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2 dimensional collision confusion

  1. May 5, 2014 #1

    NKC

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    1. The problem statement, all variables and given/known data
    A 2 kg mass with initial velocity v = (5i + 7j) collides perfectly elastically with a 3 kg
    mass with initial velocity v = (-1i -3j) After the collision, the 2kg mass has a speed of
    √50 m/s and the 3 kg mass is traveling at an angle of 329.77Θ as measured from the positive x
    axis. Determine the speed of the 3 kg mass after the collision and the angle of the 2 kg mass
    after the collision (as measured from the positive x axis).
    i and j are the x and y axis respectively.
    2. Relevant equations
    P = MV
    KE = 0.5MV^2
    A*B = XYCosΘ
    3. The attempt at a solution
    Initial:
    KEm1 = 0.5(2)(5i + 7j)^2
    KEm2 = 0.5(3(-1i - 3j)^2
    Pm1 = 2(5i + 7j)
    Pm2 = 3(-1i - 3j)
    Final:
    KEm1 = 0.5(2)(√50)^2 Cosø
    KEm2 = 0.5(3)V^2 Cos(329.77)
    Pm1 = 2(√50)
    Pm2 = 3V
    I know that initial momentum and KE of the system should equal the final momentum and KE of the system, but I can't figure out how to set that up with a 2 dimensional collision. Normally it would be KEi = KEf and Pi = Pf, but with i and j coordinators I can't figure out how to make that work. Should KE and P for the y coordinate and the x coordinate be calculated separately?
     
  2. jcsd
  3. May 5, 2014 #2

    Qube

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    Gold Member

    Yes.
     
  4. May 6, 2014 #3

    NKC

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    Yes to both KE and Momentum? I thought kinetic energy didn't have a direction being a scalar.
     
  5. May 6, 2014 #4

    BvU

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    So you answer your own question. "Should KE and P for the y coordinate and the x coordinate be calculated separately?": Yes on three counts: KE, px and Py.
     
  6. May 6, 2014 #5

    NKC

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    Just to be clear, that leaves me with 3 equations for initial values, and 3 for final values right?
     
  7. May 6, 2014 #6

    BvU

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    Yes. The initial ones have no unknowns, the final ones 2.

    You will have to do something about the final ones: where do the cosines in the KE come from ? And why aren't the P vectors instead of numbers ?
     
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