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Physics · Forces

Changes in momentum

Use \(F = m\Delta v \div \Delta t\) and explain safety features such as air bags, seat belts, crumple zones and helmets in terms of rate of change of momentum (Higher tier).

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  • 6 key terms
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Teacher resources

The teacher copies: slides with the questions built in, the answers, and anything else attached to this lesson for whoever is teaching it.

Student handouts

The same files the students see, to print or hand out.

Warm-up

Answer each one, then check.

  1. 1

    What is momentum?

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    Mass times velocity

  2. 2

    What is acceleration?

    Show answerHide answer

    Change in velocity divided by time, \(a = \Delta v \div t\)

  3. 3

    What is F = ma?

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    Resultant force equals mass times acceleration

  4. 4

    Give a safety device in a car.

    Show answerHide answer

    Seat belt, airbag or crumple zone

  5. 5

    What is a collision?

    Show answerHide answer

    Two objects hitting each other

Learning Objectives

  1. 1Explain that force equals the rate of change of momentum.
  2. 2Apply \(F = m\Delta v \div \Delta t\).
  3. 3Explain safety features in terms of increasing the time of a collision.
  4. 4Explain how changes in force, mass, velocity and time are related.

RATE OF CHANGE OF MOMENTUM

force \(=\) change in momentum \(\div\) time taken \(F = \dfrac{m\Delta v}{\Delta t}\)

Combining \(F = ma\) and \(a = \dfrac{v - u}{t}\) gives \(F = \dfrac{m\Delta v}{\Delta t}\), where \(m\Delta v\) is the change in momentum. This equation is given on the equation sheet.

Force in a Crash

A car of mass 1000 kg travelling at 20 m/s stops in 0.50 s. Calculate the average force.

Show the solutionHide the solution
  1. 1 Change in momentum \(1000 \times 20 = 20\,000\) kg m/s
  2. 2 Substitute \(F = 20\,000 \div 0.50\)
  3. 3 Answer \(F = 40\,000\) N

Answer40 000 N

Increasing the Time

The same car is stopped in 0.10 s by hitting a wall. Calculate the average force and compare with the answer above.

Show the solutionHide the solution
  1. 1 Substitute \(F = 20\,000 \div 0.10 = 200\,000\) N
  2. 2 Compare Five times greater

Answer200 000 N: a much shorter time gives a much greater force.

Safety Features

Explain how an air bag reduces injury in a collision.

Show the solutionHide the solution
  1. 1 Momentum The change in the person's momentum is the same
  2. 2 Time The air bag increases the time for the person to stop
  3. 3 Force \(F = m\Delta v \div \Delta t\): longer time gives a smaller force

AnswerIt increases the collision time so the average force on the person is smaller.

Other Safety Features

  • Seat belts

    Stretch slightly, increasing the stopping time.

  • Crumple zones

    Deform on impact, increasing the stopping time.

  • Cycle helmets

    The foam compresses, increasing the stopping time.

  • Crash mats and playground surfaces

    Cushion the landing, increasing the time.

Key Points

For exam answers.

  • Same momentum change

    The change in momentum is the same, whatever the time.

  • Force depends on time

    Smaller rate of change of momentum means smaller force.

  • Say it clearly

    'Increases the time of the collision, so decreases the force.'

  • Units

    Force in N, momentum in kg m/s, time in s.

Ball Catch

A 0.40 kg ball moving at 15 m/s is stopped by a catcher in 0.020 s. A second catcher uses a glove that stops it in 0.10 s. Calculate the force in each case.

1. Find the momentum change.

2. Divide by time.

A good answer shows: Change in momentum = 6.0 kg m/s. First: 300 N. Second: 60 N.

Can I...?

  1. 1State F = mΔv ÷ Δt.
  2. 2Calculate a change in momentum.
  3. 3Calculate a force.
  4. 4Explain an air bag.
  5. 5Explain a seat belt.
  6. 6Explain a crumple zone.
  7. 7Explain a cycle helmet.
  8. 8Explain a crash mat.

Summary & Exam Focus

  • \(F = m\Delta v \div \Delta t\).
  • Longer collision time means a smaller force.
  • Air bags, seat belts, crumple zones, helmets, crash mats.
  • Change in momentum is the same.

Exam focus

Explain how a crumple zone reduces the force on the passengers. (3 marks) (3 marks)

Increases the time of the collision.

Key terms

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

Rate of change of momentum
Change in momentum divided by time.
Air bag
A cushion that inflates in a collision.
Crumple zone
Part of a vehicle designed to deform in a crash.
Seat belt
A strap that holds a passenger and stretches slightly.
Impact time
The time a collision lasts.
Average force
The mean force over the collision time.

Questions and answers

10 questions set on this lesson, with the mark schemes and model answers open.

1. Exam question Calculate 3 marks Easier

A car of mass 1000 kg travelling at 20 m/s stops in 0.50 s. Calculate the average force on the car. Use the equation: force = mass × change in velocity ÷ time

Mark scheme — 3 marks available

  • Change in momentum 20 000 kg m/s — 1 mark
  • Correct substitution — 1 mark
  • 40 000 N — 1 mark

Model answer

\(F = 1000 \times 20 \div 0.50 = 40\,000\) N

2. Exam question Explain 3 marks Easier

Explain how an air bag reduces the force on a driver in a collision.

Mark scheme — 3 marks available

  • Increases the time to stop — 1 mark
  • Same change in momentum — 1 mark
  • Force = change in momentum ÷ time, so smaller force — 1 mark

Model answer

The air bag increases the time taken for the driver to come to rest. The change in momentum is the same, so the force (change in momentum ÷ time) is smaller.

3. Exam question Explain 3 marks Easier

A cyclist wears a helmet containing soft foam. Explain how the helmet reduces the risk of head injury in a fall.

Mark scheme — 3 marks available

  • Foam compresses — 1 mark
  • Increases the stopping time — 1 mark
  • Reduces the force — 1 mark

Model answer

The foam compresses, so the head takes longer to stop. The change in momentum is the same, so the force on the head is smaller.

4. Exam question Calculate 4 marks Easier

A ball of mass 0.40 kg moving at 15 m/s is caught and stopped in 0.020 s. Calculate the average force on the ball. Then state the force if a soft glove makes the stopping time 0.10 s.

Mark scheme — 4 marks available

  • 6.0 kg m/s — 1 mark
  • 300 N — 1 mark
  • 60 N — 1 mark
  • Comparison: longer time, smaller force — 1 mark

Model answer

Change in momentum \(= 0.40 \times 15 = 6.0\); \(F = 6.0 \div 0.020 = 300\) N; with the glove \(6.0 \div 0.10 = 60\) N

5. Exam question Explain 3 marks Easier

A gymnast lands on a thick crash mat rather than a hard floor. Use the idea of rate of change of momentum to explain why the mat reduces the risk of injury.

Mark scheme — 3 marks available

  • Mat increases the stopping time — 1 mark
  • Same change in momentum — 1 mark
  • Smaller rate of change of momentum, smaller force — 1 mark

Model answer

The mat increases the time taken to stop the gymnast. The change in momentum is the same so the rate of change of momentum, and therefore the force, is smaller.

6. Multiple choice 1 mark Easier

Force equals...

  1. A rate of change of momentum Correct
  2. B momentum × time
  3. C mass × distance
  4. D speed ÷ time

Why: F = mΔv ÷ Δt.

7. Multiple choice 1 mark Core

A longer collision time means a...

  1. A larger force
  2. B smaller force Correct
  3. C the same force
  4. D zero force

Why: Same change in momentum.

8. Multiple choice 1 mark Core

Which is NOT a safety feature that increases stopping time?

  1. A Air bag
  2. B Crumple zone
  3. C A sharper bumper Correct
  4. D Seat belt

Why: A rigid stop shortens the time.

9. Multiple choice 1 mark Core

A change in momentum of 20 000 kg m/s in 0.5 s gives a force of...

  1. A 10 000 N
  2. B 20 000.5 N
  3. C 4000 N
  4. D 40 000 N Correct

Why: 20 000 ÷ 0.5.

10. Multiple choice 1 mark Stretch

A cycle helmet works by...

  1. A increasing the stopping time Correct
  2. B adding mass
  3. C reducing the speed
  4. D removing momentum

Why: The foam compresses.