One kind of elevator has the elevator car hanging from a cable, which then passes over...

One kind of elevator has the elevator car hanging from a cable, which then passes over a pulley and connects to a counterweight. The mass of a fully-loaded elevator (that is, the elevator and all its passengers) is 1850 kg , the mass of the counterweight is 1750 kg , and the pulley has a radius of 0.5 mm and a mass of 450 kg . A motor drives the motion of the elevator by exerting a torque on the pulley. Assume that friction is negligible.

A) What is the magnitude of the torque the motor must exert in order to lift a fully-loaded elevator with a constant acceleration of magnitude 1.0m/s²?

B) What is the magnitude of the torque the motor must exert in order to lower a fully-loaded elevator with a constant acceleration of magnitude 1.0m/s²?

C) A group of people get on a fully-loaded elevator and ride it up three floors (a distance of about 9 meters), where they exit the elevator. If it took 5 seconds for the elevator to travel up those three floors, how much power did the motor need to provide?

D) To see the value of the counterweight, repeat the calculation in Part C if the elevator had no counterweight (or alternatively, if the mass of the counterweight were 0kg).

Solutions

Expert Solution

genius_generous answered 1 year ago

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