Forces, Movement, Shape and Momentum » Force, Momentum and Safety Features
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 1.26P, 1.28P
- How force is linked to change in momentum and time taken
- How to use F = (mv − mu) / t for objects that stop, start and rebound
- Why a longer stopping time means a smaller force
- How to explain car safety features, cycle helmets and crash mats using momentum
🔒 Unlock Full Course Content
Sign up to access the complete lesson and track your progress!
Unlock This CourseForce changes momentum
This lesson is examined in Paper 2 only.
Remember, a moving object has momentum, and an unbalanced force changes its velocity. So a force also changes its momentum. The bigger the force, the faster the momentum changes.
force = change in momentum / time taken
F = (mv − mu) / t
- F is the force in newtons (N)
- m is the mass in kilograms (kg)
- u is the initial velocity and v is the final velocity, both in m/s
- t is the time taken for the momentum to change, in seconds (s)
This equation is given on the formulae page of the exam paper, so you do not need to memorise it. You do need to be able to use it.
The top line, mv − mu, is the momentum at the end take away the momentum at the start. Always work it out in that order. The force you calculate is the average force during the time t.
Key terms:
- Change in momentum: the final momentum minus the initial momentum, mv − mu. It is measured in kg m/s.
- Crumple zone: a part of a car, at the front or the back, that is designed to crush slowly in a crash.
Stopping and starting
Worked example 1: stopping
A cricket ball of mass 0.15 kg moves at 20 m/s. A fielder catches it and stops it in 0.1 s. Calculate the force on the ball.
F = (mv − mu) / t
F = ((0.15 × 0) − (0.15 × 20)) / 0.1
F = (0 − 3) / 0.1
F = −30 N
The minus sign shows that the force acts in the opposite direction to the ball's movement. That is what you expect for a force that stops something.
Worked example 2: starting
A tennis player serves a ball of mass 0.06 kg. The ball starts at rest and leaves the racket at 50 m/s. The racket touches the ball for 0.005 s. Calculate the force on the ball.
F = (mv − mu) / t
F = ((0.06 × 50) − (0.06 × 0)) / 0.005
F = 3 / 0.005
F = 600 N
The time is very short, so the force is large.
You can rearrange the equation to find the other quantities:
- change in momentum = force × time taken
- time taken = change in momentum / force
Rebounding objects
When an object bounces back, its direction changes. Momentum is a vector, so one of the two velocities must be negative. Choose a positive direction before you start.
Worked example 3: rebounding
A rubber ball of mass 0.2 kg hits the floor at 6 m/s. It rebounds upwards at 4 m/s. The ball touches the floor for 0.05 s. Calculate the force on the ball.
Take upwards as positive. So u = −6 m/s and v = +4 m/s.
mv − mu = (0.2 × 4) − (0.2 × (−6))
mv − mu = 0.8 − (−1.2) = 2.0 kg m/s
F = 2.0 / 0.05
F = 40 N upwards
Notice that the change in momentum (2.0 kg m/s) is bigger than the momentum the ball arrived with (1.2 kg m/s). The floor has to stop the ball and then send it back the other way. If you forget the minus sign you get 0.8 − 1.2 = −0.4 kg m/s, which is wrong.
Longer time, smaller force
Look at the equation again. For the same change in momentum, a longer time gives a smaller force. This one idea explains every safety feature in this lesson.
Worked example 4: the same crash, two different times
A crash test dummy of mass 80 kg sits in a car moving at 15 m/s. The car hits a wall and the dummy is brought to rest.
Change in momentum = (80 × 0) − (80 × 15) = −1200 kg m/s
Stopped by the hard dashboard in 0.05 s: F = −1200 / 0.05 = −24 000 N
Stopped by a seat belt and air bag in 0.4 s: F = −1200 / 0.4 = −3000 N
The time is 8 times longer, so the force is 8 times smaller.
The dummy loses the same momentum both times. Only the time changes. A force of 3000 N is far less likely to cause a serious injury than a force of 24 000 N.
Safety features in cars
🚗 Crumple zones
The front and back of the car crush steadily in a crash. The car takes longer to stop, so the force on the car and the people inside is smaller.
💺 Seat belts
A seat belt stretches a little as it holds you. Your body takes longer to stop than it would if you hit the dashboard or the windscreen.
🎈 Air bags
An air bag fills with gas in a crash. Your head sinks into the soft bag and slows down gradually, so it takes longer to stop.
Safety away from the road
- Cycle helmets: the foam inside the helmet crushes when it hits the ground. The head takes longer to stop, so the force on the head is smaller.
- Crash mats: a thick, soft mat squashes when a gymnast or high jumper lands on it. The landing takes longer, so the force is smaller.
- Bending the knees: if you bend your knees as you land from a jump, your body keeps moving down for longer. The time to stop goes up, so the force on your legs goes down.
The fielder in worked example 1 can use the same idea. Pulling the hands back while catching makes the ball take longer to stop, so the ball stings less.
Model explanation: a 4 mark answer
Question: Explain how a crumple zone reduces the risk of injury to the people in a car during a crash. [4 marks]
Answer: The crumple zone crushes during the crash (1). This increases the time taken for the car and passengers to stop (1). The change in momentum is the same as it would be without the crumple zone (1). Force = change in momentum / time taken, so a longer time gives a smaller force on the passengers (1).
Every safety feature answer follows this pattern: what the feature does, the time goes up, the change in momentum stays the same, so the force goes down.
Investigating crumple zones
The specification suggests an investigation into how crumple zones can be used to reduce the forces in collisions. It is an optional extra, not a required practical. One way to do it:
- Let a trolley roll down a ramp from the same starting point each time, so it always hits a fixed barrier at the same speed.
- A force sensor on the barrier, connected to a data logger, records the largest force in each collision.
- Test the trolley with nothing on the front, then with different crumple zones taped on, such as folded card or sponge.
- The crumple zone that gives the smallest force is the one that makes the collision last longest.
Common mistakes
- Saying the safety feature reduces the momentum. The change in momentum is the same. It is the time that increases and the force that decreases.
- Writing "it absorbs the force". This gets no marks. Say that it increases the time taken for the momentum to change.
- Forgetting the minus sign on a rebound. The velocities before and after are in opposite directions, so one of them is negative.
- Working out mu − mv. It is always final momentum minus initial momentum.
- Not converting units. Change grams to kilograms and milliseconds to seconds first. 1 ms = 0.001 s.
Exam-style question
A gymnast of mass 50 kg jumps down from a beam. She is moving at 6 m/s when she lands.
(a) Calculate the momentum of the gymnast just before she lands. [2 marks]
(b) She lands on a crash mat and comes to rest in 0.5 s. Calculate the size of the average force that stops her. [2 marks]
(c) Explain why the gymnast is more likely to be injured if she lands on a hard floor instead of the crash mat. [3 marks]
(d) On a hard floor, the average force that stops her is 6000 N. Calculate the time taken for her to stop. [3 marks]
Model answer
(a) p = m × v = 50 × 6 (1)
p = 300 kg m/s (1)
(b) F = (mv − mu) / t = (0 − 300) / 0.5 (1)
Size of force = 600 N (1)
(c) On the hard floor she stops in a shorter time (1). Her change in momentum is the same as on the mat (1). Force = change in momentum / time taken, so the force on her is larger (1).
(d) time taken = change in momentum / force (1)
t = 300 / 6000 (1)
t = 0.05 s (1)
Exam tip
In part (c), "the floor is harder" just repeats the question. The three marks are for the shorter time, the same change in momentum and the larger force, so make sure all three are in your answer. In part (b) the question asks for the size of the force, so you can leave out the minus sign.