Work, energy and power
Connect force and displacement with energy transfer, then distinguish energy from the rate of transfer.
In this guide
Physics work has a specific meaning
For a constant force and straight displacement, the work done by that force is W = Fd cos(theta), where theta is the angle between force and displacement. If the force points in the same direction as the displacement, W = Fd. If it is perpendicular, its work is zero. If it opposes the displacement, its work is negative. This definition is narrower than everyday effort: holding a stationary object can feel tiring even though its displacement is zero.
Worked example: applied work and net work
A box moves 5 m horizontally while a constant 18 N horizontal pulling force acts forward and a constant 6 N friction force acts backward. The pulling force does 18 × 5 = 90 joules of work. Friction does -6 × 5 = -30 joules. If weight and the support force are perpendicular to the horizontal displacement, they do no work in this model. Net work is 90 - 30 = 60 joules. Do not confuse the work of one force with the sum of work by all forces.
Net work changes kinetic energy
Kinetic energy is K = (1/2)mv^2 for the nonrelativistic motion considered here. The work-energy theorem relates net work to the change in kinetic energy. If the box in the example has mass 3 kg and starts from rest, its final kinetic energy is 60 J. Solve (1/2)(3)v^2 = 60 to get v^2 = 40 and v approximately 6.32 m/s. Doubling speed would multiply kinetic energy by four, not two, because speed is squared.
Potential energy and power
Near Earth's surface, a change in gravitational potential energy can be modeled as mgh when the gravitational field is treated as constant. Lifting a 4 kg object upward by 1.5 m with g = 10 m/s^2 increases this energy by 4 × 10 × 1.5 = 60 J. If a device transfers 60 J in three seconds, its average power is 60/3 = 20 watts. Power measures how quickly energy is transferred, while energy measures the amount transferred.
Track energy without claiming it disappears
Friction can reduce a moving object's mechanical energy while increasing thermal energy in the object and surroundings. That does not mean total energy has been destroyed. Specify which system and which energy forms you are counting. Similarly, useful output energy divided by input energy gives an efficiency for a defined device and interval. The simplified examples here ignore losses only when that assumption is stated. A large power rating alone does not tell you how much energy a device uses without a duration.
- Use joules for work and energy, watts for power.
- Distinguish net work from work by a selected force.
- Use the gravitational acceleration supplied in the problem.
- Check the square on speed before comparing kinetic energies.
Try it yourself
A constant 14 N force acts along a 3 m displacement. Calculate its work. If an opposing force does -12 J and all other forces do zero work, find the net work. Separately, find the kinetic energy of a 2 kg object moving at 5 m/s, and the average power of a device that transfers 360 J in 12 seconds.
Reveal the worked answer
A constant 14 N force acts along a 3 m displacement, so it does 42 J of work. If an opposing force does -12 J and the other forces do zero work, net work is 30 J. Separately, a 2 kg object moving at 5 m/s has kinetic energy (1/2) × 2 × 25 = 25 J. A device that transfers 360 J in 12 seconds has average power 30 W. State each unit rather than reporting bare numbers; they describe different physical quantities.
A constant 14 N force acts along a 3 m displacement, so it does 42 J of work. If an opposing force does -12 J and the other forces do zero work, net work is 30 J. Separately, a 2 kg object moving at 5 m/s has kinetic energy (1/2) × 2 × 25 = 25 J. A device that transfers 360 J in 12 seconds has average power 30 W. State each unit rather than reporting bare numbers; they describe different physical quantities.
Put one idea into practice.
Try a short science session, then use the explanations to choose what to review next.
Start a short sessionSources & further reading
OpenStax College Physics 2e — Work and the work-energy theoremOpenStax College Physics 2e — PowerSomething unclear or incorrect? Suggest a correction to this guide.
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