Re: momentum

[Gordon Smith <slipstk@OLEMISS.EDU>]

At 03:56 PM 7/2/99 -0500, you wrote:
> Michael Edmiston <edmiston@BLUFFTON.EDU> wrote:
> > 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.

This 1G force is always present.  Jumping out of a plane doesn't change it.
 All you have done is remove the restoring force that is exerted by the
floor of the plane that kept you from falling in the first place.

> 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.

Agreed.

> "Acceleration" doesn't break bones.
> "Force" doesn't break bones.

These are related.  What is trying to be put forth is that a) you have an
initial velocity V.0 and a final velocity V.1.  The acceleration that you
undergo from 0 to 1 is dependant on how quickly you want to make this
transition.

        V.0 - V.1
A =     -----------
            time

The longer the time, the smaller the acceleration, and hence smaller the
force.  The shorter the time, the larger the force.  Bones will break when
enough force is applied quickly enough.  I can take a bone (in free-fall)
and and smack it with a stick hard enough to break it.  Why?  Well, now
we're talking about inertias, which will bring us back to time-of-impact
impulses.

Perhaps we're focusing a bit too much on the trees here.

> The fact that sufficiently DIFFERENT forces are acting on
> DIFFERENT parts of the SAME bone causes it to break.

I think that's implied, but it's always good to explicitly state the
assumptions.  Personally, I don't think there is a problem with looking at
impulses for crash criteria.  I can apply a 100N force on my father's hood
by gradually pushing a hammer on the hood with no damage, but when I smack
it with that 100N force?  So much for my inheritance.

-G-
-----------------------------------------
Gordon Smith
National Center for Physical Acoustics
Coliseum Drive
University, MS 38655
slipstk@olemiss.edu