Jim Green states that the energy change of a car is what correlates
with the damage. He also asks why people keep talking about momentum.
Energy change is not what causes the damage (nor is momentum change).
Consider coming to rest by applying the brakes (gently). Almost all
kinetic energy ends up as thermal energy, first in the brakes,
eventually in the surrounding air. Next consider crashing into a wall.
Almost all kinetic energy ends up as thermal energy, partly in the
wall and partly in the crumpled car. In fact, from an energy viewpoint
one might assume the braking situation is worse, because almost all
energy initially stays in the car (brakes) before being absorbed into
the air, whereas in the wall collision some of the energy goes into the
wall. But that's just a digression.
As a passenger in a car, my kinetic energy must convert to thermal
energy anytime the car and I come to rest. So if turning my body's
kinetic energy into thermal energy is injurious to me, then I am in
deep trouble anytime I ride in a car. Likewise, my momentum must
change to zero anytime I come to rest. So if my body's momentum change
from something to nothing is injurious to me, then I am in deep trouble
anytime I ride in a car. The point here is that our kinetic energy and
our momentum change quite frequently when we ride in cars, and that, in
itself, is not injurious to us.
Now, in order to bring my body to rest, we have to exert a force on it.
We can exert a small force for a long time, or a large force for a
short time, or anywhere between. Does this make a difference to us?
You bet. The small force for a long time is what we want. When we
brake slowly, the friction between our body and the seat does the
trick. This doesn't hurt at all. When we brake suddenly we may slide
on the seat and have the seat belt restrain us (and that may hurt) or
we may lean forward and hit our head on the dashboard and that may hurt
a lot. If we have a crash, the time of deceleration is even shorter
and the forces can be quite large, perhaps enough to crack our skull,
or break a rib, or rupture an organ.
So it's neither the kinetic energy change nor the momentum change that
does the damage. It's the magnitude of the force on our body. With
what physical tools shall we study this force... energy?...
momentum?... something else? It is obvious to me that examining the
momentum change is the tool of choice, because it directly relates to
the force and time. Newton's 2nd law is dp/dt = F. This rearranges to
dp = Fdt. Integrating both sides yields delta-p = integral(Fdt).
Integral(Fdt) is called "impulse." It is the area under the
force-versus-time curve for the momentum change. Impulse is equal to
change in momentum. The same impulse (the same change in momentum) can
be had with a small force for a long time, or a large force for a short
time, or any force-versus-time graph that yields the same area (same
momentum change).
Viewed in this way it is obvious that force, time, and momentum are
related as by Newton's second law... and these are the primary things
needed to ascertain injuries in a collision... and kinetic energy to
heat analysis just isn't needed.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817