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Question:

Work calculus 2 help?

A 1300-lb wrecking ball hangs from a 20-ft cable with mass density 11 lb/ft3 attached to a craneCalculate the work done if the crane lifts the ball from the ground level to 20 ft in the air by drawing in the cable.

Answer:

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11 lb/ft3 referring to a cable is a bit confusingI can answer only if I assume it's 11 lb/ft so that the total mass of the cable is 1120 220 lb (but not relevant) When the ball has been lifted a distance of x ft, the length of cable still to be raised is (20-x) ft which has a mass 11(20 - x) lb Hence the total weight to be lifted at this point is (1300 + 11(20-x))g poundal (1520 - 11x)g poundal If x is increased by a small amount dx the work done (in ft poundal) is g(1520 - 11x) dx Hence the total work done in raising the ball through 20 ft is g ∫ (1520 - 11x) dx g(1520x - 11x?/2 from 0 to 20 g(3040 - 2200) 840g From memory, I think the value of g is 32, but I've been metric for 35 years and will have to leave you to fix up the unitsAll the best.

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