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Collision in a free fall

  1. Oct 5, 2013 #1
    1. The problem statement, all variables and given/known data
    A ball A is dropped from the top of a building of height h and simultaneously a ball B is thrown upwards and both balls collide. After the collision the ball A has the double the velocity of ball B
    Determine the fraction of the building where the balls collide.


    2. Relevant equations
    mA.VA+mB.VB=mA.2V'+mB.V'
    VA=-g.t
    VB=Vo-g.t

    3. The attempt at a solution
    I tried with conservation of momentum, conservation of energy, but I can't get rid of the masses, they are always there and can't get them out of the equations, so I can't finish the problem.
    Is there a special case when an object gets the double of the other's object velocity after a collision? I looked for it but I didn't find anything


    PS: The answer is a fraction (obviously) but there are only numbers in it, so that's the reason I put it here and not in the Advanced Physics Homework.


    Thanks in advance.
     
  2. jcsd
  3. Oct 5, 2013 #2

    haruspex

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    I think you have to assume the masses are the same. You are already assuming work is conserved, which seems the greater assumption, but I think you need that too.
     
  4. Oct 5, 2013 #3
    Are you sure about that? Then the problem will state that "An equal ball B is thrown simultaneously" but I'll try that out and see where it takes me. Thanks.
     
  5. Oct 6, 2013 #4

    haruspex

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    I analysed the number of unknowns and number of equations, and it seemed to you needed to assume both conservation of work and equal masses. On that basis i obtained a solution, and it appears entirely consistent.
     
  6. Oct 6, 2013 #5
    Can you tell me which equations you used? I can't conclude the problem yet.
     
  7. Oct 7, 2013 #6
    How about initial speed of B? Will the result be independent of it, even assuming equal mass and elastic collision?
     
  8. Oct 7, 2013 #7

    haruspex

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    In this problem, no specific values emerge for anything - it's all a matter of ratios. There are specific ratios between all the speeds. If the speeds before collision are vA down and vB up, and the speeds after collision wA up and wB down, you are given wA = 2*wB. It follows from conservation laws and equal masses that 2*vA = vB. you will also find that the initial upward speed of B is 3*wB.
     
  9. Oct 7, 2013 #8
    Are you saying that you determined the fraction of the building's height with just the given data?
    What is this fraction?
     
  10. Oct 7, 2013 #9
    I got it. Thank you haruspex!

    @Nasu: If you care the answer is
    1/3 from the top or 2/3 from the bottom
     
  11. Oct 7, 2013 #10
    So there is only one initial speed that satisfies the conditions. Nice.:smile:
     
  12. Oct 8, 2013 #11

    haruspex

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    Hmm... I got 1/6 from the top.
     
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