A car travelling at high speed collides with a stationary barrier and comes to rest. Explain, using Newton's laws of motion and the concept of momentum, why a longer collision time reduces the force experienced by the car's occupants.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Modern cars are designed with crumple zones at the front and rear. These crumple zones are designed to increase the time taken for the car to stop during a collision.
Model answer (5 marks)
The car and its occupants have an initial momentum
p_i = m v
where m is the mass and v the speed before impact. During the collision the car comes to rest, so the final momentum is zero. The change in momentum is
Δp = p_f – p_i = 0 – m v = – m v
According to Newton’s second law, the average force acting on the car is
F = Δp / Δt
where Δt is the collision time. The magnitude of Δp is fixed by the initial speed and mass, so the only variable that can reduce the force is Δt. A longer collision time means the rate of change of momentum is smaller, giving a smaller average force on the occupants. Crumple zones increase Δt, therefore they reduce the force experienced during a collision.
p_i = m v
where m is the mass and v the speed before impact. During the collision the car comes to rest, so the final momentum is zero. The change in momentum is
Δp = p_f – p_i = 0 – m v = – m v
According to Newton’s second law, the average force acting on the car is
F = Δp / Δt
where Δt is the collision time. The magnitude of Δp is fixed by the initial speed and mass, so the only variable that can reduce the force is Δt. A longer collision time means the rate of change of momentum is smaller, giving a smaller average force on the occupants. Crumple zones increase Δt, therefore they reduce the force experienced during a collision.
Examiner tips
- Show the momentum equation first, then the change in momentum, then Newton’s second law, and finally link the longer time to a smaller force.
- Use the symbol Δt for collision time and Δp for change in momentum to match the mark scheme.
- Explain that the force is the rate of change of momentum, not just the change itself.
Common mistakes
- Confusing force with momentum, e.g. writing F = Δp instead of F = Δp/Δt.
- Forgetting to state that Δp is the same regardless of collision time.
- Using the wrong sign for Δp or not recognising that the magnitude of the force is what matters for occupants.
Mark scheme (5 marks)
- The car (and occupants) have momentum before the collision / momentum = mass × velocity
- During the collision the momentum changes / the car goes from moving to stationary so its momentum changes to zero
- By Newton's second law, force is related to the rate of change of momentum / force equals change in momentum divided by time
- The change in momentum is the same regardless of collision time (same initial and final momentum)
- A longer collision time means the rate of change of momentum is smaller, so the force on the occupants is smaller / crumple zones increase collision time and therefore reduce the force
Key terms in this question
Related
- All OCR A-Level Physics B: Advancing Physics (H557) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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