Estimating Collision Duration in Rear-End Car Crashes

[Frank_Horrigan]

For school I have to explain how whiplash can occur if a driver is at a read light and he seat doesn't support his head, and he gets hit from behind. Now I was thinking that I needed to find the velocity of the car after it had been hit from behind, so that I could find the corce acting on the drivers head. Upon investigation I found that collisions have to do with momentum, But i was unable to find out the key thing i was looking for, which is :

If car one is stopped at a red light, and car 2 is moving at a known velocity (and you know both cars masses) how do u figure out the velocity of each car after a rear collision?

I've been looking at this site so far and it has confused me:
http://www.physicsclassroom.com/mmedia/momentum/momentumTOC.html

On that site there are examples where the ars bounce backwards after impact, is this wha owuld happen on a normal road? I would think that either car 2 would stop and car 1 would get car 2's velocity, or that both of there velocitys would be positive after collision. Also would the force of friction on the road cause momentum to be lost after the collision? or can I assume it's negligable for this car crash senario?

 

[HallsofIvy]

Well, remember that most such collisions occur when "car 1" is stopped and the driver has his foot on the brake! In that case you certainly would have to take into account the friction force (in the brakes). The may be more complicated than what you intend. Assuming car 1 does NOT have brake set and that car 1 and car 2 have the same mass, then, you need to take into account the "elasticity" of the collision. With a perfectly elastic collision using both conservation of momentum and conservation of energy, car 2 will come to a stop and car 1 will start moving with car 2's speed.
But the question you want to consider is how much time will this take! In an "ideal", textbook problem, you would probably assume a perfectly elastic collision and that would become "infinitesmally" small and the force, for that instant, would be infinite. In reality both cars will crumple, spreading the force over some period of time. The total change in the speed of the cars, times their mass, is the "impulse" and the average force is that impulse divided by the time.

 

[jdavel]

Frank Horrigan,

Picking up on Halls of Ivy's suggestion, a reasonable approximation might be that after the collision, each car is going at half the original speed of car 2 (that conserves momentum and cuts KE in half). So suppose car 2 was going at 30 mph before the collision, how could you estimate the duration of the collision?