One was to write Newton's laws is:
I don't understand what is the force there. I believe that $F$ is the net external force on the system. So supposedly I have a mass which is moving right and then it collides with another mass which is hanging on a rope from the ceiling.
Supposedly my system is the mass, mass on rope and the Earth. This would make forces of gravity internal. The only external force is the tension on rope(assume massless rope). Now, would the tension of the rope be before the collision, or after the collision? The mass on rope swings up obviously. At that particular instant when it is at max angle, the $T$ is obviously not equal to $T$ when before collision. So does the $T= dp/dt$, is the $T$ before or after collision?
Ok edit. In this system the momentum is not conserved right? Since there is a net external force $T$. So I supposed taking ceiling as part of the system would make $T$ an internal force.