Question

A bucket weighing 5 lbs is lifted at a constant rate from the bottom of a 100 ft well by a rope which weighs 5 lbs. The bucket has a small hole in it so that water leaks out at a constant rate. Initially, the bucket contains 30 lbs of water, but has only 25 lbs of water when it reaches the top of the well. What is the work done to raise the bucket of water to the top of the well

Answer 1

Answer:

$W_{bucket} = 24934.85\,lbf\cdot ft$

Explanation:

The system is modelled after the Principle of Energy Conservation and the Work-Energy Theorem:

$W_{bucket} = U_{g,B, bucket} - U_{g,A,bucket} +U_{g, B, water}-U_{g,A,water} +U_{g, B, rope} -U_{g,A,rope}$

$W_{bucket} = (5\,lb) (32.174\,\frac{ft}{s^{2}})\cdot (100\,ft-0\,ft) + (25\,lb)\cdot (32.174\,\frac{ft}{s^{2}})\cdot (100\,ft) - (30\,lb)\cdot (32.174\,\frac{ft}{s^{2}})\cdot (0\,ft)+(5\,lb) (32.174\,\frac{ft}{s^{2}})\cdot (100\,ft-50\,ft)$

$W_{bucket} = 24934.85\,lbf\cdot ft$