LucidSTEM
A-LEVEL 9702 · AS · TOPIC 5
Work, energy and power
The chain of the topic: a force doing work transfers energy, that energy is conserved as it changes form, and the two store forms examiners care about most, kinetic energy and gravitational potential energy, are derived straight from work done. Around the hexagon are the four ideas; above is what it builds on, below is where it leads.
TOPIC 5: WORK, ENERGY AND POWER
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
TheLucidSTEM · thelucidstem.com
BUILDS ON
T2 Kinematics T3 Newton's laws, F = ma T4 Forces, weight W = mg 5.1
5.1
5.2
5.2
TOPIC 5
ENERGY
& POWER
1 · WORK AND POWER
A force doing work transfers energy.
Work = force × displacement in the force direction
Only the component F cosθ along the motion does work
Power is the rate of doing work, in watts (J s−¹)
W = F s cosθ
P = W / t = F v
F
θ
s
work done = (F cosθ) × s
2 · CONSERVATION & EFFICIENCY
Energy is never lost, only transferred.
Total energy of an isolated system stays constant.
It changes form but the grand total is unchanged.
Useful output is always less than the total input;
the rest is dissipated, mostly as thermal energy.
efficiency = useful output / total input
total in
useful out
wasted (heat)
total input = useful + wasted
3 · KINETIC ENERGY
Energy stored in motion.
Derived from W = F s with F = ma and v² = 2as
Work to accelerate a body from rest equals the KE gained
Scales with v²: double the speed, quadruple the energy
Eₖ = ½ m v²
v
Eₖ
∝ v²
kinetic energy rises with the square of speed
4 · GRAVITATIONAL POTENTIAL ENERGY
Energy stored by raising a mass.
Work done against gravity, W = (mg) × Δh
Valid near Earth, where g is effectively uniform
In free fall, lost GPE converts to gained KE
ΔEₚ = m g Δh
mgΔh = ½mv²
Δh
mg
raise mass m through Δh to store mgΔh
LEADS TO
T6 Deformation: elastic strain energy ½Fx T13 Gravitational fields: potential energy −GMm/r T16 Thermodynamics: heat & internal energy Each extends the same idea: work transfers energy between stores, and the grand total is always conserved.
← Builds on IGCSE: Energy, work & power