Changes in momentum (physics only) — AQA GCSE Physics
Test yourself on Changes in momentum (physics only) with AQA GCSE practice questions.
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Changes in momentum (physics only) explained
A force acting on an object that can move changes its momentum.
Read the full explanation
The size of the force is the rate of change of momentum: F = change in momentum ÷ time taken, which on Higher Tier is written F = m Δv ÷ Δt. Two things follow. For a given change of momentum, a longer contact time means a smaller force; for a short contact time, the force is large. Work out the change of momentum as m v − m u, remembering that a rebound reverses the sign, so a ball hitting a wall at 5 m/s and bouncing back at 4 m/s has a change of velocity of 9 m/s, not 1 m/s. Because the change of momentum is fixed by the masses and velocities involved, the only way to cut the force is to make the collision last longer.
Students should be able to explain safety features such as: air bags, seat belts, gymnasium crash mats, cycle helmets and cushioned surfaces for playgrounds with reference to the concept of rate of change of momentum.
Air bags, seat belts, crash mats, cycle helmets and cushioned playground surfaces all work the same way. In a crash the person's momentum has to fall to zero, and that change in momentum is fixed by their mass and how fast they were going: the safety feature cannot alter it. What the feature does is crumple, stretch or compress, so the person is brought to rest over a longer time. Since force is the rate of change of momentum, spreading the same change over more time makes the rate smaller, so the force on the body is smaller and the injury less serious. Examiners want the time, then the rate, then the force, in that order. The same physics works in reverse: a car striking a rigid concrete wall stops in a very short time, so the force on the occupants is enormous.
Students should be able to apply equations relating force, mass, velocity and acceleration to explain how the changes involved are inter-related.
The equations in this topic interlock. Acceleration is the rate of change of velocity, a = Δv ÷ t; resultant force is mass × acceleration, F = m a; and putting them together gives F = m Δv ÷ t, which is the rate of change of momentum. Reading them together shows why a longer collision time means a smaller force: the change of velocity is fixed, so a larger t makes a smaller a and therefore a smaller F. The same chain explains why a heavier vehicle needs a larger force to change its velocity in the same time. Choose the equation that contains the quantity you want and the quantities you are given. Units are the quickest check on a rearrangement, since a force must come out in kg m/s², which is the newton.
Your focus
- Calculate the change in momentum of an object that rebounds, using signs for the two directions.
- Determine the average force on an object from its change in momentum and the contact time.
- Explain why the same change in momentum produces a smaller force when it is spread over a longer time.
Show all 9 objectives
- Explain how an air bag reduces the force on a passenger, referring to contact time and rate of change of momentum.
- Explain how a gymnasium crash mat reduces the force on a falling gymnast, giving the three linked steps of longer contact time, smaller rate of change of momentum and smaller force.
- Identify which quantity a safety feature changes and which quantity it cannot change.
- Write down the equation linking acceleration, change in velocity and time taken, using change in velocity rather than velocity, and rearrange it to make the change in velocity the subject.
- Calculate the average force on a passenger from their mass, change of velocity and the time of a collision.
- Explain, using two linked equations, why doubling the collision time halves the force on the object.
Changes in momentum (physics only) exam tips
Marking Points
- one mark for stating that force equals the rate of change of momentum
- one mark for writing F = m Δv ÷ Δt, or change in momentum ÷ time taken
- one mark for calculating the change in momentum as final momentum minus initial momentum
- one mark for dividing by the contact time to give the force, with the unit N
- one mark for stating that the change in momentum is the same with or without the safety feature
- one mark for the feature increasing the time taken for the collision
- one mark for the rate of change of momentum therefore being smaller
- one mark for concluding that the force on the person is smaller, so the risk of injury falls
- one mark for selecting the correct equation, a = Δv ÷ t or resultant force = mass × acceleration
- one mark for a correct substitution with consistent units
- one mark for showing the rearrangement of the equation
- one mark for the answer with the correct unit
- one mark for linking a longer contact time to a smaller acceleration and so a smaller force
Examiner Tips
- 💡Write down u and v with signs before you subtract; sign errors cost more marks here than anywhere else in the topic.
- 💡Convert a contact time given in milliseconds to seconds before dividing.
- 💡State clearly whether the force you have found acts on the object or on what it hit.
- 💡Use the exact phrase 'rate of change of momentum'; 'momentum changes more slowly' is weaker but often accepted.
- 💡Name the feature and say what it physically does, such as stretching or compressing, before the physics.
- 💡Three-mark questions here follow a three-step chain: longer time, smaller rate of change, smaller force.
- 💡List what you are given with units before choosing an equation; the choice then makes itself.
- 💡Show the rearranged equation as its own line so a substitution slip does not cost every mark.
- 💡Where two equations are needed, calculate the acceleration first and carry the full value forward.
Common Mistakes
- using the final velocity rather than the change in velocity
- forgetting that a rebound reverses the sign, so the change of velocity is larger than the rebound speed
- using the time for the whole journey rather than the time of the collision
- quoting the unit of a change in momentum as N rather than kg m/s
- writing that an air bag 'slows down time', which mark schemes explicitly refuse
- saying only that it 'reduces the impact', which examiners treat as insufficient
- claiming the feature reduces the change in momentum rather than spreading it over a longer time
- saying a seat belt stops the person instantly, which would increase the force
- writing a = t ÷ Δv, which mark schemes specifically refuse
- using a final velocity where a change in velocity is required
- mixing a mass in grams with a force in newtons in the same substitution
- giving acceleration the unit m/s instead of m/s²