An elevator system in a tall building consists of a800-kg car and a 950-kg counterweight

Chapter 10, Problem 68

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An elevator system in a tall building consists of a800-kg car and a 950-kg counterweight joined by a lightcable of constant length that passes over a pulley ofmass 280 kg. The pulley, called a sheave, is a solid cylinderof radius 0.700 m turning on a horizontal axle. Thecable does not slip on the sheave. A number n of people,each of mass 80.0 kg, are riding in the elevator car,moving upward at 3.00 m/s and approaching the floorwhere the car should stop. As an energy-conservationmeasure, a computer disconnects the elevator motorat just the right moment so that the sheavecarcounterweight system then coasts freely without frictionand comes to rest at the floor desired. There it iscaught by a simple latch rather than by a massive brake.(a) Determine the distance d the car coasts upward asa function of n. Evaluate the distance for (b) n 5 2,(c) n 5 12, and (d) n 5 0. (e) For what integer valuesof n does the expression in part (a) apply? (f) Explainyour answer to part (e). (g) If an infinite number ofpeople could fit on the elevator, what is the value of d ?