10.6 Impact Forces

A free GCSE Physics lesson for AQA (8463) from OBA School: (Higher tier, physics only) Force as rate of change of momentum, impact time and two-vehicle collisions. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

• (Higher tier) explain that force equals the rate of change of momentum, F = m Δv ÷ Δt
• (Higher tier) calculate decelerations, changes of momentum and impact forces from data
• (Higher tier) explain why increasing the impact time reduces the impact force
• (Higher tier) explain why two colliding vehicles exert equal and opposite forces and have equal and opposite changes of momentum

Key words

• Impact force: The force between two objects while they are in contact during a collision.
• Impact time: The time for which the colliding objects are in contact (also called contact time).
• Change of momentum: Mass × change of velocity, m Δv, in kg m/s.
• Rate of change of momentum: The change of momentum per second. It equals the resultant force.
• Crumple zone: A part of a car designed to fold up in a crash, which increases the impact time.
• Newton’s third law: When two objects interact, they exert equal and opposite forces on each other.

Force is the rate of change of momentum

Acceleration is change of velocity ÷ time, a = Δv ÷ Δt. Putting this into F = m a gives:

force = mass × change of velocity ÷ time taken F = m Δv ÷ Δt

F in newtons, N; m in kg; Δv = final velocity − initial velocity, in m/s; Δt in seconds, s

m Δv is the change of momentum, so the resultant force on an object equals its rate of change of momentum.

Worked example: a car speeding up

A 1200 kg car speeds up from 10 m/s to 25 m/s in 6.0 s. Calculate the resultant force.
change of momentum = 1200 × (25 − 10) = 18 000 kg m/s
F = 18 000 ÷ 6.0

Answer: F = 3000 N

Impact time

When a moving object hits something and stops, its change of momentum is fixed by its mass and velocity. The impact force depends on how quickly that change happens:

• For a given change of momentum, F is inversely proportional to the impact time. Double the time and the force halves.
• Soft or squashable materials – cushions, padding, crumple zones – make the impact time longer, so the force is smaller.

Worked example: dropping an egg

A 0.060 kg egg hits the ground at 4.0 m/s. Change of momentum = 0.060 × 4.0 = 0.24 kg m/s.
Hard floor, stopped in 0.004 s: F = 0.24 ÷ 0.004 = 60 N on average – the shell breaks.
Thick cushion, stopped in 0.050 s: F = 0.24 ÷ 0.050 = 4.8 N – the egg survives.

Answer: the longer impact time gives a force about 12 times smaller

Key fact: Sometimes a large force is wanted, for example when hitting a ball with a bat or driving in a nail with a hammer. Then a hard surface and a short contact time are used.

Calculating decelerations and impact forces

Worked example: catching a cricket ball

A 0.15 kg ball moving at 30 m/s is caught. The fielder pulls her hands back so the ball stops in 0.12 s.
deceleration: a = (0 − 30) ÷ 0.12 = −250 m/s²
change of momentum: 0.15 × (0 − 30) = −4.5 kg m/s
force: F = −4.5 ÷ 0.12 = −37.5 N (minus: the force opposes the motion)
If she kept her hands still and the ball stopped in 0.015 s, the force would be 4.5 ÷ 0.015 = 300 N.

Answer: about 38 N, instead of 300 N

Exam tip: If an object bounces back, the change of velocity is bigger than its speed. A ball hitting a wall at +8.0 m/s and rebounding at −6.0 m/s has Δv = −6.0 − 8.0 = −14 m/s.

Crumple zones and two-vehicle collisions

Crumple zones at the front and rear of a car fold up in a collision. This makes the impact time longer, so the force on the car and the people inside is smaller. In a front-end impact the car’s momentum is reduced; in a rear-end impact (hit from behind) its momentum is increased – a crumple zone helps in both.

When two vehicles collide, they exert equal and opposite forces on each other (Newton’s third law) for the same time. So the change of momentum of one vehicle is equal and opposite to the change of momentum of the other, and the total momentum is conserved (if no external forces act).

Worked example: car into van

A 1500 kg car at 20 m/s hits a stationary 2500 kg van. They lock together. The impact lasts 0.25 s.
velocity after: 1500 × 20 = 4000 v, so v = 7.5 m/s
car: Δp = 1500 × (7.5 − 20) = −18 750 kg m/s; van: Δp = 2500 × (7.5 − 0) = +18 750 kg m/s
force on each = 18 750 ÷ 0.25 = 75 000 N

Answer: equal and opposite changes of momentum, and forces of 75 kN on each vehicle

Common mistakes

• Using the final velocity instead of the change of velocity in F = m Δv ÷ Δt.
• Forgetting that a rebound increases the change of velocity (add the speeds).
• Saying a longer impact time reduces the change of momentum. The change of momentum is the same; the force is smaller.
• Thinking the heavier vehicle exerts the larger force in a collision. The forces are always equal and opposite.
• Not converting milliseconds to seconds (25 ms = 0.025 s).

Revision questions

Try these, then check your answers below each one.

Question 1. (Higher tier) A 0.16 kg ball is hit from rest to 30 m/s. The bat is in contact with it for 0.0080 s. Calculate the average force on the ball.

Answer: 600 N

Working: Δp = 0.16 × 30 = 4.8 kg m/s. F = 4.8 ÷ 0.0080 = 600 N.

Question 2. (Higher tier) The resultant force on an object is equal to its… (Choose from: rate of change of momentum, change of momentum, momentum × time, mass × velocity.)

Answer: rate of change of momentum

Working: F = m Δv ÷ Δt = change of momentum ÷ time taken, which is the rate of change of momentum.

Question 3. (Higher tier) True or false? A crumple zone reduces the change of momentum of a car in a crash.

Answer: False

Working: False. The change of momentum is the same. The crumple zone increases the impact time, so the rate of change of momentum (the force) is smaller.

Related lessons

• Previous lesson: 10.5 Using Conservation of Momentum
• Next lesson: 10.7 Safety First
• In this chapter: 10.1 Force and Acceleration
• In this chapter: 10.2 Weight and Terminal Velocity
• In this chapter: 10.3 Forces and Braking

Continue in the full course

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