Last reviewed 30 Sept 2026 · 7 min read
Work
In science, work is done when a force acts on a body and the body moves in the direction of the force (or a component of it).
where is the force, the displacement and the angle between them. The SI unit is the joule (J): 1 J is the work done when a force of 1 N moves a body through 1 m in the direction of the force. Work is a scalar.
| Case | Angle | Work |
|---|---|---|
| Force along the displacement | 0° | positive () |
| Force opposite to the displacement (friction, brakes) | 180° | negative |
| Force perpendicular to the displacement | 90° | zero |
| No displacement | — | zero |
Examples of zero work: a person pushing a wall that does not move; a coolie carrying a load along a level road (the force is vertical, motion horizontal); the Moon in circular motion around the Earth (gravity is perpendicular to the motion); a satellite in a circular orbit.
Other units: erg (CGS; ), kilowatt-hour (), electron volt (about J), calorie (about 4.18 J).
A force of 50 N pulls a box 4 m along the ground at 60° to the horizontal. Work done = .
Energy
Energy is the capacity to do work. It is measured in joules, is a scalar, and exists in many forms.
Kinetic energy (KE)
The energy of a body due to its motion: . It depends on the mass and the square of the velocity — doubling the speed makes the KE four times as large (which is why speeding vehicles are so dangerous).
Potential energy (PE)
The energy stored due to position or configuration.
- Gravitational PE: (near the Earth's surface).
- Elastic PE: for a stretched or compressed spring.
- Chemical, electrical and nuclear energies are also kinds of potential energy.
Work–energy theorem
The work done by the net force on a body equals the change in its kinetic energy:
Conservation of energy
Energy can neither be created nor destroyed; it can only be changed from one form to another. The total energy of an isolated system remains constant. For a freely falling body, the sum of PE and KE stays the same: PE falls as KE increases. A pendulum bob has maximum PE at the extremes and maximum KE at the lowest point.
A 2 kg stone is dropped from a height of 20 m. Find its speed just before it hits the ground ( m/s²).
Solution. By conservation of energy . Its energy just before impact is all kinetic: , equal to the original PE, .
Forms of energy and common conversions
| Device | Conversion |
|---|---|
| Electric bulb | electrical → light + heat |
| Electric motor / fan | electrical → mechanical |
| Generator (dynamo) | mechanical → electrical |
| Battery / cell | chemical → electrical |
| Solar cell | light → electrical |
| Microphone | sound → electrical |
| Loudspeaker | electrical → sound |
| Photosynthesis | light → chemical |
| Steam engine | heat → mechanical |
| Hydroelectric plant | gravitational PE → KE → electrical |
| Nuclear power plant | nuclear → heat → electrical |
| Thermal power plant | chemical (fuel) → heat → mechanical → electrical |
| Wind turbine | wind KE → electrical |
| Candle burning | chemical → heat and light |
| Rubbing hands | mechanical → heat |
Mass–energy relation
Einstein's equation shows that mass can be converted into energy; it explains the energy released in nuclear fission and fusion.
Sources of energy
- Conventional (non-renewable): coal, petroleum, natural gas.
- Renewable (non-conventional): solar, wind, hydro, tidal, biomass, geothermal.
- Nuclear energy from fission (uranium) and fusion (the Sun's source).
- Renewable sources are pollution-free or low-pollution and replenished by nature.