Energy, Work and Power
Energy forms and conservation
The SEC syllabus tests work, energy transfer, power and efficiency in mechanical and electrical contexts. Energy is measured in joules and is conserved: it transfers between stores but is not created or destroyed.
- Work done by a constant force: W = Fs cos θ, where θ is the angle between the force and the displacement.
- Kinetic energy: KE = ½mv²; gravitational potential energy near Earth: ΔGPE = mgΔh.
- Power = work done/time = energy transferred/time; for constant speed P = Fv.
- Efficiency = useful output energy (or power) ÷ total input energy (or power) × 100%.
Friction and air resistance transfer mechanical energy to thermal energy, so useful energy falls even though total energy is conserved. At constant speed, the driving force equals the total resistive force.
Worked example
A 60 kg student climbs 12 m vertically in 20 s. Taking g = 10 N/kg, find the gain in gravitational potential energy and the average useful power.
ΔGPE = mgΔh = 60 × 10 × 12 = 7200 J.
Average power = 7200 J ÷ 20 s = 360 W.
Reasoning: the vertical height gained, not the distance walked, sets the GPE gain; power is the rate of that gain.
Traps
Using total distance travelled instead of vertical height for GPE; forgetting cos θ so that a force perpendicular to motion is wrongly said to do work; mixing energy (J) with power (W); giving efficiency as a decimal without converting to a percentage when asked; assuming energy is used up rather than dissipated.