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Q3. A winch motor drives a pinion with 320 teeth. Friction at the motor bearings is constant at 20 Nm. The pinion then meshes with a gear wheel having 640 teeth which drives a shaft of 120 mm diameter. This shaft is supported in bearings having a coefficient of friction of 0.12 and drives a winch drum of diameter 340 mm. Calculate EACH of the following:

(a) The driving torque required by the motor when raising a mass of 2 tonnes at a steady speed;

(b) The input power required by the motor when raising the mass of 2 tonnes at a steady speed of 0.3 m/s if the motor efficiency is 90%.