1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Conserved kinetic energy in collisions in different frames

  1. May 10, 2010 #1

    bon

    User Avatar

    1. The problem statement, all variables and given/known data

    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?



    2. Relevant equations



    3. The attempt at a solution

    Not sure what to do...

    thanks
     
  2. jcsd
  3. May 10, 2010 #2

    collinsmark

    User Avatar
    Homework Helper
    Gold Member

    Re: Collisions

    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:
     
  4. May 10, 2010 #3

    bon

    User Avatar

    Re: Collisions

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

    How does this help?

    thanks
     
  5. May 10, 2010 #4

    collinsmark

    User Avatar
    Homework Helper
    Gold Member

    Re: Collisions

    Hello bon,

    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: May 10, 2010
  6. May 11, 2010 #5

    bon

    User Avatar

    Re: Collisions

    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?
     
  7. May 11, 2010 #6

    bon

    User Avatar

    Re: Collisions

    edit: yes that works!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook