Theme A — Space, Time and Motion
A.3 Work, Energy and Power — IB Physics SL Revision Notes & Topical Questions
5 min read 10 parts Lesson 30 of 41 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
A.3 Work, Energy and Power — IB SL Notes — IB PHYSICS SL notes: Use work, the conservation of energy, power and efficiency to analyse mechanical energy transfers, and interpret energy density and Sankey diagrams.Work done — W = Fs cos θ, the energy transferred by a force.θ is the…
- Perpendicular force
- Varying force
- Dissipation
- Work–energy theorem
- Gravitational potential
- Elastic potential
Part 1 of 8Work
Work done
- W = Fs cos θ, the energy transferred by a force.
- θ is the angle between the force and the displacement.
- The unit is the joule, 1 J = 1 N m.
Perpendicular force
- Perpendicular force it does no work.
Varying force
- Varying force the work is the area under the force–displacement graph.
Part 2 of 8Conservation of energy
Principle
- Principle energy cannot be created or destroyed, only transferred or transformed.
Dissipation
- Dissipation no transfer is 100% efficient, and the wasted energy usually becomes thermal energy of the surroundings.
Work–energy theorem
- Work–energy theorem the net work done on a body equals its change in kinetic energy.
Part 3 of 8Energy stores in mechanics
| Store | Equation | Depends on |
|---|---|---|
| Kinetic | Ek = ½mv2 = p2/2m | Mass and speed |
| Gravitational potential | ΔEp = mgΔh | Mass, field strength, height change |
| Elastic potential | EH = ½k(Δx)2 | Spring constant and extension |
Gravitational potential
- Gravitational potential only changes matter, and the zero level is a free choice.
Elastic potential
- Elastic potential it equals the area under the force–extension line for a spring obeying Hooke's law.
Part 4 of 8Mechanical energy
Mechanical energy
- Mechanical energy the sum Ek + Ep + EH.
No resistive forces
- No resistive forces mechanical energy is conserved.
With resistive forces
- With resistive forces work done against them equals the mechanical energy transferred to thermal energy.
Part 5 of 8Power and efficiency
Power
- P = ΔW/Δt, with unit the watt, 1 W = 1 J s−1.
Steady motion
- Steady motion for a constant driving force at constant velocity, P = Fv.
Efficiency
- η = useful output / total input, for energy or power.
- It has no unit and is below 1 for real machines.
Part 6 of 8Sankey diagrams and energy density
Sankey diagram
- Sankey diagram the width of each arrow is proportional to the energy or power it represents.
- Total energy in = useful energy out + wasted energy.
Energy density
- Energy density the energy released per unit volume of fuel, in J m−3.
Specific energy
- Specific energy the energy per unit mass of fuel.
Part 7 of 8Solving energy problems
1
Identify the system and the initial and final states.
2
List the energy stores at each state: kinetic, gravitational and elastic.
3
Write initial total energy = final total energy + work done against resistive forces.
4
Solve for the unknown and check the units.
Part 8 of 8More from the specification
More from the specification
Work done against resistive forces
- Work done against resistive forces integrating applied mechanical force along displacement paths provides an analytical means to evaluate expended work.
Work Done by a Force at an Angle
- Work done on an object is calculated as W = F * s * cos(theta),
- where only the component of force acting parallel to the direction of displacement along the horizontal or vertical axis performs mechanical work.
Dissipative Forces and Friction
- When an object slides across a rough surface, friction opposes motion and dissipates mechanical energy into thermal energy,
- meaning the total amount of mechanical work input exceeds useful kinetic or potential energy gained.
Gravitational Potential Energy and Position
- The gravitational potential energy stored in an object or a mass of water depends on its vertical position in a gravitational field, calculated using Delta Ep = m * g * Delta h.
Power Output of an Electric Motor
- Power is defined as the rate of energy transfer or work done; the useful power of an electric motor pumping water or lifting a load reflects electrical power minus internal dissipated losses.
- (P = W / Delta t = F * v)
Friction
- Force parallel to the surface opposing relative motion or its tendency.
Component
- Part of a vector along one axis.
Position
- Location relative to a reference point.
Distance
- Total length of path travelled, a scalar.
Resultant force
- Another name for net force.
W
Fs = 25.6 × 20 = 512 J
What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)
Key terms
| Term | Meaning |
|---|---|
| Work done | The product of the force and the displacement in the direction of the force |
| Kinetic energy | The energy a body has because of its motion |
| Gravitational potential energy | The energy a body has because of its position in a gravitational field |
| Elastic potential energy | The energy stored in a deformed elastic object |
| Power | The rate at which work is done or energy is transferred |
| Efficiency | The ratio of useful output energy (or power) to total input energy (or power) |
| Energy density | The energy released per unit volume of a fuel |
Avoid these mistakes
1
Counting a force perpendicular to the motion as doing work — only the component along the displacement does work.
2
Using mechanical energy conservation when friction acts — include the energy dissipated.
3
Using P = Fv when velocity is not constant — it applies to constant force at constant velocity (or instantaneous values).
4
Writing efficiency with a unit — it is a ratio.
5
Mixing joules and kilowatt-hours — 1 kW h = 3.6 × 106 J.
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