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Object falling with non-constant gravity

  1. Sep 15, 2012 #1
    The exact problem reads: The acceleration of gravity g is a constant only for a limited
    range of height differences. A better approximation, one that
    might hold over a larger range of height differences, is that g decreases
    linearly with height, g = go - hg', where h is the
    height measured from the ground surface and s' is a (small) constant
    of the appropriate dimensions. (a) Find the speed of a
    dropped object as a function of height assuming it was dropped
    starting from rest from a height ho. (b) Find the speed of
    a dropped object as a function of time assuming it was dropped
    starting from rest from a height ho.

    What I've tried to do so far for part a was to integrate acceleration in terms of h. I'm not sure if that is even allowed, but I ended up getting v = g0h - 0.5g'h^2

    Then on part b, I more or less got stuck trying to get a formula for h in terms of t, and I'm not quite sure where to start.

    I may just be thinking about this incorrectly, so any input on the best method for starting this problem would be welcome.
     
  2. jcsd
  3. Sep 16, 2012 #2

    rl.bhat

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    Homework Helper

    At any instant, acceleration is given as
    g = dv/dt= dv/dh*dh/dt = v*dv/dh = go - hg'
    Now find the integration to find v in terms of h.
    Now g = go - hg' = go + ( ho - 1/2*gt2)g'
    Collect the terms containing g and write g = ......
    Then write g = dv/dt and find the integration to find v in terms of t.
     
    Last edited: Sep 16, 2012
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