Work, Energy and Power

This guide covers Topic 5, Work, energy and power, in full — subtopics 5.1 Energy conservation and 5.2 Gravitational potential energy and kinetic energy — from Cambridge International AS & A Level Physics 9702, 2025–2027 series. This is AS Level content, and an understanding of forms of energy and energy transfers from Cambridge IGCSE/O Level Physics or equivalent is assumed.

Before studying this

This resource assumes forces and Newton’s laws from Dynamics: Newton’s Laws and Momentum, and a basic IGCSE/O Level familiarity with energy forms and transfers.

Syllabus coverage

CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 — AS Level, Topic 5

5.1 Energy conservation — the concept of work, and work done = force × displacement in the direction of the force; the principle of conservation of energy; efficiency as the ratio of useful energy output to total energy input, and solving problems with it; power as work done per unit time, using P = W/t and deriving and using P = Fv.

5.2 Gravitational potential energy and kinetic energy — deriving, using W = Fs, the formula ∆Eₚ = mg∆h for gravitational potential energy changes in a uniform field; recalling and using it; deriving, using the equations of motion, the formula for kinetic energy Eₖ = ½mv²; recalling and using it.

Work done

Work done = force × displacement in the direction of the force. Where the force and displacement are not in the same direction, only the component of the force along the direction of displacement contributes — this connects directly back to the vector resolution introduced in Topic 1.

Conservation of energy and efficiency

The principle of conservation of energy states that energy cannot be created or destroyed, only transferred from one form to another. Efficiency is the ratio of useful energy output to total energy input, often expressed as a percentage:

efficiency = (useful energy output / total energy input) × 100%

Most practical devices have some unwanted energy transfer (commonly to heat, through friction or resistance), so their efficiency is below 100%. Efficiency can never exceed 100% – that would mean creating energy. But 100% is not physically impossible for every process: it depends on what counts as “useful” output. An electric heater that is meant to produce heat can convert essentially all of its electrical input into that intended output, giving an efficiency very close to 100%, because none of the energy has left by a route other than the one being counted as useful.

Worked example. A pump raises 300 kg of water through 10 m in 25 s, while drawing 1500 W of electrical power. Find its efficiency.

useful power = mgh / t = 300 x 9.81 x 10 / 25 = 1177 W

efficiency = (useful output / total input) x 100 = (1177 / 1500) x 100 = 78.5%

Worked example. A 0.40 kg ball is dropped from 6.0 m and rebounds to 3.5 m. Find the energy dissipated during the bounce.

GPE lost falling         = mgh1 = 0.40 x 9.81 x 6.0 = 23.5 J
GPE regained on rebound  = mgh2 = 0.40 x 9.81 x 3.5 = 13.7 J
energy dissipated        = 23.5 - 13.7 = 9.81 J

The energy is not destroyed in the bounce — it is transferred to internal energy in the ball and the surface, and to sound, becoming too dissipated to be recovered as useful kinetic or potential energy.

Power

Power is defined as work done per unit time:

P = W/t

Since work done = force × displacement, and displacement/time = velocity, this can be rewritten (deriving from W = Fs) as:

P = Fv

P = Fv is a general result for instantaneous power (force and velocity parallel, or F taken as the component of force along the direction of motion) – it holds while an object is accelerating just as much as while it moves at constant velocity. The constant-velocity case is simply the one where it’s easiest to apply: a vehicle moving at constant speed has its driving force exactly equal to the resistive force, so a known speed and resistive force give the driving power directly, without needing to consider acceleration at all.

Gravitational potential energy and kinetic energy

Gravitational potential energy change, for an object of mass m raised through height ∆h in a uniform gravitational field, is derived from W = Fs (work done against gravity, force = mg, displacement = ∆h):

∆Eₚ = mg∆h

Kinetic energy is derived using the equations of motion — starting from work done = force × displacement and substituting v² = u² + 2as (with u = 0 for an object starting from rest, or more generally by considering the change in kinetic energy as the work done by a resultant force):

Eₖ = ½mv²

Worked example. A 0.50 kg ball is thrown upward at 8.0 m s⁻¹. Using conservation of energy, its maximum height (where all kinetic energy has converted to gravitational potential energy, ignoring air resistance):

½mv² = mg∆h
½ × 0.50 × 8.0² = 0.50 × 9.81 × ∆h
16 = 4.905∆h
∆h ≈ 3.3 m

Common mistakes

• Using the object’s total displacement instead of the component in the direction of the force when calculating work done — only the parallel component counts.
• Assuming a process is 100% efficient unless told otherwise. Most real processes lose some energy to non-useful forms, so don’t assume 100% by default – but don’t rule 100% out either where the intended “useful” output happens to be the only form the energy can end up in (e.g. an electric heater producing heat).
• Thinking P = Fv only applies at constant velocity. P = Fv is a general instantaneous-power result and holds during acceleration too; what’s specific to the constant-velocity case is just that driving force then equals resistive force, making the calculation simpler — not that the formula itself stops applying otherwise.
• Forgetting that ∆Eₚ = mg∆h only applies to a uniform gravitational field — it is not valid for large height changes where g varies appreciably (see Gravitational Fields at A Level for the general case).

Quick revision checklist

• Work done = force × displacement in the direction of the force
• Conservation of energy and calculating efficiency
• P = W/t, and deriving/using P = Fv
• Deriving and using ∆Eₚ = mg∆h and Eₖ = ½mv²
• Using conservation of energy to solve combined KE/PE problems

Related resources

• Forces, Density and Pressure — the previous AS topic
• Deformation of Solids: Stress, Strain and the Young Modulus — the next AS topic, using elastic potential energy
• Cambridge AS & A Level Physics hub

Written against Cambridge International AS & A Level Physics 9702, 2025–2027 series. Always check the current syllabus for your examination year.