# Linear momentum ball bounce

## Main Question or Discussion Point

All right, so, we just went over linear momentum in school, and one thing is confusing me:

If I throw something at a wall, why does it bounce back? (I'm assuming both the object and the wall are infinitely hard and don't get deformed, and the wall won't move)

It seems pretty straight-forward, but I can't get my mind around it, which makes me feel dumb. My dad tries to explain it with conservation of energy -- it has kinetic energy, and it can't just lose all that energy, so it has to keep some being kinetic energy, and that makes it go back. All right, so it has to. But I still don't understand how. I tried to ask him to explain what was happening in terms of forces instead, but he couldn't.

The way I see it, is that the wall exerts normal force on the object thrown (ball). The normal force is a reaction force, right, so it ought only exert so much force on the ball that the ball stops and doesn't go through it. Why would it go ahead and exert extra force on the ball to make it bounce back? Where would it come from?

I realize I'm probably just missing something simple, but could someone try to explain to me? It's really frustrating to not understand.

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Nothing forces it to come back --- it's really a property of the material. Imagine throwing a sponge --- it wouldn't bounce much...

To elaborate ganneth's point:
An object bounces back because the initial normal force compresses it a bit. Then the object will try to decompress after it stopped and thus extern another normal force on the wall. Via Newton's third law, the wall pushes back and makes it bounce. That is why a basketball will bounce back, while your "infinitely hard" object will not.

All right, so, we just went over linear momentum in school, and one thing is confusing me:

If I throw something at a wall, why does it bounce back? (I'm assuming both the object and the wall are infinitely hard and don't get deformed, and the wall won't move)

It seems pretty straight-forward, but I can't get my mind around it, which makes me feel dumb. My dad tries to explain it with conservation of energy -- it has kinetic energy, and it can't just lose all that energy, so it has to keep some being kinetic energy, and that makes it go back. All right, so it has to. But I still don't understand how. I tried to ask him to explain what was happening in terms of forces instead, but he couldn't.

The way I see it, is that the wall exerts normal force on the object thrown (ball). The normal force is a reaction force, right, so it ought only exert so much force on the ball that the ball stops and doesn't go through it. Why would it go ahead and exert extra force on the ball to make it bounce back? Where would it come from?

I realize I'm probably just missing something simple, but could someone try to explain to me? It's really frustrating to not understand.

The infinitely hard object would just fall to the ground. This is to say the object would lose all it's kinetic energy but then gravity will accelerate it towards the ground. However energy is conserved because that wall is planted in the ground. Momentum transfers to the wall which will transfer it to the ground. Some of the objects kinetic energy will also be dissipated in the form of heat energy.

The bounce effect you talk about is an extrinsic property of an object. It is called the coefficient of restitution: http://en.wikipedia.org/wiki/Coefficient_of_restitution. It really a measure of how much energy is lost in a collision of a particular object.

However energy is conserved because that wall is planted in the ground. Momentum transfers to the wall which will transfer it to the ground. Some of the objects kinetic energy will also be dissipated in the form of heat energy.
But if the wall won't move, it can't have any momentum, can it? And if both ball and wall are infinitely hard, there will be no heat or sound upon impact, will there?

What was said about the ball not bouncing back if it were infinitely hard, was very helpful, though. Thanks! <3

no, the wall HAS momentum

Shooting Star
Homework Helper
A perfectly elastic body is that which regains its shape completely after the deforming force is removed, which implies that perfectly rigid bodies are perfectly elastic bodies in the limit of deformation tending to zero. Collision between two perfectly rigid bodies would be a perfectly elastic collision. The KE and momentum would both be conserved. The molecules in an ideal gas are indeed modelled after such a concept.

An “infinitely hard” sphere, meaning a perfectly rigid body, after hitting the wall, would not fall to the ground. How much it rebounds will of course depend on the properties of both the wall and the ball, i.e., on the co-efficient of restitution of these two materials, but it will rebound considerably if the wall is not very plastic. On the other extreme, a perfectly plastic body would indeed splat on the wall and fall to the ground.

To answer the original question, when a ball hits a wall, both the ball and the wall are deformed like “springs”. After the relative motion becomes zero, both of them tries to come back to their original shapes, and this makes the ball rebound. A part of the original energy is permanently absorbed by both the bodies as heat and sound or used for permanent deformation.

A perfectly elastic body is that which regains its shape completely after the deforming force is removed, which implies that perfectly rigid bodies are perfectly elastic bodies in the limit of deformation tending to zero. Collision between two perfectly rigid bodies would be a perfectly elastic collision. The KE and momentum would both be conserved. The molecules in an ideal gas are indeed modelled after such a concept.

An “infinitely hard” sphere, meaning a perfectly rigid body, after hitting the wall, would not fall to the ground. How much it rebounds will of course depend on the properties of both the wall and the ball, i.e., on the co-efficient of restitution of these two materials, but it will rebound considerably if the wall is not very plastic. On the other extreme, a perfectly plastic body would indeed splat on the wall and fall to the ground.

To answer the original question, when a ball hits a wall, both the ball and the wall are deformed like “springs”. After the relative motion becomes zero, both of them tries to come back to their original shapes, and this makes the ball rebound. A part of the original energy is permanently absorbed by both the bodies as heat and sound or used for permanent deformation.
There wouldn't be a deforming force to begin with if it is "completely hard"

Shooting Star
Homework Helper
There wouldn't be a deforming force to begin with if it is "completely hard"
"Completely hard" things don't exist in nature. When the deformation is very small, the time of impact is very small and the co-eff of restitution is almost equal to 1, we idealize something as perfectly rigid. Very little energy is lost in such macroscopic collisions. They are like almost perfectly elastic collisions.

EDIT: Saw the above link after I had submitted my post. Overall, I feel, that thread is saying the same thing as me. But this sentence, form post #5 in the above thread, is erroneous:
"Ah, ok, so the force that causes the ball to bounce is contained in the ball, and is not related to the surface it is bouncing against."

The amount of bounce depends on both the objects.

Last edited:
ahrkron
Staff Emeritus
Gold Member
One interesting point, marginally related with the issue, is that infinitely rigid objects are incompatible with special relativity. If you had a 1-km infinitely rigid rod, you could push one end to send a signal instantaneously to the other end.

Shooting Star
Homework Helper
One interesting point, marginally related with the issue, is that infinitely rigid objects are incompatible with special relativity. If you had a 1-km infinitely rigid rod, you could push one end to send a signal instantaneously to the other end.
Hi ahrkron,

I feel that a thread should be kept focused on the original discussion, at least until it is resolved to a satisfactory degree, instead of digressing. This has become a problem in PF, where a thread may gradually veer off to an absolutely unrelated subject, or is sometimes hijacked by people just because it contains a particular term which they wish to discuss. I have voiced my concerns over this to certain mentors.

Please understand that I am NOT saying that you are one of these people, and the point you raised is extremely interesting, but I'm afraid that the original questions will never be cleared if new and more sophisticated points are inserted continually in a discussion. A new thread should be started for that.

Thank you.