Key Equations

Work, Energy & Power — AQA A-Level Physics

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Work done (force at angle)
$$W = Fs \cos \theta$$
  • Where:
    • $W$ = work done (J)
    • $F$ = applied force (N)
    • $s$ = displacement (m)
    • $θ$ = angle between force and displacement
General form. Reduces to W = Fs when theta = 0.
Work done (parallel force)
$$W = Fs$$
  • Where:
    • $W$ = work done (J)
    • $F$ = force parallel to displacement (N)
    • $s$ = displacement (m)
Only when force is in the direction of displacement.
Power (from force and velocity)
$$P = Fv$$
  • Where:
    • $P$ = power (W)
    • $F$ = driving force (N)
    • $v$ = velocity (m s⁻¹)
Valid at constant velocity. F must be in the direction of v.
Power (from work done)
$$P = \frac{\Delta W}{\Delta t}$$
  • Where:
    • $P$ = power (W)
    • $ΔW$ = work done (J)
    • $Δt$ = time (s)
1 W = 1 J s^-1.
Kinetic energy
$$E_k = \frac{1}{2}mv^2$$
  • Where:
    • $E_k$ = kinetic energy (J)
    • $m$ = mass (kg)
    • $v$ = speed (m s⁻¹)
Scalar quantity. Proportional to v squared.
Efficiency
$$\eta = \frac{\text{Useful output}}{\text{Total input}} \times 100\%$$
  • Where:
    • $η$ = efficiency (%)
    • $output$ = useful energy or power output
    • $input$ = total energy or power input
No units. Always between 0% and 100%.
Gravitational potential energy
$$\Delta E_p = mg \Delta h$$
  • Where:
    • $ΔE_p$ = change in gravitational potential energy (J)
    • $m$ = mass (kg)
    • $g$ = gravitational field strength (9.81 N kg⁻¹)
    • $Δh$ = change in height (m)
Only valid in a uniform gravitational field (near Earth's surface).
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