A lift system consists of a cage of mass 4000kg and a winding drum of mass 5000kg, which has a radius of gyration of 0.8m and an outside diameter of 3 metres. The lift is stationary with the cage at the bottom of the shaft. The driving motor develops a constant torque to give the an upwards acceleration of 2m/s2 against a frictional resistance to motion of 2kNm Determine the minimum output torque from the motor to wind both the drum and the cage.

You have to ask a specific question, like, how do I use frictional resistance? Or does it matter if the drum is like a wheel or a hollow cylinder? Another thing is it is not clear what minimum output torque they mean: minimum torque to pull the lift with the specified acceleration or just pull it up at any rate?

Set up an equation of the torques presented in this problem. The torque that the motor provides must overcome (a) the torque due to the weight of elevator cage and (b) the torque due to the frictional forces. It must then provide enough additional torque to accelerate the cab at 2m/s^2:


I \ddot \theta = T_{motor} - T_{Cage\ Weight}-T_{Friction}


Rearrange:


T_{motor} = I \ddot \theta +T_{Cage\ Weight} + T_{Friction}


Can you take it rom here?