Power: Videos & Practice Problems

A road worker moves a 32 kg road marking machine by pushing it with a force of magnitude F, making an angle of 25 ° below the horizontal. The marking machine rolls at a constant speed of 0.5 m/s on a horizontal asphalt road surface. The coefficient of rolling friction between the marking machine and the asphalt is 0.18. Find the power delivered by the worker.

A 2.0-kg weight plate is moving on a rough, horizontal surface where the coefficient of kinetic friction is 0.100. It is moving at 5.00 m/s until friction causes it to stop. Calculate the average power generated by friction on the plate as it comes to a stop.

Based on the equation T - (130 kg)(9.8 m/s²) = (130 kg)(1.25 m/s²) and P = T(3.0 m/s), draw the figure that represents these mathematical relationships.

For T - (250 kg)(9.8 m/s²) = (250 kg)(2.15 m/s²) and P = T(4.0 m/s), determine the values of P and T                             

Drag force from the air is the dominant resistive force acting on a motorcycle moving at constant speed on a flat surface (other forms of friction can be ignored). The work done by the engine is dissipated as work is done against drag force. We'll treat the motorcycle with the rider as having a cross-sectional area of 0.65 m² and a drag coefficient of 0.75. We'll also take the density of air to be 1.2 kg/m³. The motorcycle's engine generates power by burning gasoline. Taking the energy value of gasoline as 45 MJ/kg and the engine/transmission to be 28% efficient at converting chemical energy in gasoline to mechanical energy, find the engine's rate of consuming gasoline (in watts) when driving at a constant speed of 40 km/h.

An 85 kg sprinter accelerates from rest to a peak speed of 9.2 m/s in 4.0 seconds. A 65 kg cheetah accelerates from rest to 27 m/s in 3.0 seconds. Determine the mean power output of the sprinter and the cheetah. The expression for average power is ∆E/∆t, where ∆t is the time interval.

A construction worker of mass 72 kg wishes to deliver a 25 kg pack of cement to the top of a 25 m building under construction using the stairs. Determine the worker's power that will enable them to make the delivery in 70 s.

A motor pulls a 255 kg cart filled with crushed stone up rail bars inclined at 30 degrees at a uniform speed of 200 cm/s. The kinetic friction coefficient between the cart and the rail bars is 0.25. Determine the power output of the motor.

Determine the power a crane engine requires to raise a 4500 kg container by 4.20 m in 15.0 s at a constant speed.

Air exerts a significant drag force on moving objects. A motorcycle rider needs to keep the engine on when riding at constant speed on a flat surface to counter drag effects. Presume that all the engine's mechanical energy output is converted to work against drag, the rider/motorcycle has a cross-sectional area of 0.80 m², and a drag coefficient of 0.85 due to aerodynamic inefficiency. Take the density of air to be a typical 1.2 kg/m³ and the engine/transmission to be 31% efficient at converting chemical energy to mechanical energy. Determine the chemical energy intake of the engine in kCal ( 1 kCal = 4.19 kJ) when a rider travels at 50 km/h for 40 minutes. 

A telescope with a diameter of 1.8m is used to view a star far away. During a 30 s duration, the telescope's detector records 8.25 × 10^-11 J from the light energy received. Using the temperature and size data of the star, it is known that the star radiates at a constant 4.0 × 10²⁶ W for the 30 s duration. Determine the star's distance from the Earth, reporting the result in light years. The speed of light is 3.0 × 10⁸ m/s, and 1 light year is the distance light travels in one year.

A prototype in an engineering school demonstrating a new design of water turbines uses water from a tank located 15.0 m above the turbine. Take the turbine design to be 72% efficient in transforming the potential energy of water to the kinetic energy of the shaft. Determine the water flow rate (in kg/s) required to supply the turbine shaft with energy at a rate of 20 MW. This is a realistic value during electricity generation.

A water turbine at a dam uses water kinetic energy to turn a shaft connected to an impeller that pumps water from the same dam. Assume a 90% efficiency in converting the kinetic energy of water into the kinetic energy of the shaft (that is, 90% of the kinetic energy is successfully used to pump water). A typical water pump pushes water at a rate of 22.5 KW. If the velocity of the water hitting the turbine is 20 m/s, determine the flow rate of water hitting the turbines that facilitates pumping water at 22.5 KW.

Food containers are commonly made of aluminum. A 20 kg aluminum food crate slides against an aluminum table that has a kinetic coefficient of friction, μ_k = 0.46. A worker pushes the crate at a uniform speed of 0.80 m/s for 5s. Determine the worker's power output.

A trolley weighing 55 kg travels along a track with a velocity of 1.5 m/s. A worker brings it to a stop in 2.0 seconds. Determine the magnitude of the average power required to halt the trolley.

A pumped-storage facility operates by pumping water from a lower reservoir to an upper reservoir during off-peak electrical demand hours, using excess power from the grid. The upper reservoir is $600$ meters above the lower one. If the facility uses $200$ MW of power for $6.0$ hours to pump the water uphill, calculate the volume of water in cubic meters that is moved to the upper reservoir. Water has a mass of $1.00 \times 10^{3}$ kg for every $1.0 \mathrm{~m}^{3}$.

Suppose there's a system where water is pumped to a rooftop tank 80 m above ground level. The water is pumped at a steady rate of 1.2$\times$10⁵ kg/s for 12 hours. Calculate the total energy consumption, in kWh, needed to pump water to the rooftop tank.

In a facility for water storage, a tank holds water at an elevation of 150 m above ground level. Water is continuously pumped into the tank at a rate of 8000 kg/s for 12 hours. Assuming all the stored energy is discharged over 16 hours with an efficiency of 80%, what is the average power output during the release phase?

On a flat horizontal highway, a 350 kg motorcycle's speed drops from 86 km/h to 70 km/h in 5.0 s while it is in neutral gear. Calculate what the approximate value of power (both in watts and hp) that will be needed for the motorcycle to maintain a constant speed of 72 km/h on the highway.

A skateboarder with a total mass of $60 \mathrm{~kg}$ can skateboard down a ramp inclined at $4.0^{\circ}$ to the horizontal at a steady speed of $8.0\ \text{km/h}$. By pushing off more forcefully, the skateboarder can increase their speed to $16.0 \mathrm{~km} / \mathrm{h}$. Using the same effort, at what speed can the skateboarder climb up the same ramp? Assume the force of air resistance and rolling friction is proportional to the square of the speed $v$; that is, $F_{friction}=kv^2$ , where $k$ is a constant.

An electric car with a mass of $1,500$ kg is moving along a straight road. The car's position (in meters) as a function of time is given by the equation x(t) = 3t³ - 15t² + 24t, where t is in seconds. Calculate the average net power delivered to the car's wheels during the intervals from t = 0 s to t = 3.0 s, and from t = 3.0 s to t = 6.0 s.

A marathon runner runs with 2.5 hp. Calculate the work done by her if she runs for 1.5 hours with the same power.

A small motorcycle is pulling a trolley by a rope at a constant speed of 25 km/h. Given that the power output of it is 27 hp, calculate the force exerted by the trolley on it. (Ignore friction)

A bicyclist travels 72 m up along a road inclined at an angle of 45° with the horizontal on her bicycle. Given that the total mass of the bicyclist and her bicycle is 95 kg and the time she takes to travel the distance is 65 s, calculate the average power output of the bicyclist. Assume that friction and air resistance are negligible.

A storage tank is located on top of a roof of a 95-meter-tall building. This storage tank contains a liquid. Through smooth pipes, the liquid is able to flow vertically down into a generator which produces electricity by using the mechanical energy of the liquid. Given that the efficiency of the generator is 44% and the rate at which the liquid flows down is 32 kg/s, evaluate what the rate of transfer of mechanical energy from the liquid to the generator will be.

A mountain reservoir supplies water to a town's hydroelectric power plant. The water from the reservoir flows down through a penstock with a height of 50 m to the turbines. The plant maintains a constant flow rate of 25 m³/s. Assuming that the conversion of the gravitational potential energy of the water to electrical energy is 100% efficient, calculate the amount of electrical power generated by the power plant. Use: g=9.8 m/s² and density of water 𝜌=1000 kg/m³.

A small aircraft engine produces 92 kW of power. How much is this power in horsepower?