A load of 250 kg is raised by a winch similar to that shown.

The winch has a winding drum of mass 52 kg, a diameter of 400 mm and radius of gyration 125 mm.

When the winch first starts, it lifts the load with an acceleration of 1 m/s² from rest through a distance of 3m. The winch system has an overall friction torque of 1.3 kNm.

The final angular velocity of the drum = 12.22 rad/s

The angular acceleration of the drum = 5.1rad/s

Calculate the following:

1. the work done by the driving motor (to calculate the work done you need to find the work done overcoming friction, then the work done in each part then add them together)                  
2. the input torque to the drum (T=work done as calculated above / 15rad)                
3. the maximum power developed by the driving motor (Power = T x work Done)

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