3.2 Work-Energy Theorem

The Work-Energy Theorem

The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = KE_f − KE_i. If net work is positive, kinetic energy increases (speeds up); if negative, kinetic energy decreases (slows down). This links force and displacement directly to changes in motion.

Calculating Work

Work is done when a force causes displacement: W = F·d·cos(θ), where θ is the angle between force and displacement. Only the force component parallel to displacement does work. A force perpendicular to motion (like normal force on a flat surface) does zero work.

Applying the Theorem

To find an object's final speed or stopping distance, set W_net = ΔKE and solve. This avoids needing acceleration or time — powerful for variable forces or curved paths. Works with multiple forces: sum all works (or use net force) to get total energy change.

Key terms

Work-Energy Theorem

W_net = ΔKE; the net work done on an object equals its change in kinetic energy.

Work formula (constant force)

W = F·d·cos(θ), where θ is the angle between force and displacement.

When is work zero?

When force is perpendicular to displacement (θ = 90°), since cos(90°) = 0.

Positive net work effect

Increases an object's kinetic energy (speeds it up).

Negative net work effect

Decreases an object's kinetic energy (slows it down), e.g., due to friction.

Try an AP-style question

A 10 N force pushes a box 5 m in the direction of motion. How much work does it do?

1. 2 J
2. 0 J
3. 15 J
4. 50 J