A bucket full of water weighs 5 kg , it is pulled with constant speed from a well 20 m deep. There is a small hole in the bucket through which water leaks at a constant rate of 0 .2 kg m - 1 . Ignore

Question

A bucket full of water weighs 5 kg , it is pulled with constant speed from a well 20 m deep. There is a small hole in the bucket through which water leaks at a constant rate of 0 .2 kg m - 1 . Ignore the force due to leakage. The total work done in pulling the bucket up from the well is g = 10 m s - 2

TestHub · Accepted Answer

The weight of bucket when it has been pulled up a distance $x i s$ (5-0.2 $x) .$ Hence, the required work is

$W = \int_{x = 20}^{x = 0} (5 - 0.2 x) \times 10 \times dx$

$= {[50 x]}_{x = 0}^{x = 20} - {[2 \frac{x^{2}}{2}]}_{x = 0}^{x = 20}$

$W = 50 \times 20 - {(20)}^{2} = 600 J$

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