Work, Energy & Power

Work done by constant and variable forces, power, efficiency, conservation of energy, kinetic energy, and gravitational potential energy.

Spec Points Covered
  • Calculate 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 constant force, including forces at an angle to the displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m)..
  • Determine 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 a force-displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). graph.
  • Define powerThe rate of energy transfer. Measured in watts (W). and apply $P = W/t$ and $P = Fv$.
  • Calculate efficiencyThe ratio of useful energyThe capacity to do work. Measured in joules (J). output to total energyThe capacity to do work. Measured in joules (J). input, expressed as a fraction or percentage. from useful and total energyThe capacity to do work. Measured in joules (J). or powerThe rate of energy transfer. Measured in watts (W)..
  • State and 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..
  • Use $E_{k} = 0.5mv^2$ and $\Delta E_{p} = mg \Delta h$ in energy transfer problems.
Notes
01 Work done is the energy transferred when a force moves an object Work done 3.4.1.7 → 02 Work done equals the area under a force-displacement graph 3.4.1.7 → 03 Power is the rate of doing work Power 3.4.1.7 → 04 Efficiency measures how much input energy is usefully transferred Efficiency 3.4.1.7 → 05 Energy cannot be created or destroyed, only transferred between forms Conservation of energy 3.4.1.7 → 06 Kinetic energy depends on mass and the square of speed Kinetic energy 3.4.1.7 → 07 Gravitational potential energy depends on mass, g, and height change Gravitational potential energy (near Earth's surface) 3.4.1.7 → 08 In free fall without air resistance, GPE converts entirely to KE $mg \Delta h = \frac{1}{2}mv^2$ 3.4.1.7 →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
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.
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.
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).
Q Retrieval Practice All 12 Questions →
Q1. Define 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)..
  • The energy transferred when a force causes an object to move a distance.
  • W = Fs (or W = Fs cos theta if the force is at an angle).
Q2. How do you find work done from a force-displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). graph?
Calculate the area under the graph.
Q3. Define powerThe rate of energy transfer. Measured in watts (W). and state its unit.
  • Power is the rate of doing work (or rate of energy transfer).
  • P = W/t.
  • Unit: watt (W).
Q4. Write the equation linking power, force and velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹..
  • P = Fv.
  • Valid when force is constant and in the direction of velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹..
Q5. How is efficiencyThe ratio of useful energy output to total energy input, expressed as a fraction or percentage. calculated?
EfficiencyThe ratio of useful energy output to total energy input, expressed as a fraction or percentage. = useful output / total input (as a ratio) or multiplied by 100 for percentage.