Power Practice Test

A 90 kg load is lifted 6.0 m using an ideal block-and-tackle with mechanical advantage 2, so the rope tension is $T=\tfrac{mg}{2}$ while the load rises at constant speed. Because two rope segments support the load, the free end of the rope must be pulled 12 m to raise the load 6.0 m. The pull takes 8.0 s, and friction is negligible. Use $g=9.8,\text{m/s}^2$. In the given system, what is the average power output of the system described?

A uniform disk in a lab is spun by a motor that applies a constant torque of 12 N·m while the disk rotates at a steady angular speed of 15 rad/s. Assume the angular speed is constant during the interval so the motor’s torque transfers energy at a constant rate. Neglect bearing friction and air resistance so essentially all motor work becomes rotational energy transfer. Use the rotational power relation $P=\tau\omega$. In the given system, calculate the power exerted by the torque in the scenario.