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Physics · Forces

Momentum and its conservation

Use \(p = mv\), and apply conservation of momentum to collisions and explosions (Higher tier).

  • Higher
  • 6 key terms
  • All boards
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Warm-up

Answer each one, then check.

  1. 1

    What is velocity?

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    Speed in a given direction

  2. 2

    What is mass?

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    The amount of matter in an object

  3. 3

    What is a closed system?

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    A system with no external forces or energy transfer

  4. 4

    What does conserved mean?

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    Stays the same in total

  5. 5

    What is a collision?

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    When two objects hit each other

Learning Objectives

  1. 1Define momentum and recall the equation.
  2. 2State the principle of conservation of momentum.
  3. 3Calculate momentum before and after collisions and explosions.
  4. 4Explain examples such as collisions using momentum.

MOMENTUM

momentum \(=\) mass \(\times\) 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.

Calculating Momentum

A car of mass 1500 kg moves at 20 m/s. Calculate its momentum.

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  1. 1 Write the equation \(p = mv\)
  2. 2 Substitute \(p = 1500 \times 20\)
  3. 3 Answer \(p = 30\,000\) kg m/s

Answer30 000 kg m/s

Collision: Objects Stick Together

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.

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  1. 1 Momentum before \(2.0 \times 3.0 + 1.0 \times 0 = 6.0\) kg m/s
  2. 2 Momentum after \((2.0 + 1.0) \times v = 3.0v\)
  3. 3 Conservation \(3.0v = 6.0\)
  4. 4 Answer \(v = 2.0\) m/s

Answer2.0 m/s in the original direction.

Explosion

A 4.0 kg gun fires a 0.020 kg bullet at 200 m/s. Calculate the recoil velocity of the gun.

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  1. 1 Momentum before 0 (both at rest)
  2. 2 Bullet \(0.020 \times 200 = 4.0\) kg m/s forwards
  3. 3 Gun \(4.0 \times v = -4.0\)
  4. 4 Answer \(v = -1.0\) m/s

Answer1.0 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.

Stick Together

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.

Can I...?

  1. 1Define momentum.
  2. 2Use \(p = mv\).
  3. 3State conservation of momentum.
  4. 4Solve a sticking collision.
  5. 5Solve a recoil problem.
  6. 6Use positive and negative directions.
  7. 7Explain momentum in collisions.
  8. 8Give units.

Summary & Exam Focus

  • \(p = mv\).
  • Closed system: momentum before = momentum after.
  • Momentum is a vector.
  • Explosion from rest: total momentum zero.

Exam focus

A car of mass 1500 kg moves at 20 m/s. Calculate its momentum. (2 marks) (2 marks)

Multiply mass by velocity.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Momentum
Mass multiplied by velocity.
Conservation of momentum
Total momentum before an event equals total momentum after in a closed system.
Closed system
A system with no external forces.
Collision
Two objects hitting each other.
Recoil
The backward movement of a gun when fired.
Explosion
When objects push apart from rest.

Practice questions

Have a go at each one before you open its answer.

  1. Question 1 Calculate 2 marks

    A car of mass 1500 kg travels at 20 m/s. Calculate the momentum of the car. Use the equation: momentum = mass × velocity

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    Model answer

    \(1500 \times 20 = 30\,000\) kg m/s

    Mark scheme

    • Correct substitution — 1 mark
    • 30 000 kg m/s — 1 mark
  2. Question 2 Calculate 4 marks

    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.

    Trolley A of 0.50 kg at 2.0 m/s about to collide with a stationary trolley B of 1.5 kg.
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    Model answer

    Momentum before \(= 0.50 \times 2.0 + 0 = 1.0\) kg m/s. After: \((0.50 + 1.5) \times v = 1.0\), so \(v = 0.50\) m/s

    Mark scheme

    • 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
  3. Question 3 Explain 3 marks

    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.

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    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.

    Mark scheme

    • Total momentum before equals after — 1 mark
    • Closed system — 1 mark
    • Momentum transferred between the balls — 1 mark
  4. Question 4 Calculate 4 marks

    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.

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    Model answer

    Momentum of bullet \(= 0.020 \times 200 = 4.0\) kg m/s. Gun: \(4.0 \times v = 4.0\), so \(v = 1.0\) m/s (opposite direction)

    Mark scheme

    • 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
  5. Question 5 Explain 2 marks

    Explain why momentum is a vector quantity.

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    Model answer

    It has both magnitude (mass × speed) and direction (the direction of the velocity).

    Mark scheme

    • Mass times velocity — 1 mark
    • Has direction — 1 mark

Quick check

  1. Momentum is calculated by...

    1. Amass ÷ velocity
    2. Bmass + velocity
    3. Cforce × time only
    4. Dmass × velocity
    Show answerHide answer

    D: mass × velocity

    p = mv.

  2. A 2 kg object at 5 m/s has a momentum of...

    1. A10 kg m/s
    2. B7 kg m/s
    3. C2.5 kg m/s
    4. D0.4 kg m/s
    Show answerHide answer

    A: 10 kg m/s

    2 × 5.

  3. In a closed system the total momentum is...

    1. Aalways increasing
    2. Bconserved
    3. Calways zero
    4. Ddestroyed
    Show answerHide answer

    B: conserved

    Before = after.

  4. Momentum is a...

    1. Ascalar
    2. Bforce
    3. Cvector
    4. Denergy
    Show answerHide answer

    C: vector

    It has direction.

  5. A gun recoils because...

    1. Aenergy is destroyed
    2. Bair pushes it
    3. Cgravity
    4. Dmomentum is conserved
    Show answerHide answer

    D: momentum is conserved

    The bullet gains momentum forwards so the gun gains it backwards.

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