Collisions Damage

## Question:

Sorry to bother you, but I have an on going argument at work
concerning damage at impact with two cars. Both cars are same
weight or mass and traveling same velocity (say 60mph) I say that
each car will suffer the same amount of damage as if they hit an
immovable object like a solid wall going 60 mph. My co-workers
claims the damaged would be the same as one car hitting a solid
wall at 120mph. I realize the total amount of force or energy
would be equal to one car hitting that wall at 120 but since all
that energy is divided by two vehicles then the impact force for
each vehicle would have to be halved so each car would look like
it just hit a solid wall at 60 mph? Right or Wrong?
p.s. Do you think it unhealthy for air traffic controllers to
discuss such things?.

## Answer:

Here is the way I would think about the problem. Imagine a car to
be a moving crushable object which hits a much more massive
object and dissipates the entire energy of its motion by the heat
generated in crushing so that it comes to a stop in contact with
the "immovabal" object. The one vehicle at 60 mph case.
It will be crushed enough to account for all its kinetic energy,
an amount equal to one half its mass times its velocity squared.
If two identical cars each moving at 60 miles per hour have a
perfect head on collision, each coming to rest in contact with
the other at the point of impact, the total kinetic energy of the
two vehicles will be twice that of the previous case. That energy
will be shared between the two vehicles equally so each will
crush the same amount as in the first case as you suggest. Only
if one vehicle came away undamaged would the whole kinetic energy
go into damage on the other vehicle.
You might make the point to your fellow worker that the
infinite mass of the wall in the first case has been replaced by
the 60 mph velocity of the second car in the two vehicle case so
that the collision from the perspective of one of the cars is the
same. It is sort of like the second car, coming along at 60 mph
renders the point of impact an "immovable" object.

Regarding the p.s., I hold a ComSEL license so I have always
suspected that ATC guys had their minds on things other than
airplanes:). Seriously though, a healthy curiosity about how the
universe works is a prerequisite to sound decision making in your
line of work. I hope this answer to your question is adequate. If
you need more, let me know.

J. D. Jones

M. Casco Associates