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  4. 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

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Q. 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

AIIMSAIIMS 2015System of Particles and Rotational Motion

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,
$\tau =F r=(135 N -45 N )(0.08 m )$
$=7.2\, N m$
The power output of the motor is therefore
$P= \tau \omega=(72 N \cdot m )\left(200 rad s ^{-1}\right)$
$=1440\, W =1.44\, kW$