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

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 (A) 1.44 kW (B) 14.4 kW (C) 2.88 kW (D) 28.8 kW

Tardigrade Admin · Accepted Answer

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)

= 7.2 N m

The power output of the motor is therefore

P = τ ω = (72 N \cdot m) (200 r a d s^{- 1})

= 1440 W = 1.44 kW

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

1.44 kW

14.4 kW

2.88 kW

28.8 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=Fr=(135N−45N)(0.08m) =7.2Nm The power output of the motor is therefore P=τω=(72N⋅m)(200rads−1) =1440W=1.44kW

Q. An air compressor is powered by a $200 r a d / s$ 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

Since the net force on the belt is the difference between the two tensions, the torque exerted by the motor on the belt is,
$τ = F r = (135 N - 45 N) (0.08 m)$
$= 7.2 N m$
The power output of the motor is therefore
$P = τ ω = (72 N \cdot m) (200 r a d s^{- 1})$
$= 1440 W = 1.44 kW$