The big idea: Lift something up and it stores gravitational potential energy (PE) — energy because of its height.
From height to motion
- Let it fall and that PE turns into kinetic energy (KE) — energy because of its motion.
- No energy is lost: the PE the object loses becomes the KE it gains.
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Spot it: Top of a fall = all PE, no KE. Bottom = all KE, no PE. At any height in between, PE + KE adds up to the same total — that total is the mechanical energy, and it stays constant.
Conservation of energy: Energy cannot be created or destroyed. It can only be transferred from one store or object to another, so the total energy of a closed system stays the same.
Mechanical energy = kinetic energy + gravitational potential energy + elastic potential energy. With no friction or air resistance, the mechanical energy stays the same too.
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The change in gravitational PE when an object moves up or down a height Δh is given in the data booklet:
- change in gravitational PE (J)
- mass (kg)
- gravitational field strength (≈ 9.8 N kg⁻¹ on Earth)
- change in height (m)
What 'conservation of energy' means here: For a falling body with no air resistance, the mechanical energy (PE + KE) is conserved — it stays the same.
So the PE lost = the KE gained: mgΔh = ½mv².
The kinetic energy of a moving object is also given in the booklet:
- kinetic energy (J)
- mass (kg)
- speed (m s⁻¹)
Δh is always the vertical height. On a ramp or a pendulum, find it first:
A big object: use its centre of mass: For a large object (a ladder, a block of water), Δh is how far its centre of mass rises.
A uniform 4.0 m pole lying on the ground is stood upright: its centre rises 2.0 m, so with a mass of 15 kg, ΔEp = 15 × 9.8 × 2.0 = 290 J.
A 2.0 kg ball is lifted 5.0 m above the ground (g = 9.8 N kg⁻¹). Find the gravitational PE it gains.
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How this is tested — falling-body energy comes up in two predictable forms:
Paper 1A
- A quick MCQ — often a ratio of KE part-way down to the PE at the top.
- Or 'where is PE = KE?'
Paper 2
- A short calculation setting PE lost = KE gained (mgΔh = ½mv²).
- …to find a landing speed.
The classic trap: The mass cancels — speed at the bottom doesn't depend on m. And falling half the height means only half the energy is KE so far, not all of it.
The ratio shortcut: Because KE gained = PE lost, an object that has fallen a fraction f of its total height has turned a fraction f of its starting PE into KE. Fall half the height → KE = ½ of the starting PE.
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A stone is released from rest at the top of a cliff (air resistance negligible). When it has fallen one-quarter of the way down, find the ratio (KE there) : (PE at the release point).
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When friction acts
Mechanical energy is lost, total energy is not: Friction and air resistance do work against the motion. Mechanical energy lost = work done against friction, and that energy becomes thermal energy in the surfaces and the air.
Sliding down a rough ramp: Ek at the bottom = mgh − F × d, where d is the distance along the ramp.
A 4.0 kg crate slides from rest down a ramp 5.0 m long, dropping through 2.0 m. A steady friction force of 9.0 N acts along the ramp (g = 9.8 N kg⁻¹). Find its speed at the bottom.
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