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Falling chain through a hole.

  1. Jun 16, 2011 #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) = A eγt+ B e−γt where γ is a constant.)
    Calculate the time when 1/2 of the chain has gone through the hole.
    Data: M = 0.7 kg; L = 3.0 m; L0 = 0.5 m.

    2. Relevant equations

    E=U(y)+.5m(dy/dt)^2
    dm=M/L

    3. The attempt at a solution

    U(y)=integral of(-gydm)
    dm=M/L
    then integral of(-g(M/L)ydm)=(-Mg/(2L))(y^2)=U(y)

    then i plug into E(which is constant by conversation of energy)=U(y)+.5M(dy/dt)^2

    don't know where to go from there.
    thanks.
     
  2. jcsd
  3. Jun 16, 2011 #2
    Google "sliding chain brown university"
     
  4. Jun 16, 2011 #3
    Thank you
     
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