# by Christopher Erickson

In recent years, the automobile industry has attempted to improve safety through a number of technological developments. One technique which has been proven to be successful, involves the use of crumple zones positioned in specific areas of an automobile. Crumple zones are created by the integration of variable grades of steel and fiberglass into the front and rear-end assemblies of the automobile.  Occasionally, crumple zones are used in the actual frame of the automobile, creating a point for the frame to buckle when subjected to extreme stress.  These crumple zones yield during impact, redirecting the energy of the collision---often reducing the chance of injury to the driver.
Example of front and rear crumple zones in a recent Volvo model

The following diagrams illustrate the effect of crumple zones in automobiles. In figure 1, a steel block travels at a constant velocity towards a cement wall, representing an automobile without crumple zones. Initially, the block has kinetic energy, represented by the expression, mv2/r. As the block collides with the wall, it exerts a force on the wall, after which the wall exerts an equal and opposite force on the block. The magnitude of this force is illustrated by the amount of kinetic energy regained by the block. At the moment of impact, the steel block immediately rebounds in an elastic manner, regaining nearly all of its kinetic energy, and consequently experiencing a large force.
In figure 2, an aluminum can travels at a constant velocity towards a cement wall, representing an automobile with crumple zones. As the can collides with the wall, it does not regain all of its initial kinetic energy. Instead, some of the kinetic energy is transferred into heat and sound energy, resulting in a smaller force experienced by the can.
CORRECTION!
(replace any MV^2/R expressions with 0.5*MV^2)

Figure 1

Figure 2

The energy equation governing the previous example is as follows:
Where m is mass, vo is initial velocity, and vf is the final velocity of objects 1 and 2.  NC refers to non-conservative kinetic energy, or the sound and heat energy lost in the collision.

Crumple zones in action at the Toyota crash testing site

The amount of force experienced by the car has been shown in the previous example to have been lessened by the action of crumple zones.  Crumple zones also decrease the severity of an accident by creating a phenomenon known in the automobile industry as "controlled deceleration."  Generally, this means that if the time it takes for an automobile to come to rest or change direction is increased, the force experienced by the automobile is decreased.
This phenomenon is expressed more formally through the application of Newton's second law of motion, or:

where a can be represented by the change in velocity over the change in time, or:

Substituting the previous equation for a in Newton's second law yields:
From this equation, it is clear that as the time of the collision decreases, the force experienced by the automobile increases dramatically.  For example, if a 1000 kg car collides with a wall at 14 m/s (32 mph), the force experienced by the car is expressed as:

The graph of this function is shown below, illustrating how force changes as time changes:

The key point is that at small intervals of time, a slight increase in time results in a large decrease in force.  The better the crumple zone, the more effective it is in increasing the time of a collision.

Be sure to also check out these sites:

Elevators              A experiment I performed involving acceleration and deceleration in elevators.
The B.U. Page         A collection of links relating to B.U. and the Boston area.
Apple Computer        Need I say more?

References:

Cutnell and Johnson. Physics. 4th ed, New York: John Wiley and Sons, 1997.

Bueche, Frederick. College Physics. 8th ed, New York: McGraw-Hill, 1989.

Mashaw, Jerry. The struggle for auto safety. Cambridge, Mass: Harvard Press, 1990.

Toyota Automobiles Inc.  http://www.toyota.com

Volvo Motors Inc.   http://www.volvo.com