Question

Consider the two situations. In the first a machine must pull a box up a rough slope at constant speed. The mass of the box is 800 kg, the coefficient of kinetic friction is 0.2, and the slope is inclined at 15 degrees to the horizontal. In the second situation the machine must pull an equally massive wheel up the same slope. The cable is attached to the axle of the wheel and exerts negligible torque about the axis. If both the box and the wheel move up the slope at 0.5 m/s then how much power (in Watts) must the machine supply for each task?

Answer 1

Sliding box:
Power = (Friction force + Weight component up ramp) x velocity
= (M*g*cos15*0.2 + M*g*sin15)*V
= (800*9.8)(0.1932 +0.2588)*0.5
= 1772 W

Wheel:
Power = (Weight component up ramp) x velocity
component up ramp) x velocity
= (M*g*sin15)*V
= (800*9.8)(0.2588)*0.5
= 1015 W