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Consider a 30-foot chain that weighs 4 pounds per foot hanging from a winch 30 feet above ground level. Find the work done by the winch in winding up the entire chain.

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sqdancefan

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Answer:

  1800 ft·lb

Step-by-step explanation:

The weight of the chain is ...

  (4 lb/ft)(30 ft) = 120 lb

The center of mass of the hanging chain is its midpoint, 30/2 = 15 ft below the winch. The work done winding the chain is the work done lifting the center of mass 15 ft to the winch:

  (120 lb)(15 ft) = 1800 ft·lb

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