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According to newtons third law or the law of conservation of momentum. When one body loses momentum the other gains the momentum. But what would happen in the following case?

A snooker ball hits the wall so the ball stops after hitting the wall so ideally the momentum of the ball should have been transferred to the wall but the wall stays still. So how does momentum get conserved?

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    $\begingroup$ The wall did move ,its just that we did not noice. $\endgroup$ – Lapmid Feb 3 '17 at 10:45
  • $\begingroup$ Lets gather some more info and then we could put the pieces together. As an example what if you wore skates and you held a ball and you threw the ball. Then you would be pushed back as you throw the ball forward but you would move only slightly. This is because you have a greater mass than the ball and so you have a lot of inertia. $\endgroup$ – avito009 Feb 3 '17 at 10:56
  • $\begingroup$ @avito009 You just answered your own question. The earth has an immense mass so the motion that happened is negligible - but it IS there. In non rigid (non ideal) more realistic situations, you can take into account deformations, heat loss etc. as answers below are talking about. $\endgroup$ – Steeven Feb 3 '17 at 11:59
  • $\begingroup$ More on momentum conservation in collision with wall. $\endgroup$ – Qmechanic Feb 3 '17 at 12:27
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I think asgardian's point was what you're eluding at in your comment.

The momentum of the snooker ball is insignificant compared to the mass of the wall. Any movement caused by the transfer of momentum likely isn't clear just from the human eye. You might feel a vibration if you were touching the wall when it happened.

Most of the movement was also potentially within the elastic range of the material. The momentum may have deformed the wall at the impact point; but if it didn't hit hard enough the wall likely went back to it's initial position after the impact.

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One part of the energy is used for deformation of the wall which changes the potential energies of the atoms. But if no deformations occured, then the wall got heated up according to the energy lost by the ball. So it goes into heat energy. It's what happens when you keep on hitting a metal with a hammer. If you touch it you will feel it is now warmer.

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I think I have the answer. Lets suppose the momentum of the ball before the movement was zero and so likely the momentum of the wall was also zero before the ball hit the wall. Now when the mass of the ball is 2 kg and the velocity is 10 m/s the momentum is 20 kg m/s. Now the mass of the wall is say 100 kg and the velocity would have to be 0.2 m/s. So the momentum both of the wall and the ball cancel each other out. But now the question arises as to how 0.2 m/s was derived?

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  • $\begingroup$ Why would the wall start moving, just because you give speed to the ball? Also, to use the mass of the wall will only make sense if it isn't attached to anything and hanging freely. $\endgroup$ – Steeven Feb 3 '17 at 12:03
  • $\begingroup$ "But now the question arises as to how 0.2 m/s was derived?" No it doesn't. It came from the conservation of momentum. You literally just did the math in the answer. If you mean how does that 2 m/s velocity manifest itself, that seems to be covered in the other answers. $\endgroup$ – JMac Feb 3 '17 at 12:44

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