Conserved kinetic energy in collisions in different frames

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Homework Help Overview

The discussion revolves around the conservation of kinetic energy in collisions, specifically in the context of non-relativistic frames of reference. The original poster seeks to understand how conservation of kinetic energy in one frame implies it holds in all frames moving with constant velocity.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss starting with the conservation of momentum equation from a stationary frame and modifying it for a moving frame. There are attempts to relate momentum conservation to kinetic energy conservation through algebraic manipulation.

Discussion Status

Some participants have provided guidance on how to approach the problem, suggesting algebraic expansions and substitutions to explore the relationship between momentum and energy conservation. Multiple interpretations of the steps involved are being explored, but there is no explicit consensus on the final approach.

Contextual Notes

There is an emphasis on non-relativistic conditions and the need to consider different frames of reference, which may influence the assumptions being made in the discussion.

bon
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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
 
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bon said:
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. :cool:
 


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

How does this help?

thanks
 


Hello bon,

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

How does this help?

thanks

That's a great start! :approve:

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.]
 
Last edited:


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?
 


edit: yes that works!
 

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