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From Stewart CalculusConcepts and Contexts4th edition pg.473 section 6.6 #15...

:A leaky 10-kg bucket is lifted from the ground to a height of 12 meters

at a constant speed with a rope that weighs 0.8kg/m. Initially the bucket contains 36kg of water but the water leaks at a constant rate and finishes draining just as the bucket reaches the 12 meter level. How much work is done

2. Relevant equations

3. The attempt at a solution

I am able to do these kind of problems, but the only thing different about this one is the weight is constantly changing. The total weight of the water/bucket/rope initially is 55.6 kg, and at the end its just the 10 kg bucket left.

I dont know how to approach the change in weight of the water leaking out of the bucket. So far I think you integrate from 0-12 meters, and the distance an arbitrary part of the rope has to travel is 12-x. Any hints?

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# Homework Help: Calc II word problem(work needed to lift a leaky bucket)

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