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Simpler equation for perfectly elastic collisions.

  1. Dec 3, 2011 #1
    Perfectly elastic collisions problems usually involve calculating the final velocities of two masses from their initial momenta. Trying to derive such formula I got a different result, a shorter formula to solve the same problem:
    Take two masses a and b with their respective initial volocities;
    First I assumed the velocity of the center of mass to be constant;
    vc=const.
    Then I moved my referential to the mass a. In this referential I assumed that the absolute value of the relative velocites between the mass a and the center of mass to be also constant.
    What I imagined what more or less like this:
    Before the collision I would see the center of mass move towards my referential with a velocity "via-vc". After the collision I would see the center of mass move in the opposite direction with the same speed;
    Based on this what I got was:
    |via-vc|=|vfa-vc|=const.
    via-vc=vc-vfa
    via+vfa=2*vc
    That's it. The oddity is that it uses a rather faster thought, works perfectly and I've never seen before.
    Now you can solve collisions problems with a quicker equation :)
    Did you knew about this equation? Tell me what you think.
     
  2. jcsd
  3. Dec 4, 2011 #2

    Doc Al

    User Avatar

    Staff: Mentor

    That works. Another equation that you may find useful is the following (quoting from our Introductory Physics Formulary entry on Linear Momentum and Collisions):

    Special Case: Elastic Collisions in one dimension:

    For a perfectly elastic straight-line collision, the relative velocity is reversed during the collision:

    [tex]v_1 - v_2 = v_2' - v_1'[/tex]​
     
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