How do crumble zones on cars work in relation to Newton's 2nd Law (F=ma)?
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.
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.
Separate names with a comma.