Category: ramps

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.

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!