Elastic collision conceptual problem

[alingy2]

Hello,

My textbook says that if two equal masses, with the second one of them at rest initially, collide in an elastic collision. The first mass will stop and the second one will have the initial speed of the first mass.

WHY? This makes no sense to me. Elastic collision only means momentum + energy is conserved.

Why can't the first ball rebound?

 

[AlephZero]

WHY? This makes no sense to me. Elastic collision only means momentum + energy is conserved.

Why can't the first ball rebound?

Because if you work out the math, conserving energy and momentum, the answer is that first ball doesn't rebound. If you don't believe it, play with one of these toys: http://en.wikipedia.org/wiki/Newton's_cradle.

If you know about relative velocities, the math is very easy. Suppose the velocities before the collision are v and 0. Now, imagine you are moving with velocity v2. You see the balls approaching each other with velocities +v/2 and -v/2. When they bounce, conserving energy and momentum, they have velocities -v/2 and +v/2. In other words, the two velocities "swap over". Relative to the ground, the first ball stops and the second one moves with velocity v.

This is only true if the two masses are equal. If the moving ball is lighter than the other one, it will rebound back. If it is heavier, both balls will be moving forwards after the collision.