# Object collisions: momentum and force

2 semi-related questions:
1)If momentum is conserved in a system of 2 objects colliding and we are aware of their masses and initial velocities, let's say object 1 is moving at a certain velocity towards object 2 at rest, is there any way to solve for their final velocities without knowing one of their final velocities? I know you can solve for this in a perfectly inelastic collision but how about in an elastic or inelastic collision? If not can this be explained by forces?

2) if object 1 was initially at rest and an a certain amount of force acted on it for a brief moment but then subsides, setting object 1 at a constant velocity on a collision course with object 2 (at rest) and after the collision object 2 has the same momentum as object 1 at a constant velocity before the collision (object 1 comes to rest after) will the given force on object 1 be equal to the magnitude of the force on object 2 in the collision?

## Answers and Replies

Formula: vf=vi^2-2ad

Vf= Final velocity
Vi= Initial velocity
A= Acceleration
D= Distance

That's a kinematic equation for a single object, I don't think that was what I was looking for

sophiecentaur
Science Advisor
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2020 Award
If you really want to analyse an inelastic collision, then it may be necessary to examine what happens to the shape of the objects involved during the collision. If you know the details of the shapes and the materials involved, you can estimate the amount of energy lost during the collision. It isn't easy because the forces, during the collision will vary (Hookes Law ideas - but worse- relating deformation to force) This will give you the change in momentum (integrating the elemental Impulses dP in terms of Force and Time). In most problems you try to lump it all together as a single Impulse and ignore the details. The intermediate step of using Coefficient of Restitution is often used.

Many inelastic collisions are analysed, using the 'COR (beloved of A Level Mechanics) which is the ratio of parting velocity to approach velocity. That assumes linearity, of course, but it's a good start with bouncing balls problems. Look at the Wiki article on COR and, if you want to look further then there are several references at the end.
You can always rely on Conservation of Momentum and then include the Coeff of Restitution in the equation describing the relative velocities. That will give you the loss on energy.
It all depends upon how involved you want to get and how easy you find the Maths.