Work, Energy and Power
What this domain tests
Work done by constant and variable forces, the work–energy theorem, conservative versus non-conservative forces, power, and elastic and inelastic collisions.
Core rules
- W = Fd cosθ: zero when force is perpendicular to displacement, negative when it opposes motion.
- Work–energy theorem: W_net = ΔK for any combination of forces.
- Spring potential energy ½kx²; gravitational PE mgh near the Earth; for a conservative force F = −dU/dx.
- Power P = W/t = F·v; SI unit watt; 1 kWh = 3.6×10⁶ J.
- Momentum is conserved in every collision without external forces; kinetic energy only in elastic collisions. Coefficient of restitution e = separation speed ÷ approach speed, with e = 1 elastic and e = 0 perfectly inelastic.
- In a head-on elastic collision of equal masses, the bodies exchange velocities.
Worked example
A 2 kg block at rest is pushed 3 m along a frictionless floor by a constant 10 N force. Find the final speed. W = Fd cos0° = 30 J. The work–energy theorem gives 30 = ½(2)v², so v² = 30 and v ≈ 5.5 m/s. There is no need to find acceleration and time; energy is the shorter route.
Traps that cost marks
- Believing the centripetal force does work; it is always perpendicular to velocity.
- Assuming kinetic energy is conserved in a perfectly inelastic collision - it is minimum there, not conserved.
- Using mgh for spring energy or ½kx² for gravitational energy.
- Omitting cosθ when the force acts at an angle to the displacement.