Theme A — Space, Time and Motion
A.3 Work, Energy and Power — IB Physics HL Revision Notes & Topical Questions
5 min read 11 parts Lesson 31 of 63 1 quiz
Lesson summary
A.3 Work, Energy and Power — IB PHYSICS HL notes: Use work, conservation of energy, power, efficiency, Sankey diagrams and energy density to analyse energy transfers.Energy cannot be created or destroyed — it is only transferred from one form to another.The total energy of a clos…
- Mechanical energy types
- No transfer is 100% efficient
- With friction, loss in kinetic energy
- Parallel force
- What the symbols mean
- Force at an angle θ to the displacement
Part 1 of 9Conservation of energy
Conservation of energy
Energy cannot be created or destroyed
- Energy cannot be created or destroyed it is only transferred from one form to another.
- The total energy of a closed system stays constant.
A system
A system an object or group of objects chosen to focus on what is relevant.
Mechanical energy types
- Mechanical energy types kinetic, gravitational potential and elastic potential.
No transfer is 100% efficient
- No transfer is 100% efficient some energy is dissipated, usually as thermal energy that is hard to reuse and is regarded as wasted.
Examples.
- A falling object in a vacuum transfers gravitational potential energy to kinetic energy.
- A horizontal mass on a spring swaps elastic potential energy and kinetic energy.
- A battery transfers chemical energy to electrical energy;
- a car transfers fuel chemical energy to kinetic energy.
With friction, loss in kinetic energy
With friction, loss in kinetic energy gain in gravitational potential energy + work done against friction.
Part 2 of 9Work done
Work done
Work
Work the transfer of energy when an external force moves an object — unit joule, 1 N m = 1 J.
Parallel force
- W = Fs.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)
Force at an angle θ to the displacement
- W = Fs cos θ.
- Only the component of force parallel to the displacement does work.
- A force perpendicular to the motion does no work.
The area under a force–displacement graph
The area under a force–displacement graph work done.
The work done by the resultant force
The work done by the resultant force the change in kinetic energy.
Part 3 of 9Kinetic, gravitational and elastic energy
Kinetic, gravitational and elastic energy
Kinetic energy Ek
½mv2 = p2/2m — energy due to motion.
- It is a scalar, so a loss of kinetic energy carries no minus sign.
Gravitational potential energy ΔEp
Gravitational potential energy ΔEp mgΔh — stored due to position in a uniform gravitational field.
- Only changes matter; the zero level is a free choice.
- Ep against height is a straight line.
Elastic potential energy EH
½k(Δx)2 = ½FΔx — for a material obeying Hooke's law.
- It equals the area under the force–extension graph.
- When a stretched wire breaks, EH = Ek, so v is proportional to the extension.
Part 4 of 9Mechanical energy
1Mechanical energy
Ek + Ep + EH.
2Conserved when no resistive (non-conservative) forces act
- Conserved when no resistive (non-conservative) forces act e.g. pendulums, free fall and skiing.
- Loss in gravitational potential energy = gain in kinetic energy.
- Loss in elastic potential energy = gain in kinetic energy, for a horizontal spring.
3With friction, the change in mechanical energy
With friction, the change in mechanical energy work done by the non-conservative force.
4
Vertical spring-mass.
| Position | GPE | KE | EPE |
|---|---|---|---|
| Top | Maximum | Zero | Some |
| Equilibrium | Some | Maximum | Some |
| Bottom | Minimum | Zero | Maximum |
Part 5 of 9Power
Power
Power
Power the rate of work done, or energy transfer.
- P = W/t = Fv, in watts; 1 W = 1 J s-1.What the symbols mean: P = power (W = J s−1) · W or E = work done / energy transferred (J) · t = time (s) · F = force (N) · v = velocity (m s−1)
P
Fv is for a constant force at constant velocity — the force acts in the direction of motion.
Power is needed to produce acceleration
- Power is needed to produce acceleration more power does the same work in a shorter time.
Appliance power ratings give the energy transferred per second, e.g. 1000 W.
For drag problems the driving force equals the drag force at constant speed.
Part 6 of 9Efficiency and Sankey diagrams
Efficiency and Sankey diagrams
Efficiency
Efficiency the ratio of useful output to total input.
- η = Eout/Ein = Pout/Pin, with no unit; multiply by 100 for a percentage.
Total energy in
Total energy in useful energy out + wasted energy.
A Sankey diagram represents energy transfers.
- Arrow width is proportional to the amount of energy.
- The right-hand arrow shows useful output and downward arrows show wasted energy.
- An efficient light bulb has a smaller wasted-energy arrow.
Which energy is useful depends on the system
- Which energy is useful depends on the system a kettle heating water versus losses to casing and air.
Part 7 of 9Energy density
Energy density
Energy density the energy per unit volume of a fuel — unit J m-3.
- Specific energy is the energy per unit mass.
Different fuels suit different uses, e.g. petrol for vehicles.
| Fuel | Energy density (MJ L-1) |
|---|---|
| Coal | 38 |
| Diesel | 39 |
| Biodiesel | 33 |
| Vegetable oil | 30 |
| Liquid hydrogen | 9 |
| Wood | 3 |
| Methane | 0.3 |
1 L
0.001 m3.
Fuel choice also depends on safety and pollutants released in combustion.
Part 8 of 9More from the specification
More from the specification
Work done
- W = F x d x cos theta, the energy transferred when a force moves an object a distance
Power
- Power rate of energy transfer, and for a motor pulling with a force at speed P = F x v
Energy equation
- Energy equation work done by the net force equals the change in kinetic energy, so final speed follows from 1/2 m v2 relation
Energy density
- Energy density energy stored per unit mass or volume of a fuel, helping to compare sources
Work-energy theorem
- The total work done by all external forces acting on an object is equal to the change in its kinetic energy: Wnet = ΔEk = 1/2 m v² - 1/2 m u².
Sankey diagrams
- Standardized graphical representations of energy transfers where the width of each branch is strictly proportional to the amount of energy or power flowing through that pathway.
Energy density and specific energy
- Energy density is the energy released per unit volume (J/m³), whereas specific energy is the energy released per unit mass (J/kg) of a fuel source.
Part 9 of 9More from the specification
- Scalar product definition of mechanical work
- evaluating the dot product of force and displacement vectors provides an exact mathematical means for work.
Key terms
| Term | Meaning |
|---|---|
| Work done | Energy transferred when a force moves an object, W = Fs cos θ. |
| Kinetic energy | Energy of motion, ½mv2. |
| Gravitational potential energy | Energy stored due to position in a gravitational field. |
| Power | Rate of doing work, P = W/t. |
| Efficiency | Useful output divided by total input. |
| Energy density | Energy per unit volume of a fuel. |
| Mechanical energy | Sum of kinetic, gravitational and elastic potential energy. |
| Work-energy theorem | The net work done on an object by all acting forces equals the change in its kinetic energy: Wnet = ΔEk = 1 ÷ 2m vf2 - 1 ÷ 2m vi2. |
| Conservative force | A force where the total work done moving a particle between two points is independent of the path taken, permitting the definition of a potential energy function. |
| Dissipative forces | Non-conservative forces such as friction and aerodynamic drag that convert mechanical energy into internal thermal energy. |
| Instantaneous power | The instantaneous rate of energy transfer or work performed, given by P = F · v = F v cosθ. |
Avoid these mistakes
1
Using W = Fs when the force is at an angle — use the component parallel to the displacement.
2
Giving kinetic energy loss a negative sign — energy is a scalar.
3
Assuming mechanical energy is conserved when friction or drag act.
4
Using P = Fv with a varying force or when velocity is not constant.
5
Writing efficiency above 100% or with units.
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