AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Students should recognise that energy and momentum are conserved in…
Full specification wording
Applications of conservation laws: Students should recognise that energy and momentum are conserved in interactions.
Energy conservation includes rest energy, so a decrease in rest mass appears as an increase in kinetic energy or as photon energy.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 3 of 3
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Energy conservation includes rest energy, so a decrease in rest mass appears as an increase in kinetic energy or as photon energy. Momentum is a vector, so you must consider direction as well as magnitude. A useful method is to write a before-and-after statement: total energy before equals total energy after, and total momentum before equals total momentum after. For example, in electron-positron annihilation at rest, the total momentum is zero, so the two produced photons must travel in opposite directions with equal magnitudes of momentum. Recognising these principles allows you to set up equations and solve for unknown speeds, masses or energies.
What earns the marks
- State that total energy is conserved in an interaction, including rest energy and kinetic energy.
- State that total momentum is conserved in an interaction, treating momentum as a vector with direction.
- Set up a before-and-after equation for energy, converting rest mass to energy where necessary using E = mc².
- Set up a before-and-after vector equation for momentum, taking account of opposite directions with positive and negative signs.
- Apply the principles to examples such as collisions, decays and annihilation to determine unknown quantities.
- Recognise that in annihilation at rest the total momentum is zero, so product particles must have equal and opposite momenta.
Common mistakes and how to put them right
Treating momentum as a scalar and ignoring direction, which gives incorrect results.
Put it right: Assign positive and negative signs to momenta according to direction.
Forgetting to include rest energy in energy conservation, so mass changes appear to violate conservation.
Put it right: Include rest energy using E = mc² for each particle.
Assuming kinetic energy is always conserved in every interaction.
Put it right: Recognise that kinetic energy may change while total energy remains conserved.
Exam tips
- Draw a simple before-and-after diagram with arrows to show directions, which helps you assign correct signs to momentum values.
- Write the general conservation statements first, then substitute values, so your method is clear even if the final arithmetic is wrong.
- Check that your final answer is physically sensible, for example that a photon momentum is not zero when the initial momentum was non-zero.
Try the lesson
The start of the Applications of conservation laws: Students should recognise that energy and momentum are conserved in interactions. lesson, made from checked teaching notes for this specification point.
Have a go first
Which of the following pairs of quantities are always conserved in every particle interaction?
Listen
Energy conservation includes rest energy, so a decrease in rest mass appears as an increase in kinetic energy or as photon energy. Momentum is a vector, so you must consider direction as well as magnitude. A useful method is to write a before-and-after statement: total energy before equals total energy after, and total momentum before equals total momentum after. For example, in electron-positron annihilation at rest, the total momentum is zero, so the two produced photons must travel in opposite directions with equal magnitudes of momentum. Recognising these principles allows you to set up equations and solve for unknown speeds, masses or energies. A strong answer earns marks for these points. State that total energy is conserved in an interaction, including rest energy and kinetic energy. State that total momentum is conserved in an interaction, treating momentum as a vector with direction. Set up a before-and-after equation for energy, converting rest mass to energy where necessary using E = mc². Set up a before-and-after vector equation for momentum, taking account of opposite directions with positive and negative signs. A common slip: Treating momentum as a scalar and ignoring direction, which gives incorrect results. Instead, assign positive and negative signs to momenta according to direction. Exam tip: Draw a simple before-and-after diagram with arrows to show directions, which helps you assign correct signs to momentum values.
Key words
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Conservation of energy including rest energy
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Conservation of momentum as a vector quantity
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Collisions, decays and annihilation processes
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Energy-mass equivalence
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See every definition
- Conservation of energy including rest energy
- The total energy of the system remains constant in any interaction, and this includes rest energy, so a decrease in rest mass appears as an increase in kinetic energy or as photon energy.
- Conservation of momentum as a vector quantity
- The total momentum of the system remains constant in any interaction, and because momentum is a vector you must consider direction as well as magnitude.
- Collisions, decays and annihilation processes
- Interactions in which the total energy and the total momentum of the system remain constant, whether a collision, decay or annihilation.
- Energy-mass equivalence
- Rest mass can be converted to energy where necessary using E = mc², so a decrease in rest mass appears as an increase in kinetic energy or as photon energy.
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