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Homework Help: 2D elastic collision

  1. Aug 5, 2016 #1
    1. The problem statement, all variables and given/known data
    A 2D elastic collision:
    Two pucks (masses m1 = 0.5 kg and m2 = 0.3 kg) collide on a frictionless air-hockey table. Puck 1 has an initial velocity of 4 m/s in the positive x direction and a final velocity of 2 m/s in an unknown direction, θ. Puck 2 is initially at rest. Find the final speed of puck 2 and the angles θ and φ.

    I get stuck at the end of this problem when I have to use the two equations to solve for 2 unknown angles. If someone could show me how to do that last step that would be great. Thanks in advance!
    2. Relevant equations

    3. The attempt at a solution
    Since the collision is elastic I found the final kinetic energy using Ei = Ef and it equals 4.47 m/s

    Then conservation of the x and y components of total momentum:

    X DIRECTION: Pi = Pf
    m1v1 + m2v2i = m1v1 + m2v2f
    (0.5)(4) = (0.5)(2cosθ) + (0.3)(4.47cosφ)
    2 = cosθ + 1.341cosφ

    Y DIRECTION: Pi = Pf
    m1v1 + m2v2i = m1v1 + m2v2f
    0 = (O.5)(2sinθ) -(0.3)(4.47sinφ)
    0 = sinθ - 1.341sinφ
  2. jcsd
  3. Aug 5, 2016 #2


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    Hint: cos2θ + sin2θ = 1

    (Your work looks good so far.)
  4. Aug 5, 2016 #3
    So I solve the first equation for cosφ and the second equation for sinφ?
    1.341cosφ = 2-cosθ
    -1.341sinφ = sinθ

    then square each term:
    1.3412cos2φ = 22-cos2θ
    -1.3412sin2φ = sin2θ

    then I added them but I'm still a bit lost/don't know the next step :/

    1.3412cos2φ + (-1.341)2sin2φ = 22-cos2θ + sin2θ
  5. Aug 5, 2016 #4
    Take another look at (2-cosθ)2. It doesn't look right. Also, I thought it might have been a little simpler to solve for sinθ and cosθ, then square, then add the equations and then implement TSny's hint.
  6. Aug 5, 2016 #5


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    Note that (2 - cosθ)2 ≠ 22-cos2θ. In general (a + b)2 ≠ a2 + b2.

    In order to use the trig identity cos2θ + sin2θ = 1, you could solve the first equation for cosθ. You already have an expression for sinθ, except I believe you have a sign error in -1.341sinφ = sinθ.
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