You have a vacation cabin that has a nearby solar (black) water container used t

Question

You have a vacation cabin that has a nearby solar (black) water container used to provide a warm outdoor shower. For a few days last summer, your pump went out and you had to personally haul the water up the 3.9 m from the pond to the tank. Suppose your bucket has a mass of 5.2 kg and holds 14.3 kg of water when it is full. However, the bucket has a hole in it, and as you moved it vertically at a constant speed v, water leaked out at a constant rate. By the time you reached the top, only 5.5 kg of water remained.

I figured out that (a) is 19.8-2.26y. I cannot figure out part (b) please include steps and explanation.

(b) Find the work done by you on the bucket for each 5.5 kg of water delivered to the tank.
W = kJ

Explanation / Answer

mass of the bucket m = (5.5 + 14.3) - ry                                      m = (19.8 kg) - ry    ............. (1) the rate at its losing water is r = dm/dy                                                  r = (14.3 - 5.5)/(3.9 m)                                                   r = 2.26 m substitute these values in eq (1), we get                                  m = (19.8 kg) - (2.26 kg/m)y           ................................................................................................... work W = F.dy                = mg.dy               = mg.dy                = g m.dy   limits : y = 0 m to 3.9 m ................. (2) from eq (2), ................................................................................................... work W = F.dy                = mg.dy               = mg.dy                = g m.dy   limits : y = 0 m to 3.9 m ................. (2) from eq (2),                = g m.dy   limits : y = 0 m to 3.9 m ................. (2) from eq (2), work W = (9.8) [ [(19.8 kg) - (2.26 kg/m)y] dy]   limits : 0 to 3.9 m           W = [(9.8)(19.8) [y] - (9.8)(2.26)[y2/2]]   limits : 0 to 3.9 m            W = [(9.8)(19.8) [3.9] - (9.8)(2.26)[(3.9)2/2]]             W = 588.32 J             W = 0.588 kJ

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