An escalator at a metro station is designed to transport 40 passengers per minute from the ground floor to a vertical height of 12 m . The average mass of a passenger is 60 kg . If 20\% of the electrical input power is

Question

Quantrex Academy · Accepted Answer

Correct answer: D. 6.00 kW

Total mass of passengers transported per minute is

M = 40 \times 60 = 2400\text{ kg}

.

The useful work done by the escalator per minute in lifting the passengers is

W = Mgh = 2400 \times 10 \times 12 = 288000\text{ J}

.

The useful power output of the motor is

P_{out} = \dfrac{W}{t} = \dfrac{288000}{60} = 4800\text{ W} = 4.8\text{ kW}

.

Since

20\%

of the electrical input power is lost against friction, the efficiency of the motor is

80\%

.

Let the electrical input power be

P_{in}

. Then

0.8 P_{in} = P_{out}

.

P_{in} = \dfrac{4.8}{0.8} = 6.0\text{ kW}

.

Answer:

6.00\text{ kW}

An escalator at a metro station is designed to transport 40...

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