1.5.4Dynamics
Kinetic Energy
5 min read 6 parts Lesson 19 of 22
Section 1 of 6Energy of Motion
A fast moving lorry has far more energy than a slow cyclist, and the equation shows exactly how much.
Definition
- Kinetic energy is the energy a moving object has because of its motion.
Equation
- Use Ek = ½ m v², with Ek in joules, m in kilograms and v in metres per second.
Mass
- Doubling the mass doubles the kinetic energy at the same speed.
Speed
- Doubling the speed quadruples the kinetic energy, because the speed is squared.
Section 2 of 6Why Speed Matters So Much
Why Speed Matters So Much
Squared
- Because v is squared, small increases in speed give large increases in kinetic energy.
Stopping
- The work done by brakes must equal the kinetic energy, so a faster car needs a longer stopping distance.
Safety
- Speed limits reduce the kinetic energy which would be released in a crash.
Transfer
- Kinetic energy is transferred to heat in brakes, and to sound and deformation in a collision.
| Speed (m/s) | Ek for 1000 kg car (J) |
|---|---|
| 10 | 50 000 |
| 20 | 200 000 |
| 30 | 450 000 |
Section 3 of 6Calculation Steps
1
Write the mass in kilograms and the speed in metres per second.
2
Square the speed first, before multiplying by the mass.
3
Multiply by one half and by the mass to find kinetic energy.
4
Quote the final answer in joules, with a sensible number of significant figures.
5
Rearrange for speed using v = √(2 Ek ÷ m) when the energy is known.
Section 4 of 6Everyday Contexts
Everyday Contexts
Cyclists
- A cyclist and bike of total mass 80 kg at 10 m/s have 4000 J of kinetic energy.
Braking
- Brakes must convert all this kinetic energy to heat, so doubling speed means four times as much energy to remove.
Cricket ball
- A fast bowler gives a 0.16 kg ball a speed of 40 m/s, giving it 128 J of kinetic energy.
Wind turbines
- Moving air has kinetic energy, and turbines transfer part of it into electrical energy.
Section 5 of 6Worked Example
Question
- Calculate the kinetic energy of a 1200 kg car at 20 m/s.
- A 0.20 kg ball has 90 J of kinetic energy;
- find its speed.
- Ek = ½ m v² = 0.5 × 1200 × 20² = 0.5 × 1200 × 400 = 240 000 J.
- Rearrangev² = 2 Ek ÷ m = (2 × 90) ÷ 0.20 = 900.
- v = √900 = 30 m/s.
Answer 240 000 J (2.4 × 10⁵ J); 30 m/s.
Section 6 of 6Exam Checklist & Tips
1.5.4 – Key Points for the Exam
- Kinetic energy Energy due to motion.
- Joule The unit of energy.
- Speed squared The speed multiplied by itself, v².
- Stopping distance The distance a vehicle travels after the brakes are applied until it stops.
Common Mistakes
- Forgetting to square the speed.
- Squaring the whole expression including the one half.
- Using the speed in km/h without converting to m/s.
- Thinking doubling the speed doubles the kinetic energy.