Why does stopping slowly help?
Moving things have momentum (mass x speed). To stop, a force must remove it. The force you feel depends on how fast it is removed.
A simple way to find the average force: F = m x v^2 / (2 x d), where m is mass, v is speed and d is the stopping distance. If d doubles, F halves.
So safety means: stop more slowly, over a longer distance and time, and spread the force over a bigger, stronger area.
Protecting the human body: safety technology
- Crumple zone: the front and back of the car squash and take energy, so the passenger cell stays whole and the stop is longer.
- Seat belt: holds you in the seat so you slow with the car and do not hit the dashboard. It pulls on the strong chest and hips. It stretches a little.
- Airbag: a soft cushion that spreads the force over a big area and adds a few more centimetres of stopping distance.
- Helmet: hard shell spreads the hit, foam inside squashes slowly.
- Other: safety glass, speed limits, anti-lock brakes, guard rails, fire doors, gloves and goggles.
Remember: safe design does not stop the crash. It makes the crash less harmful.
Risk analysis: chance x effect
A hazard is anything that can hurt. Risk is how much danger it brings in real life.
Risk = chance (how likely) x effect (how bad).
Give each a score from 1 to 5. A rare but deadly thing (chance 1, effect 5) scores 5. A common but small thing (chance 5, effect 1) also scores 5. A common and deadly thing (5 x 5 = 25) needs fixing first.
Steps: 1) list hazards, 2) score chance and effect, 3) multiply, 4) fix the biggest first, 5) check again.
Lowering risk: three ways
- Lower the chance: speed limits, guards, training, checking brakes.
- Lower the effect: belts, helmets, airbags, crumple zones, fire exits.
- Remove the hazard: a safer design, or a different method.
Note: even a lowered risk is never zero. We choose a level that society accepts.
Try it: stretch the stop
At home: drop an egg-sized soft ball on a hard floor, then on a folded towel. Which stops it more gently? The towel adds stopping distance. In step 6, set the speed to 50 and note the force with no belt and no crumple zone, then switch them on one at a time.
Key formulas and definitions
- F = m x v^2 / (2 x d)
- Risk = chance x effect
- v (m/s) = v (km/h) / 3.6
Worked examples
1. A 70 kg dummy at 50 km/h (13.9 m/s) stops in 0.03 m. Find the average force.
F = 70 x 13.9^2 / (2 x 0.03) = 70 x 193 / 0.06 = about 225,000 N (225 kN).
2. The same dummy stops in 0.6 m with a crumple zone and belt. Find the force.
F = 70 x 193 / (2 x 0.6) = 13,510 / 1.2 = about 11,260 N (11 kN). The stopping distance is 20 times longer, so the force is 20 times smaller.
3. A danger has chance 4 and effect 3. Another has chance 2 and effect 5. Which has more risk?
First: 4 x 3 = 12. Second: 2 x 5 = 10. The first has slightly more risk, so fix it first.
Common mistakes
- Thinking a crumple zone makes the car "weak". It sacrifices the front to keep the passenger area safe.
- Forgetting to change km/h into m/s before using F = m v^2 / 2d.
- Thinking risk is only how bad something is. Chance matters just as much.
- Thinking a seat belt is needed only for fast cars. Even at low speed a sudden stop can throw you.