4. A wagon of mass 14 tonnes is hauled up an inclineof 1 in 20 by a rope which is parallel to the incline and is beingwound round a drum of 1 m diameter. The drum, in turn, is driventhrough a 40 to 1 reduction gear by an electric motor. Thefrictional resistance to the movement of the wagon is 1.2 kN, andthe efficiency of the gear drive is 85 per cent. The bearingfriction at the drum and motor shafts may be neglected. Therotating parts of the drum have a mass of 1.25 tonnes with a radiusof gyration of 450 mm and the rotating parts on the armature shafthave a mass of 110 kg with a radius of gyration of 125 mm.
At a certain instant the wagon is moving up the slope with avelocity of 1.8 m/s and an acceleration of 0.1 m/s2. Find thetorque on the motor shaft and the power being developed. [T= 154Nm, P=22,24 kW]
