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Math Help - Help learning how to calculate work

  1. #1
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    Help learning how to calculate work

    Hello everyone,

    I can't teach myself to how to solve problems involving work. I've watched many videos, tutorials, and read my textbook many times. I can't get the information to click.

    Here is the problem I am working on:

    A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is 80 ft deep. The bucket is filled with 40 lb of water and is pulled up at a rate of 2 ft/s, but water leaks out of a hole in the bucket at a rate of 0.2 lb/s. Find the work done in pulling the bucket to the top of the well.

    I don't know how/where to start.

    What I have done:

    Total weight = 44 lb
    Total distance is 80 ft and we are suppose to integrate from 0 to 80

    F = (44 - 0.2x)?

    then integrate f fomr 0 to 80?
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Help learning how to calculate work

    Not quite. Be careful with units. The bucket loses 0.2 pounds per second, not per foot, so the equation  W = \int F dx gives  \int (44-0.2t)dx. But now the problem is that we have the variable time inside an integral with dx in feet, so we need to relate time and distance traveled. We know the bucket moves at 2 ft/s, so you have x = 2t, or rearranging: t = 2/x. Now we can sub that into the integral:

     W = \int_0 ^{80} (44 -0.2(\frac x 2))dx

    Hope this helps.
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