Re: [Phys-l] Pcons from N's Laws (Was: [PHYSHARE] Darwinism under attack? and the physicsclassroom

["Dan L. MacIsaac" <danmacisaac@mac.com>]

> > Begin forwarded message:
> > > From: chuck britton <cvbritton@embarqmail.com>
> > > Date: August 1, 2008 10:13:52 AM EDT (CA)
> > > To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
> > > Subject: Re: [Phys-l] [PHYSHARE] Darwinism under attack? and the  
> > > physicsclassroom
> > > Reply-To: Forum for Physics Educators <phys- 
> > > l@carnot.physics.buffalo.edu>
> > >
> > > care to summarize - or must I dig around for the set and the
> > > time? ;-)   (lazy)
> > >
> > >
> > > On Jul 31, 2008, at Jul 31(Thu) 10:30 , Jack Uretsky wrote:
> > >
> > > > Hi all-
> > > >  	Feynman (I-10-1) seens ti equate the 3d Law with conservation of
> > > > Momentum.  The argument strikes me as making the 3d law a  
> > > > corollary of
> > > > Laws I & 2.
> > > >  				Regards,
> > > >  					Jack


My off-the-cuff quick-and-dirty shot at this (literally too lazy to  
pick up Feynman down the hall) follows.  Ps and Fs below should have  
vector symbols over them; read F_12 as "force of object one on object  
two" etc.

start with (only) two objects interacting
N3:  F_12 = - F_21

recall N2 and P defns:
F_net = ma = d (mv) / dt = dP / dt

assume net forces are the interacting forces (only)
therefore F_12 = dP_2 / dt and F_21 = dP_1 / dt

substitute back into N3 above:
dP_2 / dt = - dP_1 / dt

regroup, et voila:
dP_1 / dt + dP_2 / dt = 0 = d(P total) / dt

conservation of linear momentum for the two interacting objects

...so conservation of linear momentum seems a direct implication from  
N2  and N3 (and definitions which probably ropes N1 into the game as  
well).  That'd seem to me to make Newton's Laws a consequence of the  
conservation of linear momentum (or vice versa).

Feynman I'm not, and I stand happy to be corrected in my hand waving.

Dan MacIsaac, Associate Professor of Physics, SUNY-Buffalo State College
222SciBldg BSC, 1300 Elmwood Ave, Buffalo NY 14222 USA 716-878-3802
<macisadl@buffalostate.edu>  <http://PhysicsEd.BuffaloState.edu>
Physics Graduate Coordinator & Dept Chair Pro Tem (acting Jan-Aug 2008)