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Simple Elastic Collision

  1. May 21, 2015 #1
    The problem statement, all variables and given/known data

    An object of mass m1 traveling with velocity v1i has a perfectly elastic collision in which it rear ends and object of mass m2 (m2>>m1) traveling with velocity v2i. How must the velocity v1i relate to v2i if the mass m1 is to stop in its tracks (v1f=0)? What happens if velocity v1i is greater than this? If it is smaller?

    Relevant equations
    KE = .5mv^2
    P = mv

    The attempt at a solution
    Cons Energy
    .5m1v1i^2 + .5m2v2i^2 = .5m2v2f^2

    V2f = sq.rt(( m1v1i^2 + m2v2i^2 )/(m2))

    Cons Momentum
    m1v1i + m2v2i = m2v2f

    V2f = ( m1v1i + m2v2i )/(m2)

    Set equal to each other, but my answer keeps getting more complex? It's a math error, but I'm not sure what it is…

    I get to here:

    (m1^2v1i^2)+(2m1v1im2v2i)+(m2^2v2i^2) = (m1v1i^2)+(m2v2i^2)

    Can anyone help me continue to work this out? I'm frustrated because this is a simple problem but I can't get it.

  2. jcsd
  3. May 21, 2015 #2
    Okay, I think I found my error, I've worked out that v1i = (m2(1 - 2v2i))/(m1), how can I plug this back in to check it? I'm struggling to find a way to do so but I know there must be a way…
  4. May 21, 2015 #3


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    Is there a typo there? 1-velocity is dimensionally invalid.
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