Edexcel IGCSE Physics · Spec 1.26P-1.28P
Momentum Change and Vehicle Safety (Paper 2)
Covers use force = change in momentum / time, Explain vehicle safety features and Solve impulse-style calculations.
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Momentum Change and Vehicle Safety (Paper 2)
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Explained
Force from a change in momentum, and why cars are built to crumple
Force equals the change in momentum divided by the time taken. It is Newton's second law written another way, and it is the equation behind every vehicle safety feature on the specification.
Change in momentum means final momentum minus initial momentum, and it is measured in kilogram metres per second. Divided by a time in seconds, it gives a force in newtons.
The logic of a safety feature
In a crash, the change in momentum is fixed. The car was moving and it has to stop, so the momentum has to go from whatever it was to zero, and nothing about the design of the car changes that.
What can be changed is the time it takes. If the same change in momentum happens over a longer time, the force is smaller, because the momentum change is on the top of the fraction and the time is underneath.
Crumple zones deform, so the front of the car takes longer to stop than a rigid front would. Airbags inflate and the occupant decelerates against something soft rather than against a steering wheel. Seat belts stretch slightly instead of holding rigid. Crash helmets and crash mats do the same thing for a head and a falling gymnast.
Every one of them works the same way, and that is the answer to give: it increases the time over which the momentum changes, so the rate of change of momentum is smaller, so the force is smaller, so the injury is less severe.
Saying only that a feature cushions the impact or absorbs the shock describes the effect without explaining it, and it is the version that scores one mark out of three.
Signs and direction
Momentum is a vector, so choose a positive direction before writing anything down.
An object slowing down has a negative change in momentum, so the force comes out negative, and that negative sign means the force acts in the opposite direction to the motion. A car braking is pushed backwards while travelling forwards, which is exactly what a braking force is.
Many mark schemes ignore the sign in the final answer, but the direction is often a separate mark, so state it in words rather than relying on the minus.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme works a momentum change question in three marks: find the change as the initial momentum minus the final momentum, substitute into the given formula, and evaluate. The worked figures are 120 000 minus 63 000, giving a change of 57 000 kilogram metres per second, then divided by a force of 6100 newtons to give 9.3 seconds.
Its notes then do something worth studying. They award one mark to an answer that rounds to 20 seconds, and one mark to an answer that rounds to 10 seconds.
Neither is close to 9.3. They are the two answers you get from the two things that go wrong here. Twenty comes from dividing the initial momentum by the force without subtracting, and ten from using the final momentum instead of the change.
So the mark scheme has worked out in advance which errors candidates make, calculated what those errors produce, and decided that each still shows a correct use of the formula. Both keep the substitution mark and lose the two that depend on getting the change in momentum right.
The lesson is where the difficulty in these questions actually is. Not in the division, which is one keystroke, but in working out what number goes on the top. Write change in momentum equals 120 000 minus 63 000 as a line of its own, and the rest follows.
Earlier in the same question the mark scheme asks for a velocity from a momentum, and requires the answer to two significant figures, accepting anything that rounds to 8.6 metres per second.
Working through a safety calculation
A 1200 kg car travelling at 20 metres per second stops in 0.10 seconds against a rigid wall.
Its initial momentum is 1200 multiplied by 20, which is 24 000 kilogram metres per second. Its final momentum is zero, so the change is 24 000. Divided by 0.10 seconds, the force is 240 000 newtons.
With a crumple zone the stop takes 0.50 seconds instead. The change in momentum is still 24 000, but divided by 0.50 the force is 48 000 newtons.
Five times the time, one fifth of the force, and the same crash. Setting the two calculations side by side like this is the clearest way to answer a question asking you to explain the benefit, because the identical number on the top of both is the whole argument.
Spec 1.26P-1.28P
What you need to know
- Use force = change in momentum / time
- Explain vehicle safety features
- Solve impulse-style calculations
Active recall
Quick check
Answer each question before opening the answer.
Write the force-momentum equation
F = change in momentum / time
How does a crumple zone reduce force?
It increases stopping time
What does a negative force sign show?
The force acts opposite the chosen positive direction
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