Consider the physics of a rear-end automobile collision between two identical automobiles on a high speed highway. One of the vehicles is stopped by traffic. and the other runs into it from the rear at 100 km/h. Assume both vehicles have a mass of 1600 kg (that's typical of an SUV) and that there are unrestrained occupants in both with masses of 80 kg (the average American). While this is representative of a real situation, it's one we hope you will never experience.

There are two scenarios to this disaster. In one, the collision is elastic and after the collision the pair of cars together have the same total kinetic energy as the pair had before the collision. In another, a significant fraction of the kinetic energy is lost to crumpled metal.

1. In the event of a fully elastic collision, why does the occupant of the stationary car experience an acceleration backward into the seat? Assume the collision duration is 0.2 seconds from being at rest to being fully in final motion. What is this acceleration in units of m/s², and in multiples of the acceleration of gravity, g = 9.8 m/s². If a human cannot survive more than 9 "g" of even momentary acceleration, is the collision survivable?

2. In the moment of an elastic collision, why does the unrestrained occupant of the incident car continue forward with his initial velocity of 100 km/h even after his car has come to a full stop? How much time elapses from the moment of the car's impact until this driver meets the windshield, 1 meter in front of him?

3. When an airbag deploys before the driver of the moving car strikes the windshield or interior of the car, explain why this makes the collision survivable for the driver?

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In the event of a fully elastic collision the occupant of the stationary car experiences an acceleration backward into the seat due to the conservatio... View the full answer