Answer to Question #251840 in Mechanics | Relativity for Gghvvbnh

Question

Suppose you want to design an air bag system that can protect the driver in a head-on collision at a speed of 100 km/hr. Estimate how fast the air bag must inflate to effectively protect the driver. Assume the car crumples upon impact over a distance of about 1 m. (tip: find the acceleration then find the unknown time). (reminder: only answer the unknown which is time).

Answer 1

Depends on how quickly the car slows down, and what you mean by “effectively protect”, but there’s a whole lot more important factors in play here than just the speed the airbag inflates at.

First off, you’re going to need substantial crush space in the front end.

We assume that the head and shoulders after the impact continue to move at a speed of 28 m/s, then in order to avoid their collision with objects located at a distance of about 0.5 m in the direction of their movement, the pillow should inflate faster than 0.5/28 = 0.02 s, i.e. for a time of about 0.01 s.