An elevator system in a tall building consists of an (800kg) car and a (950kg) counterweight joined by a light cable of constant length that passes over a pulley of mass (280kg). The pulley, called a sheave, is a solid cylinder of radius (0.7m), turning on a horizontal axle. The cable does not slip on the sheave. A number of (n) people, each of mass (80kg), are riding in the elevator car, moving upward at (300m/s) and approaching the floor where the car should stop. As an energy-conservation measure, a computer disconnects the elevator motor at just the right moment so that the sheave-car-counterweight system then coasts freely without friction and comes to rest at the floor desired. There it is caught by a simple latch rather than by a massive brake.

a. Determine the distance (d) the car coasts upward as a function of (n)

b. Evaluate the distance for [b] n=2 [c] n=12 [d] n=0

c. For what integer values of (n) does the expression in [a] apply?

d. Explain your answer for part [e].

e. If an infinite number of people could fit on the elevator, what is the value of distance (d)?