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Elastic collision of 3 balls

  1. Oct 31, 2013 #1
    1. The problem statement, all variables and given/known data
    A ball with an initial speed of v1 = 21.5 m/s collides elastically with two identical balls whose centers are on a line perpendicular to the initial velocity and that are initially in contact with each other. The first ball is aimed directly at the contact point and all motion is frictionless.
    >What is the speed of ball 1 after the collision?
    >What is the speed of ball 2 after the collision?


    2. Relevant equations
    m1v1i + m2v2i = m1v1fcos(θ) + m2v2fcos(θ)
    KE = 1/2 mv12 + 1/2 mv22


    3. The attempt at a solution
    So I know that the velocities have two components, x and y. I also know that at the collision point, the angle of the centers of mass are 30° (since the balls form an equilateral triangle).
    For the x-component, I tried using the conservation of momentum equation above with cos(30°) and using the KE equation to substitute for unknown values of v1 and v2.
    For the y-component I tried doing the same, but since the original velocity in the y-component is 0, I used
    0 = m1v1sin(θ) + m2v2sin(30). For θ I tried 30, 60, and 180, but none of them worked.
    Now I'm a bit stuck and I'm getting confused from all the variables I'm trying here. Any direction is appreciated!
     
  2. jcsd
  3. Oct 31, 2013 #2

    tiny-tim

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    hi baubletop! :smile:

    what directions are you assuming for the three balls after the collision? :wink:
     
  4. Oct 31, 2013 #3
    Should the first one go backwards since it's an elastic collision?
     
  5. Oct 31, 2013 #4

    tiny-tim

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    i'm not worried about backwards or forwards, just the line :wink:

    (and now i'm off to bed :zzz:)
     
  6. Oct 31, 2013 #5
    This is the diagram that came with the problem:
    prob04a.gif

    So the first ball would go forward, and the other two would move outwards 30° from that straight line, right?
     
  7. Nov 1, 2013 #6

    tiny-tim

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    (just got up :zzz:)
    (forwards or backwards)

    yup! :smile:

    ok, now do components of momentum in the forwards direction, and energy :wink:
     
  8. Apr 21, 2014 #7
    I have exactly the same problem.
    Can someone please explain and solve this? Please?

    (baubletop have you ever solve this?)

    Many thanks.
     
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