Key Equations

Work, Energy & Power - OCR A-Level Physics

On Data Sheet
Not on Data Sheet
Work done by a force at an angle
$$W = Fs\cos\theta$$
  • Where:
    • $W$ = J
    • $F$ = N
    • $s$ = m
theta is the angle between force and displacement. When parallel, theta = 0 and W = Fs.
Kinetic energy
$$E_k = \frac{1}{2}mv^{2}$$
  • Where:
    • $E_k$ = J
    • $m$ = kg
    • $v$ = m \(s^{-1}\)
Always positive. Proportional to v squared: double the speed means four times the kinetic energy.
Gravitational potential energy
$$\Delta E_p = mg\Delta h$$
  • Where:
    • $\Delta E_p$ = J
    • $m$ = kg
    • $g$ = m \(s^{-2}\)
    • $\Delta h$ = m
Valid near the Earth's surface where g is approximately constant. Delta h is the vertical height change.
Power (rate of work)
$$P = \frac{W}{t}$$
  • Where:
    • $P$ = W (J \(s^{-1}\))
    • $W$ = J
    • $t$ = s
Power is the rate of doing work or the rate of energy transfer.
Power (force and velocity)
$$P = Fv$$
  • Where:
    • $P$ = W
    • $F$ = N
    • $v$ = m \(s^{-1}\)
Derived from P = W/t = Fs/t = Fv. Use for vehicles at constant velocity where driving force = resistive force.
Efficiency
$$\text{efficiency} = \frac{\text{useful output energy}}{\text{total input energy}}$$
Dimensionless ratio. Multiply by 100 for percentage. Can also use power instead of energy. Always less than 1 for real machines.
Back to Work, Energy & Power Overview