# A chain 64 meters long whose mass is 20 kilograms is hanging [closed]

A chain 64 meters long whose mass is 20 kilograms is hanging over the edge of a tall building and does not touch the ground. How much work is required to lift the top 3 meters of the chain to the top of the building? Use that the acceleration due to gravity is 9.8 meters per second squared. Your answer must include the correct units.

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## closed as too localized by David Z♦Sep 29 '12 at 23:34

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Hi Ryan, and welcome to Physics Stack Exchange! We don't allow homework-like questions like this where you just ask the question directly; you should narrow it down to focus on a specific physics concept first. See our FAQ and homework policy for more information. – David Z Sep 29 '12 at 23:35

$$W =\int^b_a \! F \, \mathrm{d}x$$

This is the relationship between work and force, you'll need to work out what the force might be. Where a and b are the positions where you are moving from and to against the force.

If you've never done integration before $$\int^b_a \! F \, \mathrm{d}x = [bF - aF]$$

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Since the gravity is uniform and the chain is freely suspended, we just need to consider the change in height and the change in potential energy.

$$W = \Delta P.E. = mg(h_2 - h_1)$$

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The density of the chain is $\rho = \frac{20}{64}$. The amount of work is made with respect to the force $F=mg$, but the mass is changing according how far the chain is lifted.

I think the answer is $\rho g \int_{0}^{3}(64-x)dx$, since the work done (absolute value) is $W= \int_{a}^{b}F.dx$

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