GCSE Physics Kinetic & Potential Energy Notes
Kinetic energy depends on speed squared; gravitational potential energy depends on height. Combine them with conservation of energy to solve falling-object questions.
Key concepts
- Kinetic energy
- The energy of a moving object: Eₖ = ½mv². Doubling the speed quadruples the kinetic energy.
- Gravitational potential energy
- The energy stored by an object raised in a gravitational field: Eₚ = mgh.
- Energy conservation
- For a falling object with no air resistance, the loss in gravitational PE equals the gain in kinetic energy.
Key formulas
Kinetic energy
Eₖ = ½ × m × v²
mass in kg, speed in m/s.
Gravitational PE
Eₚ = m × g × h
g = 9.8 N/kg.
Conservation
Eₚ lost = Eₖ gained
when air resistance is ignored.
Worked example
A 0.5 kg ball is dropped from 20 m. Find its speed just before it hits the ground. (g = 10 N/kg)
- 1Find the gravitational PE lost: Eₚ = mgh = 0.5 × 10 × 20 = 100 J.
- 2This equals the kinetic energy gained: Eₖ = 100 J.
- 3Use Eₖ = ½mv² and rearrange: v² = 2Eₖ ÷ m = 200 ÷ 0.5 = 400.
- 4Square root: v = √400 = 20 m/s.
Answer: v = 20 m/s
Common mistakes
✗ Forgetting to square v (or to square-root at the end).
✓ Eₖ uses v²; when finding speed you must take the square root.
✗ Using weight instead of mass in the equations.
✓ Both equations use mass in kg, not weight in newtons.
✗ Mixing up h (height) with distance travelled along a slope.
✓ h is the vertical height gained or lost.
Quick check
Try these, then reveal the answers.
If speed doubles, what happens to kinetic energy?Reveal answer
It quadruples (×4), because Eₖ ∝ v².
A 2 kg mass is raised 3 m. Find Eₚ. (g = 10 N/kg)Reveal answer
Eₚ = 60 J
For a falling object (no air resistance), what does the loss in PE equal?Reveal answer
The gain in kinetic energy.
Exam tips
- Write both equations first, then decide which value connects them (usually energy).
- Keep track of units — a common trap is mixing grams with kilograms.
- When solving for speed, show v² first, then square-root — it protects your method marks.
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Frequently asked questions
Why does kinetic energy depend on speed squared?+
Because Eₖ = ½mv²; the v² term means small increases in speed cause much larger increases in energy — this is why stopping distances rise sharply at higher speeds.
Where does the kinetic energy go when an object lands?+
It is transferred to the thermal store of the object and surroundings (and to sound), by heating on impact.
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