Problem 11.43 Part A If the motor is to accelerate the elevator car upward at 1.
ID: 1788241 • Letter: P
Question
Problem 11.43 Part A If the motor is to accelerate the elevator car upward at 1.8 m/s2, how much torque must it generate? One elevator arrangement includes the passenger car, a counterweight, and two large pulleys, as shown in (Figure 1).Each pulley has a radius of 1.3 m and a moment of inertia of 400 kg·m: The top pulley is driven by a motor. The elevator car plus passengers has a mass of 3300 kg, and the counterweight has a mass of 2700 kg Express your answer to two significant figures and include appropriate units Hints alueUnits Submit My Answers Give Up Figure 1 of 1 Provide Feedback Continue Pulley Electric motor Passenger car Counterweight PulleyExplanation / Answer
To accelerate the elevator car upward at 1.8 m/s², we need a rope tension
T2 = 3300kg * (9.8 + 1.8)m/s² = 38280 N
and to have the counterweight accelerate downward at 1.8 m/s²,
T1 = 2700kg * (9.8 - 1.8)m/s² = 21600 N
When the linear acceleration is 1.8 m/s², the angular acceleration of the pulleys is
= a / r = 1.8m/s² / 1.3m = 1.38 rad/s²
Each pulley has a moment of inertia
I = ½mr² = ½ * 400kg * (1.3m)^2 = 338 kg·m²
and there are two of them.
So, I'd say that the total required torque is
= 2*I* + (T2 - T1)*r
= 2 * 338kg·m² * 1.8rad/s² + (38280 - 21600)N * 1.3m
= 22901 N·m