Question
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
1.44 kW
14.4 kW
2.88 kW
28.8 kW
Solution
A.
1.44 kW
Since the net force on the belt is the difference between the two tensions, the torque exerted by the motor on the belt is
Τ = F r
= ( 135 N 45 N ) ( 0.08 m )
Τ = 7.2 N m
The power output of the motor is therefore
P = Τ ω
= ( 72 N.m ) ( 200 rad s-1 )
P = 1440 W
P = 1.44 kW
