Crumple Zones & Car Safety: How F=ma Applies

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SUMMARY

Crumple zones in cars function by extending the time over which a collision occurs, thereby reducing the average force experienced by occupants, as described by Newton's second law (F=ma). The average acceleration during a collision is calculated as a = v^2 / 2L, where L represents the length of the crumple zone. By increasing L, the acceleration—and consequently the force—experienced by the occupants is minimized. This principle effectively reduces the momentum change (Impulse) during a crash, enhancing passenger safety.

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How do crumble zones on cars work in relation to Newton's 2nd Law (F=ma)?
 
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They work by reducing the "a" in F = ma.

If you are moving in your car with velocity v, and you have to slow down to 0 over a distance of L, then you will experience an (average) acceleration of

a = v^2 / 2L

If you assume that you collide with a really hard body that is not deformed at all during the collision, then L is identical with the length of your crumble zone. So the acceleration you experience is inversely proportional to the length of your crumble zone.
 
Last edited:
physium said:
How do crumble zones on cars work in relation to Newton's 2nd Law (F=ma)?
You can think of this in terms of reducing the momentum (P) of the car to zero. The change in momentum is called Impulse (J) and we can write its magnitude as:

J = (average force) F * (time) T.

This is derived from Newton's second law in the form F = dP/dt.
So for a given J we can reduce F by increasing T. This is what the crumple zone does.
 

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