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Consider a wall and a ball that is traveling towards the wall with uniform velocity. Assuming no friction of any kind in this situation. When ball collides with the ball, the ball gets squished as its kinetic energy is changed to elastic potential energy and bounces back with Potential energy changing back to kinetic energy.

Now, suppose at the instant when ball is in contact with the ball and its potential energy is maximum the wall disappears. Then what will be the ball's behavior (or motion)?

I think that the ball will start oscillating- expand and contract horizontally repeatedly; with no more translation motion. Am I thinking in right direction?

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  • $\begingroup$ By oscillating do you mean it will expand and contract and repeat. $\endgroup$ – Protein Aug 4 '20 at 5:14
  • $\begingroup$ @Protein yes. I meant the oscillation of the size of ball - expand & contract :-) $\endgroup$ – Hiro Aug 5 '20 at 12:46
  • $\begingroup$ If pls take moment and accept my ans If you liked it. You know the tick below voting buttons right? $\endgroup$ – Protein Aug 5 '20 at 13:43
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I think that the ball will start oscillating at its position.

I don't think it oscillates—rather, its size oscillates.

At the moment of maximum potential energy in the ball, its velocity is zero. If the wall disappears at this instant, the ball just falls vertically downwards with its size oscillating in a damped manner (due to continuous expansion and contraction, the oscillations are ultimately converted to heat).

the moment of Max potential energy is the moment of Max deformation

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    $\begingroup$ please note that conservation of momentum is a strict law. $\endgroup$ – anna v Aug 4 '20 at 5:19
  • $\begingroup$ @ Anna v am I wrong in saying that velocity of ball is zero for an instant. $\endgroup$ – Protein Aug 4 '20 at 8:06
  • $\begingroup$ to become negative it has to pass through zero, but oscillations (of the ball body ) wil be there whether the wall "disapears" or not. It "appears"only at the dt of impact, as far as the ball is concerned $\endgroup$ – anna v Aug 4 '20 at 13:13
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If the wall disappears after the touch impact, the ball will bounce back,even if the impact is infisinitessimal in time.

You are forgetting conservation of momentum, which is calculated by what is taken up at impact by the wall , and the bounced ball. No possible oscillations .

Thinkof it. As far as the ball is concerned, the impact is at one point in time, the wall only appears to it at that one point, and can be considered "disappeared" at all other times.

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    $\begingroup$ You can't argue with conservation of momentum in a scenario where momentum carrying objects are allowed to just disappear. $\endgroup$ – Vercassivelaunos Aug 4 '20 at 6:07
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    $\begingroup$ @Vercassivelaunos sorry, did you read my last sentence? and conservation of momentum is absolute in a physics discussion $\endgroup$ – anna v Aug 4 '20 at 6:25
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    $\begingroup$ The collision between the ball and the wall will occur over a period of time as will the conversion of the kinetic energy of the ball to elastic potential energy. If the wall disappears at the instant that the velocity of the centre of mass of the ball relative to the ground is zero the ball will not undergo an further translational motion. $\endgroup$ – Farcher Aug 4 '20 at 6:58
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    $\begingroup$ a) impact is not instantaneous, in direct contradiction to your last sentence. The ball is compressed and then decompresses over a short amount of time, not instantaneously. b) Conservation of momentum is only a given in a world with translational symmetry, which a world with a magic appearing and disappearing wall at one specific point in space is not. $\endgroup$ – Vercassivelaunos Aug 4 '20 at 7:16

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