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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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3 Answers 3

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

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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