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Suppose I strike an object with my hand and I stop moving my hand as soon as I make contact with the object. This sends the object moving in a straight line with some velocity.

Part 1: Is it valid to say the following? (assuming no friction is present)

$m_{hand} * v_{hand} = m_{obj} * v_{obj}$

Part 2: And if friction was present, is it valid to assume that momentum will be conserved in the time delta immediately following the collision (for an infinitesimally small time delta)?

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Momentum is not conserved at all here. If you apply a force to stop your hand then you have exerted an external force to the hand-object system. Therefore your equation in part 1 is incorrect, and you can't apply momentum conservation.

If you knew the impulse you provide to your hand to stop it, then you could incorporate that into the change in momentum. $$p_0=m_hv_h$$ $$p_f=m_{\text {obj}}v_{\text {obj}}$$ $$p_f=p_0+J$$ where $J$ is the additional impulse you have supplied to your hand. Notice how if your hand happened to stop on it's own due to the collision you have $J=0$ and now momentum is conserved.

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  • $\begingroup$ Makes sense. Is there a way to model such a scenario using elementary physics then? $\endgroup$ – hashnsalt Jul 31 at 17:45
  • $\begingroup$ And what about Part 2 in typical perfectly elastic collision scenario? Block of mass $m$ striking another block of mass $m$ $\endgroup$ – hashnsalt Jul 31 at 17:48
  • $\begingroup$ @hashnsalt If you know impulse you apply to your hand to stop it after hitting the object, then you would be able to know how much momentum the object has $\endgroup$ – Aaron Stevens Jul 31 at 17:49
  • $\begingroup$ Since impulse equals the change in momentum, I'd apply an impulse of $m_{hand}*(v_{hand, final} - v_{hand, initial}) = -m_{hand}*v_{hand, initial}$...correct? And therefore, $m_{obj}*(v_{obj, final} - v_{obj, initial}) = m_{obj}*v_{obj, final}$. So we're back to my original equation... Where am I going wrong? $\endgroup$ – hashnsalt Jul 31 at 18:05
  • $\begingroup$ @hashnsalt See my edit. $\endgroup$ – Aaron Stevens Jul 31 at 18:28

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