Practice
Power
Average power for lifting at constant speed, the time a motor needs for a job, and instantaneous power from force and velocity.
The skill
Power is the rate at which energy is transferred, so average power is work divided by time, . When a job is described by what gets done, such as lifting a load at constant speed, find the energy it takes first, then divide by the power to get the time. For a force on something already moving, the instantaneous power is , with the angle between the force and the velocity. Watch the units: a watt is a joule per second, so kilowatts have to become watts before you divide joules by them.
A worked example
A 4500 W motor lifts a 470 kg crate straight up at constant speed through 25 m. Use g = 10 m/s².
How long does the lift take, in seconds? Give your answer to three significant figures.
Solution
- The work needed is mgΔy = (470)(10)(25) = 117500 J.
- , so Δt = 117500 ÷ 4500 = 26.1 s.
Answer: 26.1