The auto collision problem is the staple topic of every physics student, starting in high school. We begin with the easy ones: Car A is moving and Car B is standing still. A little later on, we crash them at different speeds, weights and angles. If you remove the possibility of injury or death from the equation, mathematical analysis of collisions can be a lot of fun. What happens when a semi-truck T-bones a Fiat? What material should a bumper be made of so that two Volvos stick together in a head-on collision? These are the questions that physicists love to answer. Add the human component, and we may even save some lives.

The Newtonian Collision

Newton’s Laws of Motion is the governing science for collision theory. If you don’t remember your fifth grade science class, the laws state that a body in motion will stay in motion, there is an equal but opposite force to all static situations, and force is equal to the mass of the object times its acceleration. A person in the car will tend to stay in motion until another force acts on it. For a moment as the two cars collide, the person inside keeps going forward. The body goes until the seat belt engages, causing a rapid deceleration. More accurately, this is an acceleration in the opposite direction of the motion and the force for a person weighing 160 pounds is calculated to be about 4,800 pounds.

The Energy of a Crash

Energy transfer is an extension of Newton’s Laws. Energy cannot be created nor destroyed; it can only be transferred. The moving  body has energy, called kinetic energy, and this energy will be transferred into something else as the body slows. Likewise, the car  crashing into you will transfer its kinetic energy to you. The other type of energy is potential energy, or stored energy. Think of a  spring. When you pull it, you are storing energy. When you let it go, this potential energy is transferred into kinetic energy as  motion. Car manufacturers engineer a purposeful flaw into the structure, the Crumble Zone. This Crumble Zone is a structurally assigned  place for kinetic energy to be transferred into potential energy in the case of an accident. When two cars collide, the kinetic energy is used up to fold the metal of the auto, keeping the destructive energy out of the passengers. The same science is behind the recommendation that motorcyclists wear helmets and body armor. Auto crumble zones, as well as air bags, helmet foam and Kevlar, are all methods for converting harmful kinetic energy into safe potential energy.

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The Effects of Chaos

Studies show that whiplash from auto accidents are not predicted by the change in velocity of the crash. This is because Newtonian physics is not the only rules at play. The Chaos Theory has a foothold for accidents over 30 mph as well. According to Chaos Theory, a small change in the system can multiply, overcoming the whole structure. Called bifurcation, this multiplicative process of chaos means that a microscopic fracture in the structure of the car can cause an overall collapse of the whole car. The higher the combined speed of the accident, the more that chaos will affect the physical system.