Tag: ramps

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.

Without gravity in space, what would happen to the recoil if a gun were shot off? — DZ, Illinois

Even in the depths of space, so far from any planet that gravity is virtually absent, a gun will have its normal recoil. When you push on something, it pushes back on you just as hard as you push on it. That rule, known as Newton’s third law of motion, is as true in empty space as it is on earth. Thus when the gun pushes the bullet forward, the bullet pushes the gun backward equally hard and you feel the gun itself jump backward as result. This recoil effect is the very basis for rocket propulsion—the rocket pushes its exhaust backward and the exhaust pushes the rocket forward. That’s why rockets can work outside the earth’s atmosphere and away from any celestial objects—the rocket only has to push on its exhaust in order to obtain a push forward.

How does a surface know how hard it must push upward on an object to support that object?

If you put a piano on the sidewalk, the piano will settle into the sidewalk, squeezing the sidewalk’s surface until the sidewalk stops it from descending. At that point, the sidewalk will be pushing upward on the piano with a force exactly equal in magnitude to the piano’s downward weight. The piano will experience zero net force and will not accelerate. It’s stationary and will remain that way.

But if the sidewalk were to exert a little more force on the piano, perhaps because an animal under the sidewalk was pushing the sidewalk upward, the piano would no longer be experiencing zero net force. It would now experience an upward net force and would accelerate upward. The piano would soon rise above the sidewalk. Of course, once it lost contact with the sidewalk, it would begin to fall and would quickly return to the sidewalk.

For an example of this whole effect, put a coin on a book. Hold the book in your hand. The book is now supporting the coin with an upward force exactly equal to the coin’s weight. Now hit the book from beneath so that it pushes upward extra hard on the coin. The coin will accelerate upward and leap into the air. As soon as it loses contact with the book, it will begin to fall back down.

Thus, if the sidewalk pushed upward too hard, the piano would rise upward and leave the sidewalk’s surface and if the sidewalk pushed upward too weakly, the piano would sink downward and enter the sidewalk’s surface. A balance is quickly reached where the sidewalk pushes upward just enough to keep the piano from accelerate either up or down.

If a falling egg weighs only 1 newton, how can it exert a force of 1000 newtons on a table when it hits?

As the egg falls, it is experiencing only one force: a downward weight of 1 N. But when it hits the table, it suddenly experiences a second force: an upward support force of perhaps 1000 N. The table is acting to prevent the egg from penetrating its surface. The net force on the egg is then 999 N, because the upward 1 N force partially cancels the downward 1000 N force. If the egg could tolerate such forces, it would accelerate upward rapidly and wouldn’t enter the table’s surface. Because the egg is fragile, it shatters. The force that the egg exerts on the table is also 1000 N, this time in the downward direction. The egg and table push on one another equally hard. The table doesn’t move much in response to this large downward force because it’s so massive and because it’s resting on the floor. But if you were to put your hand under the falling egg, you would feel the egg push hard against your hand as it hit.

If every force always has an equal and opposite force pushing against it (like the bowling ball and your arm in today’s lecture), how can anything at all accelerate? Wouldn’t forces always cancel each other out?

The two equal but opposite forces are being exerted on different objects! In many cases, those two objects are free to accelerate independently and they will accelerate—in opposite directions! For example, when I push on a bowling ball, it pushes back on me with an equal but opposite force. If my force on the bowling ball is the only force it experiences, it will accelerate in the direction of my force on it. Since it exerts an opposite force on me, I will accelerate in the opposite direction—we will push apart!

If it takes less force to push something up a ramp, why doesn’t it also take less work?

When you lift an object using a ramp, the uphill force you exert on it is less than its weight but the distance you must travel along the ramp is more than if you simply lifted the object straight up. Since the work you do on the object is the product of the force you exert on it times the distance it travels in the direction of that force, the work isn’t changed by using the ramp. For example, if you lift a cart weighing 15 N straight up for 0.2 meters, you do 3 newton-meter or 3 joules of work on it. To raise that cart that same 0.2 meters upward on the ramp, you’d have to exert a 3 N force on it as you pushed it 1.0 meter along the ramp. The work you’d do to raise the cart by pushing it up the ramp would be 3 joules again. No matter how you raise the cart to the height of 0.2 meters, you’re going to do 3 joules of work on it.

If Newton’s third law is true – then how can you move anything? If it exerts the exact same amount of force on you that you exert on it, wouldn’t the net force be zero and the object wouldn’t move?

The total force on the two of you (the object you’re pushing on and you yourself) would be zero, but the object would be experiencing a force and you would be experiencing a force. As a result, the object accelerates in one direction and you accelerate in the other! To see this, imaging standing on a frozen pond with a friend. If the two of you push on one another, you will both experience forces. You will push your friend away from you and your friend will push you in the opposite direction. You will both accelerate and begin to drift apart. Each of you individually will experience a net force. (It’s true that the two of you together will experience zero net force, which means that as a combined object, you won’t accelerate. The way this appears is that your overall center of mass won’t accelerate. It will remain in the middle of the pond even as the two of you travel apart toward opposite sides of the pond.)

If the downward motion of lifting a weight transfers energy to you, why does your arm get tired?

Your body is unable to store working that’s done on it and also wastes energy even when it is not doing any work. When you lower a weight, the weight does transfer energy to you, but your body turns that energy into thermal energy. You get a little bit hotter. If you were made out of rubber, you might store it as elastic potential energy (like a stretched rubber band). Instead, your muscles don’t save the energy in a useful form. As for getting tired, your muscles turn food energy into thermal energy even when you aren’t doing work. That’s what happens during isometric exercises. There’s nothing you can do about it. It’s like a car, which wastes energy when it’s stopped at a light.

Is it impossible to do work on a ball while carrying it horizontally, or were you only referring to the force of gravity in the demonstration? Or must you be “pushing” the ball?

When I carried the ball horizontally at constant velocity, I did no work on the ball. That’s because the force I exerted on the ball was directly upward and the direction the ball moved was exactly horizontal. Since work is force times distance in the direction of that force, the work I did was exactly zero. But when I first started the ball moving horizontally, there was a brief period during which I had to push the ball forward horizontally. That’s when I “got the ball moving.” During that brief period, I did do work on the ball and I gave it kinetic energy. It needed that kinetic energy to move horizontally. When I reached my destination, there was a brief period during which I had to pull the ball backward horizontally. That’s when I “stopped the ball from moving.” During that brief period, I did negative work on the ball and removed its kinetic energy.

What forces are involved when a football player who is running is tackled by another player?

If the two players collide hard, they will both exert enormous forces on one another. The player running toward the right will experience a force to the left and will accelerate toward the left (slowing down). The player running toward the left will experience a force to the right and will accelerate toward the right (slowing down). The forces involved would cause bruises if they weren’t wearing pads. The pads reduce the magnitudes of the forces on their skin by prolonging the accelerations (smaller forces exerted for longer times). If one player simply trips up the other player, then the player who falls will still come to a stop. However, that player will be experiencing most of the stopping force from the ground by way of sliding friction.