You are in charge of installing a small food-service elevator (called a dumbwait

Question

You are in charge of installing a small food-service elevator (called a dumbwaiter in the food industry) in a campus cafeteria. The elevator is connected by a pulley system to a motor, as shown in the figure below. The motor raises and lowers the dumbwaiter. The mass of the dumbwaiter is 34 kg. In operation, it moves at a speed of 0.38 m/s upward, without accelerating (except for a brief initial period, which we can neglect, just after the motor is turned on). Electric motors typically have an efficiency of 86%. If you purchase a motor with an efficiency of 86%, what minimum power rating should the motor have? Assume that the pulleys are frictionless.
kW

Explanation / Answer

The work done in one second is F * s, where F = m * g and s is the distance covered in one second. So that work is 34 * 9.8 * 0.38 J/s = 126.616 W With an efficiency of 86%, the motor needs to have 126.616/0.86 W = 147.23 W.

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