Kinetic Energy

Crumple zones built into modern cars also serve the purpose of reducing force by increasing the collision time and minimizing bounce. Crumple zones cause cars to be totaled more often, but cars can be replaced and people can’t be. Notice that the presenter in the previous video isn’t talking about impulse or momentum, but he does keep mentioning absorbing energy. This energy that he is claiming will be absorbed by the crumple zone is the energy stored in the motion of the car. Any moving object has this type of energy, known as kinetic energy (KE). The amount of kinetic energy an object has depends on its mass and its speed:

(1)  

Notice that the kinetic energy depends on speed, but not velocity because KE doesn’t have a direction (an object can’t have negative KE). Even if we input a negative velocity into the KE equation, it gets squared so KE would come out positive anyway. The SI unit of kinetic energy is a Nm, which has it own name, the Joule (J).

Elastic Potential Energy

During the collision the car materials were compressed by the wall. If the stress remained below the yield points of the materials, so they were remained in the elastic region, then the kinetic energykinetic energy from the car would have been transferred into elastic potential energy stored in the compression of the materials. This stored energy has the potential to become kinetic energy, which is exactly what would happens when the materials then spring back  causing the car to “bounce” back from the wall.

If the car had bounced back at the same speed that it had entering the collision, then the final kinetic energy would be the same as the initial, and we would say that kinetic energy had been conserved. Collisions that conserve kinetic energy are known as elastic collisions. Collisions that don’t are known as inelastic collisions. In the previous chapter we learned that bounce was bad when it comes to minimizing the force on the body during a collision. The purpose of crumple zones is to ensure that very little of the kinetic energy remains after the collision by making them very inelastic.  The key to accomplishing that is to ensure that kinetic energy is transferred into thermal energy instead of elastic potential energy by designing the materials to break instead of bounce.

Thermal Energy

If you watch the video carefully, you see that the car was moving forward, then for a moment it was stopped and thus had zero kinetic energy, and then it was moving backward (though not as fast), so once again it had kinetic energy.  Some of the original kinetic energy was stored as elastic potential energy and then released as kinetic energy again, but most of it was not. If you are wondering where that energy went, then you are was very perceptive, because in fact the Principle of Conservation of Energy tells us that energy cannot be created or destroyed, only transferred from one form to another and/or one object to another, via work.

The force applied to the materials during the collision caused a stress on the materials. Some materials were stressed above their ultimate strength so they fractured. Some other materials didn’t fracture, but were stressed beyond their elastic limit and into their plastic region so that they were permanently deformed. In either case, the work done to deform the materials transferred kinetic energy into thermal energy, effectively slowing the car down, but warming it up. Crumple zones are designed to deform permanently in order to convert kinetic energy into thermal energy.

Microscopic Kinetic Energy

Now that we have introduced thermal energy as a new type of energy, we will reverse course and say that thermal energy is not actually a new type of energy, but rather just kinetic energy on a microscopic scale. Thermal energy is the energy stored in the motion of atoms and molecules that make up a material. Transferring thermal energy to a system really just means that you caused it’s atoms and molecules to move faster. The work done in compressing objects past their elastic limit and the work done by kinetic friction will always transfer some energy into thermal energy.  You can visualize this microscopic process for kinetic friction using the simulation below.

Coefficient of Restitution

The relative elasticity of collisions is defined by the coefficient of restitution (COR) which relates the final kinetic energy and the initial kinetic energy. For a moving object striking a stationary object that doesn’t move, as in the crumple zone video, the COR is calculated as final speed divided by initial speed.

(2)  

A perfectly elastic collision would have a COR of one.  If any materials are permanently deformed during a collision then you can be sure the collision was not perfectly elastic. In fact, perfectly elastic collisions don’t really occur, but many situations come very close and we can approximate them as perfectly elastic.

Check out this simulation that allows you to visualize different types of collisions.