# Velocity when two object collide in an elastic collision

When two objects collide in an elastic collision, aren't there an infinite number of possible velocities that the objects can gain? Let's consider two objects each of mass 1kg. One of them is moving at 1 ms-1 and the other is stationary.
After the collision, the first object (the one which was moving) could come to rest and the other object could start moving at 1 ms-1.
That's one scenario in which the 1st object transfers all it's kinetic energy to the other object.

Couldn't the first object keep some of it's energy and only transfer a fraction of it's total KE to the other object? (In which case both objects would be moving after the collision). If that happens, then couldn't there be a several pairs of values for the velocity of Object 1 and object 2 which would comply with the conservation of momentum and the conservation of kinetic energy? How can we determine which one of these combinations of velocities will occur ?

tiny-tim
Homework Helper
Hi mahela007!
… If that happens, then couldn't there be a several pairs of values for the velocity of Object 1 and object 2 which would comply with the conservation of momentum and the conservation of kinetic energy? How can we determine which one of these combinations of velocities will occur ?

No, conservation of both energy and momentum always gives a unique answer.

Try it and see.

Saw
Gold Member
We have been discussing more or less about this in the thread "Acceleration in an elastic collision", which you may want to look at for more detail. Conservation of momentum alone does allow for many final velocities. But, as tiny-tim implied, if you stipulate that the collision is perfectly elastic, that is to say, if all kinetic energy is conserved in the system, then there is only one possible solution. In particular, it's one complying with the requirement that the relative velocity of approach (before collision) = the relative velocity of separation (after collision).

Hm... Ok.. I'll check that and post back.