Work is force times distance moved along the force. Energy is what work transfers, and power is how fast that happens.
This lesson is part of SPM Physics force and motion I. It follows applying Newton’s laws in context.
How do the three quantities compare?
| Quantity | Symbol | Formula | Unit |
|---|---|---|---|
| Work | W | F × s | J |
| Gravitational potential energy | Eₚ | mgh | J |
| Kinetic energy | Eₖ | ½mv² | J |
| Power | P | W ÷ t | W (J s⁻¹) |
Before you calculate, ask whether the question is about how much or how fast. How much means work or energy, in joules. How fast means power, in watts.
Worked example: lifting a box
A student lifts a 12 kg box through 1.5 m in 3.0 s at a steady speed. Use g = 9.8 m s⁻².
- Work done = mgh = 12 × 9.8 × 1.5 = 176.4 J, so about 176 J.
- Power = W ÷ t = 176.4 ÷ 3.0 = 58.8 W, so about 59 W.
If the student took 6.0 s, the work would still be 176 J, but the power would be half, 29 W.
Worked example: a falling ball
A 0.50 kg ball falls from rest through 2.0 m. Ignore air resistance.
The energy lost as potential energy is mgh = 0.50 × 9.8 × 2.0 = 9.8 J. This becomes kinetic energy: ½ × 0.50 × v² = 9.8, so v² = 39.2 and v = 6.3 m s⁻¹ (2 s.f.).
Sense check: v = √(2gh) gives the same value and does not depend on the mass.
The mistake that loses marks
A student carries a 12 kg box 3.0 m along a level floor and writes “work = 12 × 9.8 × 3.0 = 353 J”. The lifting force is vertical, but the movement is horizontal.
The work by the lifting force is zero. Only use F × s when s is measured along the direction of F.
Check yourself
A motor lifts a 40 kg load through 5.0 m in 10 s. Find the work done and the power. Use g = 9.8 m s⁻².
Answer
Work = mgh = 40 × 9.8 × 5.0 = 1960 J.
Power = W ÷ t = 1960 ÷ 10 = 196 W.
What to study next
Test all six lessons together in the force and motion I practice set. If forces still cause trouble, return to drawing force diagrams.
The units and significant figure checker helps with the final line. If you want a teacher to go through energy questions with you, see online one-to-one Physics tuition.