Re: momentum before force (was: friction)

[Dave Hamilton <djhamil@teleport.com>]

Robert, Dan, James, and others,

I haven't actually taught in the sequence of 1. velocity, 2. momentum, 3. 
force, but I have also carefully considered this sequence.  I first 
thought about it when I read Newton's Principia and realized that this is 
precisely the sequence that he used to introduce his mechanics to his 
readers (he assumed that his readers knew about velocity).  Newton simply 
defined "quantity of motion" as m*v and defined a force as something that 
causes a change in quantity of motion.  No justification that "quantity 
of motion" shouldn't be m^2*v.  

I find it interesting that contemporaries of Newton (including Christian 
Huygens, Christopher Wren, and John Wallace) were investigating 
conservation of motion during collisions between "hard bodies."  There 
was some controversy over whether the conserved quantity was m*v or 
m*v^2.  I don't propose that we introduce our students to THAT 
controversy, but students might be interested enough in the question of 
what "gets conserved" during such a collision that a course in physics 
could begin with that very question.  

Didn't Decartes  propose conservation of quantity of motion (m*v) as a 
fundamental truth in his Philosophy?



> Raacc@aol.com says:
> > ...
> > It seems to me that velocity should be introduced followed immediately by
> > momentum.  Then acceleration and net force can be defined as the slopes of
> > the velocity and momentum graphs respectively.)
> > ...
>
> When you teach this sequence, how do you justify momentum before force has
> been introduced?  Using a qualitative idea of force?
>
> I can maybe imagine doing this, but I can't see how to justify that
> momentum is (m*v) (rather than, say, (m^2 *v)), since I don't know how to
> test it.  Maybe you do conservation of momentum?
>
> -- 
> --James McLean
> jmclean@chem.ucsd.edu
> post doc
> UCSD


David J. Hamilton, Ed.D.                    "And gladly wolde he lerne,
Franklin HS, Portland, OR                    and gladly teche."
djhamil@teleport.com                          Geoffrey Chaucer