Re: Momentum

[Robert A Cohen <bbq@ESU.EDU>]

On Fri, 2 Jul 1999, Jim Green wrote:

> Somebody state a problem and let's stick with it!

I've been reading the many posts regarding this problem.  I'd like to at
least address what I believe was the initial problem, which has been
addressed many times already but not succinctly.  The problem was started
by...

> ***********************************************
> In the Cover Story of the Wed 30 June 99 USA Today, Edward Moeller, a
> traffic engineer is quoted, "If you are driving 35 and hit someone coming
> at you at 35, it's the equivilent of hitting a tree at 70."
>
> Any hope of correcting this WRONG PHYSICS?
> *******************

To me, the Edward's implication is that one's reference frame has no
bearing on the "effect".  The same implication is present in Jack's
posting...

On Thu, 1 Jul 1999, JACK L. URETSKY (C)1998; HEP DIVISION

>         Does the worsity (how bad) of the collision depend upon the
> reference frame in which it is observed?

The answer to Jack's question is no, it doesn't matter, but we can't apply
that to this problem.  Yes, if two cars come together, each traveling 35
mph, we will observe the same damage as when we are in a reference frame
moving at 35 mph along with one of the cars (in which case one car is
stationary and the other is moving at 70 mph).

However, the "car-hitting-tree" example is not the same as following the
incident in a car-based reference frame.  In the land-based reference
frame, the two cars come to rest.  In the car-based reference frame, the
two cars do *not* come to rest.  Thus, the car-based reference frame is
not equivalent to a car traveling 70 mph and hitting a tree, even though
in both cases we have a 70-mph object colliding with a stationary object.

I believe arguments regarding how close the two situations actually are
(taking into account friction, heat, sound, etc.) go beyond the original
intent of the post which only wanted to identify how Edward was
inappropriately equating the two situations.

P.S. Regarding Michael's post...

On Fri, 2 Jul 1999, Michael Edmiston wrote:

> If the two cars are both going 35 mph, but do not have the same mass,
> the lighter car gets pushed backwards and the heavier car continues
> forward from the point of impact.  In the end, both cars have come to
> rest.  However, even though the lighter car eventually went from 35 mph
> to zero, it actually had a negative velocity for a while, hence its
> momentum change at impact was higher and the lighter car occupants
> likely have more severe injuries.

The momentum change of the lighter car is equal and opposite to the
momentum change of the heavier car, no?  The force is also the same
(Newton's third law).  I believe Michael meant to say that the *occupants*
of the lighter car (by experiencing a larger delta-v) will undergo a
greater momentum change than the occupants of the heavier vehicle
(assuming occupants in both cars have the same mass). Please correct me if
I am wrong, Michael.

By the way, I can bump into a 3-year-old and the 3-year-old will suffer
more damage than me even though each of us experiences the same force.  Is
it the acceleration that produces damage?  Am I missing something here?

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| Robert Cohen               Department of Physics       |
|                            East Stroudsburg University |
| bbq@esu.edu                East Stroudsburg, PA  18301 |
| http://www.esu.edu/~bbq/   (570) 422-3428              |
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