A bucket weighs $5 \mathrm { lb }$ and a rope of negligible weight are used to draw water from a well that is 40 $\mathrm { ft }$ deep. The bucket starts with $50 \mathrm { lb }$ of water and is pulled up at a rate of $10 \mathrm { ft } / \mathrm { s }$, but water leaks out of a hole in the bucket at a rate of $0.5 \mathrm { lb } / \mathrm { s }$. Find the work done in pulling the bucket to the top of the well.
A) $2,160 \mathrm { ft } - \mathrm { lb }$
B) $2,660 \mathrm { ft } - \mathrm { lb }$
C) $3,660 \mathrm { ft } - \mathrm { lb }$
D) $2,260 \mathrm { ft } - \mathrm { lb }$
E) $3,160 \mathrm { ft } - \mathrm { lb }$

Question

Quizplus · Accepted Answer

The work done is equal to the force required to lift the bucket and water minus the work done by the leaking water. The force required to lift the bucket and water is:$$F = (5 + 50) lb 	imes 40 ft = 2200 ft - lb$$The work done by the leaking water is:$$W = 0.5 lb/s 	imes 40 ft = 20 ft - lb$$Therefore, the work done in pulling the bucket to the top of the well is:$$W = 2200 ft - lb - 20 ft - lb = 2180 ft - lb$$

A Bucket Weighs 5lb5 \mathrm { lb }5lb And a Rope of Negligible Weight Are Used to Draw

A Bucket Weighs $5 \mathrm { lb }$ And a Rope of Negligible Weight Are Used to Draw