Question

a. given F v. T, how would you calculate average force during a collision? Give an equation or two and explain with calculus.

b. List experimental effects that could change your results in such a way that it would look like momentum is not conserved.

Answer 1

(a) We know ........(1)

Now impulse    ...........(2)

Hence average force during collision will be.   

(b) in the following example the momentum is not conserved. 1. coin sliding on a table experiences a friction force. If you give it some speed and let it go it spontaneously stops. In the theory that takes only the coin into account, the momentum is not conserved. Of course the momentum hasn't disappeared. It went in imperceptible movement of the table, the ground, etc which were neglected.

Fundamentally, momentum conservation is linked to invariance under space translations. See Noether's theorem. If you want to find a system that does not conserve momentum you should look for situations where space is not uniform, e.g. balls rolling on the surface of a bowl, a planetary system (when the dynamics of the sun is neglected), etc.