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

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