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.