a bucket that weighs 4 lb and a rope of negligible weight are used to draw water

Question

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 the 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.

Explanation / Answer

v = 2 ft/s constant h = 80 ft w = 40 lbs The work on the bucket is a function of height--->h dwork = F(h)*dh dwork = weight(h)*dh weight(t) = 40 - 0.2t but t = h/v weight(h) = 40 - 0.2(h/v) --->[40 - 8] = 32 lbs at top work = ? weight(h) * dh work = ?[40 - 0.2(h/v)] dh ft work = ?[40 - 0.1h] dh ft work = 40h - 0.1*0.5*h^2 ft work = 40*80 - (0.1*0.5*80^2) = 3200 ft-lbs

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