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Math Help - work problem

  1. #1
    Junior Member
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    work problem

    a piano weighing 200 pounds to lifted from the ground level to the roof of a 60 ft building using a chaining weighing pounds per ft. find the work done

    so i know that W=Fd and that d=60. and i think that F=(200)(2), is that correct, or does gravity come into play?
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  2. #2
    Senior Member
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    Use the change in potential energy to find the work done.
    W = \Delta E = \Delta T + \Delta U

    In this case
    W = U_f - U_i

    Remember you need to take into account the potential energy change in the chain also (use integration).
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  3. #3
    MHF Contributor

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    The weight is the force necessary to lift it- 200, not 2(200). Of course, work= force times distance so the work necessary to lift just the piano is 200(60)= 12000 foot-pounds.

    But you must add to that the work necessary to lift the chain- and only the weight of the chain below the roof. To start off, you must lift 60 feet of chain but by the time the chain is completely on the roof, you are lifting only the piano. Since the length of chain is changing continuously, you will need an integral to find the work done lifting the chain: if, at some point the piano is at height x, there are 60- x feet of chain still to be lifted. To lift that a short distance, \Delta x, you must do work \delta (60- x)\Delta x. To lift the entire chain its entire length, sum over different x: \delta \sum (60- x)\Delta x. That is a "Riemann sum" and as \Delta x goes to 0, it becomes the integral \delta\int_0^{60}(60- x)dx. " \delta" is the density of the chain in pounds per foot but you seem to have left that out of your post.
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