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The case of the leaky pendulum

  1. Oct 22, 2009 #1
    1. The problem statement, all variables and given/known data
    There is a cubical pendulum with a side of 2a filled with water that is leaking at a constant rate. Determine the period of the pendulum in terms of variables.


    2. Relevant equations
    T = 2π√(l/g)
    v = s³ for a cube
    v = s²h for a rectangle


    3. The attempt at a solution
    v=s²h
    v=4a²h
    The length varies with the new center of mass which is h/2, so l = h/2.
    v=8a²l
    differentiate with respect to time and
    dv/dt = 8a²dl/dt
    dl/dt = 1/(8a²)dv/dt
    to avoid the problem from looking too complicated, let's set dv/dt = r
    li= initial length
    T = 2π√((li-(rt/(8a²)))/g)

    I multiplied by time so that we would be left with the change in length, and I subtracted it because dl/dt is negative, and the length should obviously be increasing. Is this right?
     
  2. jcsd
  3. Oct 22, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper

    It is correct.
     
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