One elevator arrangement includes the passenger car, a counterweight, and two la

Question

One elevator arrangement includes the passenger car, a counterweight, and two large pulleys. Each pulley has a radius of 1.1 m and a moment of inertia of 370 kgm2. The top pulley is driven by a motor. The elevator car plus passengers has a mass of 3000 kg, and the counterweight has a mass of 2700 kg.

If the motor is to accelerate the elevator car upward at 1.9 m/s2, how much torque must it generate? Express your answer to two significant figures and include appropriate units.

Explanation / Answer

Given,

I1 = I2 = 370 kg-m^2 ; r1 = r2 = 1.1 m

Me = 3000 kg ; Mw = 2700 kg ; a = 1.9 m/s^2

the angular acceleration of the pulley is:

alpha = a/r = 1.9/1.1 = 1.73 rad/s^2

The tensionin elevator rope is:

Te = 3000 (1.9 + 9.8) = 35100 N

that in counter weight rope

Tw = 2700 (9.8 - 1.9) = 21330 N

Fnet = 35100 - 21330 = 13770 N

Torque will be:

Tau = 2 I alpha + Fnet r

Tau = 2 x 370 x 1.73 + 13770 x 1.1 = 16427.2 N-m

Hence, Tau = 1.60 x 10^4 N-m

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