Work, Energy, and Power
Core ideas
Work is W = Fd cosθ, the component of force along displacement times displacement. The work-energy theorem says net work equals change in kinetic energy. Conservative forces (gravity, springs) have potential energy; nonconservative forces (friction) dissipate mechanical energy as heat.
Mechanical energy E = K + U is conserved when only conservative forces do work. Gravitational potential energy near Earth is mgh; elastic potential energy is ½kx². Power is the rate of energy transfer, P = W/t = Fv cosθ.
Candidates must distinguish work done on a system from work done by a system and must recognize when to use energy methods versus Newton's laws. Energy is often faster when speed–height trade-offs appear.
Traps
- Assuming a force doing no work (e.g., centripetal force, normal force on a level floor) transfers energy.
- Forgetting that friction does negative work and reduces mechanical energy.
- Using mgh when height changes are small compared to Earth's radius - fine - but forgetting sign conventions for ΔU.
- Confusing power (rate) with work (amount).
Rule of thumb
If a problem asks for speed after a height change or a spring compression, try conservation of energy first. Always account for nonconservative work: E_final − E_initial = W_nc.
Worked example
A 1 kg block slides from rest down a 5 m frictionless ramp of height 3 m. Then mgh = ½mv² gives v = √(2gh) = √(2·10·3) ≈ 7.7 m/s. If friction does −10 J of work, subtract: ½mv² = mgh − 10 = 30 − 10 = 20 J, so v ≈ 6.3 m/s.