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Impulse-momentum question

  1. Sep 16, 2009 #1
    1. The problem statement, all variables and given/known data

    A buffer stop at the end of a railway track has a moving part of mass, 2 Mg, which can move 2.3m parallel to the track. The force resisting the motion of the moving part is given by cxdot where xdot is the velocity and c is 200kn/m s

    What is the greatest speed with which a train, of mass 100 Mg, can hit the buffer stop if, at the end of its 2.3m travel is not to exceed 1.5m/s?

    Assume that after impact, the train and the moving part of the buffer stop move together.

    2. Relevant equations




    3. The attempt at a solution

    I started with the impulse momentum equations

    Train: -F t = 100x10^3 (1.5-x) where x is the initial velocity of the train
    Buffer: (F-cxdot) t = 2x10^3 (1.5-0)

    I do not know how to proceed because I have not seen an impulse momentum equation which includes a damper. Please help!
     
    Last edited: Sep 16, 2009
  2. jcsd
  3. Sep 16, 2009 #2
    I've come to the conclusion that the x and xdot are the same thing as the damping force does not apply until after impact. However I also notice that i only have 2 equations and 3 unknowns: xdot, t and F, and so I'm unable to continue, can anyone think of another equation I'm missing?
     
  4. Sep 16, 2009 #3
    Never mind people I got it!

    Okay so what i did was start off with the integral form because the damping force changes over time:

    Train: -Ft = 100 (1.5 - xdot)
    Buffer: Int(F-cxdot) dt = 2(1.5-0) note that the two xdots are not necessarily the same as it changes over time.

    The buffer eqn can reduce to Ft - c Int(xdot)dt = 2(1.5)
    Since Int(xdot)dt = 2.3m, I now only have the initial velocity of the train, xdot, to deal with, and everything cancels out!

    Yay me! :D
     
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