76 Crumple Zones

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 or , but he does keep mentioning absorbing . 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 (KE)The amount of kinetic energy an object has depends on its and its :

(1)   \begin{equation*} KE = \frac{1}{2}mv^2 \end{equation*}

Notice that the depends on , but not 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 unit of kinetic energy is a Nm, which has it own name, the  (J).

Reinforcement Activity

What is the of a person with 65 kg running with a of 10 m/s?

What is the of a meteorite with 100x less mass than the person above, but entering the atmosphere at 100x greater speed (0.65 kg and 1000 m/s)?

Which is larger, the KE of the runner or the meteorite?

What matters more in determining , or ?

Elastic Potential Energy

During the collision the car materials were compressed by the wall. If the stress remained below the of the materials, so they were remained in the , then the kinetic energy from the car would have been transferred into elastic stored in the 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.

Reinforcement Exercise

Grab a paperclip. Bend it just enough so that it springs back when released. You applied a force over a distance to bend the clip, therefore you did and transferred into the paperclip.

When you release the paperclip, what happens to that potential energy?

If the car had bounced back at the same that it had entering the collision, then the final would be the same as the initial, and we would say that kinetic energy had been . Collisions that conserve kinetic energy are known as . Collisions that don’t are known as inelastic. 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.

Reinforcement Exercises

Try the springy paperclip experiment again. Did the paperclip continue to oscillate between being in motion and being bent so that it was transferring energy back and forth from kinetic to potential forever?

Is the bending paperclip a totally elastic process?

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 , 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 tells us that energy cannot be created or destroyed, only transferred from one form to another and/or one object to another, via .

The applied to the materials during the collision caused a on the materials. Some materials were stressed above their so they . Some other materials didn’t fracture, but were stressed beyond their and into their so that they were permanently deformed. In either case, the done to deform the materials transferred into , 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.

Reinforcement Exercises

Grab a paperclip  and bend it rapidly back and forth, being sure to bend it past its each time (far enough that it won’t spring back to its original position on its own). Now touch the crease. You might notice that the paperclip feels warm. This is because you have done on the paperclip to cause the plastic deformation, which requires reconfiguration of molecules, and that reconfiguration gave them more microscopic kinetic energy, or .

Doing work implies a transfer of energy, where do you think the thermal energy received by the paper clip was transferred from?

Microscopic Kinetic Energy

Now that we have introduced as a new type of , we will reverse course and say that thermal energy is not actually a new type of energy, but rather just 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 and the work done by will always transfer some energy into thermal energy.  You can visualize this microscopic process for kinetic friction using the simulation below.

Friction

Coefficient of Restitution

The relative elasticity of collisions is defined by the (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 divided by initial speed.

(2)   \begin{equation*} COR = \sqrt{\frac{KE_f}{KE_i}} = \sqrt{\frac{1/2mv_f^2}{1/2mv_i^2}}= \frac{final\, speed}{initial\, speed} \end{equation*}

A 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.

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