Is it possible, knowing the velocities and masses of metal balls after the colli

Question

Is it possible, knowing the velocities and masses of metal balls after the collision to determine,

uniquely what the motion of the objects were prior to the collision?

If not, how much more do you need to know?

Conversely, would you have enough information prior to the collision (knowing both initial

velocities and masses) to definitively determine how the balls will move after the collision?

If not, how much more do you need to know?

Why is this different from what you can tell prior to an inelastic collision?

Explanation / Answer

Is it possible, knowing the velocities and masses of metal balls after the collision to determine, uniquely what the motion of the objects were prior to the collision?

Yes.

Conversely, would you have enough information prior to the collision (knowing both initial velocities and masses) to definitively determine how the balls will move after the collision?

Yes.

Explanation: On elastic collisions, both the momentum and the kinetic energy of the system of two objects are conserved.

So, you have a set of two equations and two unknow variables for both cases.

Why is this different from what you can tell prior to an inelastic collision?

In this case, you need know information before and after collision because the kinetic energy is not conserved and produce that you have a ser of one equation and two unknow variables that it's not possible of resolve .

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