Key Equations
Work, Energy & Power — AQA A-Level Physics
On Data Sheet
Not on Data Sheet
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).