Confusion about nature of collision

[Inspiron]

I have a problem with understanding the nature of collisions and their outcomes.
From my understanding, I come to think that when a mass collides with another, both of them should always have equal velocities post-collision. For example, when a mass moving at v₁, m₁, collides with a mass at rest, m₂, their velocity after collision should always be m₁v₁ / m₁ + m₂. My justification for this is that once they reach that said velocity, they are not colliding anymore, they are moving along together, they have zero kinetic energy, relative to each other. I don't understand how is it that there are cases in which one mass loses it momentum completely to the other mass and other cases in which m₁ may even rebound: how can any change in momentum still occur after they have equal velocities?

I also have problems understanding what governs the magnitude of impulse at collision: is it possible to predict the magnitude of the force and the duration of which the applied force will last? It seems, from all the problems on impulse that I have seen, it's impossible because the problems always have to give some information about the momentum pre and post collision, never only pre collision.

What am I failing to understand?

 

[mfb]

My justification for this is that once they reach that said velocity, they are not colliding anymore

They can be deformed at that point, e.g. compressed in the direction of the collision. They "want" to retain their original shape again, which does not work without moving away from each other - there is still a force between them.

I also have problems understanding what governs the magnitude of impulse at collision: is it possible to predict the magnitude of the force and the duration of which the applied force will last?

Only if you know details about the deformation of the objects.

 

[Inspiron]

I don't clearly understand.

So if two undeformable objects collides with another, will both of them always have equal velocities, as I said? And is there such thing as an undefromable object in the real world?

If two deformable objects collide, do they deform like springs, where kinetic energy is converted fully into potential energy and then into kinetic energy?

What are the details about the deformation should I know, and how is it used?

Thanks in advance.

 

[A.T.]

And is there such thing as an undefromable object in the real world?

No.

 

[OldYat47]

Remember that it's momentum that's conserved in inelastic collisions, not velocity.

The results of any collision between two objects will depend on the characteristics of the two objects. For example, if you stage a collision between a bowling ball and a small lump of sticky clay the two may stick together and have exactly the same velocity post-collision, but decidedly different momenta. Modern automobiles, for example, are designed to collapse so as to absorb energy and reduce momentum on both cars. It's not a simple issue.