A leaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant

Question

A leaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weighs 0.7 kg/m. Initially the bucket contains 45 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15-m level. Find the work done. (Use 9.8 m/s2 for g.)

Thank you!

A leaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weighs 0.7 kg/m. Initially the bucket contains 45 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15-m level. Find the work done. (Use 9.8 m/s2 for g.)

Explanation / Answer

The initial total mass of the bucket is:
m = (10 kg) + (45 kg) = 55 kg

It uniformly looses 45 kg of water over a distance of 15 m, so it looses:
(45 kg) / (15 m) = 3 kg/m

The mass of the bucket as a function of its height is:
m = (55 kg) - (3 kg/m)

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