Re: A Parent's Day gem

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

I have been away from phys-l while my wife was in the hospital for a 
few days.  (She is now well into recovery, thanks.)  It's sobering to 
see that the list can survive without me for awhile.  ;-)

At any rate I wanted to respond to a few of the comments that my 
remarks on the bullet problem provoked.

Leigh wrote:

> I thought John Mallinckrodt's observation about a retarding force
> having a greater than first power velocity dependence providing
> effective lift to be a revelation here. I'd never heard of such a
> thing, but it is obviously true - and significant. It explains for
> me why bullets fired from a rifle don't fall with acceleration g.
> I have written an authority for information on this topic and I
> will, of course, share it when I get it.)

It is always gratifying (and more than a little surprising!) to 
teach Leigh something he didn't already know about physics.  
However, this result is probably known to most anyone who has 
written a numerical simulation of projectile motion.  One is 
forced in the process specifically to formulate the x and y 
components of the drag force and any velocity dependence that is 
not linear will end up involving both components of the velocity 
in both components of the drag.  This serves as a good example of 
the insight that can be obtained simply from *writing* simulations 
before ever actually *running* them.

Later Leigh wrote:

> I think that v-squared dependence is not an issue here. The only issue
> is whether the drag term for the vertically falling bullet is less than
> the vertical component of drag for the horizontally fired bullet. This
> is a question about objects which inevitably fall; they have downward
> velocity components despite the brief horizontal motion.

I was thinking about this too.  In general, of course, the drag 
depends on lot's of things other than velocity and the velocity 
dependence alone is only *crudely* modeled over *limited* regimes 
by simple power laws.  Furthermore, the form of the velocity 
dependence will change with angle of attack and, since the angle 
of attack generally changes with time ...  Well, it's just a very 
complicated problem.  But the only thing that ultimately matters 
here is whether or not the upward force on the fired bullet ends 
up being a different function of time than that on the dropped 
bullet.  All of the foregoing considerations only make me more 
confident in predicting that it will be so.

Finally, David Bowman contributed a typically thorough and more 
formal analysis of the problem in the oversimplified limit that 
I suggested.  Thanks David. 

John
-----------------------------------------------------------------
 A. John Mallinckrodt      http://www.intranet.csupomona.edu/~ajm
 Professor of Physics    mailto:ajmallinckro@csupomona.edu
 Physics Department       voice:909-869-4054
 Cal Poly Pomona            fax:909-869-5090
 Pomona, CA 91768-4031   office:Building 8, Room 223