Friday, June 24, 2005

Why does a Bigger Truck always win?

Truck Collision

In a head-on collision:
Which truck will experience the greatest
Which truck will experience the greatest
Which truck will experience the greatest
change in momentum?
Which truck will experience the greatest change in velocity?
Which truck will experience the greatest acceleration?
Which truck would you rather be in during the collision?


Comparison of the collision variables for the two trucks:

In a head-on collision:

Newton's Third Law dictates that the forces on the trucks are equal but opposite in direction.

Impulse is force multiplied by time, and time of contact is the same for both, so the impulse is the same in magnitude for the two trucks. Change in momentum is equal to impulse, so changes in momenta are equal. With equal change in momentum and smaller mass, the change in velocity is larger for the smaller truck. Since acceleration is change in velocity over change in time, the acceleration is greater for the smaller truck.

Ride in the bigger truck! There are good physical reason!

Truck Collision

In a head-on collision the forces on the two vehicles are constrained to be the same by Newton's Third Law. But from both Newton's Second Law and the Work Energy's Principles it becomes evident that it is safer to be in the bigger truck.

The change in velocity of the driver will be the same as the truck in which he/she is riding. A greater change in velocity implies a greater change in kinetic energy and therefore more work done on the driver.

Vehicle Mass and Accidents

The more massive vehicle in a two-vehicle collision would be presumed to be safer since it would undergo less change in velocity during the collision. Not so evident is the fact that the more massive car is safer in a single-car accident. Leonard Evans collected data from the FARS database for a Fatality vs Mass comparison. His problem in assessing the rate of incidence of fatal accidents was to have a base for comparison since non-fatal single car accidents are not included in the database, nor are the number of cars in a given mass range. He used the number of pedestrian fatalities as a base, a "surrogate" for the number of serious accidents of all types, since it was presumed that the ratio of collisions with pedestrians to other types of collisions, e.g. with trees, would be similar for any mass class. It was also presumed that the pedestrian fatality rate would be more-or-less independent of car mass since even the lightest car is so much more massive than a pedestrian. The self-consistency of the curves for different ages of driver offers some evidence of validity since their accident rates were much different.


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