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Figure 11-31 shows an arrangement of pulleys designed to facilitate the lifting of a heavy load L. Assume that friction can be ignored everywhere and that the pulleys to which the load is attached weigh a total of 20.0 lb. An 840-lb load is to be raised 12.0 ft. (a) What is the minimum applied force F that can lift the load? (b) How much work must be done against gravity in lifting the 840-lb load 12.0 ft? (c) Through what distance must the applied force be exerted to lift the load 12.0 ft? (d) How much work must be done by the applied force F
(a) There are four cords which are attached to the bottom load L. Each supports a tensionF, so to lift the load 4F = (840 lb) + (20:0 lb), or F = 215 lb.(b) The work done against gravity is W = ~F ~s = (840 lb)(12:0 ft) = 10100 ft lb.(c) To lift the load 12 feet each segment of the cord must be shortened by 12 ft; there are foursegments, so the end of the cord must be pulled through a distance of 48.0 ft.(d) The work done by the applied force is W = ~F ~s = (215 lb)(48:0 ft) = 10300 ft lb.
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