Work, energy and power

What the syllabus demands

• —Define work done: W = Fs cos θ for force at angle θ to displacement
• —Derive and use KE = ½mv² from the equations of motion
• —Derive and use ΔEp = mgΔh for uniform fields
• —Apply the principle of conservation of energy including work against resistive forces
• —Define power; use P = W/t and P = Fv; calculate efficiency

Definitions that earn marks

Clear definitions to practise — check your course mark scheme

Work done

The product of the force and the displacement in the direction of the force: W = Fs cos θ.

Kinetic energy

The energy of a body due to its motion: Ek = ½mv², derived from v² = u² + 2as with W = Fs.

Power

The rate of doing work or transferring energy: P = W ÷ t. For constant velocity, P = Fv.

Efficiency

The ratio of useful output energy (or power) to total input energy (or power), expressed as a fraction or percentage.

The equations

More equations to practise: the Edexcel IAL formula sheet.

Where the marks die

Common mistakes to check

1. 01

   Ignoring the cos θ. A force perpendicular to the motion does no work at all — the normal force on a sliding block, the tension in a whirling string, gravity on a horizontal journey.

2. 02

   Energy chains that skip work done against friction. On a real slope: GPE lost = KE gained + work done against resistance. Omitting the last term is the most common lost mark on this topic.

3. 03

   P = Fv used when velocity is changing without noticing it gives instantaneous power only. At maximum speed (a = 0), driving force = resistive force — that special case unlocks most 'top speed' questions.

4. 04

   Deriving KE = ½mv² by memory instead of physics. Start from W = Fs, substitute F = ma and v² = u² + 2as with u = 0 — the examiner wants the logic, not the result.

One worked example, done properly