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Collision Question problem with question itself!

  1. Mar 12, 2006 #1
    This is a problem that though I've solved has had me racking my brains trying to figure out whether or whether not I actually understand what I'm doing..here goes:

    Particles A and B have mass m and are moving in the same direction along a line, A with speed 3u and B with speed u. They collide and after the impact they both move in the same direction, A with speed u and B with speed ku. The coefficient of restitution is e

    a) show that e = (k-1)/2
    b) Deduce that 1 =< k =< 3
    c) Find the loss in kinetic energy in terms of m, k, and u.

    As I said above...reaching the answers to these questions is not the problem...the bit thats bothering me is that before getting to the bit where I could solve part a) I had come to the conclusion that k can only = 3. My reasoning is as follows:

    The total momentum of the system before impact is 3mu + mu, and given that I know the momentum of A after impact (mu) I can say that:
    mu + kmu = 4mu...k = 3...the other way I look at it is as follows:

    B imparts an impulse on A that changes it's velocity from being 3mu to mu, in doing this A must impart the same impulse to B such that:
    -(mu - 3mu) = (kmu - mu)...k still = 3 (the minus sign is because J acts in different directions)

    The question implies however that e and k are not already determined and can take any value beween 0,1... 1,3 respectively.
    The only conclusion that I can reach however is that this is wrong and that given the mass of both objects, their initial speeds and either the value of e or just the speed of either A or B any other values are forced...this question stated otherwise :frown:
    Last edited: Mar 12, 2006
  2. jcsd
  3. Mar 12, 2006 #2

    Doc Al

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    Staff: Mentor

    Your thinking seems correct to me. The problem--as stated--makes no sense. Since you are given the final velocity of one of the masses, all else is determined.
  4. Mar 12, 2006 #3
    ah cheers for backing me up Doc Al...I've spent too long torturing myself over this one :smile: (The question I have stated is quoted word for word from the book (forgot the period at the end of the paragraph though :smile: ))
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