Work, Energy and Power
What this domain tests
Work, Energy and Power tests work done by constant and variable forces, kinetic and potential energy, conservation of mechanical energy, power and collisions. Expect problems combining a force, a distance and a speed.
Core rules
- Work W = F·s = Fs cosθ. Work is zero when force is perpendicular to displacement; negative when force opposes displacement.
- Work-energy theorem: W_net = ΔK = 1/2 mv² - 1/2 mu².
- Conservative forces have potential energy: gravitational U = mgh near Earth; spring U = 1/2 kx². Mechanical energy is conserved if only conservative forces do work.
- Power P = W/t for average, P = F·v for instantaneous. SI unit watt = J/s.
- In elastic collisions, momentum and kinetic energy are conserved; in perfectly inelastic collisions, bodies stick together and kinetic energy is lost.
Worked example
A 2 kg block starts from rest and is pulled 4 m by a 10 N horizontal force against 4 N friction. Find its final speed. Net work = (10 - 4) × 4 = 24 J. By the work-energy theorem, 24 = 1/2 × 2 × v² = v², so v = √24 ≈ 4.9 m/s. The reasoning separates the work done by each force; friction contributes -16 J and the applied force +40 J.
Traps
Do not use conservation of mechanical energy when friction acts. Do not confuse power with energy. In a collision, momentum is conserved even when kinetic energy is not. For a spring, the work done is 1/2 kx², not kx.