Edexcel IGCSE Physics · Spec 1.11E
Momentum: Using the Equation (Worked Examples)
Worked examples calculating momentum.
Physics revision video
Momentum: Using the Equation (Worked Examples)
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Explained
Momentum, and why direction decides the sign
Momentum equals mass multiplied by velocity, written p equals m v. Mass in kilograms, velocity in metres per second, and momentum in kilograms metres per second, a unit with no shorter name.
Because velocity is a vector, momentum is a vector too. It has a direction, and in every collision question that direction is what the working depends on.
Conservation of momentum
In a collision or an explosion, the total momentum before equals the total momentum after, provided no external force acts.
To use it, choose a direction and call it positive before you write anything down. Anything moving the other way then has a negative velocity and a negative momentum. Add up the momentum of everything before, add up the momentum of everything after, and set the two totals equal.
An explosion is the same principle from a standing start. A stationary object has zero total momentum, so after it separates the two pieces must have equal and opposite momenta, which is why a gun recoils and why a rocket moves forward.
A worked collision
A 3 kg trolley moving at 4 m/s to the right hits a stationary 5 kg trolley and they stick together.
Before: 3 times 4 gives 12 kg m/s, plus 5 times 0 which is nothing, so 12 kg m/s in total.
After: the combined mass is 8 kg moving at some velocity v, so 8v equals 12, giving v equals 1.5 m/s to the right.
Check it makes sense. The moving object has picked up extra mass, so it must be slower, and 1.5 is less than 4.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme awards a mark for stating that the total momentum before a collision equals the total momentum after. Its note then says to ignore the equation, and prints the algebraic version it will not accept on its own.
That is unusual and worth reading twice. Writing the symbols is not a statement of the principle. The words before and after are what is being marked, because they are what show you know what the equation means.
On the calculation that follows, the mark scheme gives the momentum as 39 kg m/s and adds ignore sign, so a negative answer is not penalised there. It allows standard symbols and any rearrangement for the equation mark, and it accepts a range of final values, including a value rounded to a single significant figure.
The pattern across these papers is consistent. The physics has to be in words when words are asked for, and the arithmetic is marked generously once the method is visible.
Force and change of momentum
Force equals change in momentum divided by time taken. This is Newton's second law written another way, and it explains most safety features.
A crumple zone, an airbag and a crash helmet all work by increasing the time over which the momentum changes. The change in momentum is fixed, because the car or the head still has to stop, so a longer time means a smaller force, and a smaller force means less injury.
If a question asks how a safety feature works, that is the chain: it increases the time taken to stop, so the rate of change of momentum is smaller, so the force is smaller. Saying only that it cushions the impact describes the effect without explaining it.
Spec 1.11E
What you need to know
- Use p equals m v
- Rearrange it to find mass or velocity
- Use conservation of momentum in a collision
Active recall
Quick check
Answer each question before opening the answer.
What is the momentum of a 2 kg object moving at 3 m/s?
6 kg·m/s (2 × 3).
What quantity is conserved in a collision (with no external force)?
The total momentum.
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