. Can you explain once again how the bowling ball and the tennis ball drop at the same time. Are weight and mass proportional? If mass is the resistance to acceleration and weight is a gravitational force pulling down on the ball, doesn't the weight of the bowling ball make it fall faster? Or does the bowling ball's increased mass in a way cancel out the bowling ball's increased weight? - HC
Weight and mass are proportional to one another and the bowling ball's increased mass does effectively cancel out its increased weight. Let's suppose that the bowling ball is 100 times as massive as the tennis ball—meaning that it takes 100 times as much force to make the bowling ball accelerate at a certain rate as it does to make the tennis ball accelerate at that same rate. Because weight is proportional to mass, the bowling ball also weighs 100 times as much as the tennis ball. So if the only force on each ball is its weight, each ball will accelerate at the same rate. The bowling ball will experience 100 times the force but it will be 100 times as hard to accelerate. The two factors of 100 will cancel and it will accelerate together with the tennis ball.
. If forces are always equal but opposite, how can a hammer drive a nail into a wall? Don't the forces on the nail cancel?
Although forces always appear in equal but oppositely directed pairs, the two forces in each pair act on different objects. The nail and hammer experience one of these force pairs—the hammer pushes on the nail just as hard as the nail pushes on the hammer. Because the nail's force on the hammer is the only force that the hammer experiences, the hammer accelerates away from the nail and the wall. The nail and wall experience the other force pair—the wall pushes on the nail just as hard as the nail pushes on the wall. The nail thus experiences two horizontal forces: the hammer pushes it toward the wall and the wall pushes it away from the wall. As long as all the forces are gentle, the two forces on the nail cancel and it doesn't accelerate at all. But if you hit the nail hard with the hammer, the wall can't exert enough support force on the nail to prevent it from enter the wall. The two forces on the nail no longer cancel and it accelerates into the wall.
. If the net force on an object is zero and it has no acceleration, then what causes it to have velocity? Doesn't a force give it velocity? And doesn't this make the gravitational and support forces unequal? - EH
The great insights of Galileo and Newton were that an object doesn't need a force on it to have a non-zero velocity. Objects tend to coast along at constant velocity when they are free of forces, or when the net force on them is zero. Inertia keeps them going even though nothing pushes on them. While it takes an acceleration and thus a non-zero net force to get an object moving in the first place, it will continue to move even if the net force on it drops to zero. So while I was lifting the bowling ball upward at constant velocity, the net force on the bowling ball was truly zero—it was coasting upward because its weight and the support force from my hand were canceling one another. However, to start the bowling ball moving upward, I had to push upward on it harder than gravity pushed downward. For a short time, the bowling ball experienced an upward net force and it accelerated upward. After that, I stopped pushing extra hard and let the bowling ball coast upward at constant velocity.
. What would it be like if Newton's third law weren't true? Can we imagine that?
Many strange things would happen. For example, suppose that you pushed on your neighbor and your neighbor didn't push back—you wouldn't feel any force pushing against your hand so you wouldn't even notice that you were pushing on your neighbor. Your neighbor would feel you pushing on them and they would accelerate away from you.
Among the many consequences of such a change would be that energy wouldn't be conserved—you would be able to create energy out of nowhere. To see how that would be possible, imagine lifting a heavy object and suppose that as you pushed upward on it, it didn't push downward on you. As you lifted it upward, you would do work on it—you would exert an upward force on it and it would move upward. But it wouldn't do negative work on you—it would exert no force on you as your hands lifted it upward. As a result, its energy would increase but your energy wouldn't decrease. Energy would be created. In fact, you wouldn't even notice that you were lifting it because it wouldn't push on you as you lifted it.
. Would a small-mass hammer that accelerated rapidly exert more horizontal force on a nail than a large-mass hammer that didn't accelerate very much?
Yes. Since the only horizontal force acting on the hammer is that exerted on it by the nail, the hammer's acceleration is entirely determined by that force. The force on the hammer is equal to the hammer's mass times the hammer's acceleration (Newton's second law). If both hammers experienced the same acceleration, then the large-mass hammer would have to be experiencing the larger force from the nail and would therefore be exerting the larger force on the nail. But because the small-mass hammer is experience a larger acceleration, the force that the nail is exerting on it may be quite large. If the small-mass hammer's acceleration is large enough, the force on it may exceed the force on the large-mass hammer.
. You said that if I push on a friend they will push back (even if they are asleep). But if I push hard enough, they will fall to the ground, whereas I will not. Therefore, I don't see how the reaction is equal. Can you please explain this? - JK
Newton's third law only observes that the forces two objects exert on one another are equal in amount but opposite in direction. The law doesn't make any statement about the consequences of those forces on the objects involved. Moreover, it doesn't say that those forces are the only forces on the objects. When you push on an awake friend, your friend will obtain additional forces from the ground or a nearby wall, and will manage to avoid falling over. Even though you push your friend away from you, your friend will see to it that the ground pushes them toward you. As a result, they will probably stay in one place. But when your friend is asleep, they won't be able obtain the additional forces necessary to compensate for the force you exert on them and they may accelerate away from you or fall over.
. In "Empire Strikes Back", when Luke learns that Darth Vader is his father, he falls/jumps off a platform in Cloud City without his hand. Given the fact that objects reach terminal velocity, which would have a faster terminal velocity and which would hit the ground first if in the movie that fell from a height of 1000 meters?
Luke would probably reach the ground before his hand. An object reaches a terminal velocity as it fall because the upward force of air resistance becomes stronger as the object's downward speed increases and this upward force eventually stops the object from accelerating downward. The object's downward speed at the point when it stops accelerating is its terminal velocity. Since air resistance is what sets this terminal velocity, an object that experiences a great deal of air resistance relative to its weight will have a smaller terminal velocity than an object that experiences relatively little air resistance relative to its weight. Because Luke is much larger than his hand, he has lots of weight relative to his surface area. Since surface area largely determines air resistance, he experiences relatively little air resistance relative to his weight. His hand has less weight relative to its surface area and it experiences a lot of air resistance relative to its weight. So Luke's terminal velocity is larger than that of his hand. He reaches the ground first. This tendency for large objects to descend faster than small objects explains why small animals, such as insects, can fall from incredible heights without injury. They reach their terminal velocities quickly and descend rather slowly to the ground.
. Some friends and I are having a debate. They maintain that if a person sleeps on an unheated waterbed, heat might be drawn from their body to the point that hypothermia would occur. Is it possible for a waterbed to do this? — JS, College Park, MD
The answer depends on how cold you allow room temperature to become. Without a heater, the water temperature in the bed will be very close to room temperature. When you then lie on the bed, you will be in contact with a surface that's at room temperature and heat will flow out of you and into the water. Your heat will warm the water and it will tend to float upward and remain at the top surface of the waterbed, forming an insulating layer that will slow your heat loss. However, heat will continue to diffuse into the water as a whole and you will continue to lose heat. As long as the water isn't too cold, your metabolism will be able to replace the lost heat and you'll stay warm. But if the room and waterbed are very cold, your temperature will begin to drop. I'm not sure how cold the water would have to be for this to happen, but if the room and water were almost ice cold, you'd probably have trouble.
. How does a thermostat regulate temperature? — TF, Auburn, WA
A typical thermostat turns on the furnace whenever the temperature falls below a certain temperature and turns the furnace off whenever the temperature rises above another temperature. Those two temperatures are slightly separated so that the furnace doesn't turn on and off too rapidly. In a typical home thermostat, a bimetallic coil tips a small mercury-filled glass bottle. The bimetallic coil is made from two different metal strips that have been sandwiched together and then rolled into a coil. As the temperature changes, the two metals expand differently and the coil winds or unwinds. As it does, it tips the glass bottle and the mercury rolls from one end of the bottle to the other. When the mercury falls to one end, it allows an electric current to flow between two wires and the furnace turns on. When the mercury falls to the other end of the bottle, the current stops flowing and the furnace turns off. So the winding and unwinding of the coil controls the furnace and the home temperature tends to hover at the point where the bottle of mercury is almost perfectly level. When you adjust the set point of the thermostat, you tilt the whole coil and bottle so that the average temperature in your home must shift in order for the bottle to be almost level.
. How does a dehumidifier know when to turn on and off? The one I bought from Sears doesn't use the "wet-bulb/dry-bulb" method (of which I could use a better understanding, too). How does its on-off switch work? — JS, Amherst, NY
Most humidity sensing switches or "humidistats" use the expansion or contraction of certain materials to measure humidity. The more humid the air is, the more water molecules there will be in those materials and their shapes and sizes will be affected. For example, human hair becomes longer when wet and it makes an excellent humidity sensor. On a dry day, a hair will contain relatively few water molecules and its length will be shorter. On a humid day, the hair will contain more water molecules and its length will be longer.
A wet-bulb/dry-bulb system measures humidity by looking at the temperature drop that occurs when water evaporates. As water evaporates from the bulb of the wet thermometer and the bulb's temperature drop, the rate at which water molecules leave the bulb's surface decreases. The bulb temperature drops until the rate at which water molecules leave the bulb is equal to the rate at which water molecules return to the bulb from the air. At that point, there is no net evaporation going on. In humid air, water molecules return to the bulb more often so that this balance is reached at a higher temperature than in dry air. The wet bulb temperature is thus warmer on a humid day than it is on a dry day.