Chapter 6.7, Problem 34E

Leaky Bucket A 1-kg bucket resting on the ground contains 3 kg of water. How much work is required to raise the bucket vertically a distance of 10 m if water leaks out of the bucket at a constant rate of $\frac{1}{5}\text{kg}/\text{m}$? Assume the weight of the rope used to raise the bucket is negligible. (Hint: Use the definition of work, $W={\displaystyle {\int }_a^{b}F\left(y\right)}dy$,, where F is the variable force required to lift an object along a vertical line from y = a to y = b.)