Energy, work and power
Modern Cambridge physics describes energy as being 'stored' in different ways. When you see a question about where energy comes from or goes to, identify the store.
| Energy Store | Description |
|---|---|
| Kinetic | Stored by an object due to its motion. |
| Gravitational Potential (gPE) | Stored by an object due to its position in a gravitational field (height). |
| Chemical | Stored in the bonds between atoms and molecules (e.g., food, batteries, fuels). |
| Elastic (Strain) | Stored when an object is stretched or compressed. |
| Nuclear | Stored in the nucleus of an atom. |
| Electrostatic | Stored by charged particles due to their position relative to other charges. |
| Internal (Thermal) | Stored by the random motion of particles within a substance (related to temperature). |
How is energy transferred?
Energy moves from one store to another via four main pathways:
- Mechanically: By the action of forces (e.g., pushing a box).
- Electrically: By the movement of electric charges (currents).
- By Heating: Due to a temperature difference (conduction, convection, radiation).
- By Waves: Electromagnetic waves (light), sound waves, or other wave types.
Note: Energy is never 'created' or 'destroyed', only transferred.
Complex Energy Transfers and Sankey Diagrams (LO6)
In complex processes, energy passes through intermediate stores.
Example: A hydroelectric power station
- Water behind a dam has high Gravitational Potential Energy store.
- As water falls, gPE transfers mechanically to the Kinetic Energy store of the moving water.
- The moving water hits turbine blades, transferring energy mechanically to the Kinetic Energy store of the turbine.
- The generator converts this to Electrical Energy (work done electrically).
Interpreting Sankey Diagrams:
Sankey diagrams visualize these transfers. The width of the arrow is proportional to the amount of energy.
- Thick arrows: Large energy transfer (useful or wasted).
- Thin arrows: Small energy transfer.
- Downward branches: Usually represent wasted energy (often thermal) dissipated to the surroundings.
To analyze a complex Sankey diagram:
- Identify the total input width.
- Trace the main path to the useful output.
- Identify any intermediate stores if shown (e.g., kinetic energy of a moving car before braking).
- Sum of all output widths must equal the input width (Conservation of Energy).
Equation:
W = F \times d
Where:
- W is work done (or energy transferred) in joules, J.
- F is the force applied in newtons, N.
- d is the distance moved by the point of application of the force in the direction of the force, in metres, m.
Key Principle:
The work done on an object is equal to the energy transferred to its store. For example, if you lift a box, the work done by your muscles equals the gain in the box's gravitational potential energy store.
Equation:
E_k = \frac{1}{2}mv^2
Where:
- E_k is kinetic energy in joules, J.
- m is the mass of the object in kilograms, kg.
- v is the speed (velocity magnitude) of the object in metres per second, m/s.
Note: Speed is squared, so doubling the speed quadruples the kinetic energy.
Equation:
\Delta E_p = mg\Delta h
Where:
- \Delta E_p is the change in gravitational potential energy in joules, J.
- m is the mass of the object in kilograms, kg.
- g is the gravitational field strength (approx. 9.8 \text{ N/kg} or 10 \text{ N/kg} depending on the paper) in newtons per kilogram, N/kg.
- \Delta h is the change in vertical height in metres, m.
Note: Use \Delta h for any change in height. If lifting up, energy increases. If falling down, energy decreases.
Equations:
P = \frac{W}{t} \quad \text{or} \quad P = \frac{\Delta E}{t}
Where:
- P is power in watts, W (where 1 \text{ W} = 1 \text{ J/s}).
- W is work done in joules, J.
- \Delta E is energy transferred in joules, J.
- t is the time taken in seconds, s.
Note: Always ensure time is in seconds. If given in minutes, multiply by 60.
Equations:
\text{Efficiency} = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \times 100%
or
\text{Efficiency} = \frac{\text{Useful Power Output}}{\text{Total Power Input}} \times 100%
Where:
- Efficiency is expressed as a percentage, %.
- Useful output and total input must be in the same units (both energy in J or both power in W).
Note: Efficiency is always less than 100% because some energy is always wasted (usually as thermal energy to the surroundings).
Step 1: Identify forces.
To lift the book at constant speed, the upward force F must equal the weight of the book.
F = mg = 2.0 \times 9.8 = 19.6 \text{ N}
Step 2: Calculate Work Done (W).
The force acts in the direction of motion (vertical).
W = F \times d = 19.6 \times 1.5 = 29.4 \text{ J}
(This equals the gain in gravitational potential energy store).
Step 3: Calculate Power (P).
P = \frac{W}{t} = \frac{29.4}{3.0} = 9.8 \text{ W}
Radiation from the Sun is the main source of energy for almost all resources on Earth.
| Resource | Connection to Sun / Other Sources |
|---|---|
| Fossil Fuels | Stored chemical energy from ancient plants/animals that captured solar energy via photosynthesis. |
| Biofuels | Chemical energy from recent plants (solar origin). |
| Wind | Caused by uneven heating of the Earth's surface by infrared and other electromagnetic waves from the Sun. |
| Hydroelectric | Solar energy evaporates water, which falls as rain in high places (gPE). |
| Wave/Tidal | Waves are driven by wind (solar). Tides are primarily due to gravitational attraction of the Moon/Sun. |
| Solar Cells | Direct conversion of light/electromagnetic radiation to electrical energy. |
| Geothermal | Heat from Earth's interior (radioactive decay and residual formation heat). NOT solar. |
| Nuclear | Energy from nuclear fusion in the Sun (LO13) or fission on Earth. NOT solar. |
Note: Geothermal, Nuclear, and Tidal are the main exceptions to the 'Sun is the source' rule.
Students often confuse the symbol for Work Done (W) with Weight (W or F_g). In the formula W = Fd, if lifting an object, F is the weight. Writing W = W_{eight} \times d is confusing and prone to error.
The Correction:
- Use clear symbols. Let W denote Work Done.
- Let F_g or mg denote Weight/Force due to gravity.
- When lifting vertically: W = mg \times h. Here, mg is the force, and h is the distance.
Why this matters:
If you write W = W \times d, it looks like W(1-d)=0, which is mathematically ambiguous. Always distinguish between the energy transferred (W) and the force causing it (F_g).
Students often include horizontal width or distance when calculating work done against gravity.
The Correction:
Work done against gravity depends only on the vertical height change (\Delta h). The path taken (straight up, zig-zag, stairs) does not matter for the gain in gPE. However, for work done by a person, if they walk horizontally while holding the weight, no work is done against gravity during the horizontal part because the force (up) is perpendicular to motion (horizontal).
Rule: Only include distance moved in the direction of the force.
Examiner Acceptance:
Use the phrase: 'Energy is transferred mechanically from the gravitational potential store to the kinetic store.'
Why this works:
- It identifies the source store (gravitational potential).
- It identifies the destination store (kinetic).
- It specifies the pathway (mechanically/by forces).
Avoid: Saying 'Potential energy turns into kinetic energy.' This is vague. Cambridge requires specific store names and transfer pathways.
Example: For a falling ball:
Correct: 'Energy transfers mechanically from the gravitational potential store to the kinetic store.'
Incorrect: 'The ball loses potential energy and gains speed.'
Examiner Acceptance:
Use the phrase: 'Some energy is dissipated to the surroundings as thermal energy (or sound).
Why this works:
It acknowledges that energy is conserved but 'wasted' into stores not useful for the intended purpose. The keyword dissipated is highly valued.
Example: For a light bulb:
Correct: 'Electrical work done transfers energy to the thermal store of the filament and then radiates as light. However, significant energy is dissipated to the surroundings as thermal energy.'
Incorrect: 'Energy is lost.'