Work, Energy and Power
Work, Energy and Power tests the work–energy theorem, conservative versus non-conservative forces, potential energy, collisions and power ratings.
Core rules
- W = F·s = Fs cosθ; work is zero when the force is perpendicular to the displacement.
- Work–energy theorem: W(net) = ΔK = ½mv² − ½mu².
- Conservative forces do path-independent work and have a potential energy with F = −dU/dx. Spring U = ½kx²; gravity near Earth U = mgh.
- Mechanical energy is conserved when only conservative forces do work; friction converts it into heat.
- In every collision momentum is conserved; kinetic energy is conserved only in elastic collisions. In a one-dimensional elastic collision of equal masses, the velocities exchange.
- Power P = W/t = F·v; 1 hp ≈ 746 W.
Worked example
A 2 kg block moving at 4 m s⁻¹ strikes a spring of k = 200 N m⁻¹ on a frictionless floor. All kinetic energy becomes elastic potential energy: ½ × 2 × 16 = 16 J = ½ × 200 × x², so x² = 0.16 and x = 0.40 m. With friction the compression would be smaller, because part of the energy would leave as heat.
Traps
Claiming centripetal force does work (it does not); using kinetic-energy conservation in a perfectly inelastic collision; omitting the ½ in spring energy; assuming constant power when a machine accelerates.