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ENERGY, MOMENTUM, AND DRIVING
The external forces can cause damage to the vehicle and injury to your body. The amount of damage or injury is determined by the magnitude of the force and by the part of the vehicle or the body to which the force is applied. Minimizing damage to the vehicle and injury to the occupants often present conflicting requirements.
Bumpers are designed to protect the car; air bags are designed to protect people. Neither of these does a perfect job. Both involve trade-offs. To learn more about air bags visit the
Insurance Institute for Highway Safety, where we got the air-bag picture.
The Role of MomentumNewton's second law requires that the integral of force with respect to time must be equal to the change in momentum. This implies that a given momentum change can be accomplished with a weaker force if the time of interaction is increased. Give yourself more time to brake and the forces will be more gentle. Newton's third law requires that the forces acting on two interacting (colliding) objects will be equal and opposite. Your textbook shows how Newton's third law implies conservation of total linear momentum. The change in momentum of one colliding vehicle is accompanied by an equal and opposite change of momentum of the other vehicle. This idea is usually the underlying principle used in accident reconstruction.The Role of Mass And Energy
When a light car and a massive truck collide, momentum conservation requires that Note that an object with large mass will experience a smaller change in speed than the object with the small mass. As the occupant of the vehicle it is in your interest that the vehicle does not undergo big changes in speed in a short time. Since you yourself are a moving object subject to Newton's laws, you will need external forces yourself to change your motion. These will come from the seat, the seat belt, air bags, or other parts of the vehicle such as the steering column.
Accident ReconstructionNote: What follows is based on a contribution by Prof. David Wagner of Edinboro University. Dr. Wagner is a physics professor who is also a valued accident reconstruction expert.Unfortunately, every day there are thousands of traffic accidents throughout the United States. While most accidents are minor, a significant number of accidents result in some form of legal action, either civil or criminal. When legal action occurs, the courts get technical help from
At the simplest level, a reconstruction might involve computing the location of a vehicle at various times before a collision. Or the problem might be to determine how far a vehicle traveled during the time when a driver was perceiving and reacting to the incident. Accident reconstructionists are paid up to several hundred dollars per hour for their time. Of more interest are situations involving vehicles skidding, colliding, or yawing (sideslipping while traversing a curve). In these cases, the concepts of energy, momentum, and force are central. SkiddingWhen a vehicle begins to skid, the problem becomes one of classic kinetic friction. Given a knowledge of the coefficient of friction between the tires and the road, the slope of the road surface, and the total distance of the skid, it is quite straightforward to estimate the speed of the vehicle.
With this speed known, and given typical driver reaction times, it is possible to paint a fairly complete scenario of the motion of the vehicle just prior to the accident. CollisionsCollisions pose a more severe challenge. In cases where skid marks completely document vehicle motions prior to and following a collision, the principle of conservation of momentum can be used to analyze the collision phase of an accident, for example, by means discussed above, a determination of the speed and direction of both vehicles immediately following impact (direction, of course, being determined by the line of the skid marks).With the speed and direction of both vehicles known just after impact, conservation of momentum can be used to determine the speed and direction of both vehicles just prior to impact (again, skid marks specifying pre-impact direction). Finally, skidding analysis applied to the pre-impact skid marks allows a determination of the original speeds of both vehicles. Energy and CollisionsDuring a collision, energy is also conserved. But the use of this principle requires that all the energy transformations occurring during the collision be amenable to analysis. The most difficult contribution to accurately determine is the energy of post-impact skidding.
It turns out that tests with hundreds of vehicles have shown that there is a linear relationship between the amount of residual crush (crush remaining after the collision) and the energy lost to deformation and crush.
Energy of crush is a less precise reconstruction tool than is conservation of momentum. This is because, although there is an empirical linear relationship between crush and energy loss, individual vehicles only approximately adhere to this relationship Yaw MarksWhen a vehicle is guided through a curve, even at constant speed, that vehicle is accelerating toward the center of the curve. The force that produces the acceleration is the side thrust between the tires and the road; that is to say, friction. The yaw marks have crossways striations which are different from the marks left by a skidding tire.There is a simple relationship between the radius of curvature of the yaw marks, the coefficient of friction, and the speed of the vehicle leaving the marks. The underlying physical principle is:
Clearly, once it has been determined that a vehicle left yaw marks as a result of traversing a turn at the limit of friction, the speed of the vehicle can be determined. Further study links:Here are additional info links. We spend a lot of time and money on cars. It is worth taking an hour or two to examine some of the many interesting technical issues.
The final four links are not directly related to physics but you might find them interesting.
Further Study Questions:
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If the vehicle comes to a stop, or if the speed is substantially decreased, the lost kinetic energy of the vehicle transforms into some other form. This process will involve work, the integral of force with respect to displacement. The bigger the displacement the weaker the force (and damage and injury). Hard stationary objects don't allow much displacement and cause more damage and injury than soft, movable, or breakaway objects. The next time you are driving or riding in a car, look around and see how modern vehicle and highway designs surround you with soft, breakaway barriers whenever possible—wide medians, breakaway lampposts, energy-absorbing barriers at underpasses, padded dashboards.
It should be noted that it is rare for a reconstructionist to have an opportunity to be at a "hot" accident site. The reconstructionist usually has to rely on evidence gathered by the police or other investigators.
As an example, suppose that a vehicle is found to have skidded 130 feet along a flat road, coming to a complete stop. Given that the coefficient of friction of the tire/road surface is known to be between 0.55 and 0.70, what is the range of possible speeds?
