Need help with this one please, thank you.

A 400-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 25 feet of the cable? Solution (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. 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 pounds per foot, so the weight of the ith part is 4Ax. Thus the work done on the ith part, in foot-pounds, is (4Ax) . = 4x; Ax force distance We get the total work done by adding all these approximations and letting the number of parts become large (so Ax - 0). W = lim Sax 1 - 004 4x; AX 100 4x dx = ft-lb (b) The work required to move the top 25 ft of cable to the top of the building is computed in the same manner as part (a). W1 = 4x dx = 2x2 ft - 1b Every part of the lower 75 ft of cable moves the same distance, namely 25 ft, so the work done is W2 = lim d 25 distance force = 100 dx =[ ft-lb. (Alternatively, we can observe that the lower 75 ft of cable weighs 75 . 2 = 300 lb and moves uniformly 25 ft, so the work done is 300 . 25 = ft - lb. ) The total work done is Wj + W2 = 1250 + = 8,750 ft-lb