Conservation of momentum — AQA GCSE Combined Science
Test yourself on Conservation of momentum with AQA GCSE practice questions.
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Conservation of momentum explained
In a closed system, no external resultant force acts, so the total momentum before an event equals the total momentum after it.
Read the full explanation
This is the conservation of momentum, which is assessed at Higher Tier only. The principle applies to collisions, explosions and other interactions. To use it, add the momentum of every object before the event, add the momentum of every object after the event, and set the two totals equal. For example, a 2 kg trolley moving at 3 m/s hits a stationary 1 kg trolley and they stick together. Before: (2 × 3) + (1 × 0) = 6 kg m/s. After: (2 + 1) × v = 3v, so 3v = 6 and v = 2 m/s. Momentum is a vector, so assign one direction as positive and give velocities in the opposite direction a negative sign.
This is called conservation of momentum.
In a closed system, the total momentum before an event equals the total momentum after it, provided no external resultant force acts. This concept is assessed at Higher Tier only. Momentum p = m × v, measured in kg m/s, is a vector: assign one direction positive and the opposite negative. For two trolleys colliding and sticking, m₁u₁ + m₂u₂ = (m₁ + m₂)v. For a 2 kg trolley at 3 m/s hitting a stationary 1 kg trolley and sticking: total momentum before = 2 × 3 + 1 × 0 = 6 kg m/s; after, 3 kg × v = 6 kg m/s, so v = 2 m/s. The principle explains recoil, explosions and collisions, and follows from Newton's third law: equal and opposite forces act for equal times, so total momentum change is zero.
Students should be able to use the concept of momentum as a model to describe and explain examples of momentum in an event, such as a collision.
Momentum is a model that predicts motion during interactions. In a collision, total momentum is conserved if no external resultant force acts. To describe an event, identify the masses and velocities before and after, choose a positive direction, and then calculate. For example, a 1200 kg car at 15 m/s hits a stationary 800 kg car and they stick together. Before the collision: 1200 × 15 + 800 × 0 = 18000 kg m/s. After the collision: 2000 kg × v = 18000 kg m/s, so v = 9 m/s forwards. Momentum can also be used to explain recoil and explosions, where an initially stationary object separates into parts moving in opposite directions, keeping the total momentum at zero.
Your focus
- State the principle of conservation of momentum for a closed system.
- Calculate total momentum before and after an interaction using p = m × v.
- Use conservation of momentum to find an unknown velocity or mass in a collision or explosion.
Show all 9 objectives
- State the principle of conservation of momentum for a closed system.
- Calculate total momentum before and after a collision or explosion.
- Explain a recoil or collision using conservation of momentum and direction.
- Describe a collision using masses, velocities and directions.
- Calculate total momentum before and after an event.
- Explain recoil and explosions using the conservation of momentum.
Conservation of momentum exam tips
Marking Points
- State that a closed system has no external resultant force acting on it.
- Calculate total momentum before an event by summing m × v for each object.
- Calculate total momentum after an event by summing m × v for each object.
- Equate total momentum before and total momentum after to solve for an unknown velocity or mass.
- Apply a positive direction convention and use negative values for velocities in the opposite direction.
- State that total momentum in a closed system is constant before and after an event.
- Define a closed system as one on which no external resultant force acts.
- Calculate momentum using p = m × v with mass in kg and velocity in m/s.
- Treat momentum as a vector, assigning opposite directions opposite signs.
- Apply m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ to collisions or explosions.
- Explain recoil or explosion using equal and opposite momentum changes.
- Describe the event by listing masses and velocities before and after the interaction.
- Choose a positive direction and give opposing velocities negative signs.
- Calculate total momentum before and after using p = m × v.
- Show that total momentum is unchanged in a closed system.
- Use momentum to explain recoil and explosions, noting that initial momentum is zero.
Examiner Tips
- 💡Draw a before-and-after diagram and label each mass and velocity with its direction.
- 💡Choose one direction as positive at the start and show negative signs for motion in the opposite direction.
- 💡Check that the unit of momentum is kg m/s throughout the calculation.
- 💡Remember that conservation of momentum is a Higher Tier only topic, so expect it in more challenging calculation contexts.
- 💡Write the momentum equation, substitute values with units, then solve for the unknown.
- 💡State the direction of the final velocity, not just its magnitude.
- 💡Check that total momentum before equals total momentum after as a final verification.
- 💡As this is a Higher Tier only topic, be prepared to apply it alongside other concepts like kinetic energy.
- 💡Define the positive direction at the start of your answer.
- 💡Show the before and after momentum sums separately before equating them.
- 💡When explaining explosions, explicitly state that the total momentum before the event is zero.
Common Mistakes
- Adding speeds instead of calculating momentum: correct this by multiplying each mass by its velocity before adding.
- Forgetting to include a stationary object's momentum: correct this by including its m × v term, which is zero but still part of the total.
- Mixing up before and after totals: correct this by labelling the two sides of the equation clearly before substituting values.
- Ignoring the vector nature of momentum: correct this by assigning a negative sign to velocities in the opposite direction.
- Adding speeds instead of using signed velocities: assign one direction positive and the other negative before summing momenta.
- Forgetting to combine masses after a collision in which objects stick: use (m₁ + m₂) for the combined velocity.
- Using grams or km/h directly: convert to kg and m/s before calculating momentum.
- Ignoring direction and treating momentum as scalar: assign signs to velocities before adding.
- Assuming momentum is lost in a crash: in a closed system total momentum is conserved; energy may transfer.
- Confusing momentum with kinetic energy: momentum is m × v, kinetic energy is ½mv².