An elevator system in a tall building consists of a 800 kg car and 950 kg counte

Question

An elevator system in a tall building consists of a 800 kg car and 950 kg counterweight joined by a light cable of constant length that passes over a pulley of mass 280 kg. The pulley, called a sheave, is a solid cylinder of radius 0.700 m turning on a horizontal axel. The cable des 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 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 upwards as a function of n. Evaluate the distance for (b) n = 2, (c) n = 12, and (d) n = 0. (e) For what integer values of n does the expression in part (a) apply? (f) Explain your answer to part (e). (g) If an infinite number of people could fit on the elevator, what is the value of d?

Explanation / Answer

1. Calculate the totalinertiaof the system (it is a function of n).
2. Then calculate the total force pulling down thecar(it is only positive for n=2,3,...)
3. Now you know the force and the mass, you can find the distance traveled using: energy = Fs = 1/2 mv^2 where F is the net gravitational force and v is the speed of the car at some point, and s is the distance traveled while the force is F. m is the inertia you calculated in part 1.

For part 1, you need to get an expression for the pulley: not all of the pulley mass adds to the system. However, all of the counterweight and all of the car and the people contribute to the inertia.
For part 2, just use F=mg with different masses.

Hope this helps you get started on the problem. I guess the solid cylinder pulley is the hardest part. I'd compute the effective mass through integration, but perhaps they gave you some other formulas to work with?

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