Part A You are designing a simple elevator system for an old

Part A 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 831 kg and it is 1.80 m in diameter. What mass should the counterweight have so that it will accelerate the elevator upward through 6.75 m in the first 3.00 s, starting from rest? Express your answer with the appropriate units. mValue Units Submit My Answers Give Up Part B Under these conditions, what is the tension in the cable on the elevator side of the pulley? Express your answer with the appropriate units. T,= Value Units alnie

Solution

a)

From

S=Ut+(1/2)at²

6.75 =0+(1/2)*a*3²

a=1.5 m/s²

Velocity

V=at =1.5*3 =4.5 m/s²

Moment of inertia of pulley

I=(1/2)*m_pulley*R² =(1/2)*831*(1.8/2)² = 336.555 Kg-m²

and W=V/R =4.5/(1.8/2) =5 rad/s

By Conservation of energy

(1/2)M_elevatorV²+(1/2)m_{counterweight}V²+(1/2)IW² =m_{counterweight}gh

(1/2)(22500/9.8)*4.5²+(1/2)m_{counterweight}(4.5)²+(1/2)*336.555*5²=m_{counterweight}*9.8*6.75

m_{counterweight} = 491.6 Kg

b)

Tension on elevator side

T=M_elevator(g+a) =(22500/9.8)(9.8+1.5)

T=25944 N

c)

Tension on counterweight side

T=491.6(9.8-1.5)

T=4080.3 N