amargemernindudeste passenger car, a counterweight, and two large Figure Each pu

Question

amargemernindudeste passenger car, a counterweight, and two large Figure Each pulley has a radius of 1.0 m and The top pulley is driven by a motor. The elevator car plus passengers has a 0 kg, and the counterweight has a mass of 2800 kg, Pulley Electric O Type here to search Part A the motor is to accelerate the elevator carupwardat1.6m/s how much torque must generate? Express your answer to two significant figures and include appropriate units. Value Units Bata Gave up Review Part Incorrect Try Again; 4 attempts remaining

Explanation / Answer

To accelerate the elevator car upward at 1.6 m/s², we need a rope tension
T2 = 3000kg * (9.8 + 1.6)m/s² = 34 200 N
and to have the counterweight accelerate downward at 1.6 m/s²,
T1 = 2800kg * (9.8 - 1.6)m/s² = 22 960 N

When the linear acceleration is 1.6 m/s², the angular acceleration of the pulleys is
= a / r = 1.6m/s² / 1.1m = 1.45 rad/s²

Each pulley has a moment of inertia
I = ½mr² = ½ * 360kg * (1.1m)² = 218 kg·m²
and there are two of them.

So, I'd say that the total required torque is
= 2*I* + (T2 - T1)*r
= 2 * 218kg·m² * 1.45rad/s² + (34200 - 22960)N * 1.1m
= 13 000 N·m

Let's say the car and cw aren't there, and that we have a torque of
' = (34200 - 22960)N * 1.1m = 12 364 N·m
This HAS to be overcome by the motor.
And the motor has to get the pulleys accelerating:
" = 2 * 218kg * 1.45rad/s² = 634 N·m.

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