Energy & momentum · Topic 9 of 17

Work, Energy & Power

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Physics · work and energy

Work is force times distance; energy of motion is ½mv², stored height energy is mgh; total energy is conserved; power is work per second.

01 · WorkW = F × d (joules)

02 · Kinetic energyKE = ½mv²

03 · Potential energyPE = mgh

Energy = ability to do work; both measured in joules

Falling: PE → KE; KE at the bottom = PE at the top (no air drag)

Mechanical energy = KE + PE; friction turns some into heat

Same work in less time → more power

Energy is conserved: it changes form, the total stays the same must know

Speed ×2 → KE ×4; mass ×2 → KE ×2

Work W = F × d (force along the motion); 1 J = 1 N·m must know

Kinetic energy KE = ½ m v² (energy of motion) must know

Potential energy PE = m g h (g = 9.8 m/s², h in m) must know

Power P = W / t; 1 watt (W) = 1 J/s must know

40 N × 15 m = 600 J of work

KE = ½ × 4 kg × (5 m/s)² = 50 J

PE = 10 × 9.8 × 3 = 294 J; in 6 s → P = 49 W

Commonly confused

	Kinetic energy (KE)	Gravitational potential energy (PE)
Energy of…	Motion	Position (height)
Formula	KE = ½mv²	PE = mgh
Double the mass	2× the KE	2× the PE
Double the speed / height	Speed ×2 → 4× the KE	Height ×2 → 2× the PE
During a fall	Increases	Decreases by the same amount

No work if no movement, or if force ⟂ motion

Show 3 more facts

Net work = change in kinetic energy (work-energy theorem)

Force at an angle: W = F d cos θ

Efficiency = useful output ÷ total input (always below 100%)

Pearl

Energy changes form, never amount: height energy at the top is motion energy at the bottom.

Practice this topic, then test the whole section.

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