AP Physics C Mechanics Quiz: Power

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.

A 1500 kg elevator starts from rest and reaches 4.0 m/s in 5.0 s while moving upward, rising 10 m during that interval. The cable tension does work that increases both gravitational potential energy $mgh$ and kinetic energy $\tfrac12 mv^2$. Take $g=9.8\,\text{m/s}^2$ and neglect frictional losses. Treat the power as the average rate of total mechanical energy increase over the 5.0 s. In the given system, what is the average power output of the system described?

An electric motor hoists a 120 kg load straight up 15 m in 12 s at constant speed, so the mechanical work is $mgh$. The motor draws 2.5 kW of electrical power from the outlet while lifting, and its efficiency is 78%, meaning $P_{\text{mech}}=\eta P_{\text{in}}$. Assume $g=9.8\,\text{m/s}^2$ and neglect losses other than those in the efficiency rating. In the given system, electrical energy is converted into gravitational potential energy. Determine the mechanical power output given the conditions.

An electric motor lifts a $25.0\,\text{kg}$ load vertically upward at constant speed through $10.0\,\text{m}$ in $5.0\,\text{s}$. The motor's efficiency is $80\%$, meaning $P_{\text{mech}}=0.80\,P_{\text{elec}}$. Ignore rotational kinetic energy of the motor and any frictional losses besides the stated efficiency. Take $g=9.8\,\text{m/s}^2$ and assume the tension in the cable equals the load's weight. Based on the scenario above, determine the mechanical power output given the conditions.

A flywheel is driven so that its angular speed increases uniformly from $10.0\,\text{rad/s}$ to $30.0\,\text{rad/s}$ in $4.0\,\text{s}$ while the applied torque remains constant at $8.0\,\text{N\u00b7m}$. Assume friction is negligible and the torque is always in the direction of rotation. The instantaneous rotational power is $P=\tau\omega$, so average power over the interval can be found using the average angular speed. Use SI units throughout. In the given system, what is the average power output of the system described?

A motor draws an electrical input power of $1.50\,\text{kW}$ while lifting a $50.0\,\text{kg}$ mass straight up at constant speed. The motor's efficiency is $70\%$, so only $70\%$ of the electrical power becomes mechanical power delivered to the load. Neglect frictional losses other than the stated efficiency and ignore any change in kinetic energy. Use SI units and take $g=9.8\,\text{m/s}^2$. Based on the scenario above, determine the mechanical power output given the conditions.

Two identical motors are used to lift loads. Motor A lifts a 200 kg mass at 2.0 m/s constant velocity. Motor B lifts a 400 kg mass at constant velocity. If both motors operate at the same mechanical power output, what is the ratio of the time taken by Motor B to lift its load through 20 m compared to Motor A lifting its load through the same height?

An electric motor operates at constant mechanical power output of 1.5 kW while lifting a load vertically. Initially, the load has a mass of 100 kg and is lifted at constant velocity. After 10 seconds, an additional 50 kg mass is suddenly attached to the load. Assuming the motor maintains the same power output, what is the new constant velocity of the combined load after the transient effects have died down?

A wind turbine generates electrical power according to $P = 0.4v^3$ kW, where v is the wind speed in m/s. During a particular day, the wind speed varies as $v(t) = 8 + 2\sin(\pi t/12)$ m/s, where t is time in hours. What is the average power generated during the first 12 hours?