- #1

Alettix

- 177

- 11

## Homework Statement

There are two elastic "superballs" of mass M and m placed on top of each other with a smal distance. The lighter ball of mass m is on top of the bigger ball of mass M. The balls are released from a height h and have velocity u when they hit the ground. Prove that the top ball will have velocity ## v = \frac{3M-m}{M+m} \cdot u ## when it leaves the bigger ball.

## Homework Equations

momentum conservation ## p_{before} = p_{after} ##

energy conservation ##E_{before} = E_{after} ##

zero momentum frame velocity: ##v_{ZMF} = \frac{p_{tot}}{m_tot} ##

## The Attempt at a Solution

I didn't find it problematic to prove the requried result (see attached solution). What I find problematic is the result itself. I must have made some very silly misstake in my reasoning, but the end result I get is that the speed of the top ball after all collisions is ## u + 2v_{ZMF}## and of the bottom ball ##u##. However, before the two balls collide, they both had velocity ##u##. Clearly, energy conservation cannot be satisfied!

Can somebody please point out my probably very stupid misstake to me? Thank you! :)