Question

Why can you determine final velocities after collisions when you do NOT know the detailed nature of the force? This was true for the collisions you observed in lab. That is, you don’t know the force as a function of position or time, you’re told nothing about its size. For the same reason that you can (seemingly) magically determine such things as final velocities after jarring collisions, there are certain things you cannot determine. What are examples of things you cannot determine, and remind me why it is you cannot determine them.

Answer 1

It is possible to determine velocities without knowing the exact nature of forces because we consider the colliding masses collectively as a system. When we do so, the internal forces do no matter. The internal forces do not change the total momentum of the system. The external forces are neglected as they are small compared to the high value of force involved during collision. This creates a situation that is very simple to deal with. Considering no external force, the momentum of the system remains conserved.

The force involved is variable and non-linear. It produces deformation in the colliding particles which then reverses just like a spring would do. The time required for collision to happen i.e. the time for which the bodies are in contact cannot be determined without knowing the force. Similarly how the deformation happens in the bodies and how they oscillate like a spring during and after the collisions cannot be determined. Also we cannot determine the variation of velocities of the bodies during collision.