Work, Energy & Power

Quantifying energy transfers through work done, kinetic and potential energy, power and efficiency.

Spec Points Covered
  • I can calculate the work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). times potential difference). by a force, including when the force is at an angle to the displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m)..
  • I can derive and use the equation for kinetic energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its motion. from Newton's second law and SUVAT.
  • I can calculate gravitational potential energyThe capacity to do work. Measured in joules (J).The energy an object possesses due to its position in a gravitational fieldA region of space in which a mass experiences a gravitational force.. changes near the Earth's surface.
  • I can apply the principle of conservation of energyEnergy cannot be created or destroyed, only transferred from one form to another. The total energy of a closed system remains constant. to solve problems involving energy transfers.
  • I can calculate powerThe rate of energy transfer. Measured in watts (W). as the rate of doing work and use $P = Fv$ for objects at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹..
  • I can calculate efficiencyThe ratio of useful energy output to total energy input, expressed as a fraction or percentage. and distinguish between useful and wasted energy.
  • I can interpret force-displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). graphs to find work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). times potential difference). from the area under the curve.
  • I can solve problems involving energy conservation with friction and resistive forces on inclined planes.
Notes
01 Work done Work done → 02 Kinetic energy Kinetic energy → 03 Gravitational potential energy Gravitational potential energy → 04 Conservation of energy Conservation of energy → 05 Power Power → 06 Efficiency Efficiency →
Σ Key Equations Full Reference →
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.