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I know that the straight answer to my question is no. Since the initial momentum is not zero, the final momentum is not zero.

What about when object A impacts object B that is rigidly fixed to earth and object B is very ductile, in the sense that it can endure without breaking considerable deformations. Let's assume that this ductility is enough to dissipate the energy transferred by the colliding object A and that object B is long enough so that only a fraction of its length will actually deform (move) during the impact of object A. Let's also assume that the impact prolongs over a time period that is larger than the time it takes for the impact waves to go through both objects so that all the mass is excited and involved in the impact itself.

My questions are:

  1. How to apply momentum conservation to cases where one object comes to rest after collapse and part of the other object also?
  2. Is momentum conservation applicable during the time period when the impact is taking place?
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  • $\begingroup$ Are you asking if something thrown can stick to the ground? $\endgroup$
    – Dan
    Commented Mar 3, 2022 at 4:42
  • $\begingroup$ No that's simple case. My questions are given above. Consider as an example the airbag. How to calculate the speed during impact? $\endgroup$
    – jpcgandre
    Commented Mar 3, 2022 at 8:23

2 Answers 2

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The only way to keep the principle of momentum conservation in practical situations is using the earth as a kind of bank, the lends and borrow momentum all the time.

For example, a bullet hits a wooden target and rests there. Its momentum $p$ disapeared. But when the shot was done, if we assume a rigid support for the rifle, the momentum $p$ cames from nothing.

In both cases, the explanation is: the earth changed its momentum to compensate the visible change of movement. But its velocity is totaly negligible due to the huge mass, and it is also statistically averaged by all that events.

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  • $\begingroup$ @claudio_saspinski thank you for the answer but I don't see how it helps answering the questions. $\endgroup$
    – jpcgandre
    Commented Mar 3, 2022 at 17:49
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Momentum is always conserved. The Earth's momentum changes, albeit far too little to be measurable. If, on the other hand, you had a truly ImmovableObject (see this story ), momentum conservation would demand that the moving object, after coming to a stop and probably splattering, dissipates its momentum into movement at the particle level, i.e. heat.

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  • $\begingroup$ @Carl_Witthoft Thanks my question revolves around how to apply momentum conservation to obtain the velocity of both objects. For question one issues are that all masses are excited and part of the second object does not move. For question two, for sure the velocity of the two objects does not become the same instantly so what happens during the time impact starts and two bodies come to rest? $\endgroup$
    – jpcgandre
    Commented Mar 2, 2022 at 18:36
  • $\begingroup$ For example, the airbag. During impact for sure part of the airbag follows and cushions the body but part of it moves just ever so slightly since it's fixed on the rigid car parts. In order to correctly determine the velocity of the moving part of the airbag perhaps it's necessary to know what mass of the airbag moves with this speed. There's a gradient of speed in the airbag body, some follow the object some don't move. $\endgroup$
    – jpcgandre
    Commented Mar 2, 2022 at 18:45

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