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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).

Higher
6 key terms
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Warm-up

Answer each one, then check.

1

What is momentum?

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Mass times velocity
2

What is acceleration?

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Change in velocity divided by time, \(a = \Delta v \div t\)
3

What is F = ma?

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Resultant force equals mass times acceleration
4

Give a safety device in a car.

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Seat belt, airbag or crumple zone
5

What is a collision?

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Two objects hitting each other

Learning Objectives

1Explain that force equals the rate of change of momentum.
2Apply \(F = m\Delta v \div \Delta t\).
3Explain safety features in terms of increasing the time of a collision.
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.

Why Crumple Zones Help

Two force-time curves showing a smaller peak force when the collision time is longer.

Force in a Crash

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

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1 Change in momentum \(1000 \times 20 = 20\,000\) kg m/s
2 Substitute \(F = 20\,000 \div 0.50\)
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.

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1 Substitute \(F = 20\,000 \div 0.10 = 200\,000\) N
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.

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1 Momentum The change in the person's momentum is the same
2 Time The air bag increases the time for the person to stop
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...?

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

Practice questions

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

Question 1 Calculate 3 marks

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
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Model answer

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

Mark scheme
- Change in momentum 20 000 kg m/s — 1 mark
- Correct substitution — 1 mark
- 40 000 N — 1 mark
Question 2 Explain 3 marks

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

Mark scheme
- Increases the time to stop — 1 mark
- Same change in momentum — 1 mark
- Force = change in momentum ÷ time, so smaller force — 1 mark
Question 3 Explain 3 marks

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

Mark scheme
- Foam compresses — 1 mark
- Increases the stopping time — 1 mark
- Reduces the force — 1 mark
Question 4 Calculate 4 marks

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.
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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

Mark scheme
- 6.0 kg m/s — 1 mark
- 300 N — 1 mark
- 60 N — 1 mark
- Comparison: longer time, smaller force — 1 mark
Question 5 Explain 3 marks

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.
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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.

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

Quick check

Force equals...
1. Arate of change of momentum
2. Bmomentum × time
3. Cmass × distance
4. Dspeed ÷ time
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A: rate of change of momentum

F = mΔv ÷ Δt.
A longer collision time means a...
1. Alarger force
2. Bsmaller force
3. Cthe same force
4. Dzero force
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B: smaller force

Same change in momentum.
Which is NOT a safety feature that increases stopping time?
1. AAir bag
2. BCrumple zone
3. CA sharper bumper
4. DSeat belt
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C: A sharper bumper

A rigid stop shortens the time.
A change in momentum of 20 000 kg m/s in 0.5 s gives a force of...
1. A10 000 N
2. B20 000.5 N
3. C4000 N
4. D40 000 N
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D: 40 000 N

20 000 ÷ 0.5.
A cycle helmet works by...
1. Aincreasing the stopping time
2. Badding mass
3. Creducing the speed
4. Dremoving momentum
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A: increasing the stopping time

The foam compresses.

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