A bucket that weighs 6 lb and a rope of negligible weight are used to draw water from a well that is 80 ft deep. The bucket is filled with 36 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 lb/s. Find the work done W in pulling the bucket to the top of the well.

3200 ft-lb

Step-by-step explanation:

To answer this question, we need to find the force applied by the rope on the bucket at time

At

After seconds, the weight of the bucket is

Since the acceleration of the bucket is the force on the bucket by the rope is equal to the weight of the bucket.

If the upward direction is positive, the displacement after seconds is

Since the well is 80 ft deep, the time to pull out the bucket is

We are now ready to calculate the work done by the rope on the bucket.

Since the displacement and the force are in the same direction, we can write

Use and

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step-by-step explanation: