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Re: momentum



Hello all:

Michael Edmiston <edmiston@BLUFFTON.EDU> wrote:

{snip}

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).

This reasoning (?) is wrong, and I can tell you why. Try this
"Gedanken" experiment:

You jump out of a plane. A force (1 'gee') acts on you. Any
broken bones? No.

You jump out of a plane on planet X, whose 'gee' ('gee sub X'?)
is some large factor Y larger than our 'gee'. Any broken bones?
No, because the same force is acting uniformly on all of the
little bits that make you up (modulo tidal forces, you pedants).

"Velocity" doesn't break bones.
"Acceleration" doesn't break bones.
"Force" doesn't break bones.
The fact that sufficiently DIFFERENT forces are acting on
DIFFERENT parts of the SAME bone causes it to break.

Regards,
John