An air compressor is powered by a 200 rad / s electric motor using a V-belt drive. The motor pulley is 8 ~cm in radius, and the tension in the V -belt is 135 ~N on one side and 45 ~N on the other. The power of the motor will be

Step-by-step solution

Since the net force on the belt is the difference between the two tensions, the torque exerted by the motor on the belt is, aligned & =F r=(135 ~N -45 ~N )(0.08 ~m ) & =7.2 ~N ~m aligned The power output of the motor is therefore aligned P & = =(72 ~N m ) (200 rad s ⁻¹ ) & =1440 ~W =1.44 ~kW aligned