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Elastic Collision between billiard balls

  1. Mar 21, 2012 #1
    1. The problem statement, all variables and given/known data
    Two billiard balls of equal mass undergo a perfectly elastic head on collision. If one ball's initial speed was 2.00 m/s, and the other's was 3.00 m/s in the opposite direction, what will their speeds be after the collision?

    Va = 2 m/s
    Vb = 3 m/s



    2. Relevant equations
    MaVa + MbVb = MaVa' + MbVb'
    1/2MaVa^2 + 1/2MbVb^2 = 1/2MaVa'^2 + 1/2MbVb'^2


    3. The attempt at a solution
    Let right be positive.

    MaVa + MbVb = MaVa' + MbVb'
    Va + Vb = Va' + Vb'
    2 - 3 = Va' + Vb'
    Va' = -1 - Vb'

    1/2MaVa^2 + 1/2MbVb^2 = 1/2MaVa'^2 + 1/2MbVb'^2
    Va^2 + Vb^2 = Va'^2 + Vb'^2
    4 + 9 = (1-Vb')^2 + Vb'^2
    0 = -13 + 1 + 2Vb' + Vb'^2 + Vb'^2
    0 = 2Vb'^2 + 2Vb' - 12
    0 = Vb'^2 + Vb' - 6
    0 = (Vb' + 3)(Vb' - 2)
    Vb' = -3 or Vb' = 2

    I can figure this out, but I'm not sure which answer to choose and also for future questions how I know which to choose.

    If Vb' = -3:

    Va' = -1 - Vb'
    Va' = -1 - (-3)
    Va' = 2

    If Vb' = 2:

    Va' = -1 - Vb'
    Va' = -1 - 2
    Va' = -3
     
  2. jcsd
  3. Mar 21, 2012 #2
    Compare the final answers to your initial conditions.

    What did you state Va and Vb to be?
     
  4. Mar 21, 2012 #3
    Well Va was 2m/s and Vb was -3 m/s

    If they're colliding head on would they be pushed back directly in the opposite direction, making

    Vb' = 2 m/s and Va' = -3 m/s?
     
  5. Mar 21, 2012 #4

    PeterO

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    Homework Helper

    Your duplicate answers arise since it was arbitrary which ball you chose as A and which as B - and which one was travelling in the positive direction.

    Work the problem with Va = 2 and Vb = -3 initially, then Vb = 2 and Va = -3, then Va = -2 and Vb = 3 and finally Vb = -2 and Va = 3 and you will get seemingly different answers, which when interpretted to the situation mean the same thing.

    It is a head on collision, so call the original motion Left and Right [one of those directions you will have to call one of those positive and the other negative for maths - it doesn't like left and right.

    Once you interpret your answer you will find that the ball originally doing 2 will be travelling at 3 in the opposite direction to its original, and the ball doing 3 will be travelling at 2 in the opposite direction to its original, regardless of which ball you called A, and which direction you defined as positive.
     
  6. Mar 21, 2012 #5
    Okay, I got it, thanks, now I have another question :/
    New topic ><

    I don't find the questions hard just my answers aren't really matching up with teachers so I must be doing something wrong
     
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