# A chain lying on the ground is 10 meters long and its mass is 80 kilograms. The chain is threaded...

## Question:

A chain lying on the ground is 10 meters long and its mass is 80 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 8 meters? Use that the acceleration due to gravity is 9.8 {eq}m/s^2. {/eq} You may assume that the chain slides effortlessly and without friction along the ground as its end is lifted. Your answer must include the correct units.

## Force as a function of distance

The amount of force needed to be exerted on a heavy long chain lying on the ground increases as the length of the lifted chain increases. The force needs to compensate the increasing weight of the chain since the chain varies with the displacement. We could say that the force exerted is a function of the displaced length of chain since the density or the mass per length of chain is constant.

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Given :

• {eq}\displaystyle \text{length of chain} = l = 10 \,\mathrm{m} {/eq}
• {eq}\displaystyle \text{mass of chain} = m = 80 \,\mathrm{kg} {/eq}
• {e...

Work as an Integral

from

Chapter 7 / Lesson 9
18K

After watching this video, you will be able to solve calculus problems involving work and explain how that relates to the area under a force-displacement graph. A short quiz will follow.