The amount of hot water that's cooling doesn't necessarily determine which bowl of water will cool fastest. That depends on how quickly each gram of the hot water loses heat, a rate that depends both on how much hotter the water is than its surroundings and on how that water is exposed to those surroundings. In general, hot water loses heat through its surface so the more surface that's exposed, the faster it will lose heat. But surface that's exposed to air will lose heat via evaporation and will be particularly important in cooling the water.
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.
An ordinary wire will carry electric current in either direction, while a diode will only carry current in one direction. That's because the electric charges in a wire are free to drift in either direction in response to electric forces but the charges in a diode pass through a one-way structure known as a p-n junction. Charges can only approach the junction from one side and leave from the other. If they try to approach from the wrong side, they discover that there are no easily accessible quantum mechanical pathways or "states" in which they can travel. Sending the charges toward the p-n junction from the wrong side can only occur if something provides the extra energy needed to reach a class of less accessible quantum mechanical states. Light can provide that extra energy, which is why many diodes are light sensitive—they will conduct current in the wrong direction when exposed to light. That is the basis for many light sensitive electronic devices and for most photoelectric or "solar" cells.
If we neglect the mass of the rope, the two teams always exert equal forces on one another. That's simply an example of Newton's third law—for every force team A exerts on team B, there is an equal but oppositely directed force exerted by team B on team A. While it might seem that these two forces on the two teams should always balance in some way so that the teams never move, that isn't the case. Each team remains still or accelerates in response to the total forces on that team alone, and not on the teams as a pair. When you consider the acceleration of team A, you must ignore all the forces on team B, even though one of those forces on team B is caused by team A. There are two important forces on team A: (1) the pull from team B and (2) a force of friction from the ground. That force of friction approximately cancels the pull from the team B because the two forces are in opposite horizontal directions. As long as the two forces truly cancel, team A won't accelerate. But if team A doesn't obtain enough friction from the ground, it will begin to accelerate toward team B. The winning team is the one that obtains more friction from the ground than it needs and accelerates away from the other team. The losing team is the one that obtains too little friction from the ground and accelerates toward the other team.
Most objects make no light of their own and are visible only because they reflect some of the light that strikes them. Without sunlight (or any other light source), these passive objects would appear black. Black is what we "see" when there is no light reaching our eyes from a particular direction. The only objects we would see would be those that made their own light and sent it toward our eyes.
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.
The helium balloon is the least dense thing in the car and is responding to forces exerted on it by the air in the car. To understand this, consider what happens to you, the air, and finally the helium balloon as the car first starts to accelerate forward.
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.
At low speeds, mass and energy appear to be separate quantities. Mass is the measure of inertia and can be determined by shaking an object. Energy is the measure of how much work an object can do and can be determined by letting it do that work. Conveniently enough, the object's weight—the force gravity exerts on it—is exactly proportional to its mass, which is why people carelessly interchange the words "mass" and "weight," even though they mean different things.
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.)
A superconductor is a material that carries electric current without any loss of energy. Currents lose energy as they flow through normal wires. This energy loss appears as a voltage drop across the material—the voltage of the current as it enters the material is higher than the voltage of the current when it leaves the material. But in a superconductor, the current doesn't lose any voltage at all. As a result, currents can even flow around loops without stopping. Currents are magnetic and superconducting magnets are based on the fact that once you get a current flowing around a loop of superconductor, it keeps going forever and so does its magnetism.
Nearly all metals are crystalline, meaning that their atoms are arranged in neat and orderly stacks, like the piles of oranges or soup cans at the grocery store or the cannonballs at the courthouse square. When you bend a metal, its crystals can deform either by changing the spacings between atoms or by letting those atoms slide past one another as great moving sheets of atoms. When the atoms keep their relative orientations but change their relative spacings, the deformation is called elastic. When the atom sheets slide about and move, the deformation is called plastic.
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.
Fortunately, you don't have to wait that long. From astronomical observations, we are fairly certain that the laws of physics as we know them apply throughout the visible universe. It wouldn't take large changes in the physical laws to radically change the structures of atoms, molecules, stars, and galaxies. So the fact that the light and other particles we see coming from distant places is so similar to what we see coming from nearby sources is pretty strong evidence that the laws of physics don't change with distance. Also, the fact that the light we see from distant sources has been traveling for a long time means that the laws of physics don't seem to have changed much (if at all) with time, either. While there are theories that predict subtle but orderly changes in the laws of physics with time and location, effectively making those laws more complicated, no one seriously thinks that the laws of physics change radically and randomly from place to place in the Universe.
The foam consists of tiny air bubbles surrounded by very thin films of soap and water. When light enters the foam, it experiences partial reflections from every film surface it enters or exits. That is because light undergoes a partial reflection whenever it changes speed (hence the reflections from windows) and the speed of light in soapy water is about 30% less than the speed of light in air. Although only about 4% of the light reflects at each entry or exit surface, the foam contains so many films that very little light makes it through unscathed. Instead, virtually all of the light reflects from film surfaces and often does so repeatedly. Since the surfaces are curved, there is no one special direction for the reflections and the reflected light is scattered everywhere. And while an individual soap film may exhibit colors because of interference between reflections from its two surfaces, these interference effects average away to nothing in the dense foam. Overall, the foam appears white—it scatters light evenly, without any preference for a particular color or direction. White reflections appear whenever light encounters a dense collection of unoriented transparent particles (e.g. sugar, salt, clouds, sand, and the white pigment particles in paint).
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.