Crumple Zones and Air Bags


How would you describe the function of crumple zones and/or airbags in terms of Newtons' second law?


Suppose that you and your automobile are traveling at 2 meters per second and hit a very large object like a concrete wall head on. Your speed will be reduced to zero in the time it takes to complete the collision. If that time is very short, say 10 milliseconds, the acceleration you experience will be large, 2 mps / 0.01 seconds is 200 mps/second. According to Newton's second law the force required to produce this acceleration is given by f=m*a where m in your mass. If that is 50 kg then the force of the collision on you is 50*200=10,000 Newtons. A force of that magnitude is going to do you some serious damage.

A crumple zone increases the amount of time it takes the car to stop relative to the immovable object and an air bag increases the amount of time it takes you to stop relative to the car. Suppose that together they extend the time for you to come to a stop from 0.01 seconds to 0.2 seconds. Increasing the slowing down time by a factor of 20 reduces the acceleration and therefore the force by the same factor, resulting in a force on you of 500 Newtons instead of 10,000. Still probably no fun, but likely to be survivable.

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