From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>
Date: Fri, 2 Jul 1999 14:55:33 -0500
Hi Michael-
You write, among other things,
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In a collision with a tree (or the proverbial brick wall) the car comes
to rest at the tree/wall.
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This statement is false in almost all circumstances. When a car
hits a wall, it bounces. The amount of bounce is characterized by the
inelasticity of the collision.
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In a collision with a parked car both cars
move in the direction of the original motion of the moving car. Hence
when hitting a parked car the resting place is beyond the initial point
of contact.
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This statement is generally correct for equal mass cars, except
that the two cars almost never move together.
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So even though the original car eventually comes to rest,
and the total impulse is the same, the collision is spread over a
longer time, hence the forces on the car and its occupants are less.
So it is better to hit a parked car than to hit an immovable wall or
tree.
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This statement certainly does not follow from anything that was said
before.
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In order to collide with a car and have the original car come to rest
near the point of impact (like it does with the wall or tree) the
second car must be moving toward the first car with equal momentum.
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Not true. To take an extreme case (perfectly hardened cars),
in a perfectly elastic head-on collision between a moving car and a
parked car of the same mass and no brakes, the moving car stops and the
parked car gets the momentum of the formerly moving car.
The simplest way to model these collisions is with "soft" billiard
balls, i.e. collisions with a given inelasticity. Net kinetic energy is
then not conserved; momentum is, of course, absolutely conserved. The lost
kinetic energy maybe thought of as going into destruction of vehicles and
passengers.
And it is not all that hard to carry out the calculations, which will
make a lot of verbiage unnecessary. You can characterize a whole range of
collisions by the mass ratio and the inelasticity parameter. A revealing
plot might be fractional loss of kinetic energy as a function of these two
parameters. Will the fractional loss depend upon the initial KE of the collision?
I'm talking about "head-on" collisions only.
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