Conserved kinetic energy in collisions in different frames

[bon]

Homework Statement

How do you show that in the non-relativistic case, if KE is conserved in a collision as viewed in one frame, then it is conserved in all other frames moving with constant velocity?

Homework Equations

The Attempt at a Solution

Not sure what to do...

thanks

 

[collinsmark]

Not sure what to do...
thanks

Perhaps start by stating the equation for (non-relativistic) conservation of momentum as observed from a stationary frame. Then modify that equation such that it represents conservation of momentum from the perspective of a (non-relativistic) moving frame.

Then a little algebra will show you to the light.

 

[bon]

Hmm so m1(u1' + Vcm) + m2(u2' + Vcm) = m1(v1' + Vcm) + m2(v2' + Vcm)

How does this help?

thanks

 

[collinsmark]

Hello bon,

Hmm so m1(u1' + Vcm) + m2(u2' + Vcm) = m1(v1' + Vcm) + m2(v2' + Vcm)

How does this help?

thanks

That's a great start!

Now is where the simple algebra fits in. Multiply m1 and m2 through their factors, and you should see what I mean.

[Edit: What I mean by that is expand the terms on both sides of the equation. See what cancels out.]

 

[bon]

Ok cool so i see m1u1'+m2u2' = m1v1'+m2v2'

i.e. consv of momentum in new frame...Now need to get consv. of energy..

should i subsstitute u1'+Vcm into energy equn and expand?

 

[bon]

edit: yes that works!