Question

A chain lying on the ground is 11 meters long and its mass is 95 kilograms. The chain is threaded through a pulley, which is fixed to the ground, and pulled directly up so that it forms the shape of an L. How much work is required to raise one end of the chain to a height of 7 meters?

Answer 1

Answer: 296.1 J or 6.98 kJ

Explanation:

Given

Length of chain, l = 11 m

Mass of chain, m = 95 kg

It is worthy of note that chain has two ends. So this depends which of the two ends should end up at

the given height of 7 m.

Scenario 1. If it is the leading end:

Weight of chain raised

W = mg/l

W = 9.8×95/11

W = 84.6 N

Height raised = ½ m (which is the height of the centre of gravity of the raised portion).

Work done = 84.6 × 1/2 * 7 = 296.1 Joules

Scenario 2. If it is the trailing end:

Weight of chain raised = 9.8×95 = 931 N.

Height raised (average) = 12.5 m (5.5 m for the chain midpoint + 7 m off the ground)

Work done = 931 × 7.5 = 6.98 kJoules

Thus, the work required is either of 296.1 J or 6.98 kJ