A factory uses a motor and a cable to drag a 300 kg machine to the proper place on the factory floor. What power must the motor supply to drag the machine at a speed of 0.50 m/s? The coefficient of friction between the machine and the floor is 0.60.

Friction & Power based Numerical Problem: A factory uses a motor and a cable to drag a 300 kg machine to the proper place on the factory floor. What power must the motor supply to drag the machine at a speed of 0.50 m/s? The coefficient of friction between the machine and the floor is 0.60.

Solution:

The force applied by the motor, through the cable, is the tension force T.

This force does work on the machine with power P = Tv. [we know the formula: power = force x velocity]

The machine is in equilibrium because the motion is at a constant velocity, hence the tension in the rope balances the friction and is
T = f_k = µ_kmg
The motor’s power output P is
P = Tv = µ_kmgv = 0.6 x 300 x 9.8 x 0.5 = 882 W
So, the motor must supply 882 W of power. [Answer]

[suggested reading: Friction numerical problems solved worksheet for class 11 & class 12