Work in science
In everyday life, "work" means any effort. In science, work has a specific meaning: work is done when a force moves an object over a distance, in the direction of the force.
work = force × distance (W = F × d)
Units: joules (J). 1 J = 1 N × 1 m.
Example: You push a box with 50 N across 4 m of floor. W = 50 × 4 = 200 J.
When is no work done?
- Holding a heavy backpack still: force, but no distance. No work.
- Pushing hard on a wall that doesn’t move: no distance. No work.
- Carrying a box horizontally at steady speed: the lifting force is up, but the motion is sideways. No work done by the lifting force.
Energy
Energy is the ability to do work. When work is done, energy is transferred.
Kinetic energy
Kinetic energy depends on mass and speed:
KE = ½ mv²
Because speed is squared, doubling the speed quadruples the kinetic energy. That’s why high-speed crashes are so much more dangerous.
Example: a 1000 kg car at 20 m/s has KE = ½ × 1000 × 20² = 200 000 J.
Gravitational potential energy
Gravitational potential energy depends on mass, height and gravity:
PE = mgh (g ≈ 9.8 N/kg on Earth)
Example: lifting a 2 kg book onto a 1.5 m shelf stores PE = 2 × 9.8 × 1.5 = 29.4 J.
Energy transformations
| Example | Transformation |
|---|---|
| A ball falling | Gravitational PE → KE |
| A pendulum swinging | PE ↔ KE back and forth |
| A hydroelectric dam | Gravitational PE of water → KE → electrical |
| A car braking | KE → thermal energy (brakes heat up) |
Power
Power is how fast work is done:
power = work ÷ time (P = W ÷ t)
Units: watts (W). 1 W = 1 J/s.
Two students climb the same stairs. They do the same work, but the one who runs up has more power.
Example: A student does 3000 J of work climbing stairs in 10 s. P = 3000 ÷ 10 = 300 W.
| Device | Typical power |
|---|---|
| LED bulb | 8–10 W |
| Laptop | 50 W |
| Microwave oven | 1000 W (1 kW) |
| Car engine | about 100 kW |
Electrical bills charge for energy in kilowatt-hours (kWh). A 1 kW device running for 1 hour uses 1 kWh = 3.6 million joules.
Efficiency
No machine turns all its input energy into useful output. Some is always "wasted," usually as heat.
efficiency = useful output energy ÷ total input energy × 100%
| Device | Approximate efficiency |
|---|---|
| Incandescent bulb | 5% (most energy becomes heat) |
| LED bulb | 30–50% |
| Gasoline car engine | 20–35% |
| Electric motor | 85–95% |
| Large electric generator | about 98% |
Example: A motor uses 500 J and produces 400 J of useful motion. Efficiency = 400 ÷ 500 × 100% = 80%.
Common mistakes
- Thinking effort always equals work. No movement, no work.
- Confusing power and energy. Power is the rate of using energy.
- Forgetting to square the speed in KE.
Try it yourself
- How much work is done lifting a 10 kg box 2 m? (Use F = mg.)
- A 60 kg student climbs 4 m of stairs in 5 s. Calculate the work and power.
- Which has more kinetic energy: a 2 kg ball at 4 m/s or a 4 kg ball at 2 m/s?
- A kettle uses 2000 J to heat water but only 1500 J goes into the water. What is its efficiency?
(Answers: 196 J; 2352 J and 470 W; the 2 kg ball, 16 J vs. 8 J; 75%)
Quick recap
- Work = force × distance, measured in joules.
- Kinetic energy = ½mv²; gravitational potential energy = mgh.
- Power = work ÷ time, measured in watts.
- Energy transforms but is conserved.
- Efficiency compares useful output to total input.