A cable that weighs 2 lb/ft is used to lift 800 lb of coal up a mine shaft 500 ft deep. Find the total work done.

Answer 1

The work required to lift just the coal is 800 x 500 = 400,000 ft lbs

The work required to lift the rope is (500ft)(2lbs/ft)(500 ft/2) = 250,000 ft lbs.

The rope center of mass is raised 500/2 ft. That is the appropriate avg height raised for the total mass of the rope.

Just total the work.

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