The work done by a winch winding in an 80-foot rope weighing 6 pounds per foot, in foot-pounds, is

A)15,200
B)23,500
C)29,800
D)19,200
E)18,500

Question

The work done by a winch winding in an 80-foot rope weighing 6 pounds per foot, in foot-pounds, is
​
A)15,200
B)23,500
C)29,800
D)19,200
E)18,500

Quizplus · Accepted Answer

The work done is calculated by the formula Work = Force x Distance. Here, the force is the weight of the rope, which is 6 pounds per foot for 80 feet, so the total weight (force) is 6 * 80 = 480 pounds. The distance is the length of the rope, which is 80 feet. Therefore, the work done is 480 pounds * 80 feet = 38,400 foot-pounds. However, since the rope's weight is distributed along its length and effectively halves as it is wound (since on average, half the rope is lifted at any point), the actual work done is half of 38,400, which is 19,200 foot-pounds.

The Work Done by a Winch Winding in an 80-Foot