Which Has More Momentum and Kinetic Energy After a Perfectly Elastic Collision?

[goonking]

Homework Statement

A marble with mass M rolls into a bowling ball with mass 100M, assuming the collision is perfectly elastic, which object would have higher momentum? higher Kinetic energy?

Homework Equations

The Attempt at a Solution

First of all, what's the difference between an elastic and PERFECTLY elastic collision? aren't they both defined as one in which there is no loss of kinetic energy in the collision?

So, the marble should bounce back and have a negative Velocity, therefore negative momentum, which means the momentum of the bowling ball should be higher even if it doesn't move (but it should, just barely).

This is where I'm stumped. should the KE of the marble be equal to that of the bowling ball? I imagine the bowling ball having an extremely small velocity to make up for the extreme difference in mass.

 

[Doc Al]

First of all, what's the difference between an elastic and PERFECTLY elastic collision? aren't they both defined as one in which there is no loss of kinetic energy in the collision?

Yes, saying perfectly elastic collision is a bit redundant. (But clear!)

How can you express that mathematically, so you can figure out the final speeds, momentum, and kinetic energy?