Perfectly elastic collision

  1. 1. The problem statement, all variables and given/known data
    In an isolated system, cart1 (with mass = 1 kg and vi1 = 2) has a perfectly elastic collision with cart2 (with mass = 2 kg and vi2 = 0). Find the velocity of cart1 and the velocity of cart2 after the collision.
    I have to solve this using kinetic energy and momentum equations.


    2. Relevant equations
    m1vi1 + m2vi2 = m1v1f + m2v2f
    1/2m1vi12 + 1/2m2vi22 = 1/2m1v1f2 + 1/2m2v2f2


    3. The attempt at a solution
    I have gotten to this point:
    2= V1F + 2V2F
    4= V1F2 + 2V2F

    but I cannot get the numbers to work out correctly.
    Using another equation I know that V1f = 2/3 and V2f = 4/3

    I am doing substitution wrong or something.
    Please help!!
     
  2. jcsd
  3. Doc Al

    Staff: Mentor

    This makes sense.
    How did you get this?
     
  4. I got that by solving the kinetic energy equation.
    I mutiplied both sides by 2 to get rid of the halves.

    It is actually supposed to read:

    4 = Vif^2 + 2V2f^2
     
  5. Doc Al

    Staff: Mentor

    That's good.

    Take the first equation and solve for one of your variables. Then substitute that into the second equation. Solve the quadratic.
     
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