The work done by a winch winding in a 50-meter chain weighing 3 Newtons per meter, in Newton-meters, is

A)4,500
B)4,200
C)3,750
D)3,650
E)3,500

Question

The work done by a winch winding in a 50-meter chain weighing 3 Newtons per meter, in Newton-meters, is
​
A)4,500
B)4,200
C)3,750
D)3,650
E)3,500

Quizplus · Accepted Answer

The work done is calculated by the formula Work = Force x Distance. Here, the force is the weight of the chain, which is 3 Newtons per meter for a 50-meter chain, so the total weight (force) is 3 N/m * 50 m = 150 N. The distance the force is applied over is 50 meters. Therefore, the work done is 150 N * 50 m = 7,500 Nm. However, since the chain is being wound up, it's effectively being lifted half the distance (as the average position of the chain moves from the ground to halfway up as it's wound), so the effective distance is 25 meters, not 50. Thus, the work done is 150 N * 25 m = 3,750 Nm.

The Work Done by a Winch Winding in a 50-Meter