Torque and Work Practice Test

A pulley of radius $r=0.10,\text{m}$ is rotated by a constant tangential pull on a rope. The applied force has magnitude $F=60,\text{N}$ and stays perpendicular to the radius as the pulley turns. The axle is frictionless, and the pulley rotates in its plane. The force is applied while the pulley rotates through $\Delta\theta=4.0,\text{rad}$. Assume no slipping and no dissipative losses. The torque is constant with magnitude $\tau=rF$. The work done by the torque is $W=\tau\Delta\theta$. Using the given information, calculate the total work done by the applied force.

A pulley of radius $r=0.20,\text{m}$ is turned by pulling on a light rope wrapped around its rim. A constant tangential force $F=50,\text{N}$ is applied to the rope so the force stays perpendicular to the radius. The axle is frictionless, and the pulley rotates in its plane. The force is applied while the pulley turns through an angle $\Delta\theta=2.5,\text{rad}$. Assume the rope does not slip on the rim. The torque from the pull is constant, so rotational work is $W=\tau\Delta\theta$. Using the given information, calculate the total work done by the applied force on the pulley during this rotation.