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The case of the murderous momentum

The case of the murderous momentum

It's a dark and stormy night. You are traveling in a car going 60 mph on a single-lane road. Suddenly a car's headlights appear in the gloom, barreling down upon you at 60 mph. You hit the brakes, to no avail. Your first thought is *[email protected]!-I should have had the pads replaced. Your second thought: *[email protected]! Your only options: hit the car or swerve and hit a brick wall head-on. What should you do?

Had a forensic engineer been called to the scene to investigate your accident, one of his or her objectives would be to determine the speed(s) of the vehicle(s) involved. There are several methods for obtaining this information that will be discussed in later articles. All of them require application of the basic concepts of relative velocity, momentum, and mechanical energy.

There is a lot of misleading and just plain wrong information with respect to speed and car accidents. When I was in high school, a police officer came to our school to talk about safe driving. He said that when two cars, both going 60 mph, collide head-on, the effect is like hitting a brick wall at 120 mph. If true, it would be better to hit the brick wall at 60 mph than to hit the other car traveling at 60 mph.

While the officer's statement reflects an understanding of relative velocity, it completely ignores the concepts of momentum and energy. It's true that the speed of one car is 120 mph with respect to the other car, but the assertion that hitting a car is like hitting the proverbial brick wall-assumed to have infinite mass and be perfectly rigid with no motion after the impact-is incorrect. Plastic impact with such a wall does not conserve momentum. The kinetic energy of the car is completely dissipated and all momentum is destroyed.

In fact, hitting a car is much different than hitting the idealized brick wall. The car has a finite mass and is deformable. On the other hand, it also has finite size and may have protuberances that may cause serious injury. The momentum equations provide some insight. If a car of mass m1 has a speed of v and experiences direct central impact with a car of mass m2 that has the same speed in the opposite direction, the equation for conservation of momentum indicates that the speed of the two after impact v' is:

v' = (m1 - m2) v / (m1 + m2)

Plastic impact is assumed, so that the two masses have a common velocity after impact. This equation shows that if you have two identical cars equally loaded, the speed after impact is zero. Imagine a vertical plane between the two cars at impact. In the idealized situation, neither of the cars would impact through this plane because the deformation of the cars would be symmetrical about it. This is probably the situation the policeman had in mind, and would be somewhat like hitting the brick wall at 60 mph, not 120 mph. In this case hitting the brick wall would be the best choice because the impact force is more distributed, it doesn't really have infinite weight and stiffness, and no other people are involved.

On the other hand, if m2 is very large compared to m1, the speed of m1 after impact is almost v in the opposite direction. If your subcompact hits a loaded Mack truck, the truck hardly slows down at all and your car becomes a speck on its radiator. Again, go for the wall.

In this simplified situation, if you are driving the Mack truck meeting the subcompact, the selfish choice is obvious. However, unless everyone has already baled out of the car you should go for the wall to avoid injury to other people. The wall will probably give a little anyway and maybe you can hit it at an angle.

Did Dale Earnhardt hit the wall at 190 mph? Tune in next month to find out.

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