AQA GCSE PHYSICS · PAPER 2 · HIGHER TIER ONLY
Momentum and its conservation
Forces · Lesson 19 of 20
Teacher copy - includes the notes for whoever is teaching from it.
Warm-up
Answer each one, then check.
1. What is velocity?
Speed in a given direction
2. What is mass?
The amount of matter in an object
3. What is a closed system?
A system with no external forces or energy transfer
4. What does conserved mean?
Stays the same in total
5. What is a collision?
When two objects hit each other
Learning Objectives
1. Define momentum and recall the equation.
2. State the principle of conservation of momentum.
3. Calculate momentum before and after collisions and explosions.
4. Explain examples such as collisions using momentum.
Momentum
momentum = mass × velocity p = mv
In a closed system the total momentum before an event is equal to the total momentum after the event. Momentum is a vector, measured in kg m/s.
A Collision
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Momentum before = momentum after. |
Two trolleys colliding and sticking together, with total momentum the same before and after.
Calculating Momentum
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A car of mass 1500 kg moves at 20 m/s. Calculate its momentum. |
1. Write the equation
p = mv
2. Substitute
p = 1500 × 20
3. Answer
p = 30 000 kg m/s
Answer: 30 000 kg m/s
Collision: Objects Stick Together
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A 2.0 kg trolley moving at 3.0 m/s hits a stationary 1.0 kg trolley. They stick together. Calculate their velocity after the collision. |
1. Momentum before
2.0 × 3.0 + 1.0 × 0 = 6.0 kg m/s
2. Momentum after
(2.0 + 1.0) × v = 3.0v
3. Conservation
3.0v = 6.0
4. Answer
v = 2.0 m/s
Answer: 2.0 m/s in the original direction.
Explosion
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A 4.0 kg gun fires a 0.020 kg bullet at 200 m/s. Calculate the recoil velocity of the gun. |
1. Momentum before
0 (both at rest)
2. Bullet
0.020 × 200 = 4.0 kg m/s forwards
3. Gun
4.0 × v = −4.0
4. Answer
v = −1.0 m/s
Answer: 1.0 m/s backwards.
Key Ideas
Use direction carefully.
▸ Vector. Choose a positive direction; motion the other way is negative.
▸ Closed system. No external forces (such as friction) act.
▸ Kinetic energy. Not always conserved in collisions; momentum is.
▸ Units. kg m/s.
Key Terms
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Momentum Mass multiplied by velocity. |
Conservation of momentum Total momentum before an event equals total momentum after in a closed system. |
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Closed system A system with no external forces. |
Collision Two objects hitting each other. |
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Recoil The backward movement of a gun when fired. |
Explosion When objects push apart from rest. |
Your Task: Stick Together
12 minutes
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A 1.5 kg trolley moving at 2.0 m/s collides with a stationary 0.50 kg trolley and they stick together. Find the velocity after the collision. 1. Find the total momentum before. 2. Divide by the total mass. |
A good answer shows: Momentum before = 3.0; after (2.0 kg) v = 1.5 m/s.
Note: Ask about the kinetic energy before and after.
Can I...?
☐ Define momentum.
☐ Use p = mv.
☐ State conservation of momentum.
☐ Solve a sticking collision.
☐ Solve a recoil problem.
☐ Use positive and negative directions.
☐ Explain momentum in collisions.
☐ Give units.
Summary
✓ p = mv.
✓ Closed system: momentum before = momentum after.
✓ Momentum is a vector.
✓ Explosion from rest: total momentum zero.
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EXAM FOCUS A car of mass 1500 kg moves at 20 m/s. Calculate its momentum. (2 marks) Multiply mass by velocity. |
Exam Practice: Momentum and its conservation
Answer all questions. Use the mark allocation as a guide to how much to write. · 16 minutes
▸ Question 1 · 2 marks · Calculate. A car of mass 1500 kg travels at 20 m/s. Calculate the momentum of the car. Use the equation: momentum = mass × velocity
▸ Question 2 · 4 marks · Calculate. The diagram shows a trolley A colliding with a stationary trolley B. After the collision they stick together. Calculate the velocity of the…
▸ Question 3 · 3 marks · Explain. A moving ball hits a stationary ball and they move apart. Use the idea of conservation of momentum to explain what happens to the total…
▸ Question 4 · 4 marks · Calculate. A gun of mass 4.0 kg fires a bullet of mass 0.020 kg at a speed of 200 m/s. Calculate the recoil speed of the gun.
▸ Question 5 · 2 marks · Explain. Explain why momentum is a vector quantity.
Question 1 · 2 marks · Calculate
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“A car of mass 1500 kg travels at 20 m/s. Calculate the momentum of the car. Use the equation: momentum = mass × velocity” |
HOW TO ANSWER IT Command word: Calculate. Worth 2 marks, so plan before writing.
Question 1 · mark scheme
2 marks available. Award a mark for each point made.
▸ Correct substitution. 1 mark
▸ 30 000 kg m/s. 1 mark
▸ Model answer. 1500 × 20 = 30 000 kg m/s
Question 2 · 4 marks · Calculate
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The diagram shows a trolley A colliding with a stationary trolley B. After the collision they stick together. Calculate the velocity of the trolleys after the collision. (4 marks) |
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Question 2 · mark scheme
4 marks available. Award a mark for each point made.
▸ Momentum before 1.0 kg m/s. 1 mark
▸ Total mass 2.0 kg. 1 mark
▸ Equates momentum. 1 mark
▸ 0.50 m/s. 1 mark
▸ Model answer. Momentum before = 0.50 × 2.0 + 0 = 1.0 kg m/s. After: (0.50 + 1.5) × v = 1.0, so v = 0.50 m/s
Question 3 · 3 marks · Explain
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“A moving ball hits a stationary ball and they move apart. Use the idea of conservation of momentum to explain what happens to the total momentum.” |
HOW TO ANSWER IT Command word: Explain. Worth 3 marks, so plan before writing.
Question 3 · mark scheme
3 marks available. Award a mark for each point made.
▸ Total momentum before equals after. 1 mark
▸ Closed system. 1 mark
▸ Momentum transferred between the balls. 1 mark
▸ Model answer. In a closed system the total momentum before the collision equals the total momentum after; momentum is transferred from the first ball to the second.
Question 4 · 4 marks · Calculate
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“A gun of mass 4.0 kg fires a bullet of mass 0.020 kg at a speed of 200 m/s. Calculate the recoil speed of the gun.” |
HOW TO ANSWER IT Command word: Calculate. Worth 4 marks, so plan before writing.
Question 4 · mark scheme
4 marks available. Award a mark for each point made.
▸ Momentum of bullet 4.0 kg m/s. 1 mark
▸ Total momentum before is zero. 1 mark
▸ Equates momentum. 1 mark
▸ 1.0 m/s backwards. 1 mark
▸ Model answer. Momentum of bullet = 0.020 × 200 = 4.0 kg m/s. Gun: 4.0 × v = 4.0, so v = 1.0 m/s (opposite direction)
Question 5 · 2 marks · Explain
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“Explain why momentum is a vector quantity.” |
HOW TO ANSWER IT Command word: Explain. Worth 2 marks, so plan before writing.
Question 5 · mark scheme
2 marks available. Award a mark for each point made.
▸ Mass times velocity. 1 mark
▸ Has direction. 1 mark
▸ Model answer. It has both magnitude (mass × speed) and direction (the direction of the velocity).