Momentum- elastic collisions

Dear all,

I know the equation to conservation of momentum.
How do I show that kinetic energy is always conserved if it says that the mass of the two objects are the same.

The following is the explaination I found but I don't get part of it.

The red arrow part (attached image) is where I'm stuck on.

Thanks for the help!
pino

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Doc Al
Mentor
It's unclear from the attachment as to what you are trying to do. Every line but the last is just conservation of energy, so I assume you are talking about an elastic collision. The last line looks like you attempted to also apply conservation of momentum. If you keep going you'll get an interesting conclusion for an elastic collision of equal masses where one is initially at rest.

Realize that conservation of momentum and conservation of energy are two different things--you can't use one to show the other.

Hi DocAl

The fact that mass A stops and mass B travels with velocity V is a consequence of momentum and energy conservation. That is what you proved in the attachment. (You assumed energy & momentum conservation and proved that $V_2 = U_1$.)