83 Crumple Zones

As we discussed how crumple zones reduce on the car by extending the distance over which the car’s is transferred out, you might have wondered, “transferred out to where?” If so, that 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 negative work done on the car by the wall during the crash in fact transferred into both and or both. The video is posted again below for reference:

Thermal Energy

The applied to the materials during the collision caused a on the materials. That stress caused a in 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.

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 is a 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 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

Elastic Potential Energy

Finally,  near the end of the collision the now reconfigured materials were continued to be compressed, but now the stress decreased below the of the materials, so they were being compressed in their.  The done in compressing the materials transferred from the car into elastic stored in the of the materials. This stored energy has the potential to become kinetic energy, which is exactly what happens when the materials then spring back  causing the car to “bounce” back from the wall. (The objects don’t return to the fully original shape because the were permanently deformed during the first part of the crash). The car was moving forward, then for a moment it was stopped and thus had zero , and then it was moving backward, 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. The car was not moving as fast backward after the collision as it was forward before the collision, so most of the initial became and only a small part of  was stored as and then released again as kinetic energy.

Reinforcement Exercise

Grab the paperclip again. 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?

Why doesn’t the paper clip keep vibrating for ever?

Elastic Collisions

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 conserved (remained through the collision. Such a collision is known as a (or totally elastic collision). When a collision is not elastic, we say it is inelastic and does not conserve kinetic energy. The  we discussed previously are the extreme example of inelastic collisions. 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, as in the crumple zone video, the COR is calculated as final divided by initial speed.

(1)   \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. Perfectly elastic collisions don’t really occur, but many situations come very close and we can approximate them as perfectly elastic.

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?

If not, where did the energy eventually go?

Crumple Zones

We have arrived at the most important design feature of the crumple zone. Not only does it reduce the on the car by increasing the distance over which is done, it also minimizes the bounce-back by ensuring that is not conserved. This technique requires that materials fail (crumple) so that kinetic energy is transferred into . Imagine if this did not occur and the collision was elastic, the people inside would still be moving forward due just as the dashboard came back at them, doubling the the effective impact .

We can view this result in the context of the when is :

    \begin{equation*} F_{ave} = m(v_f -v_i) \end{equation*}

If the (and ) is zero the would be:

    \begin{equation*} \Delta t F_{ave} = -m v_i \end{equation*}

However, if the collision was elastic the is equal, but opposite, to the :

    \begin{equation*} \Delta t F_{ave} = m (-v_i - v_i) = -mv_i-mv_i = -2mv_i \end{equation*}

In the perfectly elastic case the impulse on the car (and the people inside) would be twice as big. This is why cars have crumple zones instead of being made out of rubber. While rubber cars might not need repairs after an accident, the occupants surely would. Repairing cars is much less expensive than attempting to repair people, and we are much better at it.

Play with this simulation of collisions, including elastic and inelastic types.

Collision Lab

 

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