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Perfectly Elastic Collision (Easy, just confusing)

  1. Jul 5, 2011 #1
    1. The problem statement, all variables and given/known data

    Let two particles of collide in a perfectly elastic collision. Particle 1 has a mass of 2m, while particle 2 has a mass of m. Particle 1 has initial velocity v, directed to the right, while particle 2 is at rest. What are the final velocities, v1 and v2, of particle 1 and particle 2?

    2. Relevant equations

    Conservation of Momentum

    m1v1+m2v2=m1v3+m2v4

    Conservation of Energy

    (1/2)mv1^2+(1/2)mv2^2=(1/2)mv3^2+(1/2)mv4^2


    3. The attempt at a solution

    I'm not sure what to do. I've been messing around with stuff, but I can't seem to get the right answer, and I'm running out of answers on my online homework. I know you have to solve in one equation, and then substitute to the other in order to get down to a workable amount of variables, but I'm not entirely sure how. I"m pretty sure the answer has to be in the form of (constant)v, to show the ratio of the initial velocity that each object was left with, and I just don't know how to whittle it down to that.
     
  2. jcsd
  3. Jul 5, 2011 #2
    v1 and v2 are already given. You have two equations in two variables. Solve it. To make it simpler you can also use the equation from restitution instead of energy. :wink:
     
  4. Jul 5, 2011 #3
    See, I thought it would be straightforward, but I'm getting a very weird answer, with a lot of square roots and such. My answer for V4, which is the velocity of the second object after the collision, was:

    sqrt(v)*sqrt(sqrt(v^2-2)+v)

    When it should be some nice number like 1/4v.

    I don't understand what I'm doing :-\
     
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