Tag: ramps

How does the egg (sitting on a table) hold up the table? If the “weight vs. support force of table” is not always an equal pair then how is the “support force of the egg vs. the table” an equal pair?

When an egg is sitting on a table, each object is exerting a support force on the other object. Those two support forces are equal in magnitude (amount) but opposite in direction. To be specific, the table is pushing upward on the egg with a support force and the egg is pushing downward on the table with a support force. Both forces have the same magnitude—both are equal in magnitude to the egg’s weight. The fact that the egg is pushing downward on the table with a “support” force shows that not all support forces actually “support” the object they are exert on. The egg isn’t supporting the table at all. But a name is a name and on many occasions, support forces do support the objects they’re exerted on.

What is the force produced when two cars crash? — DT, Nicosia, Cyprus

There are two forces present when the cars collide: each car pushes on the other car so each car experiences a separate force. As for the strength of these two forces, all I can say is that they are exactly equal in amount but opposite in direction. That relationship between the forces is Newton’s third law of motion, the law dealing with action and reaction. In accordance with this law of motion, no matter how big or small the cars are, they will always exert equal but oppositely directed forces on one another.

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.

Please explain ideal mechanical advantage and actual mechanical advantage. How can I demonstrate these two ideas? — S

Mechanical advantage is any process that allows you to exchange force for distance (or torque for angle) while performing a particular task. The amount of mechanical work you must do (i.e., the amount of energy you must supply) to perform that task won’t change, but the relationship of force and distance (or torque and angle) will. For example, you can increase the altitude of a wooden block by 1 meter either by lifting it straight upward 1 meter or by pushing it several meters uphill along a ramp. In the first case, you’ll have to exert a large upward force on the block but you won’t have to move it very far to complete the task. In the second case, you’ll have to exert a much smaller uphill force on the block but you’ll have to move it a long way along the ramp. If you multiply the force you exert on the block times the distance that block travels while rising 1 meter, you’ll find that it’s exactly the same in either case. You’ve simply calculated the work required to raise the block 1 meter and that work won’t change, regardless of how you perform the task! That’s the crucial issue with mechanical advantage—it doesn’t let you avoid doing the work, it just lets you do that work with a small (or larger) force exerted over a longer (or shorter) distance. In a situation involving rotation, mechanical advantage lets you do the same work with a smaller (or larger) torque exerted over a larger (or smaller) angle. In all of these cases, you’re doing the same amount of work but you’re making it more palatable by adjusting the balance between force and distance or between torque and angle.

As for actual mechanical advantage, it’s simply a recognition that any mechanical system involves imperfections. The work that you do with the help of a machine doesn’t all go toward your goal. Instead, you end up doing some work against sliding friction or air resistance and that work is lost to thermal energy. For example, when you slide a block up a ramp, friction with the ramp wastes some of your energy. If you multiply the uphill force you exert on the block while pushing it up the hill times the distance it travels along the ramp, you’ll find that you must do somewhat more work while raising the block 1 meter than you would have done by simply lifting the block directly upward that 1 meter. So ideal mechanical advantage assumes no change in the work you do while actual mechanical advantage recognizes that you’re going to end up doing extra work whenever you employ a machine to obtain mechanical advantage.

What’s energy?

Formally defined as “the capacity to do work”, energy is a measure of an object’s ability to make things happen. It is interesting to physicists for one important reason: it is a conserved physical quantity. By “conserved physical quantity”, I don’t mean that it’s something that we try not to waste. I mean that the amount of energy in an isolated system can’t change—energy can’t be created or destroyed, it can only be transferred from one object to another or converted from one form to another. Because you can’t make it or consume it, energy is an important characteristic of objects and systems. You can often watch it move from object to object and observe the consequences of this movement. For example, the energy that I’m using now to type at my keyboard arrived at the earth’s surface as sunlight, was used by plants to build new molecules that eventually become part of my breakfast this morning and are now being combined with oxygen in my body to allow me to move my fingers. Nowhere along this chain was energy created or destroyed—it simply moved about and changed forms. It will still be here tomorrow, and then next day, and even the day after that.

How can people lay on a bed of nails and still survive? — LW, Marion, OH

If you push gently on the tip of one nail, it won’t pierce your finger. When you push on the nail, it pushes back on you, but the force pushing the nail against your finger isn’t strong enough to break your skin. If you push twice as hard on two nails at once, using two different fingers, then the force you exert on each nail will be the same as before and each nail will push back against one of your fingers with the same force as before. Once again, the nails won’t break your skin. If you now push 100 times as hard against 100 nails, each nail won’t push hard enough against you to break your skin. In fact, a few hundred nails will be able to push on you with an overall force equal to your weight without piercing you. That’s the idea behind a bed of nails—by lying on many nails at once, you allow so many nails to push upward on you that, while the overall force they exert on you is enough to balance your weight, the force exerted by each individual nail isn’t enough to draw blood. These nails have to be spread out around your body so that no individual nails bear more than their fair share of your weight. If one of the nails took too much of your weight, you’d be hurt by it.

In Exercise #9 on pg. 33: If you are riding on an escalator, with a suitcase, doesn’t the escalator supply the upward force? Doesn’t this also mean that the forces of the suitcase and escalator cancel one another to produce a net force of zero?

First, let’s suppose that the suitcase is resting directly on the escalator and you are not touching it (I had intend that you hold the suitcase in your hand). Because the suitcase is traveling at constant velocity, the net force on it must be zero. Since the suitcase has a downward weight, the escalator must be pushing upward on the suitcase with a force exactly equal in magnitude to the suitcase’s weight. As you suggest, the force of the suitcase’s weight and the support force of the escalator cancel one another to produce a net force of zero on the suitcase. Now, if you are holding the suitcase, it’s your job to exert this upward force on the suitcase. Once again, that upward force is equal in magnitude to the weight of the suitcase.

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.