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A 600 lb cable is 100 ft long and hangs vertically from the top of...

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Calculus

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A 600 lb cable is 100 ft long and hangs vertically from the top of a tall building a How much work is required to lift the cable to the top of the building b How much work is required to pull up only 30 feet of the cable Solution W a Here we don t have a formula for the force function but we can use an argument similar to the one that led to the definition of work Let s place the origin at the top of the building and the x axis pointing downward as in the following figure 0 x7 100 We divide the cable into small parts with length Ax If x is a point in the ith such interval then all points in the interval are lifted by approximately the same amount namely x The cable weighs 6Ax Thus the work done on the ith part in foot pounds is 6x Ax 6Ax x distance force We get the total work done by adding all these approximations and letting the number of parts become large so Ax 0 W lim 515 Ar ax 7 1 6x Ax pounds per foot

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