# Conservation of momentum — arm hitting object

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)?

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.
• And what about Part 2 in typical perfectly elastic collision scenario? Block of mass $m$ striking another block of mass $m$ – hashnsalt Jul 31 at 17:48
• 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? – hashnsalt Jul 31 at 18:05