Before you lift a book off the floor, predict: where does the energy go? It does not disappear — it is stored as gravitational potential energy (GPE), ready to be released the moment you let go. Understanding GPE and its partner kinetic energy (KE) is the key to predicting how objects move.
What is gravitational potential energy?
Gravitational potential energy is the energy an object stores because of its height above a reference point (usually the ground). The higher you lift something and the heavier it is, the more GPE it stores.
The formula is:
GPE = mass × gravitational field strength × height GPE = m × g × h
At the Earth's surface, the gravitational field strength g = 10 N/kg (to two significant figures for KS3).
Units: mass in kilograms (kg), g in N/kg, height in metres (m), GPE in joules (J).
What is kinetic energy?
Kinetic energy is the energy an object has because it is moving. Any moving object — from a rolling marble to a speeding car — has KE. The faster it moves and the heavier it is, the more KE it carries.
KE = ½ × mass × velocity² KE = ½ mv²
Units: mass in kg, velocity in m/s, KE in joules (J).
Notice the velocity is squared: double the speed and you quadruple the kinetic energy. That is why road safety experts care so much about speed limits.
How does energy transfer between GPE and KE?
Predict: what happens to GPE as a ball rolls down a ramp?
GPE is converted into KE. As height decreases, speed increases. If we ignore friction and air resistance, the total mechanical energy is conserved:
GPE lost = KE gained mgh = ½mv²
The mass cancels from both sides, which is why Galileo discovered that heavy and light objects (ignoring air resistance) fall at the same rate.
| Position on ramp | GPE | KE | Total |
|---|---|---|---|
| Top (at rest) | Maximum | Zero | 100% |
| Halfway down | Half | Half | 100% |
| Bottom | Zero | Maximum | 100% |
In reality, some energy is always converted to thermal energy by friction, so the KE at the bottom is slightly less than the GPE at the top.
How do you calculate GPE — worked examples?
Worked example 1: A 2 kg book is placed on a shelf 1.5 m above the floor. Calculate its GPE.
- GPE = m × g × h
- GPE = 2 × 10 × 1.5
- GPE = 30 J
Worked example 2: A 500 g ball (0.5 kg) is dropped from a height of 4 m. What is its speed just before it hits the ground? (Assume no air resistance.)
- GPE at top = m × g × h = 0.5 × 10 × 4 = 20 J
- All GPE converts to KE: KE = ½mv² = 20 J
- Rearrange: v² = 2 × KE ÷ m = (2 × 20) ÷ 0.5 = 80
- v = √80 ≈ 8.9 m/s
Worked example 3: A 60 kg cyclist travels at 5 m/s. Calculate their KE.
- KE = ½ × 60 × 5²
- KE = ½ × 60 × 25
- KE = 750 J
Where do we see GPE and KE in everyday life?
Spotting energy transfers in real situations cements the concept:
- A roller coaster converts GPE (at the top of each hill) into KE (at the bottom) and back again all the way around the track.
- A hydroelectric dam stores water at height (GPE) and releases it through turbines, converting GPE → KE → electrical energy.
- A pendulum swings between maximum GPE (at the top of each swing) and maximum KE (at the bottom) continuously.
- A diver on a diving board gains GPE by climbing up, then converts it to KE during the fall, entering the water at speed.
- Throwing a ball upwards converts KE (at the moment of release) into GPE (as it rises), then back into KE on the way down.
What factors affect gravitational potential energy?
Two variables control GPE:
| Factor | Effect on GPE | Why |
|---|---|---|
| Greater mass | Increases GPE | More matter for gravity to pull on |
| Greater height | Increases GPE | Further from the reference point |
| Stronger g field (e.g., Jupiter) | Increases GPE | Gravity pulls harder |
| Same object, same height on Earth | Same GPE | g and h unchanged |
On the Moon, g ≈ 1.6 N/kg (roughly one-sixth of Earth's), so the same object lifted to the same height stores about one-sixth the GPE. That is why astronauts can jump so much higher there.
How do GPE and KE connect to the conservation of energy?
Energy cannot be created or destroyed — it can only be transferred between stores. This is the conservation of energy principle, one of the most powerful ideas in all of physics.
When a ball falls:
- The gravitational field does work on the ball.
- GPE decreases; KE increases.
- If the surface is elastic (a superball, a trampoline), KE converts back to GPE on the rebound.
- Real surfaces absorb some energy as thermal energy and sound — that is why the ball does not bounce as high each time.
The total energy in the system is always accounted for; it simply changes form.
Frequently asked questions
What are the units of gravitational potential energy?
GPE is measured in joules (J), the same unit as all forms of energy and work done. One joule is equal to one newton-metre (N·m) — the energy transferred when a force of one newton moves an object one metre.
Does a stationary object have kinetic energy?
No. KE = ½mv², so if velocity (v) is zero, KE is also zero. A stationary object can still store GPE (if it is elevated) or elastic potential energy (if it is compressed or stretched), but it has no kinetic energy.
Why does mass cancel when GPE equals KE?
When you set mgh = ½mv², the mass m appears on both sides and cancels out, leaving gh = ½v². This shows that the final speed of a falling object (ignoring air resistance) does not depend on its mass — only on the height it fell from and g. Galileo demonstrated this experimentally, contradicting Aristotle's claim that heavier objects fall faster.
What is the difference between GPE and elastic potential energy?
Both are forms of stored (potential) energy, but they arise from different situations. GPE is stored due to height in a gravitational field. Elastic potential energy is stored when an object is stretched or compressed — like a spring or elastic band — and is given back when the object returns to its natural shape.
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