Power describes how quickly energy is transferred or work is done. Two machines can do the same amount of work, but the one that finishes in less time has greater power. This idea matters in engines, electric motors, appliances, sports, and any system where speed of energy transfer affects performance.
The SI unit of power is the watt, where 1 watt equals 1 joule per second.
In a real machine, input energy is split into useful output energy and wasted energy such as heat, sound, or vibration. Efficiency compares the useful output to the total input and is usually written as a percentage. Mechanical power often comes from force and velocity, while electrical power often comes from voltage and current.
These formulas let you compare devices, predict energy use, and explain why no real machine is 100 percent efficient.
Key Facts
- Power is the rate of doing work: P = W / t
- The SI unit of power is the watt: 1 W = 1 J/s
- Work done by a constant force in the direction of motion is W = Fd
- Mechanical power at constant speed can be written as P = Fv
- Electrical power in a circuit is P = IV, where I is current and V is voltage
- Efficiency = useful output energy / input energy × 100%
Vocabulary
- Power
- Power is the rate at which work is done or energy is transferred.
- Work
- Work is energy transferred when a force moves an object through a distance in the direction of the force.
- Watt
- A watt is the SI unit of power and equals one joule of energy transferred each second.
- Efficiency
- Efficiency is the fraction or percentage of input energy that becomes useful output energy.
- Wasted energy
- Wasted energy is energy transferred to forms that are not useful for the intended task, such as heat or sound.
Common Mistakes to Avoid
- Confusing power with work is wrong because work is the total energy transferred, while power tells how fast that transfer happens.
- Forgetting to convert minutes to seconds is wrong because watts use joules per second, so time must be in seconds when using P = W / t.
- Using total output instead of useful output in efficiency is wrong because efficiency only counts the energy that performs the intended task.
- Writing efficiency greater than 100 percent is wrong for a real machine because some input energy is always dissipated as heat, sound, or other waste.
Practice Questions
- 1 A motor lifts a 300 N weight through a height of 2.0 m in 4.0 s. Calculate the work done and the average power output.
- 2 An electric device uses 1200 J of electrical energy and produces 900 J of useful mechanical energy. Calculate its efficiency as a percentage.
- 3 Two motors lift the same crate to the same height, but motor A takes 5 s and motor B takes 10 s. Explain which motor has greater power and whether they do the same amount of work.