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Homework Help: Sliding Chain through Hole

  1. Feb 8, 2013 #1
    1. The problem statement, all variables and given/known data
    A flexible chain of mass M and length L lies on a frictionless table, with a very short portion of its length L0 hanging through a hole. Initially the chain is at rest. Find a general equation for y(t), the length of chain through the hole, as a function of time. (Hint: Use conservation of energy. The answer has the form y(t) = Ae^(γt) + Be^(-γt) where γ is a constant.) Calculate the time when 1/2 of the chain has gone through the hole. Data: M = 1.4 kg; L = 2.6 m; L0 = 0.3 m.

    2. Relevant equations

    3. The attempt at a solution
    This problem has been asked before, and I've worked through it, but I can't seem to get it right. I've solved the position function to be:
    x(t) = (x0/2)e^(√(g/l)t) + (x0/2)e^(-√(g/l)t)

    which can then be solved for t to get:
    t = √(L/g)*arcosh((L-x0)/x0)

    Since I want the time when half the chain has gone though, I solve using L = 1.3 m, but I can't seem to get it. Any help on where I've gone wrong would be appreciated.
  2. jcsd
  3. Feb 8, 2013 #2


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    Homework Helper
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    2017 Award

    Shouldn't the variable x appear on the right hand side of your equation for t? You might double check how you got the expression for t.
    Doesn't L denote the total length of the chain? So, you aren't free to let it be 1.3 m.
  4. Feb 8, 2013 #3
    I realized where I went wrong, I had solved for the time t when the entire chain had fallen over the side, so I went back and solved for when x(t) = L/2. Thank you for your help.
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