Category: ramps

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.

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.

When a falling egg hits a table and breaks, did it fail to push equally on the table?

No. It pushed hard against the table and the table pushed hard against it. The forces exerted were exactly equal but in exactly the opposite directions. Each object experienced a strong push from the other object. But as they say, “whether the rock hits the pitcher or the pitcher hits the rock, it’s bound to bad for the pitcher.” The egg couldn’t take the push and it broke.

When a person bumps into something or has something dropped on them and a bruise forms, does it form because of the object hitting the person or from the person exerting a force on the object to keep that object from pass through their skin?

The bruise forms because of the force exerted on the person by the object. When an object hits you, it’s obvious that the object pushes on you. But the object also pushes on you when you hit it. In fact, it’s a matter of perspective which is hitting which. To a person standing next to you when you’re hit by a ball, the ball hit you. To a person running along with the ball, you hit the ball. In each case, the ball pushes on you and gives you a bruise. You also push on the ball, causing it to accelerate away from you.

When you drop a glass on a hard floor, why does it sometimes break and sometimes not?

When the glass hits the floor, the floor exerts all of its force on the part of the glass that actually touches the floor. That small part of the glass accelerates upward quickly and comes to rest. The remainder of the glass isn’t supported by the floor and continues downward. However the glass is relatively rigid and parts of it begin to exert forces on one another in order to stop the whole glass from bending. These internal forces can be enormous and they can rip the glass apart. Glass is a remarkable material; it never dents, it only breaks. As the glass tries to come to a stop, the internal forces may bend it significantly. It will either tolerate those bends and later return to its original shape or it will tear into pieces. Which of the two will occur depends critically on the precise locations and amounts of the forces. If the forces act on a defect on the glass’s surface, it will crack and tear and the glass is history. If the forces all act on strong parts of the glass, it may survive without damage.

When you push up on an object, are you creating thermal energy or does that only occur when something does work on you?

When you lift a heavy object, you do work on that object. After all, you exert an upward force on it and it moves in the direction of that force. However your muscles are inefficient and you consume more food energy (calories) during the lifting process than you actually transfer to the heavy object. Whatever energy you consume that doesn’t go into the object remains in you as thermal energy. Any time you tighten your muscles, whether you do work on something, it does work on you, or neither does work on the other, you end up wasting some food energy as thermal energy.

Why doesn’t an egg break when it falls into a pile of feathers? Isn’t the pile of feathers exerting the same force on it (perhaps 1000 newtons) that a table would if it were to hit that table?

The egg doesn’t break because the feathers exert a much smaller force on the egg than the table would. The feathers can move so when the egg first hits them, the feathers don’t have to stop the egg so quickly. To keep the egg from penetrating into the table, the table has to stop the egg’s descent in about a thousandth of a second. That required a huge upward force on the egg of perhaps 1000 N. This large upward force, exerted on one small point of the egg, breaks the egg. But when the egg hits the feathers, the feathers can stop the egg’s descent leisurely in about a tenth of a second. They only have to push upward on the egg with a smaller force of perhaps 10 N. This modest force, exerted on many points of the egg, shouldn’t break the egg. During this tenth of a second, the feathers and the egg will both move downward and the egg will come to a stop well below the place at which it first touched the feathers.

How do you push a shopping cart and have the cart exert the same force on you, if you are still traveling forward? Friction? Air Resistance?

When you push a shopping cart straight forward down an aisle, you are pushing it forward and it is pushing you backward. If nothing else were pushing on the two of you, the cart would accelerate forward and you would accelerate backward. But the cart is experiencing friction and air resistance, both of which tend to slow it down. They are pushing the cart backward (in the direction opposite its motion). So you must keep pushing it forward to ensure that it experiences zero net force and continues at constant forward velocity. As for you, you need a force to keep yourself heading forward; otherwise the cart’s backward force on you would slow you down. So you push backward on the ground with the soles of your shoes. In return, the ground pushes on you (using friction) and propels you forward. As a result, you also experience zero net force and move forward at constant velocity.

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.