through it is proportional to the voltage difference between its two ends. The larger that voltage difference, the bigger the forces and the more current that flows. This ohmic behavior allows incandescent lightbulbs to survive decreases in voltage unscathed. They don't, however, do well with increases in voltage, since they'll then carry too much current and receive so much power that they'll overheat and break. Voltage surges, not voltage decreases, are what kill lightbulbs.
The other appliances you mention are not ohmic devices and the currents that flow through them are not simply proportional to the voltage supplied to your home. Motors are a particularly interesting case; the average current a motor carries is related in a complicated way to how fast and how easily it's spinning. A motor that's turning effortlessly carries little average current and receives little electric power. But a motor that is struggling to turn, either because it has a heavy burden or because it can't obtain enough electric power to overcome starting effects, will carry a great deal of average current. An overburdened or non-starting motor can become very hot because it's wiring deals inefficiently with the large average current, and it can burn out. While I've never heard of a refrigerator motor dying during a brownout, it wouldn't surprise me. I suspect that most appliance motors are protected by thermal sensors that turn them off temporarily whenever they overheat.
Modern electronic devices are also interesting with respect to voltage supply issues. Electronic devices operate on specific internal voltage differences, all of which are DC — direct current. Your home is supplied with AC — alternating current. The power adapters that transfer electric power from the home's AC power to the device's DC circuitry have evolved over the years. During a brownout, the older types of power adapters simply provide less voltage to the electronic devices, which misbehave in various ways, most of which are benign. You just want to turn them off because they're not working properly. It's just as if their batteries are worn out.
But the most modern and sophisticated adapters are nearly oblivious to the supply voltage. Many of them can tolerate brownouts without a hitch and they'll keep the electronics working anyway. The power units for laptops are a case in point: they can take a whole range of input AC voltages because they prepare their DC output voltages using switching circuitry that adjusts for input voltage. They make few assumptions about what they'll be plugged into and do their best to produce the DC power required by the laptop.
In short, the motors in your home won't like the brownout, but they're probably protected against the potential overheating problem. The electronic appliances will either misbehave benignly or ride out the brownout unperturbed. Once in a while, something will fail during a brownout. But I think that most of the damage is down during the return to normal after the brownout. The voltages bounce around wildly for a second or so as power is restored and those fluctuations can be pretty hard some devices. It's probably worth turning off sensitive electronics once the brownout is underway because you don't know what will happen on the way back to normal.
The evanescent wave problem is more likely. When any electromagnetic wave reflects from a conducting surface that has small holes in it, there is what is known as an evanescent wave extending into and somewhat beyond each hole. It's as though the wave is trying to figure out whether or not it can pass through the opening and so it tries. Even when it discovers that the hole is far too small for it pass through (i.e., much smaller than its wavelength), it still offers electromagnetic intensity in the region just beyond the hole. The extent of the evanescent wave increases with the size of the hole. The microwave oven's screen has very small holes and it is located inside the glass window. The evanescent waves associated with those holes cut off so quickly that you can hold your hand against the glass and not expose your skin to significant microwaves. But once you've torn a larger hole in the screen, the evanescent waves can extend farther through that screen and perhaps out beyond the surface of the glass window. If you press your hand against the window just in front of the tear while the microwave oven is on, you may burn your hand.
Finally, there is the issue of arcing. To reflect the microwaves, the conducting screen must carry electric currents. The microwaves' electric fields push electric charge back and forth in the conducting screen and it is that moving charge (i.e., electric current) that ultimately redirects the microwaves back into the cooking chamber as a reflection. Those electric currents in the screen are real and they're not going to take kindly to that tear. It's a weak spot in the conducting surface through which they flow. Weak electrical paths can heat up like lightbulb filaments when they carry currents. Moreover, charge that should flow across the torn region can accumulate on sharp edges and leap through the air as an arc. If either of these processes happens, it may scorch the window and the screen, and cause increasing trouble.
You could be lucky: the leakage could be zero, the evanescent waves could remain far enough inside the window to never cause injury, and the tear could never heat up or arc. But the risk of operating this damaged microwave oven is not insignificant. Since it's an installed unit, I'd suggest replacing the screen or the door. There are a number of websites that sell replacement parts for microwave ovens and I have used them to replace the door on our microwave oven.
Since the earth is so much more massive than the moon, their combined center of mass is 81 times closer to the middle of the earth than it is to the middle of the moon. In fact, it's inside the earth, though not at the middle of the earth. As a result, the earth's orbital motion takes the form of a wobble rather than a more obvious looping path. Nonetheless, the earth is orbiting.
I hope that you can see that there is no reason why the earth should be fixed in space while the moon orbits about it. You've been sold a bill of goods. The mistaken notion that the moon orbits a fixed earth is a wonderful example of the "factoid science" that often passes for real science in our society.
Because thinking and understanding involve hard work, people are more comfortable when the thought and understanding have been distilled out of scientific issues and they've been turned into memorizable sound bites. Those sound bites are easy to teach and easy to test, but they're mostly mental junk food. A good teacher, like a good scientist, will urge you to question such factoids until you understand the science behind them and why they might or might not be true.
When my children were young, I often visited their schools to help teach science. In third grade, the required curriculum had them categorizing things into solutions or mixtures. Naturally, I showed them a variety of things that are neither solutions nor mixtures. It was a blast. Science is so much more interesting than a collection of 15-second sound bites.
Lenses are often characterized by their f-numbers, where f-number is the ratio of effective focal length to effective lens diameter. Focal length is the distance between the lens and the real image it forms of a distant object. For example, if a particular converging lens projects a real image of the moon onto a piece of paper placed 200 millimeters (200 mm) from the lens, then that lens has a focal length of 200 mm. And if the lens is 50 mm in diameter, it has an f-number of 4 because 200 mm divided by 50 mm is 4.
Based on purely geometrical arguments, it's easy to show that lenses with equal f-numbers project images of equal brightness onto their image sensors and the smaller the f-number, the brighter the image. Whether a lens is a wide-angle or telephoto, if it has an f-number of 4, then its effective focal length is four times the effective diameter of its light gathering lens. Since telephoto lenses have long focal lengths, they need large effective diameters to obtain small f-numbers.
But notice that I referred always to "effective diameter" and "effective focal length" when defining f-number. That's because there are many modern lenses that are so complicated internally that simply dividing the lens diameter by the distance between the lens and image sensor won't tell you much. Many of these lenses have zoom features that allow them to vary their effective focal lengths over wide ranges and these lenses often discard light in order to improve image quality and avoid dramatic changes in image brightness while zooming.
You might wonder why a lens would ever choose to discard light. There are at least two reasons for doing so. First, there is the issue of image quality. The smaller the f-number of a lens, the more precise its optics must be in order to form a sharp image. Low f-number lenses are bringing together light rays from a wide range of angles and getting all of those rays to overlap perfectly on the image sensor is no small feat. Making a high-performance lens with an f-number less than 2 is a challenge and making one with an f-number of less than 1.2 is extremely difficult. There are specialized lenses with f-numbers below 1 and Canon sold a remarkable f0.95 lens in the early 1960's. The lowest f-number camera lens I have ever owned is an f1.4.
Secondly, there is the issue of depth-of-focus. The smaller the f-number, the smaller the depth of focus. Again, this is a geometry issue: a low-f-number lens is bringing together light rays from a wide range of angles and those rays only meet at one point before separating again. Since objects at different distances in front of the lens form images at different distances behind the lens, it's impossible to capture sharp images of both objects at once on a single image sensor. With a high-f-number lens, this fact isn't a problem because the light rays from a particular object are rather close together even when the object's image forms before or after the image sensor. But with a low-f-number lens, the light rays from a particular object come together acceptably only at one particular distance from the lens. If the image sensor isn't at that distance, then the object will appear all blurry. If a zoom lens didn't work to keep its f-number relatively constant while zooming from telephoto to wide angle, its f-number would decrease during that zoom and its depth-of-focus would shrink. To avoid that phenomenon, the lens strategically discards light so as to keep its f-number essentially constant during zooming.
In summary, larger diameter lenses tend to be better at producing photographic and video images, but that assumes that they are high-quality and that they can shrink their effective diameters in ways that allow them to imitate high-quality lenses of smaller diameters when necessary. But flexible characteristics always come at some cost of image quality and the very best lenses are specialized to their tasks. Zoom lenses can't be quite as good as fixed focal length lenses and a large-diameter lens imitating a small-diameter lens by throwing away some light can't be quite as good as a true small-diameter lens.
As for my sources, one of the most satisfying aspects of physics is that you don't always need sources. Most of the imaging issues I've just discussed are associated with simple geometric optics, a subject that is part of the basic toolbox of an optical physicist (which I am). You can, however, look this stuff up in any book on geometrical optics.
If a plate is "microwave safe," it will barely absorb the microwaves and heat extremely slowly. In effect, the microwave oven will be operating empty and the electromagnetic fields inside it will build up to extremely high levels. Since the walls of the oven are mirrorlike and the plate is almost perfectly transparent to microwaves, the electromagnetic waves streaming out of the oven's magnetron tube bounce around endlessly inside the oven's cooking chamber. The resulting intense fields can produce various types of electric breakdown along the walls of the cooking chamber and thereby damage the surface with burns or arcs. Furthermore, the intense microwaves in the cooking chamber will reflect back into the magnetron and can upset its internal oscillations so that it doesn't function properly. Although magnetrons are astonishingly robust and long-lived, they don't appreciate having to reabsorb their own emitted microwaves. In short, your plates will heat up slowly and you'll be aging your microwave oven in the process. You could wet the plates before putting them in the microwave oven to speed the heating and decrease the wear-and-tear on the magnetron, but then you'd have to dry the plates before use.
If a plate isn't "microwave safe," then it will absorb microwaves and heat relatively quickly. If it absorbs the microwaves uniformly and well, then you can probably warm it to the desired temperature without any problems as long as you know exactly how many seconds it takes and adjust for the total number of plates you're warming. If you heat a plate too long, bad things will happen. It may only amount to burning your fingers, but some plates can't take high temperatures without melting, cracking, or popping. Unglazed ceramics that have soaked up lots of water will heat rapidly because water absorbs microwaves strongly. Water trapped in pores in such ceramics can transform into high-pressure steam, a result that doesn't seem safe to me. And if a plate absorbs microwaves nonuniformly, then you'll get hotspots or burned spots on the plate. Metalized decorations on a plate will simply burn up and blacken the plate. Cracks that contain water will overheat and the resulting thermal stresses will extend the cracks further. So this type of heating can be stressful to the plates.
The water pressure increases quickly with depth because each layer of water must support the weight of all the water layers above it. Since water is dense, heavy stuff, the weight piles on quickly and it takes only 10 meters (34 feet) of descent to increase the water pressure from atmospheric to twice atmospheric. In contrast, the air in the hose is light, fluffy stuff, so its pressure increases rather slowly with depth. Even though each layer of air has to support the weight of all the layers of air above it, the rise in pressure is extremely gradual. It takes miles of atmosphere above the earth for the air pressure to build up to atmospheric pressure near the ground. The air pressure in your hose is therefore approximately unchanged by your descent into the water.
With the water pressure outside rising quickly as you go deeper and the air pressure in your mouth rising incredibly slowly as you go deeper, you quickly find it hard to breathe. Your muscles can push your chest outward against a modest pressure imbalance between outside and inside. But by the time you're a few feet below the surface, you just can't draw air into your lungs through that hose anymore. You need pressurized air, such as that provided by a scuba outfit or a deep-sea diver's compressor system.
Since the freezer has a nearly airtight seal, the air it contains remains inside it for a long time. That means that the odor molecules that occasionally break free of a pungent casserole at one end of the freezer have every opportunity to land on and stick to an ice cube at the other end. With time, the ice cube acquires the scent of the casserole and becomes unappealing.
To stop this migration of molecules, you should seal each item in the freezer in its own container. That way, any molecules that leave the food's surface will eventually return to it. Since ice cubes are normally exposed to the air in the freezer, keeping the odor molecules trapped in their own sealed containers keeps the freezer air fresh and the ice cubes odor-free.
Microwaves themselves have no well-defined shape but they do have firm rules governing their overall structures. Books usually draw microwaves (and all other electromagnetic waves) as wavy lines, as though something was truly going up and down in space. From that misleading representation, it's easy for people to suppose that electromagnetic waves can't get through certain openings.
In reality, electromagnetic waves consist of electric and magnetic fields (influences that push on electric charge and magnetic pole, respectively) that point up and down in a rippling fashion, but nothing actually travels up and down per say. The spatial structures of these fields are governed by Maxwell's equations, a set of four famous relationships that bind electricity and magnetism into a single, unified classical theory. Maxwell's equations dictate the structures of electromagnetic waves and predict that electromagnetic waves on one side of a conducting surface can't propagate through to the other side of that surface. Even if there are small holes in the conducting surface, holes that are much smaller that the wavelength of the waves, those waves can't propagate through the surface. More specifically, the fields die off exponentially as they try to penetrate through the holes and the waves don't propagate on the far side.
The choice of round holes in the oven mesh is simply a practical one. You can pack round holes pretty tightly in a surface while leaving their conducting boundaries relatively robust. And round holes treat all electromagnetic waves equally because they have no wide or narrow directions.
Even though pure cellulose can't be reshaped by melting, it can be softened with water and/or heat. Like ordinary sugar, cellulose is attracted to water and water molecules easily enter its chains. This water lubricates the chains so that the cellulose becomes somewhat pliable and heat increases that pliability. When you iron a damped cotton or linen shirt, both of which consist of cellulose fibers, you're taking advantage of that enhanced pliability to reshape the fabric.
But even when dry, fibrous materials such as paper, cotton, or linen have some pliability because thin fibers of even brittle materials can bend significantly without breaking. If you bend paper gently, its fibers will bend elastically and when you let the paper relax, it will return to its original shape.
However, if you bend the paper and keep it bent for a long time, the cellulose chains within the fibers will begin to move relative to one another and the fibers themselves will begin to move relative to other fibers. Although both of these motions can be facilitated by moisture and heat, time along can get the job done at room temperature. Over months or years in a tightly rolled shape, a sheet of paper will rearrange its cellulose fibers until it adopts the rolled shape as its own. When you then remove the paper from its constraints, it won't spontaneously flatten out. You'll have to reshape it again with time, moisture, and/or heat. If you press it in a heavy book for another long period, it'll adopt a flat shape again.
The stresses frozen into the tempered glass affect its polarizability and give it strange characteristics when exposed to the electromagnetic fields in light. This stressed glass tends to rotate polarizations of the light passing through it. As a result, you see odd reflections of the sky (skylight is polarized to some extent). Those polarization effects become immediately apparent when you wear polarizing sunglasses.
The force pushing mercury back down the column as it cools is tiny in comparison. Mercury certainly does contract when cooled, so that the manufacturer is telling you nonsense. But just because the mercury contracts as it cools doesn't mean that it will all flow back down the column. The mercury needs a push to propel it through its narrow channel.
Mercury is attracted only weakly to glass, so it doesn't really adhere to the walls of its channel. However, like all liquids, mercury has a viscosity, a syrupiness, and this viscosity slows its motion through any pipe. The narrower the pipe, the harder one has to push on a liquid to keep it flowing through that pipe. In fact, flow through a pipe typically scales as the 4th power of that pipe's radius, which is why even modest narrowing of arteries can dramatically impair blood flow in people. The capillaries used in fever thermometers are so narrow that mercury has tremendous trouble flowing through them. It takes big forces to push the mercury quickly through such a capillary.
During expansion, there is easily enough force to push the mercury up through the capillary. However, during contraction, the forces pushing the mercury back down through the capillary are too weak to keep the column together. That's because the only thing above the column of liquid mercury is a thin vapor of mercury gas and that vapor pushes on the liquid much too feebly to have a significant effect. And while gravity may also push down on the liquid if the thermometer is oriented properly, it doesn't push hard enough to help much.
The contracting column of mercury takes hours to drift downward, if it drifts downward at all. It often breaks up into sections, each of which drifts downward at its own rate. And, as two readers (Michael Hugh Knowles and Miodrag Darko Matovic) have both pointed out to me in recent days, there is a narrow constriction in the capillary near its base and the mercury column always breaks at that constriction during contraction. Since the top portion of the mercury column is left almost undisturbed when the column breaks at the constriction, it's easy to read the highest temperature reached by the thermometer.
Shaking the thermometer hard is what gets the mercury down and ultimately drives it through the constriction so that it rejoins into a single column. In effect, you are making the glass accelerate so fast that it leaves the mercury behind. The mercury isn't being pushed down to the bottom of the thermometer; instead, the glass is leaping upward and the mercury is lagging behind. The mercury drifts to the bottom of the thermometer because of its own inertia.
You're right that the glass tube acts as a magnifier for that thin column of mercury. Like a tall glass of water, it acts as a cylindrical lens that magnifies the narrow sliver of metal into a wide image.
Let's start with the differences in types of radiation. Basically, anything that moves is radiation, from visible light, to ultraviolet, to X-rays, to microwaves, to alpha particles, to neutrons, and even to flying pigeons. These different radiations do different things when they hit you, particularly the pigeons. While "ionizing radiations" such as X-rays, ultraviolet, alpha particles, and neutrons usually have enough localized energy to do chemical damage to the molecules they hit, "non-ionizing radiation" such as microwaves and pigeons do not damage molecules. When you and your organic friend worry about toxic changes in food or precancerous changes in your tissue, what really worry you are molecular changes. Microwaves and pigeons don't cause those sorts of changes. Microwaves effectively heat food or tissue thermally, while pigeons bruise food or tissue on impact.
Wearing a lead apron while working around ionizing radiation makes sense, although a simple layer of fabric or sunscreen is enough to protect you from most ultraviolet. To protect yourself against pigeons, wear a helmet. And to protect yourself against microwaves, use metal. The cooking chamber of the microwave oven is a metal box (including the screened front window). So little microwave "radiation" escapes from this metal box that it's usually hard to detect, let alone cause a safety problem. There just isn't much microwave intensity coming from the oven and intensity matters. A little microwaves do nothing at all to you; in fact you emit them yourself!
If you want to detect some serious microwaves, put that microwave detector near your cellphone! The cellphone's job is to emit microwaves, right next to your ear! Before you give up on microwave ovens, you should probably give up on cellphones. That said, I think the worst danger about cellphones is driving into a pedestrian or a tree while you're under the influence of the conversation. Basically, non-ionizing radiation such as microwaves is only dangerous if it cooks you. At the intensities emitted by a cellphone next to your ear, it's possible that some minor cooking is taking place. However, the cancer risk is almost certainly nil.
Despite all this physics reality, salespeople and con artists are still more than happy to sell you protection against the dangers of modern life. I chuckle at the shields people sell to install on your cellphones to reduce their emissions of harmful radiation. The whole point of the cellphone is to emit microwave signals to the receiving tower, so if you shield it you spoil its operation! It would be like wrapping an X-ray machine in a lead box to protect the patient. Sure, the patient would be safe but the X-ray machine would barely work any more.
Returning to the microwave cooking issue, once the food comes out of the microwave oven, there are no lingering effects of its having been cooked with microwaves. There is no convincing evidence of any chemical changes in the food and certain no residual cooking microwaves around in the food. If you're worried about toxic changes to your food, avoid broiling or grilling. Those high-surface-temperature cooking techniques definitely do chemical damage to the food, making it both tasty and potentially a tiny bit toxic. One of the reasons why food cooked in the microwave oven is so bland is because those chemical changes don't happen. As a result, microwave ovens are better for reheating than for cooking.
Momentum is a conserved physical quantity, meaning that it cannot be created or destroyed. It can only be passed from one object to the other. When you let go of the packaged egg and it begins to fall, the downward momentum that gravity transfers into the egg begins to accumulate in the egg. Before you let go, your hand was removing the egg's downward momentum as fast as gravity was adding it, but now the egg is on its own!
Because momentum is equal to an object's mass times its velocity, the accumulating downward momentum in the egg is reflected in its increasing downward speed. With each passing second, the egg receives another dose of downward momentum from the earth. By the time the egg reaches the pavement, it's moving downward fast and has a substantial amount of downward momentum to get rid of. Incidentally, the earth, which has given up this downward momentum, experiences an opposite response—it has acquired an equal amount of upward momentum. However, the earth has such a huge mass that there is no noticeable increase in its upward speed.
To stop, the egg must transfer all of its downward momentum into something else, such as the earth. It can transfer its momentum into the earth by exerting a force on the ground for a certain amount of time. A transfer of momentum, known as an impulse, is the product of a force times a time. To get rid of its momentum, the egg can exert a large force on the ground for a short time or a small force for a long time, or anything in between. If you let it hit the pavement unprotected, the egg will employ a large force for a short time and that will be bad for the egg. After all, the pavement will push back on the egg with an equally strong but oppositely directed force and punch a hole in the egg.
To make the transfer of momentum graceful enough to leave the egg intact, the protective package must prolong the momentum transfer. The longer it takes for the egg to get rid of its downward momentum, the smaller the forces between the egg and the slowing materials. That's why landing on a soft surface is a good start: it prolongs the momentum transfer and thereby reduces the peak force on the egg.
But there is also the issue of distributing the slowing forces uniformly on the egg. Even a small force can break the egg if it's exerted only on one tiny spot of the egg. So spreading out the force is important. Probably the best way of distributing the slowing force would be to float the egg in the middle of a fluid that has the same average density as the egg. But various foamy or springy materials will distribute the forces nearly as well.
In summary, (1) you want to bring the egg to a stop over as long as period of time as possible so as to prolong the transfer of momentum and reduce the slowing forces and (2) you want to involve the whole bottom surface of the egg in this transfer of momentum so that the slowing forces are exerted uniformly on the egg's bottom surface. As for the actual impact force on the egg, you can determine this by dividing the egg's momentum just before impact (its downward speed times its mass) by the time over which the egg gets rid of its momentum.
The walls of your home are simply hard to look through. They block visible, infrared, and ultraviolet light nearly perfectly and that doesn't leave snoopers many good options. A person sitting outside your home with a thermal camera—a device that "sees" the infrared light associated with body-temperature objects—or a digital camera is going to have a nice view of your wall, not you inside. There are materials that, while opaque to visible light, are relatively transparent to infrared light, such as some plastics and fabrics. However, typical wall materials are too thick and too opaque for infrared light to penetrate. Sure, someone can put a camera inside your home and access it via an optical fiber or radio waves, but at that point, they might as well just peer through your window.
The only electromagnetic waves that penetrate walls well are radio waves, microwaves, and X rays. If someone builds an X ray machine around your home, they'll be able to see you, or at least your bones. Don't forget to wave. And, in principle, they could use the radar technique to look for you with microwaves, but you'd be a fuzzy blob at best and lost in the jumble of reflections from everything else in your home.
As for using a laser to monitor your conversations from afar, that's a real possibility. Surfaces vibrate in the presence of sound and it is possible to observe those vibrations via reflected light. But the technical work involved is substantial and it's probably easier to just put a bug inside the house or on its surface.
Since I first posted this answer, several people have pointed out to me that terahertz radiation also penetrates through some solid surfaces and could be used to see through the walls of homes. In fact, the whole low-frequency end of the electromagnetic spectrum (radio, microwaves, terahertz waves) can penetrate through electrically insulating materials in order to "observe" conducting materials inside a home and the whole high-frequency end of that spectrum (X-rays and gamma rays) can penetrate through simple atoms (low atomic number) in order to "observe" complex atoms inside a home. Still, these approaches to seeing through walls require the viewers to send electromagnetic waves through the house and those waves can be detected by the people inside. They're also not trivial to implement. I suppose that people could use ambient electromagnetic waves to see what's happening in a house, but that's not easy, either. Where there's a will, there's a way: stealth aircraft have been detected by way of the dark spot they produce in the ambient radio spectrum and the insides of the pyramids have been studied by looking at cosmic rays passing through them. Nonetheless, I don't think that many of us need worry about being studied through the walls of our homes.
The laws of both energy conservation and thermodynamics are essentially mathematical laws—they depend relatively little on the specific details of our universe. Just about the only specific detail that's important is time-translation symmetry: as far as we can tell, physics doesn't change with time—physics today is the same as it was yesterday and as it will be tomorrow. That observation leads, amazingly enough, to energy conservation: energy cannot be created or destroy; it can only change forms or be transferred between objects. Together with statistical principals, we can derive thermodynamics without any further reference to the universe itself. And having developed energy conservation and the laws of thermodynamics, the game is over for free-energy motors and generators. They just can't work. It's not a matter of looking for one special arrangement that works among millions that don't. There are exactly zero arrangements that work.
It's not a matter of my bias, unless you consider my belief that 2 plus 2 equals 4 to be some sort of bias. You can look all you like for a 2 that when added to another 2 gives you a 5, but I don't expect you to succeed.
About once every month or two, someone contacts me with a new motor that turns for free or a generator that creates power out of nowhere. The pattern always repeats: I send them the sad news that their invention will not work and they respond angrily that I am not listening, that I am biased, and that I am part of the conspiracy. Oh well. There isn't much else I can do. I suppose I could examine each proposal individually at length to find the flaw, but I just don't have the time. I'm a volunteer here and this is time away from my family.
Instead, I suggest that any inventor who believes he or she has a free-energy device build that device and demonstrate it openly for the physics community. Take it to an American Physical Society conference and present it there. Let everyone in the audience examine it closely. Since anyone can join the APS and any APS member can talk at any major APS conference, there is plenty of opportunity. If someone succeeds in convincing the physics community that they have a true free-energy machine, more power to them (no pun intended). But given the absence of any observed failure of time-translation symmetry, and therefore the steadfast endurance of energy conservation laws, I don't expect any successful devices.
Friction's role with respect to temperature is in raising that temperature. Friction is a great disorderer. If a person running down the track falls and skids along the ground, friction will turn that person's ordered kinetic energy into disordered kinetic energy and the person will get slightly hotter. No energy was created or destroyed in the fall and skid, but lots of formerly orderly kinetic energy became disordered kinetic energy—what I often call "thermal kinetic energy."
The overall story is naturally a bit more complicated, but the basic idea here is correct. Once energy is in the form of thermal kinetic energy, it's stuck... like a glass vase that has been dropped and shattered into countless pieces, thermal kinetic energy can't be entirely reconstituted into orderly kinetic energy. Once energy has been distributed to all the individual molecules and atoms, getting them all to return their chunks of thermal kinetic energy is hopeless. Friction, even at the molecular level, isn't important at this point because the energy has already been fragmented and the most that any type of friction can do is pass that fragmented energy about between particles. So friction creates thermal kinetic energy (out of ordered energies of various types)... in effect, it makes things hot. It doesn't keep them hot; they do that all by themselves.
In actually, some of the water molecules have almost certainly left via a form of solid-to-gas evaporation known technically as "sublimation." You have seen this conversion of ice into gas when you have noticed that old ice cubes in your freezer are smaller than they used to be or when you see that the snow outside during a cold spell seems to vanish gradually without ever melting. Sublimation is also the cause of "freezer burn" for frozen foods left without proper wrapping.
Like so many "scientific" conmen, the purveyors of this particular scam claim to be victims of a hostile scientific establishment, which refuses to accept their brilliant discoveries. They typically attack the deepest and most central tenets of science and claim that a conspiracy is perpetuating belief on those tenets. Their refusal to submit their work to scientific peer review is supposedly based on a fear that such review will be biased and subjective, controlled by the conspiracy.
The sad reality is that the "scientific establishment" is more than willing to examine the claims, but those claims won't survive the process of inspection. In some cases, the authors of the claims are truly self-deluded and are guilty only of pride and ignorance. But in other cases, the authors are real conmen who are out to make a buck at public expense. They should be run out of town on a rail. >
Well ..Having the thought process that I have, kinda how should I put it? ...Stupid? or inventive or even in-between. Well, my microwave door did happen to come off. Magic Chef 900-watt microwave. Well, I did my best to try to fix it but the hinge on one side did not attach properly, therefore having a gap between the door and the appliance. Being me (stupid) I wondered if it would burn fast or would it gradually warm up. I slid my finger between...You probably dying to hear what happened... But it didn't gradually warm up at all. It was instant heat! It didn't scar me or anything like that, but sure scared the H*** out of me to find out it got so hot so quick. I didn't get any blisters either. But it just burned like touching something hot on the tip of my finger being that is the only thing I put in. Well you know the old adage, "You learn from your mistakes", stands true. lol - Anonymous
For the one-open-window problem, the solution is simple: open another window. That shifts the resonant frequency of the car's air and also helps to dampen the vibrations. Alternatively, you can close the opened window. In your case, the resonance appears to involve a less visible opening into the car, perhaps near the rear bumper. If you can close that leak, you may be able to stop the airflow from driving the air in the car into resonance. If you are unable to find the leak, your best bet is to do exactly what you've done: open another window.
However, the true meaning of the "40 foot-pound" specification is that the safety helmet is capable of absorbing 40 foot-pounds of energy during an impact on its crown. This energy is transferred to the helmet by doing work on it: by pushing its crown downward as the crown dents downward. The product of the downward force on the crown times the distance the crown moves downward gives the total work done on the helmet and this product must not exceed 40 foot-pounds or the helmet may fail to protect the wearer. Since the denting force typically changes as the helmet dents, this varying force must be accounted for in calculating the total work done on the helmet. While I'm not particularly familiar with safety helmets, I know that bicycle helmets don't promise to be useable after absorbing their rated energies. Bicycle helmets contain energy-absorbing foam that crushes permanently during severe impacts so that they can't be used again. Some safety helmets may behave similarly.
Finally, an object dropped from a certain height acquires an energy of motion (kinetic energy) equal to its weight times the height from which it was dropped. As long as that dropped object isn't too heavy and the helmet it hits dents without moving overall, the object's entire kinetic energy will be transferred to the helmet. That means that a 20-pound object dropped from 2 feet on the helmet will deposit 40 found-pounds of energy in the helmet. But if the wearer lets the helmet move downward overall, some of the falling object's energy will go into the wearer rather than the helmet and the helmet will tolerate the impact easily. On the other hand, if the dropped object is too heavy, the extra gravitational potential energy released as it dents the helmet downward will increase the energy transferred to the helmet. Thus a 4000-pound object dropped just 1/100th of a foot will transfer much more than 40 foot-pounds of energy to the helmet.
Like any black object, the stealth aircraft will heat up when exposed to intense electromagnetic waves. But trying to cook a stealth aircraft with microwaves isn't worth the trouble. If someone can figure out where it is enough to focus intense microwaves on it, they can surely find something better with which to damage it.
As for detecting the stealth aircraft with the help of cell phones, that brings up the issue of what is invisibility. Like a black bat against the night sky, it's hard to see a stealth aircraft simply by shining microwaves at it. Those microwaves don't come back to you so you see no difference between the dark sky and the dark plane. But if you put the stealth aircraft against the equivalent of a white background, it will become painfully easy to see. Cell phones provide the microwave equivalent of a white background. If you look for microwave emission near the ground from high in the sky, you'll see microwaves coming at you from every cell phone and telephone tower. If you now fly a microwave absorbing aircraft across that microwave-rich background, you'll see the dark image as it blocks out all these microwave sources. Whether or not this effect was used in the Balkans, I can't say. But it does point out that invisibility is never perfect and that excellent camouflage in one situation may be terrible in another.
But at sunrise and sunset, sunlight enters our atmosphere at a shallow angle and travels a long distance before reaching our eyes. During this long passage, most of the blue light is deflected away and virtually all that we see coming to us from the sun is its red and orange wavelengths. The missing blue light illuminates the skies far to our east during sunrise and to our west during sunset. When the loss of blue light is extreme enough, as it is after a volcanic eruption, so little blue light may reach your location at times that even the sky itself appears deep red. The particles in air aren't good at deflecting red wavelengths, but if that's all the light there is they will give the sky a dim, red glow.
At rest, the bicycle is unstable because it has no base of support. A base of support is the polygon formed by an object's contact points with the ground. For example, a table has a square or rectangular base of support defined by its four legs as they touch the floor. As long as an object's center of gravity (the effective location of its weight) is above this base of support, the object is statically stable. That stability has to do with the object's increasing potential (stored) energy as it tips-tipping a statically stable object raises its center of gravity and gravitational potential energy, so that it naturally accelerates back toward its upright position. Since a bicycle has only two contact points with the ground, the base of support is a line segment and the bicycle can't have static stability.
But when the bicycle is heading forward, it automatically steers its wheels underneath its center of gravity. Just as you can balance a broom on you hand if you keep moving your hand under the broom's center of gravity, a bicycle can balance if it keeps moving its wheels under its center of gravity. This automatic steering has to do with two effects: gyroscopic precession and bending of the bicycle about its steering axis.
In the gyroscopic precession steering, the spinning wheel behaves as a gyroscope. It has angular momentum, a conserved quantity of motion associated with spinning, and this angular momentum points toward the left (a convention that you can understand by pointing the curved fingers of your right hand around in the direction of the tire's motion; your thumb will then point to the left). When the bicycle begins to lean to one side, for example to the left, the ground begins to twist the front wheel. Since the ground pushes upward on the bottom of that wheel, it tends to twist the wheel counter-clockwise according to the rider. This twist or torque points toward the rear of the bicycle (again, when the fingers of your right hand arc around counterclockwise, your thumb will point toward the rear). When a rearward torque is exerted on an object with a leftward angular momentum, that angular momentum drifts toward the left-rear. In this case, the bicycle wheel steers toward the left. While I know that this argument is difficult to follow, since angular effects like precession challenge even first-year physics graduate students, but the basic result is simple: the forward moving bicycle steers in the direction that it leans and naturally drives under its own center of gravity. You can see this effect by rolling a coin forward on a hard surface: it will automatically balance itself by driving under its center of gravity.
In the bending effect, the leaning bicycle flexes about its steering axis. If you tip a stationary bicycle to the left, you see this effect: the bicycle will steer toward the left. That steering is the result of the bicycle's natural tendency to lower its gravitational potential energy by any means possible. Bending is one such means. Again, the bicycle steers so as to drive under its own center of gravity.
These two automatic steering effects work together to make a forward moving bicycle surprisingly stable. Children's bicycles are designed to be especially stable in motion (for obvious reasons) and one consequence is that children quickly discover that they can ride without hands. Adult bicycles are made less stable because excessive stability makes it hard to steer the bicycle.
The ant lives on the surface of the balloon, a two-dimensional world. The ant is unaware of the third dimension that you and I can see when we look at the balloon. The only directions that the ant can move in are along the balloon's surface. The ant can't point toward the center of the balloon because that's not along the surface that the ant perceives. To the ant, the balloon has no center. It lives in a continuous, homogeneous world, which has the weird property that if you walk far enough in any direction, you return to where you started.
Similarly, we see our universe as a three-dimensional world. If there are spatial dimensions beyond three, we are unaware of them. The only directions that we can move in are along the three dimensions of the universe that we perceive. The overall structure of the universe is still not fully understood, but let's suppose that the universe is a simple closed structure like the surface of a higher-dimensional balloon. In that case, we wouldn't be able to point to a center either because that center would exist in a dimension that we don't perceive. To us, the universe would be a continuous, homogeneous structure with that same weird property: if you traveled far enough in one direction, you'd return to where you started.
There is no true outward force acting on an object that's revolving around a center. Instead, that object's own inertia is trying to make it travel in a straight-line path that would cause it to drift farther and farther away from the center. The one true force acting on the revolving object is an inward one-a centripetal force. The object is trying to go straight and the centripetal force is pulling it inward and bending the object's path into a circle.
To get a feel for the experiences associated with this sort of motion, let's first imagine that you are the revolving object and that you're swinging around in a circle at the end of a rope. In that case, your inertia is trying to send you in a straight-line path and the rope is pulling you inward and deflecting your motion so that you go in a circle. If you are holding the rope with your hands, you'll feel the tension in the rope as the rope pulls on you. (Note that, in accordance with Newton's third law of motion, you pull back on the rope just as hard as it pulls on you.) The rope's force makes you accelerate inward and you feel all the mass in your body resisting this inward acceleration. As the rope's force is conveyed throughout your body via your muscles and bones, you feel your body resisting this inward acceleration. There's no actual outward force on you; it's just your inertia fighting the inward acceleration. You'd feel the same experience if you were being yanked forward by a rope-there would be no real backward force acting on you yet you'd feel your inertia fighting the forward acceleration.
Now let's imagine that you are exerting the inward force on an object and that that object is a heavy bucket of water that's swinging around in a circle. The water's inertia is trying to make it travel in a straight line and you're pulling inward on it to bend its path into a circle. The force you exert on the bucket is quite real and it causes the bucket to accelerate inward, rather than traveling straight ahead. Since you're exerting an inward force on the bucket, the bucket must exert an inward force on you (Newton's third law again). It pulls outward on your arm. But there isn't anything pulling outward on the bucket, no mysterious "centrifugal force." Instead, the bucket accelerates in response to an unbalance force on it: you pull it inward and nothing pulls it outward, so it accelerates inward. In the process, the bucket exerts only one force on its surroundings: an outward force on your arm.
As for the operation of a centrifuge, it works by swinging its contents around in a circle and using their inertias to make them separate. The various items in the centrifuge have different densities and other characteristics that affect their paths as they revolve around the center of the centrifuge. Inertia tends to make each item go straight while the centrifuge makes them bend inward. The forces causing this inward bending have to be conveyed from the centrifuge through its contents and there's a tendency for the denser items in the centrifuge to travel straighter than the less dense items. As a result, the denser items are found near the outside of the circular path while the less dense ones are found near the center of that path.
But you are wondering what controls the currents flowing in the two coils. The circuit it is connected to determines the current in the secondary coil. If that circuit is open, then no current will flow. If it is connected to a light bulb, then the light bulb will determine the current. What is remarkable about a transformer is that once the load on the secondary coil establishes the secondary current, the primary current is also determined.
Remember that the current flowing in the secondary coil is itself magnetic and because it is an alternating current, it is accompanied by its own electric field. The more current that is allowed to flow through the secondary coil, the stronger its electric field becomes. The secondary coil's electric field opposes the primary coil's electric field, in accordance with a famous rule of electromagnetism known as Lenz's law. The primary coil's electric field was pushing backward on current passing through the primary coil, so the secondary coil's electric field must be pushing forward on that current. Since the backward push is being partially negated, more current flows through the primary coil.
The current in the primary coil increases until the two electric fields, one from the primary current and one from the secondary current, work together so that they extract all of the primary current's electrostatic energy during its trip through the coil. This natural feedback process ensures that when more current is allowed to flow through the transformer's secondary coil, more current will flow through the primary coil to match.
Despite the fact that cellulose isn't as tasty as sugar, it does have one important thing in common with sugar: both chemicals cling tightly to water molecules. The presence of many hydroxyl groups (-OH) on the sugar and cellulose molecules allow them to form relatively strong bonds with water molecules (HOH). This clinginess makes normal sugar very soluble in water and makes water very soluble in cellulose fibers. When you dip your paper towel in water, the water molecules rush into the towel to bind to the cellulose fibers and the towel absorbs water.
Incidentally, this wonderful solubility of water in cellulose is also what causes shrinkage and wrinkling in cotton clothing when you launder it. The cotton draws in water so effectively that the cotton fibers swell considerably when wet and this swelling reshapes the garment. Hot drying chases the water out of the fibers quickly and the forces between water and cellulose molecules tend to compress the fibers as they dry. The clothes shrink and wrinkle in the process.
Ultraviolet light is high-energy light, meaning that whenever it is emitted or absorbed, the amount of energy involved in the process is relatively large. Although light travels through space as waves, it is emitted and absorbed as particles known as photons. The energy in a photon of ultraviolet light is larger than in a photon of visible light and that leads to interesting effects.
First, some molecules can't tolerate the energy in an ultraviolet photon. When these molecules absorb such an energetic photon, their electrons rearrange so dramatically that the entire molecule changes its structure forever. Among the organic molecules that are most vulnerable to these ultraviolet-light-induced chemical rearrangements are the molecules that are responsible for colors. The same electronic structural characteristics that make these organic molecules colorful also make them fragile and susceptible to ultraviolet damage. As a result, they tend to bleach white in the sun.
Second, some molecules can tolerate high-energy photons by reemitting part of the photon's energy as new light. Such molecules absorb ultraviolet or other high-energy photons and use that energy to emit blue, green, or even red photons. The leftover energy is converted into thermal energy. These fluorescent molecules are the basis for the "neon" colors that are so popular on swimwear, in colored markers, and on poster boards. When you expose something dyed with fluorescent molecules to sunlight, the dye molecules absorbs the invisible ultraviolet light and then emit brilliant visible light.
Note added: A reader pointed out that I never actually answered the question. He's right! So here is the answer: they use accelerometers. An accelerometer is essentially a test mass on a force sensor. When there is no acceleration, the test mass only needs to be supported against the pull of gravity (i.e., the test mass's weight), so the force sensor reports that it is pushing up on the test mass with a force equal to the test mass's weight. But once the accelerometer begins to accelerate, the test mass needs an additional force in order to accelerate with the accelerometer. The force sensor detects this additional force and reports it. If you carry an accelerometer with you on a roller coaster, it will report the force it exerts on the test mass at each moment during the trip. A recording device can thus follow the "g-forces" throughout the ride.
As far as how accelerometers work, modern ones are generally based on tiny mechanical systems known as MEMS (Micro-Electro-Mechanical Systems). Their test masses are associated with microscopic spring systems and the complete accelerometer sensor resides on a single chip.
Imagine standing in front of a 10-kilowatt light bulb (which emits about 1 kilowatt of visible light and the rest is other forms of heat) and then imagine that you can't see light at all and can only feel it when it is causing potential damage. Would you feel safe? Your video camera won't enjoy the microwave exposure, either.
If you want to videotape your experiments without having to view them through the metal mesh on the door, you can consider drilling a small hole in the side of the cooking chamber. If you keep the hole's diameter to a few millimeters, the microwaves will not leak out. Then put one of the tiny inexpensive video cameras that widely available a centimeter or so away from that hole. You should get a nice unobstructed view of the cooking process without risking life and limb.
However, if the fans are directing the cold air in a way that makes you more comfortable without having to cool all the room air or if the fans are creating fast moving air that cools you via evaporation more effectively, then you may be experiencing a real savings of electricity.
To figure out which is the case, you'd have to log the time the air conditioner cycles on during a certain period while the fans were off and the thermostat set to 75 °F and then repeat that measurement during a similar period with the fans on and the thermostat set to 78 °F. If the fans significantly reduce the units runtime while leaving you just as comfortable, then you're saving power.
In contrast, there should be very little voltage difference between the other wire (known as "neutral") and the earth. In a properly wired lamp, the large spade on the electric plug (the neutral wire) should connect to the outside of the bulb socket. That way, when you accidentally touch the bulb's base as you screw it in or out, you'll only be connecting your hand to the neutral wire and won't receive a shock. If you miswire the lamp and have the hot wire connected to the outside of the socket, you can get a shock if you accidentally touch the bulb base at any time.
The story provided SOME insight into what exactly had happened, however, it was reported that the surface of the super-heated liquid had to be broken by something for an explosion to be triggered. In the explosion with the coffee, there were no other objects in the microwave other than the mug and the coffee it held. What then, caused the explosion if nothing was present to break the surface? - MM, Denver, CO
This sort of accident happens fairly often and we rarely think much about it as we sponge up the spilled liquid inside the microwave oven. But had your friend been unlucky enough to stop heating the coffee a second or two before that POP, she might have been injured while taking the coffee out of the oven. The moral of this story is to avoid overcooking any liquid in the microwave oven. If you must drink your coffee boiling hot, pay attention to it as it heats up so that it doesn't cook too long and then let it sit for a minute after the oven turns off. If you don't like your coffee boiling hot, then don't heat it to boiling at all.
Glass containers are clearly the most likely to superheat water because their surfaces are essentially perfect. Glasses have the characteristics of frozen liquids and a glass surface is as smooth as... well, glass. When you overheat water in a clean glass measuring cup, your chances of superheating it at least mildly are surprisingly high. The spontaneous bubbling that occurs when you add sugar, coffee powder, or a teabag to microwave-heated water is the result of such mild superheating. Fortunately, severe superheating is much less common because defects, dirt, or other impurities usually help the water boil before it becomes truly dangerous. That's why most of us avoid serious injuries.
However, even non-transparent microwaveable containers often have glass surfaces. Ceramics are "glazed," which means that they are coated with glass for both sealing and decoration. Many heavy mixing bowls are glass or glass-ceramics. As you can see, it's hard to get away from trouble. I simply don't know how plastic microwaveable containers behave when heating water; they may be safe or they may be dangerous.
If you're looking for a way out of this hazard, here are my suggestions. First, learn to know how long a given amount of liquid must be heated in your microwave in order to reach boiling and don't cook it that long. If you really need to boil water, be very careful with it after microwaving or boil it on a stovetop instead. My microwave oven has a "beverage" setting that senses how hot the water is getting. If the water isn't hot enough when that setting finishes, I add another 30 seconds and then test again. I never cook the water longer than I need to. Cooking water too long on a stovetop means that some of it boils away, but doing the same in a microwave oven may mean that it becomes dangerously superheated. Your children can still "cook" soup in the microwave if they use the right amount of time. Children don't like boiling hot soup anyway, so if you figure out how long it takes to heat their soup to eating temperature and have them cook their soup only that long, they'll never encounter superheating. As for dad's coffee water, same advice. If dad wants his coffee boiling hot, then he should probably make it himself. Boiling water is a hazard for children even without superheating.
Second, handle liquids that have been heated in a microwave oven with respect. Don't remove a liquid the instant the oven stops and then hover over it with your face exposed. If the water was bubbling spasmodically or not at all despite heavy heating, it may be superheated and deserves particular respect. But even if you see no indications of superheating, it takes no real effort to be careful. If you cooked the water long enough for it to reach boiling temperature, let it rest for a minute per cup before removing it from the microwave. Never put your face or body over the container and keep the container at a safe distance when you add things to it for the first time: powdered coffee, sugar, a teabag, or a spoon.
Finally, it would be great if some entrepreneurs came up with ways to avoid superheating altogether. The makers of glass containers don't seem to recognize the dangers of superheating in microwave ovens, despite the mounting evidence for the problem. Absent any efforts on their parts to make the containers intrinsically safer, it would be nice to have some items to help the water boil: reusable or disposable inserts that you could leave in the water as it cooked or an edible powder that you could add to the water before cooking. Chemists have used boiling chips to prevent superheating for decades and making sanitary, nontoxic boiling sticks for microwaves shouldn't be difficult. Similarly, it should be easy to find edible particles that would help the water boil. Activated carbon is one possibility.
Last night's report wasn't meant to scare you away from using your microwave oven or keep you from heating water in it. It was intended to show you that there is a potential hazard that you can avoid if you're informed about it. Microwave ovens are wonderful devices and they prepare food safely and efficiently as long as you use them properly. "Using them properly" means not heating liquids too long in smooth-walled containers.
Nucleation usually occurs at hot spots during stovetop cooking or at defects in the surfaces of cooking vessels. Glass containers have few or no such defects. When you cook water in a smooth glass container, using a microwave oven, it is quite possible that there will be no nucleation on the walls of the container and the water will superheat. This situation becomes even worse if the top surface of the water is "sealed" by a thin layer of oil or fat so that evaporation can't occur, either. Superheated water is extremely dangerous and people have been severely injured by such water. All it takes is some trigger to create the first bubble-a fork or spoon opening up the inner surface of the water or striking the bottom of the container-and an explosion follows. I recently filmed such explosions in my own microwave (low-quality movie (749KB), medium-quality movie (5.5MB)), or high-quality movie (16.2MB)). As you'll hear in my flustered remarks after "Experiment 13," I was a bit shaken up by the ferocity of the explosion I had triggered, despite every expectation that it would occur. After that surprise, you'll notice that I became much more concerned about yanking my hand out of the oven before the fork reached the water. I recommend against trying this dangerous experiment, but if you must, be extremely careful and don't superheat more than a few ounces of water. You can easily get burned or worse. For a reader's story about a burn he received from superheated water in a microwave, touch here.
Here is a sequence of images from the movie of my experiment, taken 1/30th of a second apart:
As far as the food is concerned, the presence of the spoon redirected the microwaves somewhat, but probably without causing any noticeable changes in how the food cooked. There is certainly no residual radiation of any sort and the food is no more likely to cause cancer after being cooked with metal around than had there been no spoon with it. In general, leaving a spoon in a cup of coffee or bowl of oatmeal isn't going to cause any trouble at all. I do it all the time. In fact, having a metal spoon in the liquid may reduce the likelihood of superheating the liquid, a dangerous phenomenon that occurs frequently in microwave cooking. Superheated liquids boil violently when you disturb them and can cause serious injuries as a result.
By giving the sealed bottle a shake, your mother-in-law is simply speeding up the approach to equilibrium. She is helping the CO2 molecules leave the beverage and enter the gas phase. The bottle then pressurizes faster, but at the expense of dissolved molecules in the beverage itself. If there is any chance that you'll drink more before equilibrium has been reached, you do best not to shake the bottle. That way, the equilibration process will be delayed as much as possible and you may still be able to drink a few more of those CO2 molecules rather than breathing them.
Incidentally, shaking a new bottle of soda just before you open it also speeds up the equilibration process. For an open bottle, equilibrium is reached when essentially all the CO2 molecules have left and are in the gas phase (since the gas phase extends over the whole atmosphere). That's not what you want at all. Instead, you try not to shake the beverage so that it stays away from equilibrium (and flatness) as long as possible. For most opened beverages, equilibrium is not a tasty situation.
About the lens: in principle, all you need is one convex lens. A giant magnifying glass will do. But it has a couple of constraints. Because your television screen is pretty large, the lens diameter must also be pretty large. If it is significantly smaller than the TV screen, it won't project enough light onto your wall. And to control the size of the image it projects on the wall, you'll need to pick just the right focal length (curvature) of the lens. You'll be projecting a real image on the wall, a pattern of light that exactly matches the pattern of light appearing on the TV screen. The size and location of that real image depends on the lens's focal length and on its distance from the TV screen. You'll have to get these right or you'll see only a blur. Unfortunately, single lenses tend to have color problems and edge distortions. Projection lenses need to be multi-element carefully designed systems. Getting a good quality, large lens with the right focal length is going to cost you.
The other big problem is more humorous. Real images are flipped horizontally and vertically relative to the light source from which they originate. Unless you turn your TV set upside-down, your wall image will be inverted. And, without a mirror, you can't solve the left-right reversal problem. All the writing will appear backward. Projection television systems flip their screen image to start with so that the projected image has the right orientation. Unless you want to rewire your TV set, that's not going to happen for you. Good luck.
But when you carry the sack horizontally at a steady pace, the upward force you exert on the sack and the horizontal distance it travels are at right angles to one another. You don't do any work on the sack in that case. The evidence here is that the sack doesn't become any more dangerous; its speed doesn't increase and neither does its altitude. It just shifts from one place to an equivalent one to its side.
However, the ball doesn't bounce all by itself when you drop it on a flexible surface. In that case, the surface also dents and is responsible for part of the ball's rebound. If that surface handles energy inefficiently, it may weaken the ball's bounce. For example, if you drop the ball on carpeting, the carpeting will do much of the denting, will receive much of the ball's original energy, and will waste its share as heat. The ball won't rebound well. My guess is that you dropped the ball on a reasonably hard surface, but one that began to dent significantly when the ball's pressure reached 12psi. At that point, the ball was extremely bouncy, but it was also so hard that it dented the surface and let the surface participate strongly in the bouncing. The surface probably wasn't as bouncy as the ball, so it threw the ball relatively weakly into the air.
I'd suggest repeating your experiment on the hardest, most massive surface you can find. A smooth cement or thick metal surface would be best. The ball will then do virtually all of the denting and will be responsible for virtually all of the rebounding. In that case, I'll bet that the 12psi ball will bounce highest.
About the humidity caveat: if you can blow dry air across your windshield, that will defrost it faster than just about anything else, even if that air is cold. The water molecules on your windshield are constantly shifting back and forth between the solid phase (ice) and the gaseous phase (steam or water vapor). Heating the ice will help more water molecules leave the ice for the water vapor, but dropping the density of the water vapor will reduce the number of water molecules leaving the water vapor for the ice. Either way, the ice decreases and the water vapor increases. Since you car's air condition begins drying the air much soon after you start the car than its heater begins warming the air, many modern cars concentrate first on drying the air rather than on heating it.
If you send a current backward through a battery, the battery extracts energy from the current and lowers its voltage. As it takes energy from the current, the battery adds to its store of chemical potential energy so that it recharges. Battery charges do exactly that: they push current backward through the batteries to recharge them. This recharging only works well on batteries that are designed to be recharged since many common batteries undergo structural damage as their energy is consumed and this damage can't be undone during recharging.
When you use a chain of batteries to power an electric device, you must arrange them so that each one pumps charge the same direction. Otherwise, one will pump and add energy to the current while the other extracts energy from the current. If all the batteries are aligned positive terminal to negative terminal, then they all pump the same direction and the current experiences a 1.5 volt (typically) voltage rise in passing through each battery. After passing through 2 batteries, its voltage is up by 3 volts, after passing through 3 batteries, its voltage is up by 4.5 volts, and so on.
The color filters that the camera employs to obtain color information misbehave when they're dealing with infrared light and so the camera is fooled into thinking that it's viewing white light. That's why your camera shows a white spot where the remote's infrared source is located.
I just tried taking some pictures through infrared filters, glass plates that block visible light completely, and my digital camera worked just fine. The images were as sharp and clear as usual, although the colors were odd. I had to use incandescent illumination because fluorescent light doesn't contain enough infrared. It would be easy to take pictures in complete darkness if you just illuminated a scene with bright infrared sources. No doubt there are "spy" cameras that do exactly that.
In all likelihood, the manufacturer of this unit has shielded all the light so that none of it reaches your eyes. If that's not the case, you should wear laser safety glasses that block 1064 nm light. But it's also possible that the irritation you're experiencing is coming from the burned material that you are machining. Better ventilation should help. High voltage power supplies, which may be present in the laser, could also produce ozone. Ozone has a spicy fresh smell, like the smell after a lightning storm, and it is quite irritating to eyes and nose.
The flattened poles are the result of rotation—as the planet spins, the need for centripetal (centrally directed) acceleration at its equator causes its equatorial surface to shift outward slightly, away from the planet's axis of rotation. The planet is therefore wider at its equator than it is at its poles.
Water can always evaporate into dry air, but it normally only does so at its surface. When water molecules leave the surface faster than they return, the quantity of liquid water gradually diminishes. That's ordinary evaporation. However, when water is heated to its boiling temperature, it can begin to evaporate not only from its surface, but also from within. If a steam bubble forms inside the hot water, water molecules can evaporate into that steam bubble and make it grow larger and larger. The high temperature is necessary because the pressure inside the bubble depends on the temperature. At low temperature, the bubble pressure is too low and the surrounding atmospheric pressure smashes it. That's why boiling only occurs at or above water's boiling temperature. Since pressure is involved, boiling temperature depends on air pressure. At high altitude, boiling occurs at lower temperature than at sea level.
But pay attention to the phrase "If a steam bubble forms" in the previous paragraph. That's easier said than done. Forming the initial steam bubble into which water molecules can evaporate is a process known as "nucleation." It requires a good number of water molecules to spontaneously and simultaneously break apart from one another to form a gas. That's an extraordinarily rare event. Even in a cup of water many degrees above the boiling temperature, it might never happen. In reality, nucleation usually occurs at a defect in the cup or an impurity in the water—anything that can help those first few water molecules form the seed bubble. When you heat water on the stove, the hot spots at the bottom of the pot or defects in the pot bottom usually assist nucleation so that boiling occurs soon after the boiling temperature is reached. But when you heat pure water in a smooth cup using a microwave oven, there may be nothing present to help nucleation occur. The water can heat right past its boiling temperature without boiling. The water then superheats—its temperature rising above its boiling temperature. When you shake the cup or sprinkle something like sugar or salt into it, you initiate nucleation and the water then boils violently.
Fortunately, serious microwave superheating accidents are fairly unusual. However, they occur regularly and some of the worst victims require hospital treatment. I have heard of extreme cases in which people received serious eye injuries and third degree burns that required skin grafts and plastic surgery.
You can minimize the chance of this sort of problem by not overcooking water or any other liquid in the microwave oven, by waiting about 1 minute per cup for that liquid to cool before removing it from the microwave if there is any possibility that you have superheated it, and by being cautious when you first introduce utensils, powders, teabags, or otherwise disturb very hot liquid that has been cooked in a microwave oven. Keep the water away from your face and body until you're sure it's safe and don't ever hover over the top of the container. Finally, it's better to have the liquid boil violently while it's inside the microwave oven than when it's outside on your counter and can splatter all over you. Once you're pretty certain that the water is no longer superheated, you can ensure that it's safe by deliberately nucleating boiling before removing the cup from the microwave. Inserting a metal spoon or almost any food into the water should trigger boiling in superheated water. A pinch of sugar will do the trick, something I've often noticed when I heat tea in the microwave. However, don't mess around with large quantities of superheated water. If you have more than 1 cup of potentially superheated water, don't try to nucleate boiling until you've waited quite a while for it to cool down. I've been scalded by the stuff several times even when I was prepared for an explosion. It's really dangerous.
The leaving rate (the rate at which molecules break free from the liquid water) depends on the temperature. The hotter the water is, the more frequently water molecules will be able to break away from their buddies and float off into the gas. The landing rate (the rate at which molecules land on the water's surface and stick) depends on the density of molecules in the gas. The more dense the water vapor, the more frequently water molecules will bump into the liquid's surface and land.
As you raise the temperature of the water in your glass, the leaving rate increases and the equilibrium shifts toward higher vapor density and less liquid water. By the time you reach 100° Celsius, the equilibrium vapor pressure is atmospheric pressure, which is why water tends to boil at this temperature (it can form and sustain steam bubbles). Above this temperature the equilibrium vapor pressure exceeds atmospheric pressure. The liquid water and the gas above it can reach equilibrium, but only if you allow the pressure in your enclosed system to exceed atmospheric pressure. However, if you open up your enclosed system, the water vapor will spread out into the atmosphere as a whole and there will be a never-ending stream of gaseous water molecules leaving the glass. Above 100° C, liquid water can't exist in equilibrium with atmospheric pressure gas, even if that gas is pure water vapor.
So how can you superheat water? Don't wait for equilibrium! The road to equilibrium may be slow; it may take minutes or hours for the liquid water to evaporate away to nothing. In the meantime, the system will be out of equilibrium, but that's ok. It happens all the time: a snowman can't exist in equilibrium on a hot summer day, but that doesn't mean that you can't have a snowman at the beach... for a while. Superheated water isn't in equilibrium and, if you're patient, something will change. But in the short run, you can have strange arrangements like this without any problem.
A cubic foot of air weighs about 0.078 pounds so the upward buoyant force on a cubic foot of helium is about 0.078 pounds. A cubic foot of helium weighs only about 0.011 pounds. The difference between the upward buoyant force on the cubic foot of helium and the weight of the helium is the amount of extra weight that the helium can lift; about 0.067 pounds. Since you weigh 85 pounds, it would take about 1300 cubic feet of helium to lift you and a thin balloon up into the air. That's a balloon about 13.5 feet in diameter.
Ordinary incandescent bulbs produce a thermal spectrum of light with a "color temperature" of about 2800° C. A thermal light spectrum is a broad, featureless mixture of colors that peaks at a particular wavelength that's determined only by the temperature of the object emitting it. Since the bulb's color temperature is much cooler than that of the sun's (5800° C), the bulb appears much redder than the sun and emits relatively little blue light. A fluorescent lamp, however, synthesizes its light spectrum from the emissions of various fluorescent phosphors. Its light spectrum is broad but structured and depends on the lamp's phosphor mixture. The four most important phosphor mixtures are cool white, deluxe cool white, warm white, and deluxe warm white. These mixtures all produce more blue than an incandescent bulb, but the warm white and particularly the deluxe warm white tone down the blue emission to give a richer, warmer glow at the expense of a little energy efficiency. Cool white fluorescents are closer to natural sunlight than either warm white fluorescents or incandescent bulbs.
To answer your question about shaves: without blue light in the illumination, it's not that easy to distinguish beard from skin. Since incandescent illumination is lacking in blue light, a shave looks good even when it isn't. But in bright fluorescent lighting, beard and skin appear sharply different and it's easy to see spots shaving has missed. As for makeup illumination, it's important to apply makeup in the light in which it will be worn. Blue-poor incandescent lighting downplays blue colors so it's easy to overapply them. When the lighting then shifts to blue-rich fluorescents, the blue makeup will look heavy handed. Some makeup mirrors provide both kinds of illumination so that these kinds of mistakes can be avoided.
The terminal velocity of an object depends on the object's size, shape, and density. A fluffy object (a feather, a parachute, or a sheet of paper) has a small terminal velocity while a compact, large, heavy object (a cannonball, a rock, or a bowling ball) has a large terminal velocity. An aerodynamic object such as an arrow also has a very large terminal velocity. A person has a terminal velocity of about 200 mph when balled up and about 125 mph with arms and feet fully extended to catch the wind.
The secondary circuit consists of little more than a huge coil of wire and some electrodes. This coil of wire is located around the same region of space occupied by the inductor of the primary circuit. As the magnetic field inside that inductor fluctuates up and down in strength, it induces current in the secondary coil. That's because a changing magnetic field produces an electric field and the electric field surrounding the inductor pushes charges around and around the secondary coil. By the time the charges in the secondary coil emerge from the coil, they have enormous amounts of energy; making them very high voltage charges. They accumulate in vast numbers on the electrodes of the secondary circuit and push one another off into the air as sparks.
While most circuits must form complete loops, the Tesla coil's secondary circuit doesn't. Its end electrodes just spit charges off into space and let those charges fend for themselves. Many of them eventually work their ways from one electrode to the other by flowing through the air or through objects. But even when they don't, there is little net build up of charge anywhere. That's because the direction of current flow through the secondary coil reverses frequently and the sign of the charge on each electrode reverses, too. The Tesla coil is a high-frequency device and its top electrode goes from positively charged to negatively charge to positively charged millions of times a second. This rapid reversal of charge, together with reversing electric and magnetic fields means that a Tesla coil radiates strong electromagnetic waves. It therefore interferes with nearby radio reception.
Finally, it has been pointed out to me by readers that a properly built Tesla coil is resonant—that the high-voltage coil has a natural resonance at the same frequency that it is being excited by the lower voltage circuit. The high-voltage coil's resonance is determined by its wire length, shape, and natural capacitance.
A diesel engine doesn't have spark ignition. Instead, it uses the high temperature caused by extreme compression to ignite its fuel. It compresses pure air to high temperature and pressure, and then injects fuel into this air. Timed to arrive at the proper instant, the fuel bursts into flames and burns quickly in the superheated compressed air. In contrast to gasoline, diesel fuel is formulated to ignite easily as soon as it enters hot air.
The magnet is part of the system that makes the surface move. Attached to the surface itself is a cylindrical coil of wire and this coil fits into a cylindrical channel cut into the speaker's permanent magnet. That magnet is carefully designed so that its magnetic field lines radiate outward from the inside of the channel to the outside of the channel and thus pass through the cylindrical coil the way bicycle spokes pass through the rim of the wheel.
When an electric current is present in the wire, the moving electric charges circulate around this cylinder and cut across the magnetic field lines. But whenever a charge moves across a magnetic field line, it experiences a force known as the Lorenz force. In this case, the charges are pushed either into or out of the channel slot, depending on which way they are circulating around the coil. The charges drag the coil and surface with them, so that as current flows back and forth through the coil, the coil and surface pop in and out of the magnet channel. This motion produces sound.
Instead of trying to interact through a natural resonance in water, a microwave oven just exposes the water molecules to the intense electromagnetic fields in strong, non-resonant microwaves. The frequency used in microwave ovens (2,450,000,000 cycles per second or 2.45 GHz) is a sensible but not unique choice. Waves of that frequency penetrate well into foods of reasonable size so that the heating is relatively uniform throughout the foods. Since leakage from these ovens makes the radio spectrum near 2.45 GHz unusable for communications, the frequency was chosen in part because it would not interfere with existing communication systems.
As for there being a laser in a microwave oven, there isn't. Lasers are not the answer to all problems and so the source for microwaves in a microwave oven is a magnetron. This high-powered vacuum tube emits a beam of coherent microwaves while a laser emits a beam of coherent light waves. While microwaves and light waves are both electromagnetic waves, they have quite different frequencies. A laser produces much higher frequency waves than the magnetron. And the techniques these devices use to create their electromagnetic waves are entirely different. Both are wonderful inventions, but they work in very different ways.
The fact that this misleading information appears in a science book, presumably used in schools, is a bit discouraging. It just goes to show you that you shouldn't believe everything read in books or on the web (even this web site, because I make mistakes, too).
Color sets create the impression of full color by mixing the three primary colors of light—blue, green, and red—right there on the inside surface of the picture tube. A set does the mixing by turning on and off three separate electron beams to control the relative brightnesses of the three primary colors at each location on the screen. The shadow mask is a metal grillwork that allows the three electrons beams to hit only specific phosphor dots on the inside of the tube's front surface. That way, electrons in the "blue" electron beam can only hit blue-glowing phosphors, while those in the "green" beam hit green-glowing phosphors and those in the "red" beam hit red-glowing phosphors. The three beams originate at slightly different locations in the back of the picture tube and reach the screen at slightly different angles. After passing through the holes in the shadow mask, these three beams can only hit the phosphors of their color.
Since the shadow mask's grillwork and the phosphor dots must stay perfectly aligned relative to one another, the shadow mask must be made of a metal that has the same thermal expansion characteristics as glass. The only reasonable choice for the shadow mask is Invar metal, an alloy that unfortunately is easily magnetized. Your son has magnetized the mask inside your set and because moving charged particles are deflected by magnetic fields, the electron beams in your television are being steered by the magnetized shadow mask so that they hit the wrong phosphors. That's why the colors are all washed out and rearranged.
To demagnetize the shadow mask, you should expose it to a rapidly fluctuating magnetic field that gradually decreases in strength until it vanishes altogether. The degaussing coils I mentioned above plug directly into the AC power line and act as large, alternating-field electromagnets. As you wave one of these coils around in front of the screen, you flip the magnetization of the Invar shadow mask back and forth rapidly. By slowly moving this coil farther and farther away from the screen, you gradually scramble the magnetizations of the mask's microscopic magnetic domains. The mask still has magnetic structures at the microscopic level (this is unavoidable and a basic characteristic of all ferromagnetic metals such as steel and Invar). But those domains will all point randomly and ultimately cancel each other out once you have demagnetized the mask. By the time you have the coil a couple of feet away from the television, the mask will have no significant magnetization left at the macroscopic scale and the colors of the set will be back to normal.
Incidentally, I did exactly this trick to my family's brand new color television set in 1965. I had enjoyed watching baseball games and deflecting the pitches wildly on our old black-and-white set. With only one electron beam, a black-and-white set needs no shadow mask and has nothing inside the screen to magnetize. My giant super alnico magnet left no lingering effect on it. But when the new set arrived, I promptly magnetized its shadow mask and when my parent watched the "African Queen" that night, the colors were not what you'd call "natural." The service person came out to degauss the picture tube the next day and I remember denying any knowledge of what might have caused such an intense magnetization. He and I agreed that someone must have started a vacuum cleaner very close to the set and thus magnetized its surface. I was only 8, so what did I know anyway.
Finally, as many readers have pointed out, many modern televisions and computer monitors have built-in degaussing coils. Each time you turn on one of these units, the degaussing circuitry exposes the shadow mask to a fluctuating magnetic field in order to demagnetize it. If your television set or monitor has such a system, then turning it on and off a couple of times should clear up most or all of the magnetization problems. However, you may have to wait about 15 minutes between power on/off cycles because the built-in degaussing units have thermal protection that makes sure they cool down properly between uses.
But when the fly is inside the van, the fly travels about in air that is moving with the van. If the van is moving at 70 mph, then so is the air inside it and so is the fly. In fact, everything inside the van moves more or less together and from the perspective of the van and its contents, the whole world outside is what is doing the moving—the van itself can be considered stationary and the van's contents are then also stationary.
As long as the fly and the air it is in are protected inside the van, the movement of the outside world doesn't matter. The fly buzzes around in its little protected world. But if the van's window is open and the fly ventures outside just as a signpost passes the car, the fly may get creamed by a collision with the "moving" sign. Everything is relative and if you consider the van as stationary, then it is undesirable for the van's contents to get hit by the moving items in the world outside (passing trees, bridge abutments, or oncoming vehicles.
However, quantum mechanics makes controlling the die truly impossible. The problem stems from the fact that position and velocity information are not fully defined at the same time in our quantum mechanical universe. In short, you can't know exactly where a die is and how fast it is moving at the same time. And that doesn't mean that you can't perform these measurements well. It means that the precise values don't exist together; they are limited by Heisenberg uncertainty. So quantum physics imposes a fundamental limit on how well you can know the initial conditions before your throw and it thus limits your ability to control the outcome of that throw. How much quantum physics affects your ability to throw a 6 depends on the complexity of the throw. If you just drop a die a few inches onto a table, you can probably get a 6 most of the time, despite quantum mechanics and without even knowing much classical information. But as you begin throwing the die farther, you'll begin to lose control of it because of quantum mechanics and uncertainty. In reality, you'll find classical physics so limiting that you'll probably never observe the quantum physics problem. Knowing everything about a system is already unrealistic, even in a classical universe. The problems arising from quantum mechanics are really just icing on the cake for this situation.
I watched the video on the "Counter Rotation Device" and found the discussion of "Newton's Fourth Law of Motion" quite amusing. The speaker claims that this fourth law was discovered about 30 years ago by a person now at their research lab. It is based on Newton's third law, which the speaker simplifies to "for every action there is an equal and opposite reaction." In a nutshell, his fourth law claims that you can take the reaction caused by a particular action and apply it to the action in the same direction—action causes reaction which causes more action which causes more reaction and so on. Pretty soon you have so much action and reaction that anything becomes possible. The video goes on to show devices that yield more power than they consume and that can easily become net sources of energy—by using part of the output energy from one of these energy multiplying devices to power that device, you can create endless energy from nothing at all.
Sadly enough, it's all just nonsense. Newton's third law is not as flexible as the speaker supposes and this endless feedback process in which reaction is used as action to produce more reaction is ridiculous. A more accurate version of Newton's third law is: "Whenever one object pushes on a second object, the second object pushes back on the first object equally hard but in the opposite direction". Thus when you push on the handle of a water pump, that handle pushes back on you with an equal but oppositely directed force. The speaker's claim is that there is a way to use the handle's push on you as part of your push on the handle so that, with your help, the handle essentially pushes itself through action and reaction. You can then pump water almost without effort. Sorry, this is just nonsense. It's mostly just playing with the words action and reaction in their common language form: if you scare me, I react by jumping. That action and reaction has nothing to do with physics.
The speaker uses at least three clever techniques to make his claims more compelling and palatable. First, he refers frequently to a power-company conspiracy that is out to destroy his company and its products. Conspiracy theories are so popular these days that having a conspiracy against you makes you more believable. Second, he describes the fellow who discovered the fourth law of motion as a basement inventor who has taken on the rigid scientific establishment. Ordinary people love to see pompous, highly educated academics brought low by other ordinary people; it's kind of a team spirit issue. And third, he makes casual use of technical looking equipment and jargon, as though he is completely at ease in the world of advanced technology. Movies have made it easier to trust characters like Doc Brown from "Back to the Future" than to trust real scientists.
In fact, there is no power-company conspiracy because there is no free electricity. The proof is in the pudding: if these guys really could make energy from nothing, they'd be doing it every day and making a fortune. They would be the power companies. If they were interested in public welfare rather than money, they'd have given their techniques away already. If they were interested in proving the scientific establishment wrong, they'd have accepted challenges by scientific organization and demonstrated their devices in controlled situations (where they can't cheat). The fact is, they're just frauds and of no more interest to the power companies than snake oil salespeople are to doctors. No decent people want to see others defrauded of money, property, or health, but the free electricity people present no real threat to the power companies.
The popular notion that an ordinary person is likely to upset established science is an unfortunate product of the anti-intellectual climate of our present world. Becoming a competent scientist is generally hard work and requires dedication, time, and an enormous amount of serious thinking. Physics is hard, even for most physicists. The laws governing the universe are slowly being exposed but it has taken very smart, very hardworking people almost half a millennium to get to the current state of understanding. Each new step requires enormous effort and a detailed understanding of a good part of the physics that is already known. Still, there is a common myth that some clever and lucky individual with essentially no training or knowledge of what has been discovered before will make some monumental breakthrough. The movies are filled with such events. Unfortunately, it won't happen. In new or immature fields or subfields, it is possible for an essentially untrained or self-trained genius to jump in and discover something important. Galileo and Newton probably fit this category in physics and Galois and Ramanujan probably fit it in mathematics. But most of physics is now so mature that broad new discoveries are rare, and accessible only to those with extremely good understandings of what is already known. A basement tinkerer hasn't got a prayer.
Finally, real scientists don't always walk around in white lab coats looking serious, ridiculing the less educated, and trying to figure out how to trick the government into funding yet another silly, fraudulent, or unethical research project. In fact, most scientists wear practical clothes, have considerable humor, enjoy speaking with ordinary folk about their science, and conduct that science because they love and believe in it rather than as a means to some diabolic end. These scientists use the words of science in their conversations because it is the appropriate language for their work and there is meaning in each word and each sentence. The gibberish spoken by "scientists" in movies is often offensive to scientists in the same way that immigrant groups find it offensive when people mock their native languages.
I don't know about any patent history for the free electricity organization but everyone should be aware that not all patented items actually do what they're supposed to. In principle, the U.S. Patent Office only awards a patent when it determines that a concept has not been patented previously, is not already known, is not obvious, and is useful. The utility requirement should eliminate items that don't actually work. One of my readers, a patent attorney, reports that he regularly invokes the utility regulation while escorting the "inventors" of impossible devices such as "free electricity" to the door. They consider him part of the conspiracy against them, but he is doing us all a service by keeping foolishness out of the patent system. However, proving that something doesn't work often takes time and money, so sometimes nonfunctional items get patented. Thus a patent isn't always a guarantee of efficacy. Patented nonsense is exactly that: nonsense.
Finally, how do I know that Free Electricity is really not possible? Couldn't I have missed something somewhere in the details? No. The impossibility of this scheme is rooted in the very groundwork of physics; at the deepest level where there is no possibility of mistake. For the counter rotation device to generate 15 kilowatts of electricity out of nothing, it would have to be a net source of energy—the device would be creating energy from nothing. That process would violate the conservation of energy, whereby energy cannot be created or destroyed but can only be transferred from one object to another or converted from one form to another. Recognizing that our universe is relativistic (it obeys the laws of special relativity), the actual conserved quantity is mass/energy, but the concept is the same: you can't make mass/energy from nothing.
The origin of this conservation law lies in a mathematical theorem noted first by C. G. J. Jacobi and fully developed by Emmy Noether, that each symmetry in the laws of physics gives rise to a conserved quantity. The fact that a translation in space—shifting yourself from one place to another—does not change the laws of physics gives rise to a conserved quantity: momentum. The fact that a rotation—changing the direction in which you are facing—does not change the laws of physics gives rise to another conserved quantity: angular momentum. And the fact that waiting a few minutes—changing the time at which you are—does not change the laws of physics gives rise to a third conserved quantity: energy. The conservation of energy is thus intimately connected with the fact that the laws of physics are the same today as they were yesterday and as they will be tomorrow.
Scientists have been looking for over a century for any changes in the laws of physics with translations and rotations in space and with movement through time, and have never found any evidence for such changes. Thus momentum, angular momentum, and energy are strictly conserved in our universe. For the counter rotation device to create energy from nothing, all of physics would have to be thrown in the trashcan. The upset would be almost as severe as discovering that 1+1 = 3. Furthermore, a universe in which physics was time-dependent and energy was not conserved would be a dangerous place. Free electricity devices would become the weapons of the future—bombs and missiles that released energy from nothing. Moreover, as the free electricity devices produced energy from nothing, the mass/energy of the earth would increase and thus its gravitational field would also increase. Eventually, the gravity would become strong enough to cause gravitational collapse and the earth would become a black hole. Fortunately, this is all just science fiction because free electricity isn't real.
A convenient arrangement for generating electricity endlessly is to mount a permanent magnet on a spindle and to place a coil of wire nearby. Then as the magnet spins, it will turn past the coil of wire and propel currents through that coil. With a little more engineering, you'll have a system that looks remarkably like the guts of a typical permanent magnet based motor. In fact, if you take a common DC motor out of a toy and connect its two electrical terminals to a 1.5 V light bulb or a light emitting diode (try both directions with an LED because it can only carry current in one direction), you'll probably be able to light that bulb or LED by spinning the motor's shaft rapidly. A DC motor has a special switching system that converts the AC produced in the motor's coils into DC for delivery to the motor's terminals, but it's still a generator. So the easiest answer to your question is: "find a nice DC motor and turn its shaft".
To magnetize a screwdriver permanently, you should expose it briefly to a very strong magnetic field. Touching the screwdriver's tip to one pole of a strong magnet will cause some permanent magnetization. Rubbing or tapping the screwdriver also helps to free up its domains so that they can align with this external field. But the better approach is to put the screwdriver in a coil of wire that carries a very large DC electric current.
The current only needs to flow for a fraction of a second—just long enough for the domains to align. A car battery is a possibility, but it has safety problems: it can deliver an incredible current (400 amperes or more) for a long time (minutes) and can overheat or even explode your coil of wire. Moreover, it may leak hydrogen gas, which can be ignited by the sparks that will inevitably occur while you are magnetizing your screwdriver.
A safer choice for the current source is a charged electrolytic capacitor—a device that stores large quantities of separated electric charge. A charged capacitor can deliver an even larger current than a battery can, but only for a fraction of a second—only until the capacitor's store of separated charge is exhausted. Looking at one of my hobbyist electronics catalogs, Marlin P. Jones, 800-652-6733, I'd pick a filter capacitor with a capacity of 10,000 microfarads and a maximum voltage of 35 volts (Item 12104-CR, cost: $1.50). Charging this device with three little 9V batteries clipped together in a series (27 volts overall) will leave it with about 0.25 coulombs of separated charge and just over 3.5 joules (3.5 watt-seconds or 3.5 newton-meters) of energy.
Make sure that you get the polarity right—electrolytic filter capacitors store separated electric charge nicely but you have to put the positive charges and negative charges on the proper sides. [To be safe, work with rubber gloves and, as a general rule, never touch anything electrical with more than one hand at a time. Remember that a shock across your heart is much more dangerous than a shock across you hand. And while 27 volts is not a lot and is unlikely to give you a shock under any reasonable circumstances, I can't accept responsibility for any injuries. If you're not willing to accept responsibility yourself, don't try any of this.]
If you wrap about 100 turns of reasonably thick insulated wire (at least 18 gauge, but 12 gauge solid-copper home wiring would be better) around the screwdriver and then connect one end of the coil to the positively charged side of the capacitor and the other end of the coil to the negatively charged side, you'll get a small spark (wear gloves and safety glasses) and a huge current will flow through the coil. The screwdriver should become magnetized. If the magnetization isn't enough, repeat the charging-discharging procedure a couple of times, always with the same connections so that the magnetization is in the same direction.
The fact that electricity itself travels at almost the speed of light just means that when you start the electrons moving at one end of a long wire, the electrons at the other end of the wire also begin moving almost immediately. But that doesn't mean that an electron from your end of the wire actually reaches the far end any time soon. Instead, the electrons behave somewhat like water in a long hose. When you start the water moving at one end, it pushes on water in front of it, which pushes on water in front of it, and so on so that water at the far end of the hose begins to leave the hose almost immediately. In the case of water, the motion proceeds forward at the speed of sound. In a wire, the motion proceeds forward at the speed of light in the wire (actually the speed at which electromagnetic waves propagate along the wire), which is only slightly less than the speed of light in vacuum.
Note for the experts: as one of my readers (KT) points out, the water-in-a-hose analogy for current-in-a-wire is far from perfect. Current in a wire flows throughout the wire, including at its surface, and the wire's resistance to steady current flow scales as the cross-sectional area of the wire. In contrast, water in a hose only flows through the open channel inside the hose and the hose's resistance to flow scales approximately as the fourth power of that channel's diameter.
When you put your eye in water, the eye's curved outer surface stops acting as a lens. That's because light travels at roughly the same speed in water as it does in your eye and that light no longer bends as it enters your eye. Everything looks blurry because the light doesn't focus on your retina anymore. But by inserting an air space between your eye and a flat plate of glass or plastic, you recover the bending at your eye's surface and everything appears sharp again.
The problem with this real image of the sun is simply that it's dazzlingly bright and that it delivers lots of thermal power in a small area. The real image is there in space, whether or not you put any object into that space. If you put paper or some other flammable substance in this focused region, it may catch on fire. Putting your skin in the focus would also be a bad idea. And if you put your eye there, you're in serious trouble.
So my suggestion with first graders is to stay in the shade when you're working with magnifying glasses. As soon as you go out in direct sunlight, that brilliant real image will begin hovering in space just beyond the magnifying glass, waiting for someone to put something into it. And many first graders just can't resist the opportunity to do just that.
These electromechanical watches are the modern descendants of the automatic mechanical watches. An automatic watch had a main spring that was wound by the motion of the wearer's hand. A small mass inside the watch swung back and forth on the end of a lever. Because of its inertia, this mass resisted changes in velocity and it moved relative to the watch body whenever the watch accelerated. If you like, you can picture the mass as a ball that rolls about inside a wagon as you roll the wagon around an obstacle course. When the lever turned back and forth relative to the watch body, the watch was able to extract energy from it. Gears attached to the lever allowed the watch to use the mass's energy to wind its mainspring. The energy extracted from the mass with each swing was very small, but it was enough to keep the mainspring fully wound. Ultimately, this energy came from your hand—you did work on the watch in shaking it about and some of this energy eventually wound up in the mainspring.
These same sorts of motions are what power the electromechanical watches of today. Instead of winding a spring, your wrist motions swing weights about inside the watches and these moving weights spin generators to produce electric power.
In principle, you could tap into a cloud and the ground beneath and extract the capacitor's charge directly with wires. But this would be a heroic engineering project and unlikely to be worth the trouble. And catching a lightning strike in order to charge a second capacitor is not likely to be very efficient: most of the energy released during the strike would have to dissipate in the air and relatively little of it could be allowed to enter the capacitor. That's because no realistic capacitor can handle the voltage in lightning.
Here's the detailed analysis. The power released during the strike is equal to the strike's voltage times its current: the voltage between clouds and ground and the current flowing between the two during the strike. Voltage is the measure of how much energy each unit of electric charge has and current is the measure of how many units of electric charge are flowing each second. Their product is energy per second, which is power. Added up over time, this power gives you the total energy in the strike. If you want to capture all this energy in your equipment, it must handle all the current and all the voltage. If it can only handle 1% of the voltage, it can only capture 1% of the strike's total energy.
While the current flowing in a lightning strike is pretty large, the voltage involved is astonishing: millions and millions of volts. Devices that can handle the currents associated with lightning are common in the electric power industry but there's nothing reasonable that can handle lightning's voltage. Your equipment would have to let the air handle most of that voltage. The air would extract power from the flowing current in the lightning bolt and turning it into light, heat, and sound. Your equipment would then extract only a token fraction of the stroke's total energy. Finally, your equipment would have to prepare the energy properly for delivery on the AC power grid—its voltage would have to be lowered dramatically and a switching system would have to convert the static charge on the capacitors to an alternating flow of current in the power lines.
To see why this arrangement is stable, consider what would happen if something tried to upset it. For example, what would happen if this mixture were to begin losing heat to its surroundings? Its temperature would begin to drop but then the water would begin to freeze and release thermal energy: when water molecules stick together, they release chemical potential energy as thermal energy. This thermal energy release would raise the temperature back to 32 F. The bath thus resists attempts at lowering its temperature.
Similarly, what would happen if the mixture were to begin gaining heat from its surroundings? Its temperature would begin to rise but then the ice would begin to melt and absorb thermal energy: separating water molecules increases their chemical potential energy and requires an input of thermal energy. This lost thermal energy would lower the temperature back to 32 F. The bath thus resists attempts at raising its temperature.
So an ice/water bath self-regulates its temperature at 32 F. The only other quantities affecting this temperature are the air pressure (the bath temperature could shift upward by about 0.003 degrees F during the low pressure of a hurricane) and dissolved chemicals (half an ounce of table salt per liter of bath water will shift the bath temperature downward by about 1 degree F).
More manageable pressures surround us everyday. Our bodies do their part in supporting the weight of the atmosphere overhead when we're on land or the weight of the atmosphere and a small part of the ocean when we're swimming at sea. The deeper you go in the ocean, the more weight there is overhead and the harder your body must push upward. Thus the pressure you exert on the water above you and the pressure that that water exerts back on you increases with depth. Even though gravity is decreasing as you go deeper and deeper, the pressure continues to increase. However, it increases a little less rapidly as a result of the decrease in local gravity.
As for the fact that even colored soaps create only white foam, that's related to the amount of dye in the soaps. It doesn't take much dye to give bulk soap its color. Since light often travels deep into a solid or liquid soap before reflecting back to our eyes, even a modest amount of dye will selectively absorb enough light to color the reflection. But the foam reflects light so effectively with so little soap that the light doesn't encounter much dye before leaving the lather. The reflection remains white. To produce a colored foam, you would have to add so much dye to the soap that you'd probably end up with colored hands as well.
Metals that bend permanently are experiencing plastic deformation. Their atoms change their relative orientations during the bend and they lose track of where they were. Once plastic deformation has occurred, the metal can't remember how to get back to its original shape and stays bent.
Metals that bend only temporarily and return to their original shape when freed from stress are experiencing elastic deformation. Their sheets of atoms aren't sliding about and they can easily spring back to normal when the stresses go away. Naturally, springs are made from materials that experience only elastic deformation in normal circumstances. Hardened metals such as spring steel are designed and heat-treated so that the atomic sliding processes, known technically as "slip," are inhibited. When you bend them and let go, they bounce back to their original shapes. But if you bend them too far, they either experience plastic deformation or they break.
Non-crystalline materials such as glass also make good springs. But since these amorphous materials have no orderly rows of atoms, they can't experience plastic deformation at all. They behave as wonderful springs right up until you bend them too far. Then, instead of experience plastic deformation and bending permanently, they simply crack in two.
One last detail: there are a few exotic materials that undergo complicated deformations that are neither temporary nor permanent. With changes in temperature, these shape memory materials can recover from plastic deformation and spring back to their original shapes.
But when something is moving at speeds approaching the speed of light, mass and kinetic energy no longer separate so easily. In fact, the relativistic equations of motion are more complicated than those describing slow objects and the way in which gravity affects fast objects is more complicated than simply giving them "weight."
Overall, you can view the bending of light by gravity in one of two ways. First, you can view it approximately as gravity affecting not on mass, but also energy so that light falls because its energy gives it something equivalent to a "weight." Second, you can view it more accurately as the bending of light as caused by a change in the shape of space and time around a gravitating object. Space is curved, so that light doesn't travel straight as it moves past gravitating objects—it follows the curves of space itself. The second or Einsteinian view, which correctly predicts twice as much bending of light as the first or Newtonian view, is a little disconcerting. That's why it took some time for the theory of general relativity to be widely accepted. (Thanks to DP for pointing out the factor of two.)
When the car starts forward, inertia tries to keep all of the objects in the car from moving forward. An object at rest tends to remain at rest. So the car must push you forward in order to accelerate you forward and keep you moving with the car. As the car seat pushes forward on you, you push back on the car seat (Newton's third law) and dent its surface. Your perception is that you are moving backward, but you're not really. You're actually moving forward; just not quite as quickly as the car itself.
The air in the car undergoes the same forward acceleration process. Its inertia tends to keep it in place, so the car must push forward on it to make it accelerate forward. Air near the front of the car has nothing to push it forward except the air near the back of the car, so the air in the front of the car tends to "dent" the air in the back of the car. In effect, the air shifts slightly toward the rear of the car. Again, you might think that this air is going backward, but it's not. It's actually moving forward; just not quite as quickly as the car itself.
Now we're ready for the helium balloon. Since helium is so light, the helium balloon is almost a hollow, weightless shell that displaces the surrounding air. As the car accelerates forward, the air in the car tends to pile up near the rear of the car because of its inertia. If the air can push something out of its way to get more room near the rear of the car, it will. The helium balloon is that something. As inertia causes the air to drift toward the rear of the accelerating car, the nearly massless and inertialess helium balloon is squirted toward the front of the car to make more room for the air. There is actually a horizontal pressure gradient in the car's air during forward acceleration, with a higher pressure at the rear of the car than at the front of the car. This pressure gradient is ultimately what accelerates the air forward with the car and it's also what propels the helium balloon to the front of the car.
Finally, when the car is up to speed and stops accelerating forward, the pressure gradient vanishes and the air returns to its normal distribution. The helium balloon is no longer squeezed toward the front of the car and it floats once again directly above the gear shift.
One last note: OGT from Lystrup, Denmark points out that when you accelerate a glass of beer, the rising bubbles behave in the same manner. They move toward the front of the glass as you accelerate it forward and toward the back of the glass as you bring it to rest.
The fact that we see mostly reflected light makes for some interesting experiments. A red object selectively reflects only red light; a blue object reflects only blue light; a green object reflects only green light. But what happens if you illuminate a red object with only blue light? The answer is that the object appears black! Since it is only able to reflect red light, the blue light that illuminates it is absorbed and nothing comes out for us to see. That's why lighting is so important to art. As you change the illumination in an art gallery, you change the variety of lighting colors that are available for reflection. Even the change from incandescent lighting to fluorescent lighting can dramatically change the look of a painting or a person's face. That's why some makeup mirrors have dual illumination: incandescent and fluorescent.
The one exception to this rule that objects only reflect the light that strikes them is fluorescent objects. These objects absorb the light that strikes them and then emit new light at new colors. For example, most fluorescent cards or pens will absorb blue light and then emit green, orange, or red light. Try exposing a mixture of artwork and fluorescent objects to blue light. The artwork will appear blue and black: blue wherever the art is blue and black wherever the art is either red, green, or black. But the fluorescent objects will display a richer variety of colors because those objects can synthesize their own light colors.
In answer to your question, my guess is that the larger bowl of water also exposes much more of that water to the air. Although the larger bowl had more water in it, it allowed that water to exchange heat faster with its environment. If the larger bowl contained twice as much water but let that water lose heat twice as fast, the two bowls would maintain equal temperatures. If you want to see the effect of thermal mass in slowing the loss of temperature, you'll need to control heat loss. Try letting equal amounts of hot water cool in two identical containers—one wrapped in insulation and covered with clear plastic wrap (to prevent evaporation) and one open to the air. You'll see a dramatic change in cooling rate. And if you want to compare unequal amounts of water, use two indentical containers that are only exposed to the cooler environment through a controlled amount of surface area. For example, try two identical insulated cups, one full of water and one only half full. If both lose heat only through their open tops, the full cup should cool more slowly than the half full cup.
You won't get any important quantitative results from this sort of experiment, but it'll be fun anyway. I wonder what fillings will make the ball bounce best or worst?
That is what happens when you carefully weave a needle into a latex balloon—the needle separates the polymer strands locally, but doesn't actually pull them apart or break them. Since breaking the latex molecules will probably cause the balloon to tear and burst, you have to be very patient and use a very sharp needle. I usually oil the needle before I do this and I don't try to insert the needle in the most highly stressed parts of the balloon. The regions near the tip of the balloon and near where it is filled are the least stressed and thus the easiest to pierce successfully with a needle. A reader has informed me that coating the needle with Vasoline is particularly helpful.
One final note: a reader pointed out that it is also possible to put a needle through a balloon with the help of a small piece of adhesive tape. If you put the tape on a patch of the inflated balloon, it will prevent the balloon from ripping when you pierce the balloon right through the tape. This "cheaters" approach is more reliable than trying to thread the needle between the latex molecules, but it's less satisfying as well. But it does point out the fact that a balloon bursts because of tearing and that if you prevent the balloon from tearing, you can pierce it as much as you like.
When the unit is operating and pumping heat, the evaporator becomes cold and the condenser becomes hot. A fan blows warm, moist air from the room through the evaporator coils and that air's temperature drops. This temperature drop changes the behavior of water molecules in the air. When the air and its surroundings were warm, any water molecule that accidentally bumped into a surface could easily return to the air. Thus while water molecules were always landing on surfaces or taking off, the balance was in favor of being in the air. But once the air and its surroundings become cold, any water molecules that bump into a surface tend to stay there. Water molecules are still landing on surfaces and taking off, but the balance is in favor of staying on the surface as either liquid water or solid ice. That's why dew or frost form when warm moist air encounters cold ground. In the dehumidifier, much of the air's water ends up dripping down the coils of the evaporator into a collection basin.
All that remains is for the dehumidifier to rewarm the air. It does this by passing the air through the condenser coils. The thermal energy that was removed from the air by the evaporator is returned to it by the condenser. In fact, the air emerges slightly hotter than before, in part because it now contains all of the energy used to operate the dehumidifier and in part because condensing moisture into water releases energy. So the dehumidifier is using temperature changes to separate water and air.
By itself, melting ice has a temperature of 0° C (32° F). When heat flows into ice at that temperature, the ice doesn't get hotter, it just transforms into water at that same temperature. Separating the water molecules in ice to form liquid water takes energy and so heat must flow into the ice to make it melt.
But if you add salt to the ice, you encourage the melting process so much that the ice begins to use its own internal thermal energy to transform into water. The temperature of the ice drops well below 0° C (32° F) and yet it keeps melting. Eventually, the drop in temperature stops and the ice and salt water reach an equilibrium, but the mixture is then quite cold—perhaps -10° C (14° F) or so. To melt more ice, heat must flow into the mixture. When you place liquid cream nearby, heat begins to flow out of the cream and into the ice and salt water. More ice melts and the liquid cream get colder. Eventually, ice cream starts to form. Stirring keeps the ice crystals small and also ensures that the whole creamy liquid freezes uniformly.
The issue is in how well the ball's surface stores and then releases this energy. The ideal ball experiences only elastic deformation—the molecules within the ball do not reorganize at all, but only change their relative spacings during the dent. If the molecules reorganize—sliding across one another or pulling apart in places—then some of the denting energy will be lost due to internal friction-like effects. Even if the molecules slide back to their original positions, they won't recover all the energy and the ball won't bounce to its original height.
In general, harder rubber bounces more efficiently than softer rubber. That's because the molecules in hard rubber are too constrained to be able to slide much. A superball is very hard and bounces well. But there are also sophisticated thermal effects that occur in some seemingly hard rubbers that cause them to lose their stored energy.
However, because ozone molecules are chemically unstable, they can be depleted by contaminants in the air. Ozone molecules react with many other molecules or molecular fragments, making ozone useful as a bleach and a disinfectant. Molecules containing chlorine atoms are particularly destructive of ozone because a single chlorine atom can facilitate the destruction of many ozone molecules through a chlorine recycling process.
In contrast, nitrogen molecules are extremely stable. They are so stable that there are only a few biological systems that are capable of separating the two nitrogen atoms in a nitrogen molecule in order to create organic nitrogen compounds. Without these nitrogen-fixing organisms, life wouldn't exist here. Because nitrogen molecules are nearly unbreakable, they survive virtually any amount or type of chemical contamination.
Second, although there is considerable energy consumed in manufacturing the complicated components of a fluorescent lamp, it's unlikely to more than a few kilowatt-hours—the equivalent of the extra energy a 100 watt incandescent light uses up in a week or so of typical operation. So it may take a week or two to recover the energy cost of building the fluorescent light, but after that the energy savings continue to accrue for years and years.
But suppose that the bus were traveling at 99.999999% of the speed of light and you were to run toward its front at 0.000002% of the speed of light (about 13 mph or just under a 5 minute mile). Now what would happen?
First, the bus speed I quoted is in reference to some outside observer because the seated passengers on the bus can't determine its speed. After all, if the shades are pulled down on the bus and it's moving at a steady velocity, no one can tell that it's moving at all. So let's assume that the bus speed I gave is according to a stationary friend who is watching the bus zoom by from outside.
While you are running toward the front of the bus at 0.000002% of the speed of light, your speed is in reference to the other passengers in the bus, who see you moving forward. The big question is what does you stationary friend see? Actually, your friend sees you running toward the front of the bus, but determines that your personal speed is only barely over 99.999999%. The two speeds haven't added the way you'd expect. Even though you and the bus passengers determine that you are moving quickly toward the front of the bus, your stationary friend determines that you are moving just the tiniest bit faster than the bus. How can that be?
The answer lies in the details of special relativity, but here is a simple, albeit bizarre picture. Your stationary friend sees a deformed bus pass by. Ignoring some peculiar optical effects due to the fact that it takes time for light to travel from the bus to your friend's eyes so that your friend can see the bus, your friend sees a foreshortened bus—a bus that is smashed almost into a pancake as it travels by. While you are in that pancake, running toward the front of the bus, the front is so close to the rear that your speed within the bus is miniscule. Why the bus becomes so short is another issue of special relativity.
The pipe functions by evaporating the liquid working fluid into gas at its hotter end and allowing that gaseous working fluid to condense back into a liquid at its colder end. Since it takes thermal energy to convert a liquid to a gas, heat is absorbed at the hotter end. And because a gas gives up thermal energy when it converts from a gas to a liquid, heat is released at the colder end.
After a brief start-up period, the heat pipe functions smoothly as a rapid conveyor of heat. The working fluid cycles around the pipe, evaporating from the wick at the hot end of the pipe, traveling as a gas to the cold end of the pipe, condensing on the wick, and then traveling as a liquid to the hot end of the pipe.
Near room temperature, heat pipes use working fluids such as HFCs (hydrofluorocarbons, the replacements for Freons), ammonia, or even water. At elevated temperatures, heat pipes often use liquid metals such as sodium.
Two of the most common types of microphones are capacitance microphones and electromagnetic microphones. In a capacitance microphone, opposite electric charges are placed on two closely spaced surfaces. One of those surfaces is extremely thin and moves easily in response to changes in air pressure. The other surface is rigid and fixed. As a sound enters the microphone, the thin surface vibrates with the pressure fluctuations. The electric charges on the two surfaces pull on one another with forces that depend on the spacing of the surfaces. Thus as the thin surface vibrates, the charges experience fluctuating forces that cause them to move. Since both surfaces are connected by wires to audio equipment, charges move back and forth between the surfaces and the audio equipment. The sound has caused electric currents to flow and the audio equipment uses these currents to record or process the sound information.
In an electromagnetic microphone, the fluctuating air pressure causes a coil of wire to move back and forth near a magnet. Since changing or moving magnetic fields produce electric fields, electric charges in the coil of wire begin to move as a current. This coil is connected to audio equipment and again uses these currents to represent sound.
But the airstream that goes over the wing has a complicated trip. First it encounters the leading edge of the wing and is pushed upward and forward. This air slows somewhat and its pressure increases. So far, this upper airstream isn't helpful to the plane because it pushes the plane backward. But the airstream then follows the curving upper surface of the wing because of a phenomenon known as the Coanda effect. The Coanda effect is a common behavior in fluids—viscosity and friction keep them flowing along surfaces as long as they don't have to turn too quickly. (The next time your coffee dribbles down the side of the pitcher when you poured too slowly, blame it on the Coanda effect.)
Because of the Coanda effect, the upper airstream now has to bend inward to follow the wing's upper surface. This inward bending involves an inward acceleration that requires an inward force. That force appears as the result of a pressure imbalance between the ambient pressure far above the wing and a reduced pressure at the top surface of the wing. The Coanda effect is the result (i.e. air follows the wing's top surface) but air pressure is the means to achieve that result (i.e. a low pressure region must form above the wing in order for the airstream to arc inward and follow the plane's top surface).
The low pressure region above the wing helps to support the plane because it allows air pressure below the wing to be more effective at lifting the wing. But this low pressure also causes the upper airstream to accelerate. With more pressure behind it than in front of it, the airstream accelerates—it's pushed forward by the pressure imbalance. Of course, the low pressure region doesn't last forever and the upper airstream has to decelerate as it approaches the wing's trailing edge—a complicated process that produces a small amount of turbulence on even the most carefully designed wing.
In short, the curvature of the upper airstream gives rise to a drop in air pressure above the wing and the drop in air pressure above the wing causes a temporary increase in the speed of the upper airstream as it passes over much of the wing.
While salt and sugar both dissolve in water and thus both lower its freezing temperature, salt is much more effective than sugar. That's because salt produces far more dissolved particles per pound or per cup than sugar. First, table salt (sodium chloride) is almost 40% more dense than cane sugar (sucrose), so that a cup of salt weighs much more than a cup of cane sugar. Second, a salt molecule (NaCl) weighs only about 8.5% as much as a sucrose molecule (C12H22O11), so there are far more salt molecules in a pound of salt than sugar molecules in a pound of sugar. Finally, when salt dissolves in water, it decomposes into ions: Na+ and Cl-. That decomposition doubles the density of dissolved particles produced when salt dissolves. Sugar molecules remain intact when they dissolve, so there is no doubling effect. Thus salt produces a much higher density of dissolved particles than sugar, whether you compare them cup for cup or pound for pound, and thus lowers water's freezing temperature more effectively. That's why the salt water is so slow to freeze.
But before fuel is injected into the engine's compressed air, there is a side duct that allows some of that compressed air to flow toward the passenger cabin. So the engine is providing the air you breathe during a flight.
There is one last interesting point about this compressed air: It is initially too hot to breathe. Even though air at 30,000 feet is extremely cold, the act of compressing it causes its temperature to rise substantially. This happens because compressing air takes energy and that energy must go somewhere in the end. It goes into the thermal energy of the air and raises the air's temperature. Thus the compressed air from the engines must be cooled by air conditioners before it goes into the passenger cabin.
But there is something I've neglected: you aren't really at one location in space. Because your body has a finite size, the forces of gravity on different parts of your body would vary subtly according to their exact locations in space. Such variations in the strength of gravity are normally insignificant but would become important if you were extremely big (e.g. the size of the moon) or if the two planets you had in mind were extremely small but extraordinarily massive (e.g. black holes or neutron stars). In those cases, spatial variations in gravity would tend to pull unevenly on your body parts and might cause trouble. Such uneven forces are known as tidal forces and are indeed responsible for the earth's tides. While the tidal forces on a spaceship traveling between the earth and the moon would be difficult to detect, they would be easy to find if the spaceship were traveling between two small and nearby black holes. In that case, the tidal forces could become so severe that they could rip apart not only the spaceship and its occupants, but also their constituent molecules, atoms, and even subatomic particles.
So instead of measuring the "temperature of the microwave oven," people normally put thermometers in the food to measure the food's temperature. This works well as long as the thermometers don't interact with the microwaves in ways that make them either hotter or inaccurate. Electronic thermometers are common in high-end microwaves. There is nothing special about these electronic thermometers except that they are carefully shielded so that the microwaves don't heat them or affect their readings. By "shielded," I mean that each of these thermometers has a continuous metallic sheath that reflects the microwaves. This sheath extends from the wall of the oven's cooking chamber all the way to the thermometer probe's tip so that the microwaves themselves can't enter the measurement electronics. Since the sheath reflects microwaves, the thermometer isn't heated by the microwaves and only measures the temperature of the food it contacts.
On the other hand, putting a mercury thermometer in a microwave oven isn't a good idea. While mercury is a metal and will reflect most of the microwaves that strike it, the microwaves will push a great many electric charges up and down the narrow column of mercury. This current flow will cause heating of the mercury because the column is too thin to tolerate the substantial current without becoming warm. The mercury can easily overheat, turn to gas, and explode the thermometer. (A reader of this web site reported having blown up a mercury thermometer just this way as a child.) Moreover, as charges slosh up and down the mercury column, they will periodically accumulate at the upper end. Since there is only a thin vapor of mercury gas above this upper surface, the accumulated charges will probably ionize this vapor and create a luminous mercury discharge. The thermometer would then turn into a mercury lamp, emitting ultraviolet light. I used microwave-powered mercury lamps similar to this in my thesis research fifteen years ago and they work very nicely.
The most effective modern absorption cycle refrigerators use a solution of lithium bromide (LiBr) in water. What enters the boiler is a relatively dilute solution of LiBr (57.5%) and what leaves is dense, pure water vapor and a relatively concentrated solution of LiBr (64%). The pure water vapor enters a condenser, where it gives up heat to its surroundings and turns into liquid water. To convert this liquid water back into gas, all that has to happen is for its pressure to drop. That pressure drop occurs when the water enters a low-pressure evaporator through a narrow orifice. As the water evaporates, it draws heat from its surroundings and refrigerates them.
Finally, something must collect this low pressure water vapor and carry it back to the boiler. That "something" is the concentrated LiBr solution. When the low-pressure water vapor encounters the concentrated LiBr solution in the absorption unit, it quickly goes back into solution. The solution becomes less concentrated as it draws water vapor out of the gas above it. This diluted solution then returns to the boiler to begin the process all over again.
Overall, the pure water follows one path and the LiBr solution follows another. The pure water first appears as a high-pressure gas in the boiler (out of the boiling LiBr solution), converts to a liquid in the condenser, evaporates back into a low-pressure gas in the evaporator, and finally disappears in the absorption unit (into the cool LiBr solution). Meanwhile, the LiBr solution shuttles back and forth between the boiler (where it gives up water vapor) and the absorption unit (where it picks up water vapor). The remarkable thing about this whole cycle is that its only moving parts are in the pump that moves LiBr solution from the absorption unit to the boiler. Its only significant power source is the heater that operates the boiler. That heater can use propane, kerosene, electricity, waste heat from a conventional power plant, and so on.
Visualize a boat riding on a passing wave—the boat begins bobbing up and down as the wave arrives but it stops bobbing as the wave departs. Overall, the boat doesn't absorb any energy from the wave. However, if the boat rubs against a dock as it bobs up and down, it will converts some of the wave's energy into thermal energy and the wave will have permanently transferred some of its energy to the boat and dock.
However, there is one big difference between an audio player and a VCR. In an audio player, the tape moves past a stationary playback head. In a VCR, the tape moves past a spinning playback head. When you pause an audio tape player, the tape stops moving and there is no audio signal. But when you pause a VCR, the playback head continues to spin. As the playback head (actually 2 or even 4 heads that trade off from one another) sweeps across a few inches of the tape, it experiences the changing magnetic fields and fluctuating electric fields needed to produce the video and audio signals. That's why you can still see the image from a paused VCR. To prevent the spinning playback heads from wearing away the tape, most VCRs limit the pause time to about 5 minutes.
Now for the technical details: a transformer is able to make such transfers of power because (1) electric currents are magnetic, (2) the magnetic fields from an alternating electric current changes with time, (3) a time-varying magnetic field creates an electric field, and (4) an electric fields pushes on electric charges and electric currents. Overall, one of the alternating currents flowing through a transformer creates a time-varying magnetic field and thus an electric field in the transformer. This electric field does work on (transfers power to) another alternating current flowing through the transformer. At the same time, this electric field does negative work on (saps power from) the original alternating current. When all is said and done, the first current has lost some of its power and the second current has gained that missing power.
The most probable cause for this problem is some power-hungry device in or near your house that cycles on every 5 or 10 minutes. In all likelihood, this device contains a large motor—motors have a tendency to draw enormous currents while they are first starting to turn, particularly if they are old and in need of maintenance. The wiring and power transformer systems that deliver electricity to your neighborhood and house have limited capacities and cannot transfer infinite amounts of power without wasting some of it. In general, wires waste power in proportion to the square of the current they are carrying. While the amount of power wasted in your home's wiring is insignificant in normal situations, it can become sizeable when the circuits are overloaded. This wasted power in the wiring appears as a loss of voltage—a loss of energy per charge—at your lights and appliances. When the heavy equipment turns on and begins to consume huge amounts of power, the wiring and other electric supply systems begin to waste much more power than normal and the voltage reaching your lights is significantly reduced. Your lights dim until the machinery stops using so much power.
To find what device that's making your lights dim, listen carefully the next time your lights fade. You'll probably hear an air conditioner, a fan, or even an elevator starting up somewhere, either in your house or in your neighborhood. There may be nothing you can do to fix the problem, but it's possible that replacing a motor or its bearings will reduce the problem. Another possible culprit is an electric heating system—a hot water heater, a radiant heater, an oven, a toaster, or even a hair-dryer. These devices also consume large amounts of power and, in an older house with limited electric services, may dim the lights.
One final issue to consider is surface area: the more surface area there is between the liquid soda and the gas above it, the faster molecules are exchanged between the two phases. Even if you don't keep carbon dioxide gas trapped above soda, you can slow the loss of carbonation by keeping the soda in a narrow-necked bottle with little surface between liquid and gas. But you must also be careful not to introduce liquid-gas surface area inside the liquid. That's what happens when you shake soda or pour it into a glass—you create tiny bubbles inside the soda and these bubbles grow rapidly as carbon dioxide molecules move from the liquid into the bubbles. Cool temperatures, minimal surface area, and plenty of carbon dioxide in the gas phases will keep soda from going flat.
As for pouring the soda over ice causing it to bubble particularly hard, that is partly the result of air stirred into the soda as it tumbles over the ice cubes and partly the result of adding impurities to the soda as the soda washes over the rough and impure surfaces of the ice. The air and impurities both nucleate carbon dioxide bubbles—providing the initial impetus for those bubbles to form and grow. Washing the ice to smooth its surfaces and remove impurities apparently reduces the bubbling when you then pour soda of it.
But while a parachutist can't change her weight, she can change the relationship between her downward speed and the upward drag force she experiences. If she rolls herself into a compact ball, she weakens the drag force and ultimately increases her terminal velocity. On the other hand, if she spreads her arms and legs wide so as to catch more air, she strengthens the drag force and decreases her terminal velocity. Popping open her parachute strengthens the drag force so much that her terminal velocity diminishes almost to zero and she coasts slowly downward to a comfortable landing. So to answer your question—two twin parachutists will descend at very different terminal velocities if they adopt different profiles or if only one opens a parachute.
At this point, you might assert that velocities do add and that objects should be able to reach any speed. But that's not the case. The modern, relativistic understanding of the universe says that even at these small speeds, velocities don't quite add. To the stationary observer, the second runner travels at only 9.9999999999999994 mph and the third runner at only 14.9999999999999988 mph. As you can see, when two or more velocities are combined, the final velocity isn't quite as large as the simple sum. What that means is that the velocity you observe in another object is inextricably related to your own motion. This interrelatedness is part of the theory of relativity—that observers who are moving relative to one another will see space and time somewhat differently.
For objects traveling close to the speed of light, the failure of velocity addition becomes quite severe. For example, if one spaceship travels past the earth at half the speed of light and the people in that spaceship watch a second spaceship pass them at half the speed of light in the same direction, then a person on earth will see the second spaceship traveling only four-fifths of the speed of light. As you can see, relativity is making it difficult to reach the speed of light. In fact, it's impossible to reach the speed of light! No matter how you combine velocities, no observer will ever see a massive object reach or exceed the speed of light. The only objects that can reach the speed of light are objects without mass and they can only travel at the speed of light.
So while the counting numbers obey simple addition and go on forever, velocities do not obey simple addition and have a firm limit—the speed of light. The additive counting numbers are an example of a mathematical group that extends infinitely in both directions, but there are many examples of groups that do not extend to infinity. The group that describes relativistic, real-world velocities is one such group. You can visualize another simple limited group—the one associated with walking around the surface of the earth. No matter how much you try, you can't walk more than a certain distance northward. While it seems as though steps northward add, so that 5 steps north plus 5 steps north equals 10 steps north, things aren't quite that simple. Eventually you reach the north pole and start walking south!
It's interesting to note that the earth itself bulges slightly in response to these tidal forces. However, because the earth is more rigid than the water, its bulges are rather small compared to those of the water.
However, if the tree's motion is too violent, even this weight and pulley system may not save the cable. As long as everything moves slowly, the tension in the cord should be equal to the weight of the weights. But if the tree moves away from the house very suddenly, then the tension in the cord will increase suddenly because the cord must not only support the weights, it must accelerate them upward as well. Part of the cord's tension acts to overcome the weights' inertia. Just as a sudden yank on a paper towel will rip it free from the roll, so a sudden yank on your cable will rip it free from the weights. If sudden yanks of this type cause trouble for you, you can fix the problem by coupling the cord to the weights via a strong spring. On long timescales, the spring will have no effect on the tension in the cord—it will still be equal to the weight of the weights. But the spring will stretch or contract during sudden yanks on the cord and will prevent the tension in the cord from changing abruptly either up or down. The spring shouldn't be too stiff—the less stiff and the more it stretches while supporting the weights, the more effectively it will smooth out changes in tension.
As far as the weight of the weights, that depends on how much curvature you want in the cable supporting the feeders. The more weight you use, the less the cable will sag but the more stress it will experience. You can determine how much weight you need by pulling on the far end of the cable with your hands and judging how hard you must pull to get a satisfactory amount of sag.
To obtain a wide variety of colors, you'll need a wide variety of metal salts. Sodium salts, including common table salt, will give you yellow light—the same light that's produced by sodium vapor lamps. Potassium salts yield purple, copper and barium salts yield green, strontium salts yield red, and so on. The classic way to produce a colored flame is to dip a platinum wire into a metal salt solution and to hold the wire in the flame. Since platinum is expensive, you can do the same trick with a piece of steel wire. The only problem is that the steel wire will burn eventually.
To sense the ripples in the V-groove, a phonograph places a hard stylus in the groove and spins the record. As the stylus rides along the walls of the moving groove, it vibrates back and forth with each ripple in a wall. Two transducers attached to this stylus sense its motions and produce electric currents that are related to those motions. The two most common transduction techniques are electromagnetic (a coil of wire and a magnet move relative to one another as the stylus moves and this causes current to flow through the coil) and piezoelectric (an asymmetric crystal is squeezed or unsqueezed as the stylus moves and this causes charge to be transferred between its surfaces). The transducer current is amplified and used to reproduce the recorded sound.
Once we recognize that the speed of light is special and that everyone sees light traveling at that speed, our views of space and time have to change. One of the classic "thought experiments" necessitating that change is the flashbulb in the boxcar experiment. Suppose that you are in a railroad boxcar with a flashbulb in its exact center. The flashbulb goes off and its light spreads outward rapidly in all directions. Since the bulb is in the center of the boxcar, its light naturally hits the front and back walls of the boxcar at the same instant and everything seems simple.
But your boxcar is actually hurtling forward on a track at an enormous speed and your friend is sitting in a station as the train rushes by. She looks into the boxcar through its window and sees the flashbulb go off. She watches light from the flashbulb spread out in all directions but it doesn't hit the front and back walls of the boxcar simultaneously. Because the boxcar is moving forward, the front wall of the boxcar is moving away from the approaching light while the back wall of the boxcar is moving toward that light. Remarkably, light from the flashbulb strikes the back wall of the boxcar first, as seen by your stationary friend.
Something is odd here: you see the light strike both walls simultaneously while your stationary friend sees light strike the back wall first. Who is right? The answer, strangely enough, is that you're both right. However, because you are moving at different velocities, the two of you perceive time and space somewhat differently. Because of these differences, you and your friend will not always agree about the distances between points in space or the intervals between moments in time. Most importantly, the two of you will not always agree about the distance or time separating two specific events and, in certain cases, may not even agree about which event happened first!
The remainder of the special theory of relativity builds on this groundwork, always treating the speed of light as a fundamental constant of nature. Einstein's famous formula, E=mc2, is an unavoidable consequence of this line of reasoning.
However, most metals don't have any internal magnetic order at all and there is nothing to line up with an external field. Metals such as copper and aluminum have no magnetic order in them—they don't have any tiny magnets present. The only way to make aluminum or copper magnetic is to run a current through it.
To maximize the attraction between the magnets, opposite magnetic poles should be as near together as possible while like magnetic poles are as far apart as possible. With long bar magnets, you align the magnets head to toe so that you have the north pole of one magnet opposite the south pole of the other magnet and vice versa. But long magnets also tend to have weaker poles than short stubby magnets because it takes energy to separate a magnet's north pole from its south pole. With short stubby magnets, the best you can do is to bring the north pole of one magnet close to the south pole of the other magnet while leaving their other poles pointing away from one another. Horseshoe magnets combine some of the best of both magnets—they can have the strong poles of short stubby magnets with more distance separating those poles.
Returning to the paper question, size is less important than pole strength and separation. The stronger the magnets and the farther apart their poles, the more paper you can hold between them.
But regardless of counting scheme, I can still answer your question about how the four basic forces differ. Gravitational forces are attractive interactions between concentrations of mass/energy. Everything with mass/energy attracts everything else with mass/energy. Because this gravitational attraction is exceedingly weak, we only notice it when there are huge objects around to enhance its effects.
Electromagnetic forces are strong interactions between objects carrying electric charge or magnetic pole. While most of these interactions can be characterized as attractive or repulsive, that's something of an oversimplification whenever motion is involved.
Weak interactions are too complicated to call "forces" because they almost always do more than simply pull two objects together or push them apart. Weak interactions often change the very natures of the particles that experience them. But the weak interactions are rare because they involve the exchange of exotic particles that are difficult to form and live for exceedingly short times. Weak interactions are responsible for much of natural radioactivity.
Strong forces are also very complicated, primarily because the particles that convey the strong force themselves experience the strong force. Strong forces are what hold quarks together to form familiar particles like protons and neutrons.
The time slowing effect is acceleration—a person or clock that takes a fast trip around the earth and then returns to the starting point will experience slightly less time than a person or clock that remained at the starting point. This effect is a consequence of acceleration and the changing relationships between space and time that come with different velocities.
The time speeding effect is gravitational redshift—a person or clock that is farther from the earth's center experiences slightly more time than a person or clock that remains at the earth's surface. This effect is a consequence of the decreased potential energy that comes with being deeper in the earth's gravitational potential well.
During his orbit, the astronaut feels weightless because all of his "pieces" are falling together. Those pieces don't need to push on one another to keep their relative positions as they fall, so he feels none of the internal forces that he interprets as weight when he stands on the ground. A falling astronaut can't feel his weight.
To prepare for this weightless feeling, the astronaut needs to fall. Jumping off a diving board or riding a roller coaster will help, but the classic training technique is a ride on the "Vomit Comet"—an airplane that follows a parabolic arc through the air that allows everything inside it to fall freely. The airplane's arc is just that of a freely falling object and everything inside it floats around in free fall, too—including the astronaut trainee. The plane starts the arc heading upward. It slows its rise until it reaches a peak height and then continues arcing downward faster and faster. The whole trip lasts at most 20 seconds, during which everyone inside the plane feels weightless.
While some of our appliances won't work in Europe because of the change in cycles-per-second, the biggest problem is with the increase in voltage. The charges entering a U.S. appliance in Europe carry about twice the energy per change (i.e. twice the voltage) and this increased "pressure" causes about twice the number of charges per second (i.e. twice the current) to flow through the appliance. With twice the current flowing through the appliance and twice as much voltage being lost by this current as it flows through the appliance, the appliance is receiving about four times its intended power. It will probably burn up.
As one of my readers (Tom O.) points out, most modern color copiers are essentially scanners plus color printers. They use infrared lasers to write the images optically onto four light-sensitive drums, one drum for each of the four colors (some systems reuse the same drum four times).
The white wire is rather passive in this process because its voltage is always essentially zero. It never has a net charge on it. But the black wire is alternately positively charged and then negatively charged. That's what makes its voltage rise and fall. Since the black wire is capable of pushing or pulling charge from the ground instead of from the white wire, you don't want to touch the black wire while you're grounded. You'll get a shock.
The absence of such "monopoles" is an interesting puzzle and scientists haven't given up hope of finding them. Some theories predict that they should exist, but be very difficult to form artificially. There may be magnetic monopoles left over from the big bang, but we haven't found any yet.
Dan Barker, one of my readers, informed me of a NASA study showing that there is a minimum speed at which a tire will begin to hydroplane and that that speed depends on the square root of the tire pressure. Higher tire pressure tends to expel the water layer and prevent hydroplaning, while lower tire pressure allows the water layer to remain in place when the vehicle is traveling fast enough. As Dan notes, a large truck tire is typically inflated to 100 PSI and resists hydroplaning at speed of up to about 100 mph. But a passanger car tire has a much lower pressure of about 32 PSI and can hydroplane at speeds somewhat under 60 mph. That's why you have to be careful driving on waterlogged pavement at highway speeds and why highway builders carefully slope their surfaces to shed rain water quickly.
About terminal velocity: when an object descends very rapidly through the air, it experiences a large upward force of air resistance. This new upward force becomes stronger as the downward speed of the object becomes greater. Eventually this upward air resistance force balances the object's downward weight and the object stops accelerating downward. It then descends at a constant velocity—obeying its inertia alone. This special downward speed is known as "terminal velocity." An object's terminal velocity depends on the strength of gravity, the shape and other characteristics of the object, and the density and other characteristics of the air.
A cloth's color is determined by how it absorbs and emits light. Black cloth absorbs essentially all light that hits it, which is why its temperature rises so much. White cloth absorbs virtually no light, which is why it remains cool. Colored cloths fall somewhere in between black and white. Blue cloth absorbs light in the green and red portions of the spectrum while reflecting the blue portion. Red cloth absorbs light in the blue and green portions of the spectrum while reflecting the red portion. Since most light sources put more energy in the red portion of the spectrum than in the blue portion of the spectrum, the blue cloth absorbs more energy than the red cloth. So the sequence of temperatures you observed is the one you should expect to observe.
One final note: most light sources also emit invisible infrared light, which also carries energy. Most of the light from an incandescent lamp is infrared. You can't tell by looking at a piece of cloth how much infrared light it absorbs and how much it reflects. Nonetheless, infrared light affects the cloth's temperature. A piece of white cloth that absorbs infrared light may become surprisingly hot and a piece of black cloth that reflects infrared light may not become as hot as you would expect.
Since the top of the first hill is the highest point on the track, it's also the point at which the roller coaster's gravitational potential energy is greatest. Moreover, as the roller coaster passes over the top of the first hill, its total energy is greatest. Most of that total energy is gravitational potential energy but a small amount is kinetic energy, the energy of motion.
From that point on, the roller coaster does two things with its energy. First, it begins to transform that energy from one form to another—from gravitational potential energy to kinetic energy and from kinetic energy to gravitational potential energy, back and forth. Second, it begins to transfer some of its energy to its environment, mostly in the form of heat and sound. Each time the roller coaster goes downhill, its gravitational potential energy decreases and its kinetic energy increases. Each time the roller coaster goes uphill, its kinetic energy decreases and its gravitational potential energy increases. But each transfer of energy isn't complete because some of the energy is lost to heat and sound. Because of this lost energy, the roller coaster can't return to its original height after coasting down hill. That's why each successive hill must be lower than the previous hill. Eventually the roller coaster has lost so much of its original total energy that the ride must end. With so little total energy left, the roller coaster can't have much gravitational potential energy and must be much lower than the top of the first hill.
It's then time for the riders to get off, new riders to board, and for a motor-driven chain to drag the roller coaster back to the top of the hill to start the process again. The chain does work on the roller coaster, investing energy into it so that it can carry its riders along the track at break-neck speed again. Overall, energy enters the roller coaster by way of the chain and leaves the roller coaster as heat and sound. In the interim, it goes back and forth between gravitational potential energy and kinetic energy as the roller coaster goes up and down the hills.
But hardness does have an important effect on bouncing from a non-rigid surface. When a hard object collides with a non-rigid surface, the surface does some or all of the deforming so that the surface becomes involved in the energy storage and bounce. If the surface is elastic, storing energy well when it deforms, then it will make the object rebound strongly. That's what happens when a steel marble collides with a rubber block. However, if the surface isn't very elastic, then the object will not rebound much. That's what happens when a steel marble collides with a thick woolen carpet.
Most of the missing collision energy is lost because of sliding friction within the ball. Molecules move across one another as the ball's surface dents inward and these molecules rub. This rubbing produces heat and diminishes the elastic potential energy stored in the ball. When the ball subsequently undents, there just isn't as much stored energy available for a strong rebound. The classic dead "ball" is a beanbag. When you throw a beanbag at a wall, it doesn't rebound because all of its energy is lost through sliding friction between the beans as the beanbag dents.
But while both of these techniques work fine at short distances, they aren't so good at large distances in a dense forest. A better scheme is to look for his thermal radiation. All objects emit thermal radiation to some extent and the spectral character of this thermal radiation depends principally on the temperatures of the objects. If the person is hotter than his surroundings, as is almost always the case, he will emit a different spectrum of thermal radiation than his surrounds. Light sensors that operate in the deep infrared can detect a person's thermal radiation and distinguish it from that of his cooler surroundings. Still, viewing that thermal radiation requires a direct line-of-sight from the person to the infrared sensor, so if the forest is too dense, the person is untrackable.
Spreading out the contact also prevents damage to the racket and birdie. If they collided over only a tiny area, the forces they exerted on one another would be concentrated over that area and produce enormous local pressures. These pressures could cut the birdie or break a string. But with the birdie's large head, the pressures involved are mild and nothing breaks.
So there are trade offs in racket or bat mass. For badminton, the birdie has so little mass that it barely slows the racket when the two collide. Increasing the racket's mass would allow it to hit the birdie slightly farther, but only if you continued to swing the racket as fast as before. Since increasing the racket mass will make it harder to swing, it's probably not worthwhile. In all likelihood, people have experimented with racket masses and have determined that the standard mass is just about optimal for the game.
If the planet's gravity is even stronger, the flashlight will have to be tipped even more above horizontal. In fact, if the gravity is sufficiently strong, light can only avoid hitting the planet if the flashlight is aimed almost straight up. And beyond a certain strength of gravity, even pointing the flashlight straight up won't keep the light from hitting the planet's surface.
When that situation occurs, an event horizon forms around the planet and forever separates the planet from the universe around it. Actually, the planet ceases to exist as a complex object and is reduced to its most basic characteristics: mass, electric charge, and angular momentum. The planet becomes a black hole. and light emitted at or within this black hole's event horizon falls inward so strongly that it doesn't escape. Since nothing can move faster than light, nothing else can escape from the black hole's event horizon either.
The nature of space and time at the event horizon are quite complicated and counter-intuitive. For example, an object dropped into a black hole will appear to spread out on the event horizon without ever entering it. That's because, to an outside observer, time slows down in the vicinity of the event horizon. By that, I mean that it takes an infinite amount of our time for an object to fall through that event horizon. But the object itself doesn't experience a change in the flow of time. For it, time passes normally and it zips right through the event horizon.
Finally, event horizons and the black holes that have them aren't truly black—quantum mechanical fluctuations at the event horizon allow black holes to emit particles and radiation. This "Hawking radiation," discovered by Stephen Hawking about 25 years ago, means that black holes aren't truly black. Nonetheless, objects that fall into an event horizon never leave intact.
But heterodyne techniques have a side effect: they cause the radio receiver to emit radio waves. These waves originate with the local radio-frequency oscillator, and with other internal mixing frequencies such as the intermediate frequency oscillator present in many sophisticated receivers. Because these oscillators don't use very much power, the waves they emit aren't very strong. Nonetheless, they can be detected, particularly at short range. For example, it's possible for police to detect a radar detector that contains its own local microwave oscillator. Similarly, people who have tried to pirate microwave transmissions have been caught because of the microwaves emitted from their receivers. In WWII, the Japanese were apparently very successful at locating US forces by detecting the 455 kHz intermediate frequency oscillators in their radios—a problem that quickly led to a redesign of the radios to prevent that 455 kHz signal from leaking onto the antennas (thanks to Tom Skinner for pointing this out to me). As you can see, it is possible to track someone who is listening to the right type of radio receiver. However, the radio waves from that receiver are going to be very weak and you won't be able to follow them from a great distance.
If there were more than one moon, the tidal bulges would become misshapen. That is essentially what happens because of the sun. As the moon and sun adopt different arrangements around the earth, the strengths of the tides vary. The strongest tides (spring tides) occur when the moon and sun are on the same or opposite sides of the earth. The weakest tides (neap tides) occur when the moon and sun are at 90° from one another. Extra moons would probably just complicate this situation so that the strengths of the tides would vary erratically as the moons shifted their positions around the earth. Since the timing of the tides is still basically determined by the earth's rotation, there would still be approximately 2 highs and 2 lows a day.
Physical science, particularly physics itself, is completely self-consistent. By that I mean that the same set of physical rules applies to every possible situation in the universe and that this set of rules never leads to paradoxical results. Despite its complicated behavior, the universe is orderly and predictable. It's precisely this order and predictability that is the basis for the whole field of physics.
In contrast, pseudo-science is eclectic—it draws from physics and magic as it sees fit. It uses the laws of physics when it finds those laws useful and it ignores the laws of physics when they conflict with its interests. But the laws of physics only make sense if they apply universally—if there were even one situation in which a law of physics didn't apply, physics would lose its self-consistency and predictive power. That's just what happens with pseudo-science when it begins to ignore the laws of physics on occasion. Moreover, the new rules that pseudo-science introduces to replace the ones it ignores make the trouble even worse. Overall, pseudo-science is inconsistent and can't be counted on to predict anything.Pseudo-science might argue that the laws of physics are correct as far as they go, but that they're incomplete. No doubt the laws of physics are incomplete; physicists have frequently discovered improvements to the laws of physics that have allowed them to make even more accurate predictions of the universe's behavior. But in the years since the discoveries of relativity and quantum physics, the pace of such discoveries has slowed and what remains to be understood is at a very deep and subtle level. It's extraordinarily unlikely that the laws of physics as they're currently understood are wrong at a level that would allow a person to bend a spoon with their thoughts alone or predict the order of a deck of cards without assistance. Just because I haven't dropped a particular book doesn't prevent me from predicting that it will fall when I let go of it. I understand the laws that govern its motion and I know that having it fly upward would violate those laws. Similarly, I don't have to watch someone try to bend a spoon with their thoughts to know that it can't be done legitimately. Again, I understand the laws that govern the spoon's condition and I know that having it bend without an identifiable force acting on it would violate those laws. I also don't have to watch someone try to predict cards to know that it, too, can't be done legitimately. Without a clear physical mechanism for transporting information from the cards to the person, a mechanism that must involve forces or exchanges of particles, there is no way for the person to predict the cards.
When the pole-vaulter stands ready to begin his jump, he is motionless on the ground and he has no kinetic energy (energy of motion), minimal gravitational potential energy (energy of height), and no elastic energy in his pole. All he has is chemical potential energy in his body, energy that he got by eating food. Now he begins to run down the path toward the jump. As he does so, he converts chemical potential energy into kinetic energy. By the time he plants his pole at the jump, his kinetic energy is quite large.
But once he plants the pole, the pole begins to bend. As it does, he slows down and his kinetic energy is partially transferred to the pole, where it becomes elastic potential energy. The pole then begins to lift the vaulter upward, returning its stored energy to him as gravitational potential energy. By the time the vaulter clears the bar, 5 or 6 meters above the ground, almost all of the energy in the situation is in the form of gravitational potential energy. The vaulter has only just enough kinetic energy to carry him past the bar before he falls. On his way down, his gravitational potential energy becomes kinetic energy and he hits the pit at high speed. The pit's padding extracts his kinetic energy from him gently and converts that energy into thermal energy. This thermal energy then floats off into the air as heat.
One interesting point about jumping technique involves body shape. The vaulter bends his body as he passes over the bar so that his average height (his center of gravity) never actually gets above the bar. Since his gravitational potential energy depends on his average height, rather than the height of his highest part, this technique allows him to use less overall energy to clear the bar.
While you're looking at your image, the reversed direction is the forward-backward direction. But it's natural to imagine yourself in the place of your image. To do this you imagine turning around to face in the direction that your image is facing. When you turn in this manner, you mentally eliminate the forward-backward reversal but introduce a new reversal in its place: a left-right reversal. If you were to imagine standing on your head instead, you would still eliminate the forward-backward reversal but would now introduce an up-down reversal. Since it's hard to imagine standing on your head in order to face in the direction your image is facing, you tend to think only about turning around. It's this imagined turning around that leads you to say that your image is reversed horizontally.
When two atoms exchange an electron, they form an ionic bond that again lowers the overall energy of the atoms and sticks them together. Although moving the electron from one atom to the other requires some energy, the two atomic ions that are formed by the transfer have opposite charges and attract one another strongly. The reduction in energy that accompanies their attraction can easily exceed the energy needed to transfer the electron so that the two atoms become permanently stuck to one another.
You'll notice that I keep saying "relative to the earth's center of mass" when I discuss motion. I do that because there is no special "absolute" frame of reference. Any inertial frame is as good as any other frame and your current inertial frame is just as good as anyone else's. In fact, you are quite justified in declaring that your frame of reference is stationary and that everyone else's frames of reference are moving. After all, you don't detect any motion around you so why not declare that your frame is officially stationary. Since the air is also stationary in that frame of reference, flying about in the air doesn't make things any more complicated. You are flying through stationary air in your old stationary frame of reference. The only way in which the 950 mph speed appears now is in comparing your frame of reference to the rest of the earth: in your frame of reference, the earth's center of mass is moving westward at 950 mph.
Modern studies of glass show that below the glass transition temperature, which is well above room temperature, molecular rearrangement effectively vanishes altogether. The glass stops behaving like a viscous liquid and becomes a solid. Its heat capacity and other characteristics are consistent with its being a solid as well.
In effect, the charged particle "plays" with the photon of light, trying to see if it can absorb that photon. As it plays, the charged particle begins to shift into a new quantum state—a "virtual" state. This virtual state may or may not be permanently allowed. If it is, it's called a real state and the charged particle may remain in it indefinitely. In that case, the charged particle can truly absorb the photon and may never reemit it at all. But if the virtual state turns out not to be a permanently allowed quantum state, the charged particle can't remain in it long and must quickly return to its original state. In doing so, this charged particle reemits the photon it was playing with. The closer the photon is to one that it can absorb permanently, meaning the closer the virtual quantum state is to one of the real quantum states, the longer the charged particle can play with the photon before recognizing that it must give the photon up.
A colored material is one in which the charged particles can permanently absorb certain photons of visible light. Because this material only absorbs certain photons of light, it separates the components of white light and gives that material a colored appearance.
A transparent material is one in which the charged particles can't permanently absorb any photons of visible light. While these charged particles all try to absorb the visible light photons, they find that there are no permanent quantum states available to them when they do. Instead, they play with the photons briefly and then let them continue on their way. This playing process slows the light down. In general blue light slows down more than red light in a transparent material because blue light photons contain more energy than red light photons. The charged particles in the transparent material do have real permanent states available to them, but to reach those states, the charged particles would have to absorb high-energy photons of ultraviolet light. While blue photons don't have as much energy as ultraviolet photons, they have more energy than red photons do. As a result, the charged particles in a transparent material can play with a blue photon longer than they can play with a red photon—the virtual state produced by a blue photon is closer to the real states than is the virtual state produced by a red photon. Because of this effect, the speed at which blue light passes through a transparent material is significantly less than the speed at which red light passes through that material.
Finally, about quantum states: you can think of the real states of one of these charged particles the way you think about the possible pitches of a guitar string. While you can jiggle the guitar string back and forth at any frequency you like with your fingers, it will only vibrate naturally at certain specific frequencies. You can hear these frequencies by plucking the string. If you whistle at the string and choose one of these specific frequencies for your pitch, you can set the string vibrating. In effect, the string is absorbing the sound wave from your whistle. But if you whistle at some other frequency, the string will only play briefly with your sound wave and then send it on its way. The string playing with your sound waves is just like a charged particle in a transparent material playing with a light wave. The physics of these two situations is remarkably similar.
The amount of each force is determined by how fast the cars approach one another before they hit and by how stiff their surfaces and frames are. If the cars are approaching rapidly and are extremely stiff and rigid, they will exert enormous forces on one another when they collide and will do so for a very short period of time. During that time, the cars will accelerate violently and their velocities will change radically. If you happened to be in one of the cars, you would also accelerate violently in response to severe forces and would find the experience highly unpleasant.
If, on the other hand, the cars are soft and squishy, they will exert much weaker forces on another and they will accelerate much more gently for a long period of time. That will be true even if they were approaching one another rapidly before impact. When the collision period is over, the cars will again have changed velocities significantly but the weaker forces will have made those changes much more gradual. If you have to be in a collision, chose the soft squishy cars over the stiff ones—the accelerations and forces are much weaker and less injurious. That's why cars have crumple zones and airbags: they are trying to act squishy so that you don't get hurt as much.
This tungsten recycling process dramatically slows the filament's decay. Although the filament gradually develops thin spots that eventually cause it to fail, the filament can operate at a higher temperature and still last two or three times as long as the filament of a regular bulb. The hotter filament of a halogen bulb emits relatively more blue light and relatively less infrared light than a regular bulb, giving it a whiter appearance and making it more energy efficient.
For an object to vibrate strongly in response to a tone, that object must exhibit a strong natural resonance and the tone's pitch must be perfectly matched to the frequency of that resonance. A crystal wineglass vibrates well and emits a clear tone when you tap it. If you listen to the pitch of that tone and then sing it loudly, you can make the wineglass vibrate. A crystal windowpane would also have natural resonances and would vibrate in response to the right tones. But it would take very loud sound at exactly the right pitch to break this windowpane. A few extraordinary voices have been able to break crystal wineglasses unassisted (i.e., without amplification) and it would take such a voice to break the crystal windowpane.
In normal glass, this chipping would be barely noticeable. But the side and rear windows of a car are made of tempered glass—glass that has been heat processed in such a way that its surfaces are under compression and its body is under tension. Tempering strengthens the glass by making it more resistant to tearing. But once an injury gets through the compressed surface of the tempered glass and enters the tense body, the glass rips itself apart. The spider web pattern of tearing you observe is a feature of the tempered glass, not the center punch. Any deep cut or chip in the tempered glass will cause this "dicing fracture" to occur.
But when the scratch is tangential (extending around the disc and along the spiral), it may prevent the player from reading a large portion of an arc. If the player is unable to read enough of the arc to perform its error correcting work, it can't reproduce the sound. That's why a tangential scratch can ruin a CD much more easily than a radial scratch can. That's why you should never wipe a CD tangentially. Always clean them by wiping from the center out.
In each case, there is some flexibility in temperature—these coexistence conditions can be reached over at least a small range of temperature by varying the pressure on the system. In fact, at 0.03° C and a pressure of 6.11 torr; pure water, pure ice, and pure steam can coexist as a threesome. At this triple point, water molecules will be moving back and forth between all three phases but without producing any net change in the amount of ice, water, or steam.
In most cases, this exported disorder winds up in the energy used to desalinating sea water. You start with nicely ordered energy—perhaps electricity or gasoline—and you end up with junk energy such as waste heat. While some desalination techniques such as reverse osmosis can operate near the efficiency limits imposed by thermodynamics, they can't avoid those limits. If you want to desalinate water, you must consume ordered resources and those resources usually cost money (an exception is sunlight). The desalinating equipment is also expensive. Until water becomes scarce enough or energy cheap enough, desalinated water will remain uncommon in the United States.
Now suppose that you throw the cannonball overboard. The cannonball quickly sinks to the bottom. The boat now floats higher than before because it no longer needs to displaces the extra 8 cannonball volumes of water. Although the cannonball itself is displacing 1 cannonball volume of water, there are still 7 cannonball volumes less water being displaced by objects in the water. As a result, the water level of the lake drops slightly when you throw the cannonball overboard.
Fortunately, there are several effects that make controlled operation of a reactor relatively easy. Most importantly, some of the neutrons involved in the chain reactions are delayed because they come from radioactive decay processes. These delayed neutrons slow the reactor's response to changes—the chain reactions take time to grow stronger and they take time to grow weaker. As a result, it's possible for a reactor to exceed critical mass briefly without experiencing the exponentially growing chain reactions that we associate with nuclear explosions. In fact, the only nuclear reactor that ever experienced these exponentially growing chain reactions was Chernobyl. That flawed and mishandled reactor went so far into the super-critical regime that even the neutron delaying effects couldn't prevent exponential chain reactions from occurring. The reactor superheated and ripped itself apart.
When the fuel is below critical mass, there aren't quite enough nuclei around to keep the chain reactions proceeding steadily and each chain gradually dies away. While such a sub-critical mass of fuel continues to experience chain reactions, they aren't self-sustaining and depend on natural radioactive decay to restart them.
When the fuel is above critical mass, there are more than enough nuclei around to sustain the chain reactions. In fact, each chain reaction grows exponentially in size with the passage of time. Since each fission directly induces more than one subsequent fission, it takes only a few generations of fissions before there are astronomical numbers of nuclei fissioning in the fuel. Explosive chain reactions of this sort occur in nuclear weapons.
There are two classic techniques for reaching super-critical mass. The technique used in the uranium bomb dropped over Hiroshima in WWII involved a collision between two objects. A small cannon fired a piece of uranium 235 into a nearly complete sphere of uranium 235. The uranium projectile entered the incomplete sphere at enormous speed and made the overall structure a super-critical mass. But despite the rapid mechanical assembly, the bomb still wasn't able to use its nuclei very efficiently. It wasn't sufficiently super-critical for an efficient explosion.
The technique used in the two plutonium bombs, the Gadget tested in New Mexico and the Fat Man dropped over Nagasaki, involved implosions. In each bomb, high explosives crushed a solid sphere of plutonium 239 so that its density roughly doubled. With its nuclei packed more tightly together, this fuel surged through critical mass and went well into the super-critical regime. It consumed a much larger fraction of its nuclei than the uranium bomb and was thus a more efficient device. However, its design was so complicated and technically demanding that its builders weren't sure it would work. That's why they tested it once on the sands of New Mexico. The builders of the uranium bomb were confident enough of its design and too worried about wasting precious uranium to test it.
Most homes in the United States receive 240 volt power in the form of two hot wires that are 180° out of phase, in addition to a neutral wire. 120-volt lights and appliances are powered by one of the hot wires and the neutral wire, with half the home depending on each of the two hot wires. 240-volt appliances use both hot wires.
The Newtonian perspective is the most intuitive and where we will start. The airstream arriving at the forward or "leading" edge of the airplane wing splits into two separate flows that travel over and under the wing, respectively. The wing is shaped and tilted so that these two flows experience very different accelerations as they travel around the wing. The flow that goes under the wing encounters a downward sloping surface that pushes it downward and it accelerates downward. In response to this downward push, the air pushes upward on the bottom of the wing and provides part of the force that supports the plane.
The air that flows over the wing follows a more complicated route. At first, this flow encounters an upward sloping surface that pushes it upward and it accelerates upward. In response to this upward force, the air pushes downward on the leading portion of the wing's top surface. But the wing's top surface is curved so that it soon begins to slope downward rather than upward. When this happens, the airflow must accelerate downward to stay in contact with it. A suction effect appears, in which the rear or "trailing" portion of the wing's top surface sucks downward on the air and the air sucks upward on it in response. This upward suction force more than balances the downward force at the leading edge of the wing so that the air flowing over the wing provides an overall upward force on the wing.
Since both of these air flows produce upward forces on the wing, they act together to support the airplane's weight. The air passing both under and over the wings is deflected downward and the plane remains suspended.
In the Bernoullian view, air flowing around a wing's sloping surfaces experiences changes in speed and pressure that lead to an overall upward force on the wing. The fact that each speed change is accompanied by a pressure change is the result of a conservation of energy in air passing a stationary surface—when the air's speed and motional energy increase, the air's pressure and pressure energy must decrease to compensate. In short, when air flowing around the wing speeds up, its pressure drops and when it slows down, its pressure rises.
When air going under the wing encounters the downward sloping bottom surface, it slows down. As a result, the air's pressure rises and it exerts a strong upward force on the wing. But when air going over the wing encounters the up and down sloping top surface, it slows down and then speeds up. As a result, the air's pressure first rises and then drops dramatically, and it exerts a very weak overall downward force on the wing. Because the upward force on the bottom of the wing is much stronger than the downward force on the top of the wing, there is an upward overall pressure force on the wing. This upward force can be strong enough to support the weight of the airplane.
But despite the apparent differences between these two descriptions of airplane flight, they are completely equivalent. The upward pressure force of the Bernoullian perspective is exactly the same as the upward reaction force of the Newtonian perspective. They are simply two ways of looking at the force produced by deflecting an airstream, a force known as lift.
If an airplane's voltage begins to differ significantly from that of its surroundings, it's going to have trouble. Sooner or later, it will encounter something that will exchange electric charge with it and the results may be disastrous. To avoid a lightning strike, the airplane must keep its voltage near that of its surroundings. That's why it has static dissipaters on the tips of its wings. These sharp metal spikes use a phenomenon known as a corona discharge to spray unwanted electric charges into the air behind the plane. Any stray charges that the plane picks up by rubbing against the air or by passing through electrically charged clouds are quickly released to the air so that the plane's voltage never differs significantly from that of its surroundings and it never sticks out as a target for lightning. While an unlucky plane may still get caught in an exchange of lightning between two other objects, the use of static dissipaters significantly reduces its chances of being hit directly.
Just where the missing energy goes during an inelastic collision depends on the objects. When large objects collide, most of this missing energy usually becomes heat and sound. In fact, the only objects that ever experience perfectly elastic collisions are atoms and molecules—the air molecules in front of you collide countless times each second and often do so in perfectly elastic collisions. When the collisions aren't elastic, the missing energy often becomes rotational energy or occasionally vibrational energy in the molecules. Actually, some of the collisions between air molecules are superelastic, meaning that the air molecules leave the collision with more total kinetic energy than they had before it. This extra energy came from stored energy in the molecules—typically from their rotational or vibrational energies. Such superelastic collisions can also occur in large objects, such as when a pin collides with a toy balloon.
Returning to inelastic collisions, one of the best examples is a head-on automobile accident. In that case, the collision is often highly inelastic—most of the two cars' total kinetic energy is transformed into another form and they barely bounce at all. Much of this missing kinetic energy goes into deforming and heating the metal in the front of the car. That's why well-designed cars have so called "crumple zones" that are meant to absorb energy during a collision. The last place you want this energy to go is into the occupants of the car. In fact, the occupants will do best if they transfer most of their kinetic energies into their airbags.
To start herself spinning, something must exert a twist on the skater and that something is the ice. She uses her skates to twist the ice in one direction and, as a result, the ice twists her in the opposite direction. This effect is an example of the action/reaction principle known as Newton's third law of motion. Because of the ice's twist on her, she acquires angular momentum during her takeoff. Angular momentum is a form of momentum that's associated with rotation and, like normal momentum, angular momentum is important for one special reason: it's a conserved physical quantity, meaning that it cannot be created or destroyed; it can only be transferred between objects. The ice transfers angular momentum to the skater during her takeoff and she retains that angular momentum throughout her flight. She only gives up the angular momentum when she lands and the ice can twist her again.
During her flight, her angular momentum causes her to spin but the rate at which she spins depends on her shape. The narrower she is, the faster she spins. This effect is familiar to anyone who has watched a skater spin on the tip of one skate. If she starts spinning with her arms spread widely and then pulls them in so that she becomes very narrow, her rate of rotation increases dramatically. That's because while she is on the tip of one skate, the ice can't twist her and she spins with a fixed amount of angular momentum. By changing her shape to become as narrow as possible, she allows this angular momentum to make her spin very quickly. And this same rapid rotation occurs in the triple axle jump. The jumper starts the jump with arms and legs widely spread and then pulls into a narrow shape so that she spins rapidly in the air.
Finally, in landing the skater must stop herself from spinning and she does this by twisting the ice in reverse. The ice again reacts by twisting her in reverse, slowing her spin and removing her angular momentum. She skates away smoothly without much spin.
Because salty water has a lower chemical potential for water molecules than pure water, water molecules tend to move from purer water to saltier water. This type of flow is known as osmosis. To slow or stop osmosis, you must raise the chemical potential on the saltier side by applying pressure. The more you squeeze the saltier side, the higher the chemical potential there gets and the slower water molecules move from the purer side to the saltier side. If you squeeze hard enough, you can actually make the water molecules move backwards—toward the purer side! This flow of water molecules from the saltier water toward the purer water with the application of extreme pressure is known as reverse osmosis.
In commercial desalination, high-pressure seawater is pushed into jellyroll structures containing the semi-permeable membranes. The pressure of the salty water is so high that the water molecules flow through the membrane from the salty water side to the pure water side. This pure water is collected for drinking.
But air pressure can't push the water upward forever. As the column of water in the hose rises, its weight increases. Atmospheric pressure can only lift the column of water so high before the upward force on the water is balanced by the water's downward weight. Even if you remove all of the air inside the hose, atmospheric pressure can only support a column of water about 30 feet tall inside the hose. If you're higher than that on your balcony, the water won't reach you no matter how hard you try. The only way to send the water higher is to put a pump at the bottom end of the hose. This pump can push upward harder than atmospheric pressure can and it can support a taller column of water. That's why deep home wells have submersible pumps at their bottoms—they must pump the water upward because it's impossible to suck it upward more than 30 feet from above.
When you are recording sound on the tape, the microphone measures the air pressure changes associated with the sound and produces a fluctuating electric current that represents those changes. This current is amplified and used to operate an electromagnet in the recording head. The electromagnet magnetizes the tape—it flips the magnetization of some of those tiny magnetic particles so that the tape becomes effectively magnetized in one direction or the other. The larger the pressure change at the microphone, the more current flows through the electromagnet and the deeper the magnetization penetrates into the tape's surface. After recording, the tape is covered with tiny patches of magnetization, of various depths and directions. These magnetized patches retain the sound information indefinitely.
During playback, the tape moves past the playback head. As the magnetic fields from magnetized regions of the tape sweep past the playback head, they cause a fluctuating electric current to flow in that head. The process involved is called electromagnetic induction; a moving or changing magnetic field produces an electric field, which in turn pushes an electric current through a wire. The current from the playback head is amplified and used to operate speakers, which reproduce the original sound.
The rest of the cassette recorder is just transport mechanism—wheels and motors that move the tape smoothly and steadily past the recording or playback heads (which are often the same object). There is also an erase head that demagnetizes the tape prior to recording. It's an electromagnet that flips its magnetic field back and forth very rapidly so that it leaves the tiny magnetic particles that pass near it with randomly oriented magnetizations.
But despite these high speeds, the quarks never exceed the speed of light. As a massive particle such as a quark approaches the speed of light, its momentum and kinetic energy grow without bounds. For that reason, even if you gave all the energy in the world to a single quark, its speed would still remain just a hair less than the speed of light.
Applying these observations to the three objects, it's clear that the solid and liquid portions of these objects aren't affected very much by the pressure, but the gaseous portions are. In a fish or diver, the gas-filled parts (the swim bladder in a fish and the lungs in a diver) become smaller as the fish or diver go deeper in the water and are exposed to more pressure. In a submarine, the hull of the submarine must support the pressure outside so that the pressure of the air inside the submarine doesn't increase. If the pressure did reach the air inside the submarine, that air would occupy less and less volume and the submarine would crush. That's why the hull of a submarine must be so strong—it must hide the tremendous water pressure outside the hull from the air inside the hull.
Apart from these mechanical effects on the three objects, there is one other interesting effect to consider. Increasing pressure makes gases more soluble in liquids. Thus at greater depths and pressures, the fish and diver can have more gases dissolved in their blood and tissues. Decompression illness, commonly called "the bends", occurs when the pressure on a diver is suddenly reduced by a rapid ascent from great depth. Gases that were soluble in that diver's tissue at the initial high pressure suddenly become less soluble in that diver's tissue at the final low pressure. If the gas comes out of solution inside the diver's tissue, it causes damage and pain.
While nothing can travel faster than this special speed, it's easy to go slower. In fact, light itself travels more slowly than this when it passes through a material. Whenever light encounters matter, its interactions with the charged particles in that matter delay its movement. For example, light travels only about 2/3 of its vacuum speed while traveling in glass. Because of this slowing of light, it is possible for massive objects to exceed the speed at which light travels through a material. For example, if you send very, very energetic charged particles (such as those from a research accelerator) into matter, those particles may move faster than light can move in that matter. When this happens, the charged particles emit electromagnetic shock waves known as Cherenkov radiation—there is light emitted from each particle as it moves.
I suppose that the brochure could have been talking about this light/matter interaction. But since that effect has been observed for decades, there is nothing special about 1995. More likely, the brochure is talking about nonsense.
When an npn sandwich is constructed, the two junctions between layers experience a natural charge migration—mobile negative charges spill out of the n-type material on either end and into the p-type material in the middle. This flow of charge creates special "depletion regions" around the physical p-n junctions. In this depletion regions, there are no mobile electric charges any more—the mobile negative and positive charges have cancelled one another out!
Because of the two depletion regions, current cannot flow from one end of the sandwich to the other. But if you wire up the npn sandwich—actually an npn bipolar transistor—so that negative charges are injected into one end layer (the "emitter") and positive charges are injected into the middle layer (the "base"), the depletion region between those two layers shrinks and effectively goes away. Current begins to flow through that end of the sandwich, from the base to the emitter. But because the middle layer of the sandwich is very thin, the depletion region between the base and the second end of the sandwich (the "collector") also shrinks. If you wire the collector so that positive charges are injected into it, current will begin to flow through the entire sandwich, from the collector to the emitter. The amount of current flowing from the collector to the emitter is proportional to the amount of current flowing from the base to the emitter. Since a small amount of current flowing from the base to the emitter controls a much larger current flowing from the collector to the emitter, the transistor allows a small current to control a large current. This effect is the basis of electronic amplification—the synthesis of a larger copy of an electrical signal.
When dc current passes through the primary coil of wire, the coil does have a magnetic field around it, but it doesn't have an electric field around it. The electric field is what pushes electric charges through the secondary coil to transfer power from the primary coil to the secondary coil. In contrast, when ac current passes through that primary coil of wire, the magnetic field around the coil flips back and forth in direction and this changing magnetic field gives rise to an electric field around the coil. It is this electric field that pushes on electrically charged particles—typically electrons—in the secondary coil of wire. These electrons pick up speed and energy as they move around the secondary coil's turns. The more turns these charged particles go through, the more energy they pick up. That's why doubling the turns in a transformer's secondary coil doubles the voltage of the current leaving the secondary coil.
This temperature gradient has its origin in the physics of gases—when a gas expands and does work on its surroundings, its temperature decreases. To see why this effect is important, imagine that you have a plastic bag that's partially filled with valley air. If you carry this bag up the side of the mountain, you will find that the bag's volume will gradually increase. That's because there will be less and less air overhead as you climb and the pressure that this air exerts on the bag will diminish. With less pressure keeping it small, the air in the bag will expand and the bag will fill up more and more. But for the bag's size to increase, it must push the air around it out of the way. Pushing this air away takes work and energy, and this energy comes from the valley air inside the bag. Since the valley air has only one form of energy it can give up—thermal energy—its temperature decreases as it expands. By the time you reach the top of the mountain, your bag of valley air will have cooled dramatically. If it started at 20° C, its temperature may have dropped to 0° C, cold enough for snow.
If you now turn around and walk back down the mountain, the increasing air pressure will gradually squeeze your bag of valley air back down to its original size. In doing do, the surrounding air will do work on your valley air, giving it energy, and will increase that air's thermal energy—the valley air will warm up! When you reach the valley, the air in your bag will have returned to its original temperature.
Air often rises and falls in the atmosphere and, as it does, it experiences these same changes in temperature. Air cools as it blows up into the mountains (often causing rain to form) and warms as it flows down out of the mountains (producing dry mountain winds). These effects maintain a temperature gradient in the atmosphere that allows snow to remain on mountaintops even when it's relatively warm in the valleys.
Each hemoglobin molecule contains four heme groups, the iron-containing structures that actually form the reversible bond with oxygen molecules and that also give the hemoglobin its color. However, this color depends on the oxidization state of the heme group—red when the heme group is binding oxygen and blue-purple when the heme group is alone. That color difference explains why someone who is holding their breath may "turn blue"—their hemoglobin is lacking in oxygen. The clip you wore was analyzing the color of your blood to determine the extent of oxygenation in its hemoglobin. It measured your pulse rate by looking for periodic fluctuations in the opacity of your finger, brought on by changes in your finger's blood content with each heartbeat.
However, I would guess that rubber-soled shoes provide some slight protection against being hit by lightning in the first place. Lightning tends to strike objects that have acquired an electric charge that is opposite that of the cloud overhead. This opposite charge naturally appears on grounded conducting objects because the cloud's charge pulls opposite charges up from the ground and onto the objects. Once this charging has taken place, the object is a prime target for a lightning strike.
If you are standing alone and barefoot on the top of a mountain during a thunderstorm, the cloud will draw opposite charge up from the ground through your feet and you will become very highly charged. There are even photographs of people on mountaintops with their hair standing up because of this charging effect. Unfortunately, some of these people were struck by lightning shortly after experiencing this effect. If you ever experience it, run for your life down the mountain! It's possible that wearing rubber soles shoes will prevent or delay this charging effect, and it might keep you from being struck by lightning. But I sure wouldn't count on it.
While you can't see it in this unopened bottle, there is activity both at the surface of the water and within the water. At the water's surface, carbon dioxide molecules are constantly leaving the water for the gas under the cap and returning from the gas under the cap to the water. The rates of departure and return are equal, so that nothing happens overall. Within the water, tiny bubbles are also forming occasionally. But these tiny bubbles, which nucleate through random fluctuations within the liquid or more often at defects in the bottle's walls, can't grow. Even though these bubbles contain gaseous carbon dioxide molecules, the molecules aren't dense enough to keep the bubbles from being crushed by the pressurized water. So these tiny bubbles form and collapse without ever becoming noticeable.
However, once you remove the top from the bottle, everything changes. The bottle's contents are no longer in equilibrium. To begin with, carbon dioxide molecules that leave the surface of the water are no longer replaced by molecules returning to the liquid. That's one reason why an opened bottle of carbonated water begins to lose its dissolved carbon dioxide and become "flat." Secondly, without its trapped portion of dense carbon dioxide gas, the bottle is no longer pressurized and it stops being taut and hard (assuming that it's made of plastic rather than gas). Thirdly, with the loss of pressure, the water in the bottle stops crushing the tiny gas bubbles that form within it. In fact, once one of those bubbles forms, carbon dioxide molecules can enter it from the liquid just as they enter the gas at the top of the bottle. As a result, each bubble that forms grows larger and larger. Since the gas in a bubble is less dense than water, the bubble begins to float upward until it reaches the top of the bottle. Because the bottle is taller than a typical water glass, a bubble has more time to grow before reaching the top in the bottle than it would have in the glass. That's one reason why the bubbles in a bottle are taller than in a glass. Another reason is that the concentration of dissolved carbon dioxide molecules is higher while the water is in the bottle than it is by the time the water reaches the glass, so that bubbles grow faster in the bottle than in the glass.
Only the propane lamp needs a mantle to produce bright light. That's because the hot gas molecules that are produced by propane combustion aren't very good at radiating their thermal energy as visible light. The mantle extracts thermal energy from the passing gas molecules and becomes incandescent—it converts much of its thermal energy into thermal radiation, including visible light. Mantles are actually delicate ceramic structures consisting of metal oxides, including thorium oxide. Thorium is a naturally occurring radioactive element, similar to uranium, and lamp mantles are one of the few unregulated uses of thorium.
The light emitted by these oxide mantles is shorter in average wavelength than can be explained simply by the temperature of the burning gases, so it isn't just thermal radiation at the ambient temperature. The mantle's unexpected light emission is called candoluminescence and is thought to involve non-thermal light emitted as the result of chemical reactions and radiative transitions involving the burning gases and the mantle oxides.
In contrast, the acetylene miner's lamp works pretty well without a mantle. I think that's because the flame contains lots of tiny carbon particles that act as the mantle and emit an adequate spectrum of yellow thermal radiation. Many of these particles then go on to become soot. A candle flame emits yellow light in the same manner.
One last feature of a properly constructed miner's lamp, a safety lamp, is that it can't ignite gases around it even if those gases are present in explosive concentrations. That's because the lamp's flame is surrounded by a fine metal mesh. This mesh draws heat out of any gas within its holes and thus prevents the flame inside the mesh from igniting any gas outside the mesh.
Between the second impeller and the wheels is a gearbox. The second impeller of the fluid coupling causes several of the gears in this box to turn and they, in turn, cause other gears to turn. Eventually, this system of gears causes the wheels of the car to turn. Along with these gears are several friction plates that can be brought into contact with one another by the transmission to change the relative rotation rates between the second impeller and the car's wheels. These changes in relative rotation rate give the car the variable mechanical advantage it needs to be able to both climb steep hills and drive fast on flat roadways.
Finally, some cars combine parts of the gear box with the fluid coupling in what is called a "torque converter." Here the two impellers in the fluid coupling have different shapes so that they naturally turn at different rates. This asymmetric arrangement eliminates the need for some gears in the gearbox itself.
The amount of energy that a photon carries depends on the frequency of that photon—the higher the frequency, the more energy. Photons of visible light carry enough energy to induce various changes in atoms and molecules, which is why they provide our eyes with such useful information about the objects around us—we see how this visible light is interacting with the world around us.
Like all electromagnetic waves, radio waves and microwaves consist of coupled electric and magnetic fields that sustain one another in stable structures that move rapidly through empty space. Because an electromagnetic wave's electric field changes with time, it is able to create the wave's magnetic field and, because its magnetic field changes with time, that magnetic field is able to create the wave's electric field. Since they consist only of electric and magnetic fields, these waves cannot stay still—they must move (although you can trap them between mirrors so that they appear to stand in one place as they bounce back and forth). While they contain no true mass, they do contain energy and an electromagnetic wave carries energy from one place to another.
Electromagnetic waves are created whenever electrically charged particles change speed or direction; whenever they accelerate. Since there are accelerating electric charges everywhere—thermal energy keeps them moving about—there are also electromagnetic waves everywhere. But the radio waves used in communications systems are generated deliberately by moving electric charges back and forth. When charges are sent up and down a radio antenna, these charges are accelerating and they form complicated electric and magnetic fields that include electromagnetic waves. Once launched, those electromagnetic waves propagate through space at approximately the speed of light.
To send information with radio waves, a transmitter makes modifications in one or more the wave's characteristics. In an amplitude modulation scheme (AM), the transmitter changes the strength or "amplitude" of the wave to convey information—like sending radio smoke signals. In the frequency modulation scheme (FM), the transmitter changes the frequency of the wave to convey information—like whistling a tune with a complicated melody.
But as soon as the liquid water is gone (and, fortuitously, the rice is fully cooked), there is nothing left to keep the heating element's temperature from rising. As more electric energy enters the element and becomes thermal energy, the element gets hotter and hotter. A thermostat, probably a bimetallic strip like that used in most toasters, senses the sudden temperature rise. It releases a switch that turns off the electric power to the rice cooker.
Which of these possibilities occurs in a particular organic material depends on the precise structure of that material. Carbon atoms can be part of transparent organic materials, such as sugar, or of opaque organic materials, such as asphalt. The carbon atoms and their neighbors determine the behaviors of their electrons and these electrons in turn determine the optical properties of the materials.
The specific voltages and their relationships with ground or a possible fourth "neutral" wire depend on the exact type of transformer arrangement that supplies your home or business. In the standard "Delta" arrangement (which you can find discussed at sites dealing with power distribution), the voltage differences between any pair of the three phases is typically 240 VAC. In the standard "Wye" arrangement, the typical voltage difference between any pair of phases is 208 VAC and the voltage difference between any single phase and ground is 120 VAC. And in the "Center-Tapped Grounded Delta" arrangement, the voltage difference between any pair of phases is 240 VAC and the voltage difference between a single phase and neutral is 120, 120, and 208 VAC respectively (yes, the three phases behave differently in this third arrangement).
If you run a single-phase 220 VAC motor from two wires of a Delta arrangement power outlet, that motor will receive a little more voltage (240 VAC) than it was designed for and if you run it from two wires of a Wye arrangement outlet, it will receive a little less voltage (208 VAC) than appropriate. Still, the motor will probably run adequately and it's unlikely that you'll ever notice the difference.
Nonetheless, a large permanent magnet isn't really permanent. The random fluctuations of thermal energy and the influences of passing magnetic fields gradually demagnetize large permanent magnets. However, good permanent magnets demagnetize so slowly that the changes are completely undetectable. You might have to wait a billion years to detect any significant weakening in the magnetic field around such a magnet.
As for the best insulators, I'd vote for good crystals of salts like lithium fluoride and sodium chloride (table salt), and covalently-bound substances like aluminum oxide (sapphire) or diamond. All of these materials are pretty nearly perfect insulators.
Good metal detectors produce electromagnetic fields that cause currents to flow through nearby metal objects and then detect the magnetism that results. Unfortunately, identifying what type of non-ferromagnetic metal is responding to a metal detector is hard. Mark Rowan, Chief Engineer at White's Electronics of Sweet Home, Oregon, a manufacturer of consumer metal detecting equipment, notes that their detectors are able to classify non-ferromagnetic metal objects based on the ratio of an object's inductance to its resistivity. They can reliably distinguish between all denominations of U.S. coins—for example, nickels are relatively more resistive than copper and clad coins, and quarters are more inductive than smaller dimes. The primary mechanism they use in these measurements is to look at the phase shift between transmitted and received signals (signals typically at, or slightly above, audio frequencies). However, they are unable to identify objects like gold nuggets where the size, shape, and alloy composition are unknown.
What's really happening is that electrochemical processes are spontaneously separating charges from one another inside the battery and placing those separated charges on the battery's terminals—the battery's negative terminal becomes negatively charged and its positive terminal becomes positively charged. This charge separating process proceeds in a random, statistical manner until enough charges accumulate on the terminals to prevent any further charge separation. Because like charges repel one another, sufficiently large accumulations of positive charges on the positive terminal and negative charges on the negative terminal stop further arrivals of those charges.
But when you send a positive charge through a wire and onto the battery's negative terminal, you reduce the amount of negative charge there and weaken the repulsive forces. As a result, the chemicals in the battery separate another pair of charges. The battery's negative terminal returns to normal, but now there is an extra positive charge on the battery's positive terminal. This extra charge flows away through a wire. Overall, it appears that your positive charge "passed through" the battery—entering the battery's negative terminal and emerging from the positive terminal with more energy than it had when it arrived at the negative terminal. But what really happened was that the battery's chemicals separated another pair of charges.
In a warm environment, the battery's chemicals can separate charges rapidly and can keep up with reasonably large currents of arriving charges. But in a cold battery, the electrochemical processes slow down and it becomes hard for the battery to keep up. If you try to send too much current through the battery while it's cold, it is unable to replace the charges on its terminals quickly enough and it voltage sags—it doesn't have enough separated charges on its terminals to give the charges "passing through" it their full increase in energy. If you use a battery while it's very cold, you should be careful not to send too much current through it because it will become inefficient and will provide less than its usual voltage.
Let me begin to pick up the pieces by pointing out that terms like "human energy field", "vibrational medicine", and "energy imbalance" are simply meaningless and that the use of "Einstein's Theory" to justify healing-at-a-distance is typical of people who don't have a clue about what science actually is. The meaningless misuse of scientific terms and the uninformed and careless misapplication of scientific techniques is an activity called pseudo-science. Pseudo-science may sound and look like science, but the two have almost nothing else in common. Among the benefits of a good college education is learning how vast is the world of human knowledge, recognizing how little you know of that world, discovering how much others have already thought about everything you can imagine, and finding out how dangerous it is to venture unprepared into any area you do not know well. Most of these pseudo-scientific quacks are either oblivious of their own ignorance or so arrogant that they dismiss the work of others as not worthy of their attention. Either way, they make terrible students and, consequently, useless teachers. You'll do best to leave their books on the shelves.
Because real science is not buzzwords, simply stringing together the words of science does not make one a scientist. Science is an intense, self-reflective, skeptical, objective investigative process in which we try to form conceptual models for the universe and its contents, and try to test those models against the universe itself. We do this modeling and testing over and over again, improving and perfecting the models and discarding or modifying models that do not appear consistent with actual observations. Accurate models are valuable because they have predictive power—you can tell in advance how something will behave if you have modeled it correctly.
In the course of these scientific investigations, concepts arise which deserve names and so we assign names to them. In that manner, words such as "energy" and "vibration" have entered our language. Each such word has a very specific meaning and applies only in a specific context. Thus the word "force" was assigned to the concept we commonly refer to as a "push" or a "pull" and applies in the context of interactions between objects. The expression "the force be with you" has nothing to do with physics—the word "force" in that phrase doesn't mean a push or a pull and has nothing to do with the interactions between objects. As you can see, taken out of its applicable context and used carelessly in another usually renders a scientific word completely meaningless.
Alas, the average person doesn't understand science, doesn't speak its language, and cannot distinguish the correct use of the language of science from the meaningless gibberish of pseudo-science. As anyone who has spent time exploring the web ought to have discovered, highly polished prose and graphics is no guarantee of intelligent content. That's certainly true of what appears to be scientific material. I am further saddened to see that even the titles of academia are deemed fair game by the quacks. While the physics term "energy" and the biological word "medicine" can appear together in a sentence about cancer treatment or medical imaging, that's not what the person claiming to have a Ph.D. in "Energy Medicine" has in mind. That degree was probably granted by a group that understands neither physics nor medicine. There may be a place for non-traditional medicine because medicine is not an exact science—there is often more than one correct answer in medicine and there are poorly understood issues in medicine even at fairly basic levels.
However, physics is an exact science, with mechanical predictability (within the limitations of quantum mechanics) and only one truly correct answer to each question. Its self-consistent and quantitative nature leaves physics with no room for conflicting explanations. Like most academic physicists, I occasionally receive self-published books and manuscripts from people claiming to have discovered an entirely new physics that is far superior to the current one. And like most academic physicists, I flip briefly through these unreviewed documents and then, with a moment's sadness that the authors have wasted so much time, effort, and money, I toss them into the recycling bin. It's not that we scientists are close minded medieval keepers of the dogma, it's that these "new physics" offerings are the works of ignorant people who don't know what they don't know. Unlike real scientific revolutionaries like Galileo and Einstein, these people don't understand the strengths and weaknesses of the current scientific models. Their new offerings are usually inconsistent, fail to correctly model the real universe, add unnecessary complexity to simple phenomena, or all three. It's extraordinarily unlikely that anyone will ever successfully overthrow the basic laws of physics, not because no one will accept a new physics if it's actually correct but because the current physics already explains things with such incredible accuracy and predictive power. Developments in physics come almost exclusively at its frontier, where the current understanding of physics is known to be imperfect or incomplete, and that is probably where those developments will probably always occur.
So to return to your question, I would tell my students that I think that the "healing sciences" as you have identified them are neither.
A projector just reverses this process. Now light starts out from an illuminated piece of developed film—such as a slide containing an image of a tree. Now the projector lens bends all of the light striking it from a particular leaf spot on the slide together to one small spot on a distant projection screen. Again, light from each leaf on the slide is bent together to a corresponding spot on the screen and a pattern of light that looks just like the slide—a real image of the slide—forms on the surface of the projection screen. As before, this image is upside-down and backwards, which is why you must be careful how you orient a slide in a projector, lest you produce an inverted image on the screen.
What makes a metal-halide lamp so efficient is that there are relatively few ways for the lamp to waste energy as heat. While collisionally excited mercury atoms normally emit most of their stored energy as ultraviolet light—the basis for fluorescent lamps—they can't do this in a high-pressure environment. A phenomenon called "radiation trapping" makes it almost impossible for this ultraviolet light to escape from a dense vapor of mercury, so a high-pressure mercury lamp emits mostly visible light. Even without the metal-halides, a high-pressure mercury lamp emits a brilliant blue-white glow. The metal-halides boost the reds and other colors in the lamp to make its light "warmer" and more like sunlight.
Next time you watch one of these lamps warm up, observe how its colors change. When it first starts up, its pressure is low and it emits mostly invisible ultraviolet light (which is absorbed by the lamp's glass envelope). But as the lamp heats up and its pressure increases, the rich, white light gradually develops. Incidentally, if the power to a hot lamp is interrupted, the lamp has to cool down before it can restart because it only starts well at low pressures.
As for compounds that change their optical properties while in electric fields, the answer is yes—all compounds exhibit such changes, although they may be undetectably small. However, I can't think of any isolated molecules that change dramatically in normal fields. Still, electric fields can alter the "selection rules"—the symmetry-based laws that often control which optical transitions can or cannot occur. It's possible that a modest electric field will turn on or off import optical transitions in some molecules so that they exhibit large color changes in small fields. Still, I can't think of any useful examples.
Increasing the current in the generator also affects its magnetic fields because currents are magnetic. At a low current, the current's magnetism can be ignored. But when a generator is handling a very large current, the magnetic fields associated with that current are no longer small perturbations on the generator's normal magnetic fields and the generator may not perform properly any more.
Finally, a generator's job is to transfer energy from a mechanical system to the electric current passing through it. As the amount of current in the generator increases, the amount of work that the mechanical system provides must also increase—the generator becomes harder to turn. There will always be a limit to how much torque an engine or crank can exert on the generator to keep it spinning and thus there will be a limit to how much current the generator can handle.
As for how the current varies with load: the more current the load permits to pass through it, the more current will pass through the generator. Assuming that the generator is well built and has very little electric resistance, the load will serve to limit the current. The generator will then deliver just as much current as the load will permit. If the load permits more current, the generator will deliver more. As a result, the wires in the generator will waste more power as heat, the magnetic fields in the generator will become more complicated, and the device powering the generator will have to work harder to keep the generator turning.
I should point out, however, that the energy absorbed by the film does have a weight and that if the only effect of exposing film to light were that the film absorbed this additional energy, then the film's weight would increase by a fantastically small amount. But the chemistry that results from this energy absorption certainly swamps the weight of the light energy.
As if this problem weren't enough, there is another problem: if you aren't extremely patient, the lever will bend as you turn it, forming a spiral rather than a long arm that sweeps through space. That's because the lever is kept straight by internal forces. While you are twisting the lever to make it turn faster, you are unbalancing these internal forces and causing the lever to bend. The long lever you describe will actually curl into a spiral and its end speed will never come close to the speed of light.
The process you describe, bending wood while heating the wood with steam, takes advantage of the fact that cellulose molecules bind strongly to water molecules and that the water molecules then lubricate the chains so that they can move relative to one another. Water is said to be a "plasticizer" for cellulose. Heat, water, and stress allow the cellulose chains to slide slowly across one another. With enough patience, the wood's internal structure can be changed forever. When the heat, water, and stress are then removed, the wood keeps its new shape.
In real champagne, chains of bubbles do rise upward from the center of the fluid. These bubbles are clearly forming at suspended impurities. All it takes is a tiny piece of dust to trigger bubble formation. If you swirl the champagne slightly, you should be able to see these suspended chains of bubbles move, indicating that the impurities that are triggering them are also moving with the fluid.
One of the most effective tools for eliminating the unburned hydrocarbons and carbon monoxide is a catalytic converter. It is essentially a pipe containing a ceramic honeycomb on which there are countless tiny particles of platinum and palladium. As the unwanted molecules pass through the honeycomb, they land on the metal particles briefly and are combined with oxygen atoms to form water vapor and carbon dioxide. The catalytic converter is burning these molecules in a controlled way, with the precious metal particles acting as catalysts to assist the burning process.
Like all catalysts, these particles are not consumed in the process of burning the gases, but they can easily be contaminated. That's why it's so important not to put leaded gasoline in a car with a catalytic converter—one tank of leaded gas is all it takes to lead-coat the tiny platinum and palladium particles and to render them useless. Another interesting note is that the catalytic converter is usually located on the underside of the car, protected only by a thin metal shield. The converter becomes very hot in operation, both because hot exhaust gas is passing through it and because the controlled combustion taking place inside it heats it up. Don't park a car with a catalytic converter over a pile of leaves! Many an autumn car fire has started when a hot catalytic converter ignited the pile of leaves beneath it.
Even if such exotic structures do exist, there is also no evidence that people could traverse the severely distorted space-time between the two open ends without being destroyed and without having an infinite amount of time pass in the rest of the universe while they were en route. If all of these issues aren't enough to discourage you, let me add that the possibility of engineering wormholes to connect specific regions of space-time is extraordinarily remote. Working with a wormhole would be at least as difficult as working with a black hole and I, for one, hope never to encounter such a destructive and dangerous object.
When Newton formulated his theory of gravity, he viewed gravity as exerting forces on objects—it pulled them toward one another so that they no longer followed their straight inertial paths. That's why a ball arcs through the air, gradually turning toward the ground as the earth's gravity pulls it downward. This interpretation of gravity was very successful and remains extremely useful to this day.
However, there is a second interpretation of gravity: the one offered by Einstein in the general theory of relativity. According to this interpretation, concentrations of mass/energy warp space-time so that objects that are following inertial paths—called geodesics—no longer travel in simple straight lines. In effect, a ball arcs through the air because it is following a curved geodesic path and not because it is experiencing a force. While this exotic interpretation for gravity isn't all that useful for slow moving objects like balls—Newtonian gravity is much more practical in that case—it's important when dealing with fast moving objects like light. Light also follows geodesics, but because it travels so quickly its geodesics tend to be rather straight. Even light passing just above the surface of the sun bends only just enough to measure. Still, one of the most important confirmations of general relativity came during a total solar eclipse when light from a star was found to bend slightly as it passed by the sun's obscured surface.
Finally, I should say that you can also interpret the bending of light in terms of Newtonian gravity—that because light contains energy, it acquires a weight when gravity is present and this weight causes its path to bend. However, this Newtonian observation omits so much of the intrigue and beauty that comes with the bending of space-time that I prefer the more modern interpretation.
These interference effects are quite visible in wave waves, but they also make themselves apparent in microwaves. In your oven, they lead to regions of the cooking chamber that heat quickly (regions where the microwaves experience constructive interference) and regions that don't heat well at all (regions where they experience destructive interference). Because these fast and slow cooking regions can't be avoided, many microwave ovens incorporate turntables to keep the food moving through the various regions inside the oven. Some ovens use rotating metal paddles to stir that microwaves around inside the cooking chamber, so that the fast and slow cooking regions move about.
Your experience with uneven heating of coffee or milk is an example of this interference problem. The solution is to move the cups occasionally while they are being heated.
The energy in a particle of light (a photon) is related the color of that light—with blue photons having more energy than red photons. Here is where the difficulty in making blue LED's comes in: to produce a blue photon, the electron in an LED must give up lots of energy as it fills the hole in the anode. This need for a large energy release places a severe demand on the semiconductors from which the blue LED is made. These semiconductors need an unusually large band gap—the energy spacing between two types of paths that electrons can follow in the semiconductor. It wasn't until recently that good quality semiconductors with the appropriate electrical characteristics were available for this task.
Since a truck has its heavy engine in front, the front wheels bear more of its weight than the rear wheels and they experience more traction than the rear wheels. But as the truck tilts upward on the hill, the weight of its engine is born more and more by the rear wheels. In physics terms, the truck's center of gravity, which is almost over the front wheels while the truck is level, shifts to be more and more over the rear wheels as the truck tilts upward.However, the extra weight that the rear wheels are supporting as the truck tilts doesn't improve their traction. That's because this extra weight isn't being supported entirely by support forces—much of it is being supported instead by friction between the rear wheels and the roadway. In fact, the support forces exerted by the roadway on the rear wheels to keep them from sinking into the pavement actually become weaker as the truck tilts uphill, so the truck loses traction as the tilt increases. Since traction is responsible for the friction that is also supporting the truck, the truck is in danger of slipping down the road. There is clearly a limit to how steep the roadway can get before the truck begins to slide.
However, you'll notice that I said "freezing the water has virtually no effect on its weight." In reality, the water does lose a tiny fraction of its weight. That's because to freeze the water, you must remove some of the water's energy. As Einstein pointed out with his famous formula E=mc2, energy and mass are related to one another and since mass acquires weight when it's near the earth, so does energy. Because the thermal energy in liquid water has a tiny weight, when you remove some of this thermal energy from the water, the water loses some of its weight. But don't expect to measure this weight loss with a common scale—the weight change is on the order of one part in a trillion, a factor that's presently beyond the precision of even the most advanced research measuring devices.
Any type of wave will partially reflect from a surface if passing through that surface causes the wave's speed to change or, more generally, introduces a change in the "impedance" the wave experiences. Impedance is a quantity that relates various parts of a wave to one another—it relates pressure to velocity in sound and it relates the electric field to the magnetic field in a microwave. Since both sound waves and microwaves change speeds and impedances when they encounter the cooking chamber's metal walls, they both partially reflect. The sound that you hear when popcorn pops inside the oven is slightly muffled because the sound is having some trouble escaping from the cooking chamber. However, the impedance change for the microwaves is so enormous that the reflection is complete. No microwaves at all escape from the cooking chamber! The same effect occurs when you hold a large mirror up in front of your face. You can hear what's happening on the other side of the mirror because some sound can pass through the mirror. But light is completely reflected and you can't see through the mirror at all.
What matters then is just how much charge enters the appliance. The open switch would normally block the passage of electricity, which is why the appliance doesn't operate while it's turned off. But as charge accumulates on one side of the switch, the voltage at that point rises higher and higher. When the voltage becomes high enough, as it easily does after a lightning strike, the charges can leap into the air and travel to the other side of the switch even though the two sides don't touch one another. Another view of this disaster is that the like charges on one side of the switch repel one another so vigorously that some of them are pushed through the air to the other side of the switch. As a result of this movement of charges through the air—an electric arc—current passes through the appliance as though it were turned on. If this current exceeds what the appliance can tolerate, the appliance will be destroyed. Even grounding the appliance may not help—charges can flow uncontrollably through the appliance and, while some charges take paths to ground, others flow through sensitive components and destroy them.
However, because there would be air resistance unless you maintained a vacuum inside the hole, the ball wouldn't rise to its original height after each passage through the earth. It would gradually loss energy and speed, and would eventually settle down at the very center of the earth.Finally, the reason for drilling the hole from the north pole to south pole is to avoid complications due to the earth's rotation. If you were to drill the hole anywhere but through the earth's rotational axis, the ball would hit the sides of the hole as it fell and its behavior would be altered.
Another important view of flight involves air pressure in the streams of air flowing over and under the plane. When the air passing under the wing curves downward, it actually does so because the pressure just under the wing is higher than the pressure far from the wing—the air stream is experiencing an overall downward force due to this pressure imbalance and this downward force is deflecting the air stream downward. When the air passing over the wing arcs up, over, and down, it is also doing so because the pressure just above the wing is different from that far from the wing. In this case, the pressure just over the wing's leading edge is quite high—enough to deflect the air stream upward initially. But the pressure over the rest of the wing's upper surface is very low and the air stream curves inward toward the wing; arcing downward so that it leaves the wing's trailing edge with a small downward component to its motion. Overall, there is a low average pressure above the wing and a high average pressure below it. This pressure imbalance produces an overall upward force on the wing and supports the plane's weight.
These two views of flight—one involving deflection of the air stream and the other involving pressure imbalances—are intimately related to one another and really only two descriptions of the same process. Incidentally, the low pressure just over most the wing causes the air flowing over that wing to speed up. That's Bernoulli's equation in action—when air following a streamline experiences a drop in pressure, it accelerates in the forward direction.
But when the woman is walking, she often lands hard on that heel, so that it supports her entire weight and then some. The extra force comes about because she is accelerating—when she lands, she is heading downward and the floor must push upward extra hard on her to stop her downward motion. If we suppose that the total downward force she exerts on the heel reaches a peak of 200 pounds—not at all unreasonable—the pressure the shoe exerts on the floor reaches 2000 pounds per square inch. No wonder spiked heels damage floors and present a serious hazard to nearby toes!
But when you tip the mirror upward for night use, the mirrored back surface presents you only with a view of the car's darkened ceiling. However, there is a weak second reflection from the clear front surface of the mirror—whenever light changes speeds, as it does upon entering the glass, some of that light reflects. About 4% of the light striking the front surface of the mirror from behind the car reflects without entering the glass and is directed toward your eyes. Since the image you see is about 25 times dimmer than normal, it doesn't blind you the way a reflection from the mirrored surface would.
First, consider a wave traveling toward us on the surface of a lake. Suppose that this wave passes under a small boat and I ask you which way the wave is making the boat move. You would tell me that the boat is moving up and down. I would then tell you that the wave is vertically polarized because it causes objects that it encounters to move up and down rhythmically.
Unfortunately, pure water won't do for the next step because it won't support horizontally polarized waves. So let's imagine that some ecological disaster has turned the entire lake into gelatin. An explosion at the side of the lake now causes a wave to begin heading toward us on the gelatin lake, but this strange wave involves a side-to-side motion of the lake's surface. Now when the wave passes under the boat, the boat moves side-to-side rhythmically. In this case the wave is horizontally polarized because it causes objects that it encounters to move left and right rhythmically.
Now let's return to optics. When an electromagnetic wave heads toward us, its electric fields will push any electrically charged particles it encounters back and forth rhythmically. If we watch one of these charged particles as the wave passes it and observe that this particle moves up and down, then the wave is vertically polarized. If instead the charged particle moves left and right, then the wave is horizontally polarized.
There is, however, an alternative explanation: you may have seen the "green flash" that occasionally appears just as the sun reaches the horizon at sunrise or sunset. This flash is a refraction effect in the atmosphere in which only blue-green light from the sun reaches the viewer's eyes for a second or two while the sun is just below the horizon. However, this green flash should appear in the eastern sky just before dawn, not the southern sky.
To understand how this difference in speeds is possible, think about what happens when you turn on the water to a long hose. If that hose is already filled with water, water will immediately begin pouring out of the hose's end even though the water is flowing quite slowly through the hose. While the water itself moves slowly, the water's effects travel through the hose at the speed of sound in water—several miles per second! Water at the end of the hose "knows" that you have opened the faucet long before new water from the faucet arrives.
Similarly, when you turn on a flashlight, electrons begin to flow out of the battery's negative terminal at speeds of only a few millimeters per second. But these electrons don't have to travel all the way to the light bulb for the bulb to light up. When these electrons leave the battery, they push on the electrons in front of them, which push on the electrons in front of them, and so on. They produce an electromagnetic wave that rushes through the wire at an incredible speed. As a result, electrons begin flowing through the light bulb only a few billionths of a second after the first electron left the battery. So while the electrons that carry electricity through the power grid flow rather slowly, the power they deliver moves remarkably fast.
However, if you trap the air underneath the car, so that its volume can't increase, and then heat that air, its pressure will rise. This increased pressure below the car would produce an overall upward pressure force on the car and could support the car's weight. In effect, you would be creating a ground-effect hovercraft in which the elevated pressure of trapped hot air supports the weight of the vehicle. But it would be easier and less energy-intensive to pump air underneath your hovercraft with a big fan. That's what most ground-effect vehicles do. They pack extra air molecules underneath themselves and then allow those molecules to support their weight. Furthermore, because air molecules are always leaking out from beneath the vehicle, you'll need a fan to replace them anyway.
But to be even more energy efficient, the sewage that was just sterilized a minute ago and is still hot can be used to heat the sewage that is about to be treated! A well designed thermal treatment facility could employ "counter-current exchange"—that is it could pass the hot, treated material through a heat exchanger to allow it to transfer most of its excess heat to the cooler, untreated material that is about to be sterilized. By recycling the heat in this manner, the facility could avoid having to burn so much fuel. The only drawback with this technique is that the heat exchanger must be leak-proof—it must keep the sterilized material from touching and being contaminated by the unsterilized material.
Second, to make efficient use of the wind created by traffic, hundreds of wind generators would have to be installed on each mile of expressway. Since wind generators are expensive, it's much more cost effective to put them on windy ridges out in the country or by the seashore.
Third, the wind generators you propose would actually extract energy from the cars and trucks and reduce their gas mileages! That fact might surprise you, since it would seem that extracting energy from the wind wouldn't have any effect on the cars and trucks that created that wind. But the wind and the vehicles continue to interact as they move along the expressway—each vehicle drags a pocket of air with it and interfering with this air pocket has the effect of interfering with the vehicle! The vehicle uses energy to maintain this moving air pocket and it burns additional fuel. An aerodynamically well-designed vehicle has a relatively small air pocket, but there is a limit to what can be done. To reduce the energy cost of maintaining the air pocket, the vehicle's driver can steer it into the air pocket behind another vehicle so that the two vehicles share a single air pocket. The lead vehicle then provides most of the energy needed to keep the air pocket moving. This technique of sharing an air pocket is called "drafting" and is frequently used by bicycle racers. But while drafting makes it easier for many vehicles to keep their air pockets moving, the wind generators that you propose would make it harder—they would steal energy from the air pockets of every passing vehicle and make those vehicles fight harder to keep their air pockets moving.
A better way to save energy would be to encourage large-scale drafting in some safe way. Having chains of independent cars tailgate one another would be energy efficient, but would cause horrific accidents. However, assembling those cars into a tightly coupled "train" may someday become possible with advances in technology and computer controls.
The landing and leaving processes are in perpetual competition and the fastest one wins. If the air is humid and the object is cold or attractive to water molecules, the landing process dominates and water condenses out of the air and onto the object. If the air is dry and the object is hot or doesn't bind water molecules well, taking off dominates and water evaporates from the object into the air.
Your problem is that the air in your closets is very humid and landing is winning—too much water is condensing on your walls. To stop this condensation, you either have to heat the walls, so that water molecules leave them faster, or reduce the humidity of the air, so that water molecules land less often. Putting a material that binds water molecules into your closets changes the balance of landing and taking off—water molecules that land on this material don't return to the air often so the humidity of the air diminishes. With less humidity in the air, the rate at which water molecules land on the walls also diminishes.
But this drying effect only works if the air in the closet is trapped there. If your closet exchanges air quickly with outdoor air, the water molecules removed by the drying agent will be quickly replaced with new water molecules from outside. In effect, you will be trying to dry the great outdoors, a hopeless task. To make the most of this drying agent, you should let it work on as little air as possible by sealing the closet and slowing the exchange of air with outside. Better yet, replace the drying agent with a dehumidifier. A dehumidifier accumulates water molecules from the air by presenting the air with a chilled surface. Water molecules land on the cold surface and then don't have enough energy to return to the air. They are trapped by the cold rather than by chemical binding.
Your suggestions for why the bubbles appear raise two interesting points. First, in a thermal system such as hot water, you can't identify some molecules as being boiling hot and others as being cooler—temperature is a property of the entire system and not of individual molecules. However, at a given instant, there are molecules with more energy than their neighbors and it is these energetic molecules that may break free of their neighbors to form a bubble nucleus.
Second, water often contains dissolved gases and these gases come out of solution when the water is heated. While many of the gas molecules leave through the water's surface, some of them may leave as bubbles from within the water. This gas bubble formation requires nucleation as well, which is why these bubbles often appear on the inner surfaces of a metal pot on the stove—flaws in the pot's surface assist bubble nucleation. But these gas bubbles aren't what you observed; there just isn't that much dissolve gas. You can prove that the bubbles you observe are steam: repeat the experiment several times with the same water. Each time you heat the water and add sugar, it bubbles wildly—something that wouldn't be possible if you were simply releasing dissolved gases from the water.
When you wrap yourself in a wet cloth, you are ensuring that the relative humidity near the surface of your skin will be close to 100%. Air molecules will still be present around your skin but now there will be essentially no net transfer of water between your skin and the surrounding air—water molecules will leave your skin for the air at roughly the same rate as water molecules return to your skin from the air. In effect, you are stopping evaporation from your skin and very little else. Stopping evaporation from your skin will also cause it to accumulate moisture, but this time the new moisture will come from within your body. Water molecules that would have left your skin had it been surrounded by dry air are now staying in your skin, where they add to the moisture in your skin. Overall, you skin will contain more water but it will not have lost as many water-soluble chemicals and it will not have water driven into it by osmotic pressure. It may be this more gentle moisturizing effect that makes wrapping yourself in a damp sheet more pleasant for your eczema than immersing yourself in water.
When an electron, which is negatively charged, approaches the depletion region from the anode side, it first encounters the depletion region's negatively charged surface and is repelled. But when the electron approaches from the cathode side, it first encounters the depletion region's positively charged surface and is attracted. If it has enough energy when it approaches the depletion region from the cathode side, the electron can cross the depletion region to reach the anode layer. Thus electrons can move relatively easily from the photocell's cathode layer to its anode layer but they can't go back.
When a photocell is exposed to light, some of the light particles (photons) are absorbed in the diode's cathode layer. When such an absorption occurs, the photon's energy may be transferred to an electron in the cathode, giving that electron the energy it needs to cross the depletion region and reach the anode. But once the electron has arrived at the anode it can't return to the cathode directly across the depletion region. Instead, it must flow through an external circuit in order to return to the cathode. As that electron flows through the external circuit, it can give up some of its energy, obtained from the light photon, to devices in that circuit. In that manner, light energy has provided energy to an electrically powered device.
By itself, an overheated photocell won't fail dramatically; it will just stop working. If you've overheated it severely, it will remain broken from then on. But if the photocell is part of a larger collection of power generating elements that continues to produce power, that photocell may suddenly consume all of the power from the other elements. In that case, the photocell may explode as its temperature skyrockets.
The filament is formed by drawing tungsten metal into a very fine wire. This wire, typically only 42 microns (0.0017 inches) in diameter is first wound into a coil and then this coil is itself wound into a coil. The mandrels used in these two coiling processes are trapped in the coils and must be dissolved away with acids after the filament has been annealed.
The finished filament is clamped or welded to the power leads, which have already been embedded in a glass supporting structure. This glass support is inserted into a bulb and the two glass parts are fused together. A tube in the glass support allows the manufacturer to pump the air out of the bulb and then reintroduce various inert gases. When virtually all of the oxygen has been eliminated from the bulb, the tube is cut off and the opening is sealed. Once the base of the bulb has been attached, the bulb is ready for use.
Whenever you accelerate, the various parts of your body can no longer follow their inertia; they must accelerate, too. This acceleration requires forces within your body and you can feel these forces. In fact, they make it feel as though a new type of gravity were acting on the parts of your body. You can't distinguish true gravity from the experience of acceleration because they feel exactly the same. The strength of this gravity-like experience depends on how fast you accelerate and it points in the direction opposite your acceleration. If you accelerate upward, as you do when an elevator first starts moving upward, this gravity-like sensation points downward and you feel extra heavy (the experience of "positive g's") If you accelerate downward, as you do when a rising elevator comes to a stop, this gravity-like sensation points upward and you feel unusually light (the experience of "negative g's") Since there is no fundamental limit to how rapidly one can accelerate, these positive and negative g's can become extremely strong and can easily feel stronger than the true force of gravity. However, when these gravity-like sensations become a few times stronger than gravity itself, they become difficult to tolerate. That's why elevators start and stop gradually and why the turns on roller coasters aren't too sharp.
The camera's lens is a converging lens, meaning that it bends the paths of these light rays so that they diverge less after passing through it. In fact, the lens bends the rays so much that they begin to come together or "converge" after the lens and all the rays of light from the person's nose merge to a single point in space somewhere beyond the lens. Exactly how far from the lens the rays come together depends on the structure of the lens and on the distance between it and the person's nose. When you focus the lens, you're moving the lens so that the rays come together at just the right place to illuminate a single spot on a piece of photographic film. When the distance between the lens and film is just right, all the light from each point on the person comes together at a corresponding point on the film. The lens is then forming a real image of the person on the film and the film records this pattern of light to make a photograph.
In a single lens reflex camera, light passing through the lens doesn't always fall on the film. Most of the time, this light is redirected by a mirror that follows the lens so that the real image forms on a special glass sheet near the top of the camera. When you look through the viewfinder of the camera, you are actually using a magnifying glass to inspecting this real image, making the camera effectively a telescope. You (or the camera, if it is automatic) then focus the lens to form a sharp real image on the glass sheet before taking the picture. Since this glass sheet is the same optical distance from the lens as the film is, focusing on the glass is equivalent to focusing on the film. When you take the picture, the redirecting mirror quickly flips out of the way and a shutter opens to allow light from the lens to fall directly onto the camera's photographic film. For a brief moment, light from the person passes through the lens and onto the film, forming a real image that is permanently recorded on the film. Then the shutter closes and the mirror swings back to its normal position.
In that respect, people are much more vigorous producers of disorder than most other living organisms. People seek order not only in their bodies, but also in the objects around them and they achieve this ordering by consuming order in their environment—fossil fuels, minerals, pure water—at a furious pace and producing disorder in its place—burned gases, garbage, polluted water. Fortunately, sunlight is a tremendous source of order for our earth and it undoes some of the disordering caused by living organisms. However, we are consuming much of the order that sunlight stored on earth over millions of years in only a few generations. At this pace, we're destined to have troubles with the disorder we're creating. Many of the environmental issues that face us today can be viewed from this order/disorder perspective: we have to learn how to create less disorder.
The basic calculation of critical mass is straightforward in principle, but it requires a thorough understanding of the nuclear fuel. Because you need to know how likely one nuclear fission is to cause a subsequent nuclear fission, you must know both the types of fragments you can expect from the first nuclear fission and the likelihood that each fragment will induce a subsequent fission in another atomic nucleus before that it escapes from the nuclear fuel. Because the range of possible fragments, their kinetic energies, and their paths through the nuclear fuel are so vast, an accurate calculation of critical mass is extremely complicated. As an indication of the difficulty, note that fission fragments may bounce off nuclei without inducing fission, so that you must consider bent paths as well as straight ones. Not surprisingly, the calculation of critical mass is too difficult to do exactly, even with the help of computers. In fact, one of the reasons that Germany didn't develop nuclear weapons during World War II was that its scientists miscalculated the critical mass of a fission bomb based on enriched uranium and thought that they would need many tons of enriched uranium rather than the true critical mass of about 52 kilograms. Certain that a critical mass of enriched uranium was unattainable, they didn't pursue the project.
That said, a reader notes that the uneven cooking in a microwave oven can lead to bacterial safety problems—if parts of the food aren't heated sufficiently to kill dangerous bacteria, then you could be exposing yourself to those bacteria. He suggests using the microwave oven for reheating only. He also notes that the lack of surface heating leaves the food relatively tasteless, as compared to more conventional cooking.
In a sense, probability is destiny. Thermodynamics observes that vast systems tend to evolve toward the mostly likely configurations. To understand this process, consider what happens when you mix hot and cold water. The most likely final configuration for the mixed water is for it to reach a uniform temperature about half way in between the two original temperatures. While it's possible for the water to end up extremely hot in one place and extremely cold in another, that outcome is extremely unlikely. It's so unlikely that it never happens.
So in what sense does thermodynamics overwhelm things? The world is filled with relatively ordered arrangements and these ordered arrangements are unlikely by themselves (how they came to be ordered in the first place is another matter for another questions). If you take a crystal vase and drop it on the floor, it's going to evolve toward a more likely arrangement of atoms and dropping it a second time isn't going to return it toward its original unlikely state. In short, ordered systems naturally drift toward disorder when given a chance. How quickly they drift depends on their situation. A coffee cup will remain a nicely ordered object for thousands or millions of years if you don't disturb it. But in a hot environment, or one that is chemically aggressive, it may not last very long.
One last thought: how do living organisms maintain their order in the face of this tendency to disorder? They do it by consuming order and exporting disorder—they eat ordered foods and release disordered wastes to their surroundings.
However, there are several complications when using this technique to measure a person's temperature. First, anything that lies between the person and you, and that absorbs or emit thermal radiation, will affect your measurement. That's because some of the thermal radiation that appears to be coming from the person may be coming from those in between things. Fortunately, air is moderately transparent to thermal radiation but many other things aren't. In fact, to get an accurate reading of person's temperature, you'd have to cool the telescope and the light detector so that they don't add their own thermal radiation to what you observe. You'd also have to use a mirror telescope because glass optics absorb infrared light.
Second, the temperature that you observe will be that of the person's skin and not their inner core temperature. That's because the person's skin absorbs any infrared light from inside the person and it emits its own infrared light to the world around the person. You can't observe infrared light from inside the person because the person's skin blocks your view. All you see is their skin temperature.
While fusion is somewhat more energy efficient than fission, that's not the whole reason why hydrogen bombs (thermonuclear bombs) are more powerful than uranium bombs (fission bombs). The main reason is that thermonuclear bombs can be much larger than fission bombs because there is no upper limit to the amount of hydrogen you can assemble in a small region of space. In contrast, if you assemble too much fissile uranium in a small region of space, a chain reaction will begin and the material will overheat and explode. At the height of the cold war, the Soviet Union built gigantic thermonuclear weapons with explosive yields as large as 100 megatons of TNT.
If you don't want to do the polymerization yourself, you can start with a finished plastic and melt it. Most plastics that haven't been vulcanized into one giant molecule (as is done in rubber tires) will melt at high enough temperatures (although some burn or decompose before they melt). These molten plastics can be stretched, squeezed, or poured into molds to make just about any shape you like.
Because the picture tube can't direct its electron beams accurately enough to hit specific red, green, or blue phosphor regions, it needs help from a shadow mask that's located a short distance before the phosphor layer. This thin metal grillwork shades the light-producing phosphors from the wrong electrons. The picture tube has three separate beams of electrons, one for each primary color, and the grillwork ensures that electrons in the red beam are only able to strike phosphors that produce red light. The same goes for the blue beam and the green beam.
The grillwork must stay in perfect registry with the pattern of phosphors on the inside of the picture tube, even as their temperatures change. That's why this grillwork is made of Invar, a special steel alloy that doesn't change size when its temperature changes. Unfortunately, Invar can be magnetized and its magnetic fields can then steer the electrons so that they strike the wrong phosphors. If you were to hold a strong magnet near the face of a computer monitor, you would probably magnetize the Invar shadow mask and spoil the color balance of the images on the monitor.
To demagnetize the Invar, you must expose it to a magnetic field that fluctuates back and forth and gradually diminishes to zero. The Invar's magnetization would also fluctuate back and forth and would dwindle to nothing by the time the demagnetizing field had vanished. Traditionally, this demagnetizing was done with a large wire coil that was powered by alternating current so that its magnetic field fluctuated back and forth. This coil was gradually moved away from the picture tube so that the influence of its magnetic field slowly diminished to zero, leaving the Invar completely demagnetized. In good computer monitors, this coil and an automatic power source for it are built in. When you push the degauss button, you see a burst of colors as the demagnetizing coil's fluctuating magnetic field erases the magnetization of the shadow mask and also steers the electrons wildly.
Apparently, degaussing circuitry has been built into all color televisions sets for the past 20 or 30 years. When you turn on your television, a demagnetizing coil activates briefly and removes minor magnetization from the television's invar mask.
Most of the time, these waves aren't important and can be ignored. But occasionally some special event will cause enormous waves to begin traveling through a bridge. The classic example was the Tacoma Narrows Bridge in Washington State that collapsed in 1940 when wind-driven waves in its surface ripped it apart. The entire collapse was captured on film and is a fascinating to watch. When a large group of soldiers crosses a footbridge, they are often instructed to break step so that their rhythmic cadence doesn't excite intense waves that might damage the bridge. In general, modern bridges are engineered to dampen these waves—wasting their energy through friction or friction-like effects so that they die away quickly. While it might be fun to watch waves traveling along the surface of a bridge from a safe vantage point, you probably wouldn't want to be on a bridge when it was experiencing strong ones.
The instrument is based on the discovery that most tissues when illuminated by blue or UV light emit a natural fluorescence spectral signature known as autofluorescence. This fluorescence signature is the sum of the emission of the various biochemical fluorphores present in the tissue. If the tissue chemical or physical structure changes, then the spectral signature changes. By exploiting differences in the spectral signature between cancerous and healthy tissue one can create an imaging device that can "see" the difference in the color of the autofluorescence of the tissue and detect changes that may indicate the presence of cancer. The sensors used to see the low levels of fluorescence light employ similar technology to military night vision devices. Once areas of change are located and confirmed by analysis of a biopsy sample treatment can begin. This technique is primarily useful for early stage cancers that are not visually apparent to a physician.
You need only four basic components for a crystal radio: an antenna, a tank circuit, a diode, and a high-impedance earphone.
The antenna is a long wire that projects upward into the electromagnetic fields of the passing radio wave so that electric charges begin to move up and down its length. The ideal length for this wire is a quarter of the wavelength of the wave you're trying to receive, but since that's hundreds of meters for a typical AM station, you'll have to settle for a shorter than ideal antenna.
The tank circuit is a coil of wire that's connected at each end to the two ends of a capacitor. In a typical crystal radio, one of these items—either the coil or the capacitor—is adjustable and forms the tuning element that allows you to select a particular AM station. The tank circuit is a resonant device—electric charges and current flow back and forth through it rhythmically at a specific frequency. If that resonant frequency is adjusted so that it coincides with the transmission frequency of an AM radio station, the small currents flowing in the antenna that's connected to the tank circuit will excite large movements of charge and current in the tank circuit.
The diode is also connected to the tank circuit. Its job is to extract some of the charge that oscillates back and forth in the tank circuit and to send that charge to the earphone. By allowing current to flow only in one direction, the diode samples the overall amount of charge moving in the tank circuit. What it passes to the earphone is a measure of how strong the radio wave is, which is actually the form in which the AM radio station is transmitting sound information.
The high-impedance earphone uses the diode's tiny charge deliveries to reproduce sound. The diaphragm inside the earphone moves back and forth as the amount of charge passing through the diode fluctuates up and down. Each time the radio wave increases in strength, the diaphragm moves in one direction. Each time the radio wave decreases in strength, the diaphragm moves in the other direction. Thus as the radio station varies the strength of its radio wave, the earphone's diaphragm moves back and forth and it reproduces the sound.
When you place a canning jar in boiling water, what you are really doing is exposing that jar to a water bath at a temperature of 212° F (100° C). Boiling water self-regulates its temperature very accurately, making it a wonderful reference for cooking. Below water's boiling temperature, water molecules evaporate relatively slowly from the surface of water so that when you add heat to the water, it tends to get hotter and hotter. But once the water begins to boil—meaning that evaporation begins to occur within the body of the water—water molecules evaporate so rapidly that when you add heat to the water, more of it converts into steam and its temperature doesn't change much. When you boil canning jars for 5 minutes, you are simply making sure that the canning jars sit at about 212° F for about 5 minutes; long enough to kill bacteria in the jars. Since the boiling temperature of water diminishes at high altitudes and lower atmospheric pressures, you must wait longer for your jars to be adequately sterilized if you live in the mountains.
Microwave cooking wouldn't heat the jars to any specific temperature. As you cooked the jars in a microwave oven, their contents would become hotter and hotter. Even if we ignore the fact that microwave cooking is uneven, so that the temperature inside each jar won't be uniform, there will be nothing special about the temperature 212° F. If you cook the food long enough, its temperature will reach 212° F, but will then keep rising. As it does, the water vapor in the jars will become more and more dense and its pressure will rise higher and higher. If the canning jar had been properly capped, the metal lid ought to be loose enough to allow this steam to escape. However, the canning system wasn't designed to handle large amounts of escaping steam and an over-tightened jar might not permit the steam to escape at all. With the steam trapped inside, the pressure inside the jar may become large enough to cause it to explode. Since too little time in the microwave oven will leave the jars unsterilized and too much time in the microwave oven may cause them to explode, I suggest sticking to the tried and true method of sterilizing your jars in boiling water.
As energy becomes more and more precious, making the most of it becomes more and more important. I would suggest saving these 130-volt bulbs for fixtures that are so difficult to reach that you want to avoid changing bulbs at all costs. In more easily accessible fixtures, replacing bulbs is only a minor inconvenience associated with improved energy efficiency. Better still, switch to fluorescent lamps—which are much more energy efficient than even the best incandescent lamps.
Cathodic protection is a scheme in which a piece of reactive metal, typically magnesium, is connected to the steel to form an electrochemical cell. Magnesium ions (Mg2+) form more easily than iron ions and enough electrons are given up by the magnesium atoms as they become positive ions to completely dominate the hydroxide ion formation process. With nowhere for their electrons to go, the iron atoms can't become iron ions and rusting can't proceed. As long as the magnesium metal, often called the "sacrificial anode", remains intact and connected to the steel, the steel won't rust significantly.
As an alternative to this approach, some companies use a power supply to pump negative charges onto the steel to prevent it from rusting. Pipeline companies often do this and that action has led to some interesting complications: metal objects that are brought into contact with such a pipeline can be protected against rusting as well. For example, when people chained their bicycles to protected pipelines, the bicycles became part of the protected materials. This may have been good for the bicycles, but it confused the pipeline companies who found that they needed to pump extra charge onto the pipelines to handle the increased load. It was particularly bad when the bicycles accidentally grounded the pipelines and allowed the negative charges to escape.
If you're seriously interested in cleaning the air in your home, you are probably better off with a full electrostatic air cleaner. Small home versions of this common industrial workhorse are easy to obtain at a local heating and air conditioning store. Properly designed machines use positive ions to avoid producing ozone and provide a negatively charged surface for the positively charged dirt to stick to so that it doesn't deposit itself on your walls.
The best choice I can think of is nuclear magnetic resonance (NMR)—an effect that involves the flipping of an atomic nucleus's magnetic poles. Most atomic nuclei—the massive positively charged nuggets at the centers of atoms—are magnetic. When you put an atom with a magnetic nucleus in a magnetic field, the atom acquires a certain amount of potential energy that depends on whether that magnetic nucleus is aligned with the magnetic field or not. The extent to which the atom's nucleus is aligned with the field can be changed by exposing it to an electromagnetic wave of the right frequency. This electromagnetic wave provides or absorbs the required energy to allow the nucleus's magnetization to flip. The nucleus exhibits a resonance in response to the correct electromagnetic wave—a phenomenon called "nuclear magnetic resonance." This frequency at which this resonance occurs depends on the nucleus, on the magnetic field, and on the magnetic environment of the nucleus. The resonance occurs for any magnetic nucleus, in any field, but how interesting or useful the resonance is depends on the situation. So the answers to both questions are yes, but that doesn't mean the effects are important.
On the other hand, if the frequency of current in the primary is too high, the core may be unable to magnetize and demagnetize fast enough to keep up with it and the power transfer will again be inadequate. The core may also become hot due to friction-like losses in the core material. That's why high frequency transformers use special core materials such as ferrite powders or even air. Although air (or really empty space) can't store large amounts of energy in small volumes when it magnetizes, it can respond extremely quickly. Air-core transformers operate well at extremely high frequencies.
Another system that makes the movement of waves visible is a stiff, thin aluminum plate that's supported rigidly and horizontally at only one point. If you sprinkle fine sand lightly over the surface of this plate and then bow its edge with a violin bow, it will begin vibrating with a clear tone. As it vibrates, the sand will drift into places where there is very little surface motion—the nodes of the vibrating surface. Once again, sound waves are traveling back and forth across this surface and the up-down motions squeeze the sand into certain parts of the plate. In this case, the surface's vibrations and the sound waves in that surface are the same thing—in example of the fact that vibrations and sound waves are intimately related and are in many respects exactly the same thing.
Because the telephones are sharing the total current, any change in the current through your telephone causes a change in the current through your friend's telephone. Thus as you talk, the current through your friend's telephone fluctuates. A speaker in that telephone responds to these current fluctuations by compressing and rarefying the air. The resulting air pressure fluctuations reproduce the sound of your voice. Although the nature of telephones and the circuits connecting them have changed radically in the past few decades, the telephone system still functions in a manner that at least simulates this behavior.
There are thus two separate tidal bulges in the earth's oceans: one on the side nearest the moon and one on the side farthest from the moon. But the earth rotates once a day, so these bulges move across the earth's surface. Since there are two bulges, a typical seashore passes through two bulges a day. At those times, the tide is high. During the times when the seashore is between bulges, the tide is low. Because the moon moves as the earth turns, high tides occur about 12 hours and 26 minutes apart, rather than every 12 hours. Since local water must flow to form the bulges as the earth rotates, there are cases where the tides are delayed as the water struggles to move through a channel. However, even in those cases, the high tides occur every 12 hours and 26 minutes. The sun's gravity also contributes to the tides, but its effects are smaller and serve mostly to vary the heights of high and low tide.
The pattern of light that forms on the screen is called a real image because it looks just like the original object—in this case the transparency—and it's real, meaning that you can touch it with your hand. Real images are usually upside-down and backward, but the overhead projector uses its mirror to flip the image over so that it appears right side up. Because of this vertical flip, the side-to-side reversal is a good thing—the right side of the transparency becomes the left side of the screen image (as viewed by the same person) and the screen image is readable.
The blue light from the sky normally travels directly toward your eyes so that you see it coming from the sky. But when there is a layer of very hot air near the ground in the distance, some of the blue light from the sky in front of you bends upward toward your eyes. This light was traveling toward the ground in front of you at a very shallow angle but it didn't hit the ground. Instead, its entry into the hot air layer bent it upward so that it arced away from the ground and toward your eyes. When you look at the ground far in front of you, you see this deflected light from the blue sky turned up at you by the air and it looks as though it has reflected from a layer of water in front of you. This bending of light that occurs when light goes from higher-density cold air to lower-density hot air is called refraction, the same effect that bends light as light enters a camera lens or a raindrop or a glass of water. Whenever light changes speeds, it can experience refraction and light speeds up in going from cold air to hot air. In this case, the light bends upward, missing the ground and eventually reaching your eyes.
In a digital video signal, a physical quantity first represents numbers and then these numbers represent the brightness and color of the spots. The physical quantity representing the numbers doesn't have to be continuous. For example, a current that's on could represent the number 1 while a current that's off could represent the number 0. A certain pattern of on and off currents could represent larger numbers and these numbers could then represent brightness and color. This use of a continuous or non-continuous physical quantity (such as magnetization, charge, or current) to represent numbers and then these numbers to represent a continuous physical quantity (such as brightness) is called digital representation.
One advantage of digital representation is that it's relatively immune to noise. In analog representation, any disturbance in the continuous physical quantity representing the information leads directly to a disturbance in the recovered information. For example, if the strength of a radio wave is representing brightness and color on your television (the current technique), then any disturbance of the radio wave leads directly to a damaged image on your television. But in digital representation, small changes in the physical quantity that's carrying the information won't change the numbers that are obtained from that physical quantity and will thus have absolutely no effect on the recovered information. For example, if the strength of a radio wave is representing numbers in digital format, using binary (base two) encoding, then a small disturbance of the radio wave will not affect the binary numbers that are recovered from the radio wave. To see why that's true, imagine representing the number 1 as a powerful radio wave and a 0 as no radio wave at all. It's pretty easy to tell a powerful radio wave from an absent one so that, even if there is some radio interference around, it's unlikely to confuse the receiver. Moreover, even if noise does occasionally confuse the receiver about a number or two, the digital scheme can include redundant information that allows the receiver to identify errors and to fix them! That's why a compact disk is so immune to noise—even if there is a flaw or dirty spot on the disk, there is enough redundant digital information to reproduce the music flawlessly.
The other advantage to digital representation is that digital compression techniques become possible. A typical video signal contains lots of unnecessary and duplicated information. For example, when two people are standing in a room and the only things that are changing with time are the images of those two people, there is really no reason to keep sending an image of the room itself from the broadcast station to your home. Digital compression can identify redundant information and remove it from the transmission. In doing so, it can use the communication channel more efficiently.
By adopting a digital transmission scheme, the FCC has recognized that broadcasters will be able to send much clearer, more detailed images using digital representations than with the current analog representations, while still occupying the same portions of the electromagnetic spectrum. However, there is a cost—current televisions will not work directly with these new digital signals. To fix that shortcoming, there will be inexpensive converters that receive the new digital signals and recreate the analog signals needed for current televisions. This conversion will allow older televisions to keep working, but the new digital televisions will be designed to make better use of the enhanced details in the transmissions. The new transmissions will contain about 4 times the detail of current transmissions so that the images will be sharper as well as more immune to noise than the current transmissions.
First, you can view the water between the impeller blades as an object traveling in a circle. Objects don't naturally travel in a circle—they need an inward force to cause them to accelerate inward as they spin. Without such an inward force, an object will travel in a straight line and won't complete the circle. In a centrifugal pump, that inward force is provided by high-pressure water near the outer edge of the pump housing. The water at the edge of the pump pushes inward on the water between the impeller blades and makes it possible for that water to travel in a circle. The water pressure at the edge of the turning impeller rises until it's able to keep water circling with the impeller blades.
You can also view the water as an incompressible fluid, one that obeys Bernoulli's equation in the appropriate contexts. As water drifts outward between the impeller blades of the pump, it must move faster and faster because its circular path is getting larger and larger. The impeller blades do work on the water so it moves faster and faster. By the time the water has reached the outer edge of the impeller, it's moving quite fast. But when the water leaves the impeller and arrives at the outer edge of the cylindrical pump housing, it slows down. Here is where Bernoulli's equation figures in. As the water slows down and its kinetic energy decreases, that water's pressure potential energy increases (to conserve energy). Thus the slowing is accompanied by a pressure rise. That's why the water pressure at the outer edge of the pump housing is higher than the water pressure near the center of the impeller.
When water is actively flowing through the pump, arriving through a hole near the center of the impeller and leaving through a hole near the outer edge of the pump housing, the pressure rise between center and edge of the pump isn't as large. However, this pressure rise never completely disappears and it's what propels the water through the car's cooling system.
However, there are more complicated black holes—ones involving angular momentum and electric charge—that have more complicated structures. In falling into one of these black holes, it is apparently possible to miss the singularity. There is some discussion of such material reemerging from the "other end" of one of this black holes but I believe that there are serious problems with such two-ended interpretations of the equations governing such black holes.
The principal constituents of an atom are protons, neutrons, and electrons. These are three most important subatomic particles; the main building blocks of matter in the same way that wood, bricks, and steel are the major building blocks of houses. Each of these particles has a mass—the measure of their inertia—and two of them, electrons and protons, are electrically charged. Each electron has one unit of negative charge while each proton has one unit of positive charge. Because an atom is normally electrically neutral—its positive and negative charges must balance—it has an equal number of electrons and protons. The number of neutrons in an atom is somewhat flexible.
These particles, electrons, protons, and neutrons, are held together by several types of forces. The protons and neutrons, which are relatively massive, stick to one another at the center of the atom and form a dense object called the atomic nucleus. The particles in the nucleus are held together by the "nuclear" force, which binds together protons and neutrons that are touching one another. This nuclear force is quite strong and is able to overcome the strongly repulsive electromagnetic forces that the protons in the nucleus exert on one another—like electric charges repel one another and the protons are all positively charged. The electrons circulate around the atom's nucleus, held in place by the strongly attractive electromagnetic forces that protons exert on electrons—opposite electric charges attract one another and the electrons are negatively charged while the protons are positively charged.
The electrons do most of the circulating around the nucleus, rather than the other way around, because they are much less massive than the nucleus. As with the planets around the sun, the less massive objects tend to orbit the more massive objects. At a basic level, you can view an atom as a tiny solar system with its neutrons and protons at the center and its electrons orbiting around this central nucleus. Quantum physics dramatically complicates this picture, but it's a helpful picture nonetheless.
At the next level of detail, the protons and neutrons themselves have structure—they are built out of yet smaller particles known as quarks. The particles also stick to one another by tossing particles back and forth—particles including photons and gluons. But that is a whole new story.
Unfortunately, most practical heat engines work best when the hotter object is really hot. For example, a steam engine works best when the hotter object is hot enough to produce very high temperature, high pressure steam. To operate a steam engine with outside air as the hotter object and cold ice as the colder object, the steam engine would have to operate at very low pressure. In fact, it would operate well below atmospheric pressure in a carefully sealed environment. Steam might not even be the best choice for a working fluid—you might do better with a refrigerant such as the various Freon replacements. In effect, your heat engine would be an air conditioner run backward—providing electric power rather than consuming it. Although this could be done, it would probably not be cost effective. The heat exchangers needed to obtain heat from the air and to deliver most of that heat to the glacier, as well as all the machinery of the heat engine itself, would probably make the electricity you generated too expensive. Just because something can be done doesn't mean that it's worth doing. Until other sources of energy become more expensive, this one won't pay for itself.
In the other view, the blades "fly" through the fluid like the wings of an airplane. The fluid flow around each blade is such that the pressure is higher on one side of the blade than the other and the blade experiences a net force toward the lower pressure side. The blades move in the direction of this force, so the passing fluid does work on them—energy is transferred from the fluid to the blades.
These two views are completely equivalent. The fluid leaves the turbine blades traveling more slowly or at lower pressure, and it acquires a rotation in the direction opposite the turbine's rotation.
X-ray crystallography is an important tool for materials science and molecular biology. Just as the colored interference patterns that appear on a soap bubble when sunlight reflects from that bubble tell you something about the structure of that soap bubble, so the X-rays that reflect from a crystal tell you something about the structure of that crystal. X-rays experience interference after they reflect from a crystal and the interference patterns can tell you where individual atoms are located within a crystal or within the molecules from which the crystal is made. Materials scientists use this information to understand the crystals they have produced while molecular biologists use it to understand the molecular structures of complicated biological molecules.
But when the two lamps are in series with one another, each lamp carries the entire current passing through the circuit. Current arriving at the two lamps must pass first through one lamp and then through the other lamp before continuing its trip around the circuit. There is no need to add the currents passing through the lamps because it is the same current in each lamp. Moreover, the voltage drop provided by the rest of the circuit is being shared by the two lamps so that each lamp experiences roughly half the overall voltage drop. Since lamps draw less current as the voltage drop they experience decreases, these lamps draw less current when they must share the voltage drop. Thus the current passing through the circuit is much less when the two lamps are inserted into the circuit in series than in parallel.
Of course, a real metal detector is much more sensitive than your hands are, but it's using similar principles to detect nearby metal. Most often, a metal detector uses a coil of wire with an alternating current in it to create a rapidly changing magnetic field around the coil. If that changing magnetic field enters a piece of nearby metal, the metal responds. If the metal is ferromagnetic—meaning that it has intrinsic magnetic order like iron or steel—it will respond strongly with its own magnetic field. If the metal is non-ferromagnetic—meaning that it doesn't have the appropriate intrinsic magnetic order—it will respond more weakly with magnetic fields that are caused by electric currents that begin to flow through it.
In a short range metal detector, the detector looks for the direct interaction of its magnetic field and a nearby piece of metal. That nearby metal changes the characteristics of the detector's wire coil in a way that's relatively easy to detect. But in a longer-range metal detector, the electromagnetic coil must actually radiate an electromagnetic wave and then look for the reflection of this electromagnetic wave from a more distant piece of metal. That's because the magnetic field of the coil doesn't extend outward forever—it dies away a few diameters of the coil away from the coil itself. For the metal detector to look for metal farther away, it needs help carrying the magnetic field through space. By combining an electric field with the magnetic field, the long-range metal detector creates an electromagnetic wave—a radio wave—that travels independently through space. Electromagnetic waves reflect from many things, particularly objects that conduct electricity. So the long-range metal detector launches an electromagnetic wave and then looks for the reflection of that wave. This wave reflection technique is the basis for sonar (sound waves) and radar (radio waves), and it can be used to find metals deep in the ground. Unfortunately, the ground itself conducts electricity to some extent, so it becomes harder and harder to distinguish the reflections from metal from the reflections from other things in the ground.
In a video recorder, the tape moves too slowly to produce the millions of the magnetization changes needed each second to represent a video signal. So instead of moving the tape past the playback head, the video recorder moves the playback head past the tape. As the tape travels slowly through the recorder, the playback head spins past it on a smooth cylindrical support. The tape is wrapped part way around this support and two or more playback heads take turns detecting the patches of magnetization on the tape's surface. The tape is tilted slightly with respect to the spinning heads so that the heads sweep both along the tape and across its width. That way, the entire surface of the tape is used to record the immense amount of information needed to reproduce images on a television screen. During recording, currents are sent through the heads so that they magnetize the tape rather than reading its magnetization.
To make a strong permanent magnet, you must find a material that is both intrinsically magnetic and that is able to stay magnetic when it's by itself. Materials that hide their magnetism when alone do this by allowing their magnetic structure to break up into tiny pieces that all point in different directions. Each of these tiny magnetic pieces is called a magnetic domain, and iron and steel are normally composed of many magnetic domains. A good permanent magnet material is one that is intrinsically magnetic and that resists the formation of randomly oriented magnetic domains. A very effective way to make such permanent magnet materials is to assemble lots of tiny magnetic particles. Each of these particles is shaped in a way that makes one of its ends a north pole and its other end a south pole, and that makes it extremely hard for these two poles to exchange places. The particles are then aligned with one another and bonded together to form a permanent magnet. To make sure that the particles all have their north poles at one end and their south poles at the other end, the finished magnet is exposed to an extremely strong magnetic field—one so strong that it flips any misaligned magnetic particles into alignment with the others. After being magnetized in this manner, the permanent magnet is very hard to demagnetize, which is just what you want in a permanent magnet.
The most common magnet materials are Ferrite and Alnico. Ferrite magnets are made from a mixture of iron oxide and barium, strontium, or lead oxide. Alnico magnets are made from aluminum, nickel, iron, and cobalt, and consist of tiny particles of an iron-nickel-aluminum alloy inside an iron-cobalt alloy. But the strongest modern magnets are made from an iron-neodymium-boron alloy. The latter magnets are very resistant to demagnetization and the forces they exert on one another are amazingly strong.
The rail gun's projectile must conduct electricity and it completes the electric circuit formed by two parallel metal rails and a high current power source. During the rail gun's operation, current flows out of the power source through one rail, passes through the projectile, and returns to the power source through the other rail. As it passes through the two rails, the electric current produces an intense magnetic field between the rails. The projectile is exposed to this magnetic field and as charged particles pass through the projectile, they experience a Lorentz force that pushes them and the projectile in one direction along the rails. The projectile picks up speed as it travels along the rails and doesn't stop accelerating until the current ceases or it leaves the rails. In practice, the power sources used in most rail guns is a large bank of capacitors. These devices store separated electric charge and supply enormous currents to the rails for a brief period of time.
The working fluid arrives at the compressor as a cool, low pressure gas. The compressor squeezes this working fluid, packing its molecules more tightly together so that their density and pressure increase. The squeezing process also does work on the working fluid, increasing its energy and therefore its temperature. The working fluid leaves the compressor as a hot, high-pressure gas and flows into the condenser. The condenser has metal fins all around it that assist the working fluid in transferring heat to the surrounding outdoor air. As this transfer takes place, the closely spaced molecules of the working fluid begin to stick to one another, releasing additional thermal energy into the surrounding air and causing the working fluid to transform into a liquid. By the time the working fluid leaves the condenser, its temperature has almost dropped back down to the outdoor temperature but it is now a liquid rather than a gas.
This high pressure liquid then flows into the evaporator through a narrow orifice. This orifice allows the liquid's pressure to drop so that it begins to evaporate into a gas. As it evaporates, it extracts heat from the air around the evaporator because that heat is needed to separate the molecules of the working fluid. Like the condenser, the evaporator has metal fins to assist it in exchanging thermal energy with the surrounding air. By the time the working fluid leaves the evaporator, it is a cool, low-pressure gas. It then returns to the compressor to begin its trip all over again.
Overall, the working fluid releases heat into the outside air and absorbs heat from the inside air. The direction of heat transfer, from a cooler region to a hotter region, is the reverse of normal and requires an input of ordered energy so that it doesn't violate the second law of thermodynamics (the disorder of an isolated system can never decrease). This ordered energy is used to operate the compressor and is converted into thermal energy in the process. This additional disordered thermal energy enters the outside air and makes up for the additional order that's given to the indoor air as that air is cooled.
A much better choice, both in terms of energy efficiency and light color, is a fluorescent or compact fluorescent lamp. Such lamps typically use less than 25% of the energy required for comparable incandescent lighting, provide excellent color rendering that can be chosen to match that of incandescent lighting, and they last much longer than incandescent bulbs. Even though compact fluorescent lamps are more expensive than incandescent bulbs up front, they last so much longer and save so much energy that each one typically saves you about $45 over its working life.
To convey audio information (sound) to you radio, the radio station makes one of several changes to the radio wave it transmits. In the AM or Amplitude Modulation technique, it adjusts the amount of charge it moves up and down its antenna, and hence the strength of its radio wave, in order to signal which way to move the speaker of your radio. These movements of the speaker are what cause your radio to emit sound. In the FM or Frequency Modulation technique, the radio station adjusts the precise frequency at which it moves charge up and down its antenna. Your radio senses these slight changes in frequency and moves its speaker accordingly.
But in the experiment you describe, the supercooled water was having trouble nucleating the initial seed ice crystal on which the remaining water could crystallize. Given enough time, that water would have spontaneously formed a seed crystal and the growth of the ice crystal would have proceeded rapidly after that. However, Black accelerated the formation of the seed crystal by shaking the tube. A defect at the surface of the tube or a piece of dust then acted as the trigger and helped the seed ice crystal form. The water then crystallized rapidly around this seed crystal. After the ice had formed, the water was truly in equilibrium.
However, something has happened—the light wave has been delayed ever so slightly. This absorption and reemission process holds the light wave back so that it travels at less than its full speed. If the charged particles in the matter are few and far between, this slowing effect is almost insignificant. But in dense materials such as glass or diamond, the light wave can be slowed substantially.
Actually, higher frequency violet light is slowed more than lower frequency red light because violet light is more effectively absorbed and reemitted by the atoms in most transparent materials. That's because when a high frequency light wave encounters the electrons in an atom, the jiggling motion is so rapid and the electrons' motions are so small that the electrons never reach the boundaries of the atom. As a result, those electrons are able to jiggle back and forth as though they were free electrons and they do a good job of slowing the light wave down. But when a low frequency light wave encounters the electrons in an atom, the jiggling motion is slower and the electrons' motions are so large that they quickly reach the boundaries of the atom. As a result, those electrons aren't able to jiggle back and forth as far as they should and they don't slow the light wave down as well.
The waves used for standard AM radio transmissions have very long wavelengths—typically 300 meters—so that they require vertical pole antennas that are about 75 meters long for optimal reception. An antenna of that length is also optimal for radio transmission, which is why the antennas of AM radio stations are so long and slender. However, because such long antennas are inconvenient for most AM receivers, most AM receivers use small magnetic antennas. A magnetic antenna is a device containing an iron-like material called ferrite that draws in magnetic flux lines like a sponge. A coil of wire is wound around this ferrite so that as the magnetic flux lines of a passing radio wave enter the ferrite, they induces electric currents into the coil of wire. This coil then acts as the antenna.
But the waves used in FM radio transmission have much shorter wavelengths—typically 3 meters—so that antennas of about 75 centimeters are all that's needed. The vertical pole radio antenna on your car is designed to receive these FM waves. The antennas of FM radio stations are also rather short, but they are usually mounted high up on a pole so that the whole structure looks like an AM radio antenna. However, if you look near the top of an FM radio tower, you'll see the actual FM antenna as a much smaller structure.