From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>
Date: Fri, 2 Jul 1999 17:40:26 -0500
Hi all-
To clarify the discussion between Michael Edmiston and me:
******************************************************
Jack Uretsky says I am incorrect that a collision with a tree (or brick
wall) brings the car to rest at the tree/wall. I think Jack needs to
view a few test-crash videos, or visit a few accident sites. Any
"bounce back" is quite small.
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This becomes a "my experience is more relevant than yours" sort
of argument, which I decline to participate in. Cornell Aeronautical
Labs was one place that made many movies of car crashes, and there are
no doubt many other sources. What is needed here is some relevant factual
data that we can agree on. Pending such data, we seem to agree that
the inelasticity of a collision is relevant to a description of the collision.
**************************************************************
Jack says I am incorrect about a moving car hitting a parked car. He
says the parked car will shoot ahead and the first car will come to
rest. He does admit that his analysis assumes hardened cars colliding
elastically. But why would we want to make those assumptions when they
are so obviously incorrect. This is one place where I will acknowledge
that it makes some sense to bring energy analysis into the picture
(along with momentum analysis).
*************************************
I said that it depends upon the inelasticity and the masses
involved. Had you said at the beginning that you are assuming that
all relevant collisions are totally inelastic, I would have spared
you almost all of my comments.
************************************************************
Jack also says that my statement that
the time of deceleration increases does not follow. I beg to differ.
Here is the analysis.
(1) Is there damage (crumpling) of either car when a moving car hits a
parked car? Yes. Then some kinetic energy was converted to thermal
energy... perhaps quite a bit.
(2) If kinetic energy is not conserved, then (by definition) this is an
inelastic collision.
(3) ONLY in the case of an elastic collision (between equal mass and
frictionless cars) will the first car stop and the second car assume
the velocity of the first car. In an inelastic collision between equal
mass cars (one parked) the moving car CANNOT stop at the point of
impact; it must travel beyond the point of impact.
(4) If the first car travels beyond the point of impact, it must move
for a longer period of time than the time it would have traveled had it
come to rest at the point of impact. The deceleration is spread over
greater time and greater distance.
(5) If the deceleration of the car is spread over longer time, the
forces on the car are reduced (Newton's second law). Hence, the damage
is less. Incidentally, this is why you "give" with the ball when you
catch a fast baseball.
********************************
Steps 4 and 5 are where you went astray. The moving car hits the
parked car in a totally inelastic collision. The tangled mess then continues
with the momentum of the first car. Friction with the ground then eventually
brings the tangled mess to a stop. But the damage was all done in the formation
of the tangled mess. Nothing in your discussion affects the time required for
the tangled mess to form.
You can easily check that there are two different losses of kinetic
energy, (1) formation of the tangled mess and (2) coming to rest because of
friction with the ground.
Here is a model to play with: 1-dimensional collision between sliding
blocks, zero inelasticity parameter. First case, the blocks coalesce upon
impact - zero formation time. Second case, the "parked block" is protected
by a spring, but coalescence occurs when the spring is compressed by some
predetermined amount - formation time is the time to compress the spring.
In either case, the loss of kinetic energy is the same; hence the damage
is the same (the spring also collapses into the wreckage after coalescence occurs).
By the way, discussion of such collisions has long been a favorite
of mine for quizzes and finals in both calculus and non-calculus courses.
Regards,
Jack
"I scored the next great triumph for science myself,
to wit, how the milk gets into the cow. Both of us
had marveled over that mystery a long time. We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
Mark Twain, Extract from Eve's
Autobiography