Theme A · Space, Time and Motion · SL + HL · 8 hours

A.3 Work, Energy and Power

How can energetics be used as an alternative method to solve problems in kinematics?

Energy is the currency of physics. Every process — from a rocket launch to a chemical reaction to the beating of a heart — can be understood as a transformation of energy from one store to another. The principle of conservation of energy is one of the deepest laws in science: the total energy of an isolated system never changes, it only moves between forms.

Work connects force and energy: when a force has a component along the direction of displacement, energy transfers. The angle between force and displacement matters — a force perpendicular to motion (like centripetal force) does no work, which is why a satellite in circular orbit maintains constant speed. Efficiency measures how much of the input energy goes to the intended output; Sankey diagrams make the losses visible.

A 70 kg cyclist descends a hill of vertical height 30 m, starting from rest. If the cyclist and bicycle together experience 800 J of work done against friction, what is the speed at the bottom? Use energy methods.

Key equations

Work done: W = Fscosθ

Kinetic energy: E_k = ½mv² = p²/2m

Gravitational PE (near Earth's surface): ΔE_p = mgΔh

Elastic PE: E_H = ½k(Δx)²

Power: P = ΔW/Δt = Fv

Efficiency: η = E_output / E_input = P_output / P_input

What students must understand

Conservation of energy — energy cannot be created or destroyed, only transferred between stores
Work done by a force equals the energy transferred: W = Fscosθ; the component along displacement matters
Energy transfers can be represented on Sankey diagrams
Mechanical energy is the sum of kinetic, gravitational potential, and elastic potential energy
Without friction, total mechanical energy is conserved
Power is the rate of doing work or transferring energy: P = ΔW/Δt = Fv
Efficiency in terms of energy or power ratios
Energy density of fuel sources (useful for comparing fuels and energy resources)

Linking questions

Which other quantities in physics are rates of change? → A.1 Kinematics, D.4 Induction
How is the equilibrium of a star determined in terms of energy? → B.2 Greenhouse Effect, E.5 Fusion and Stars
How do travelling waves transfer energy without net displacement of matter? → C.2 Wave Model
Why does the formula ΔE_p = mgh only work close to Earth's surface? → D.1 Gravitational Fields