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8point1
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Homework Statement
A leaky 6lb bucket is lifted from the ground to a height of 30ft at a constant speed with a rope that weighs .5lb/ft. Initially, the bucket contains 60lbs of water, but the water leaks out at a constant rate and finishes draining just as the bucket reaches the 30ft level. How much total work is done lifting the bucket?
Homework Equations
Function I found for the weight of the rope: (15-.5x)
Function I found for the weight of the bucket: (60-2x)
so adding all together I got = 6 + (15-.5x) + (60-2x) (Δx) (x)
then simplified to get the work function = 81x-2.5x2dx
The Attempt at a Solution
integrated work function 81x-2.5x2 over 0 to 30 and got 13950 ft/lbs total work.
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