Math

A bucket that weighs 3.2 pounds and a rope of negligible weight are used to draw water from a well that is 82 feet deep. The bucket is filled with 42 pounds of water and is pulled up at a rate of 2.3 feet per second, but water leaks out of a hole in the bucket at a rate of 0.35 pounds per second. Find the work done pulling the bucket to the top of the well.

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  1. The net mass of the bucket as a function of time, M(t)
    =3.2+42-0.35t
    Work done as a function of time
    = M(t)*2.3 ft/s * 32.2 ft/s^2
    Over the height of the well,
    time required to go to the top
    = 82'/2.3 '/s
    = 82/2.3 s
    Total work done
    = ∫ M(t)*32.2 * 2.3dt from 0 to 82/2.3
    =[45.2t-0.175t²] from 0 to 82/2.3
    = 102872 poundal-ft
    = 3194.8 lbf-ft (after dividing by g)

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  2. what's the 32.2ft/s^2

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  3. Acceleration due to gravity

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