Can Kinetic Energy Always Be Conserved in Elastic Collisions?

[v_pino]

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 explanation 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

 

[Doc Al]

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.

 

[v_pino]

Hi DocAl

Thanks for the reply.

But if we take the situation of two balls of equal mass, mass B is stationary and mass A travels at velocity V. So after the collision mass A will become stationary and Mass B will travel with velocity V. Here, both momentum and kinetic energy are conserved- it is an elastic collision.

Would I be able to do this? (attachment)

 

[Doc Al]

So after the collision mass A will become stationary and Mass B will travel with velocity V.

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 $V_2 = U_1$.)