You are designing a simple elevator system for an old warehouse that is being co

Question

You are designing a simple elevator system for an old warehouse that is being converted to loft apartments. A 22,500-N elevator is to be accelerated upward by connecting it to a counterweight by means of a light (but strong!) cable passing over a solid uniform disk-shaped pulley. The cable does not slip where it is in contact with the surface of the pulley. There is no appreciable friction at the axle of the pulley, but its mass is 855 kg and it is 1.90 m in diameter.

Part A: What mass should the counterweight have so that it will accelerate the elevator upward through 6.75 m in the first3.00 s, starting from rest?

Part B: Under these conditions, what is the tension in the cable on the elevator side of the pulley?

Part C: Under these conditions, what is the tension in the cable on the counterweight side of the pulley?

Explanation / Answer

mass of pulley, M = 855 kg

d = 1.9 m

R = 1.9/2 = 0.95 m

mass of elevator, m1 = 22500/9.8 = 2296 kg

A) let a is the acceleraion of the elevator in ypward direction.

apply, h = u*t + 0.5*a*t^2

h = 0 + 0.5*a*t^2

==> a = 2*h/t^2

= 2*6.75/3^2

= 1.5 m/s^2

B) Tension in the cable on the elevator side, T1 = m1*g + m1*a

= 22500 + 2296*1.5

= 25944 N

C)let T2 is the Tension in the cable on the other side.

Apply,

Net torque on the pulley = I*alfa

(T2 - T1)*R = 0.5*M*R^2*a/R

T2 - T1 = 0.5*M*a

T2 = T1 + 0.5*M*a

= 25944 + 0.5*855*1.5

= 26585 N

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