An elevator system in a tall building consists of a 800-kg carand a 950-kg counterweight joined by a light cable of constantlength that passes over a pulley of mass 280 kg. The pulley, calleda sheave, is a solid cylinder of radius 0.700 m turning on ahorizontal axle. The cable does not slip on the sheave. A number nof people, each of mass 80.0 kg, are riding in the elevator car,moving upward at 3.00 m/s and approaching the floor where the carshould stop. As an energy-conservation measure, a computerdisconnects the elevator motor at just the right moment so that thesheave–car– counterweight system then coasts freely withoutfriction and comes to rest at the floor desired. There it is caughtby a simple latch rather than by a massive brake. (a) Determine thedistance d the car coasts upward as a function of n. Evaluate thedistance for (b) n = 2, (c) n = 12, and (d) n = 0. (e) For whatinteger values of n does the expression in part (a) apply? (f)Explain your answer to part (e). (g) If an infinite number ofpeople could fit on the elevator, what is the value of d ?
