Safety features and crumple zones
Newton's Laws & Momentum - OCR A-Level Physics
Key Principle
Every collision-protection device works by increasing the time $\Delta t$ over which a person or object's momentum changes. The change in momentum $\Delta p$ is fixed by the speed of the impact, so a longer $\Delta t$ produces a smaller average force $F$. The same idea covers car safety, cycle helmets, playground surfaces and packaging for fragile items.
$$F = \frac{\Delta p}{\Delta t}$$
Case 1 : Crumple zones
Crumple zonesRegions of a vehicle designed to deform in a collision, increasing the time of impact and reducing the force. are the front and rear of a car. They deform on impact, lengthening the deceleration time of the passenger compartment. The same $\Delta p$ acts over a longer $\Delta t$, so the average force on the occupants is reduced.
Case 2 : Airbags and seatbelts
AirbagsSafety devices that inflate rapidly in a collision to extend the time over which the occupant decelerates. inflate during the impact and cushion the occupant against the steering wheel or dashboard, again extending $\Delta t$. SeatbeltsRestraints that spread the decelerating force across the chest and pelvis and extend the time of deceleration. stretch slightly and spread the force across the strongest parts of the body, also extending the time of deceleration and stopping the occupant hitting the interior.
Case 3 : Helmets, surfaces and packaging
Cycle helmet foam, rubberised playground surfaces and bubble-wrap packaging all compress on impact, lengthening the time over which the moving object decelerates. The same impulse $\Delta p = F \Delta t$ is delivered, but the peak force is much smaller because $\Delta t$ is longer.
- Worked example: a 70 kg passenger going at $14 \; \text{m s}^{-1}$ comes to rest. $\Delta p = 70 \times 14 = 980 \; \text{kg m s}^{-1}$. With no airbag, $\Delta t = 0.05 \; \text{s}$: $F = 980 / 0.05 \approx 2.0 \times 10^{4} \; \text{N}$. With airbag, $\Delta t = 0.25 \; \text{s}$: $F = 980 / 0.25 \approx 3900 \; \text{N}$. Force is reduced by a factor of 5.
- Comparing force-time graphs with and without a safety feature: the AREA under both curves is the same (same $\Delta p$). The graph WITH the feature has a lower peak and a wider base.
- The lost kinetic energy is transferred to deformation, heat and sound in the crumple zone or foam. It is not "absorbed" magically; track where it goes.
Common Mistake
HIGH
Wrong: Writing that "crumple zones absorb energy" or "airbags reduce momentum" without linking to impulse.
Right: The change in momentum $\Delta p$ is the same with or without the safety feature, because the passenger still goes from $u$ to zero. The feature increases $\Delta t$. Since $F = \Delta p / \Delta t$, a longer $\Delta t$ gives a smaller peak force. State this equation in your answer.
Right: The change in momentum $\Delta p$ is the same with or without the safety feature, because the passenger still goes from $u$ to zero. The feature increases $\Delta t$. Since $F = \Delta p / \Delta t$, a longer $\Delta t$ gives a smaller peak force. State this equation in your answer.
Examiner Tips and Tricks
- For full marks on a 4-mark "explain how X reduces force on the passenger" question, you need: (1) state $\Delta p$ is fixed, (2) state $F = \Delta p / \Delta t$, (3) say $\Delta t$ is increased by the device, (4) conclude $F$ is therefore reduced.
- Mention WHERE the kinetic energy goes: heat and sound in the deformed metal, heat in the airbag gas, deformation of the foam.
- If asked to compare two force-time graphs (with and without a feature), state explicitly that the areas are equal but the peak is lower and the base is wider.
Two force-time graphs on the same axes: tall narrow peak (no crumple zone) vs short wide curve (with crumple zone). Equal shaded areas labelled "$\Delta p$ same". Peak forces labelled.