Work, Energy & Power

Cheat Sheet  ·  Physics Gr 11
Emil Oliversen
WORK
Definition
W = F·d·cosθ (Joules, J)
θ
angle between force & displacement
Sign of work
W > 0
force aids motion (θ < 90°)
W < 0
force opposes motion (θ > 90°)
W = 0
force ⊥ displacement (θ = 90°)
Work-energy theorem
W_net = ΔEk = Ek_f − Ek_i
Carrying a box horizontally: gravity does zero work (θ = 90°). Normal force also does zero work.
KINETIC ENERGY
Ek formula
Ek = ½mv²
Work-energy
ΔEk = W_net
Doubling speed → quadruples Ek
GRAVITATIONAL PE
Ep formula
Ep = mgh
h
vertical height above reference
Reference level is arbitrary — only Δh matters
ELASTIC PE (SPRING)
Ee formula
Ee = ½kx²
Hooke's Law
F = kx
k
spring constant (N/m)
x
compression / extension (m)
CONSERVATION OF ENERGY
No friction:
Total E
Ek_i + Ep_i = Ek_f + Ep_f
With friction:
With friction
subtract W_friction from total E
Friction converts mechanical energy to heat — total universe energy still conserved
PENDULUM
PositionEkEp
Top (extreme)0max
Bottommax0
Height h
h = L(1 − cosθ)
Speed
v = √(2gh)
Energy eq
mgh = ½mv²
POWER
P (basic)
P = W/t (Watts = J/s)
P (force)
P = Fv (F and v same direction)
  • Average power: total W ÷ total t
  • 1 kW = 1000 W; 1 hp ≈ 746 W
EFFICIENCY
Efficiency
eff = (E_useful / E_input) × 100%
Efficiency is always ≤ 100%
COMMON MISTAKES
  • W = Fd only when θ = 0° — always use cosθ
  • h in Ep = vertical height only (not slant)
  • v in Ek = full speed, not a component
  • Efficiency is always ≤ 100%
  • Spring PE uses x (deformation), not position
  • Pendulum top: max Ep, zero Ek (v = 0)