Re: momentum before force (was: friction)

[Raacc@aol.com]

In a message dated 96-07-16 23:16:11 EDT, Daniel L. MacIsaac writes:

<< Whoops.  I just posted:
 
> Newton worked in dP/dt -- the change in momentum (he was too cagey to
> assume constant mass like the statement F = ma is often misinterpreted).
> From IMPETUS or the better-differentiated MOMENTUM that followed, he
> defined force.
 
 ...by this murky writing I was trying to bring up the fact that 
 dP/dt = m dv/dt + v dm/dt; with which Newton was intimately aware and
 which is often overlooked in our more modern treatments of F= ma in 
 beginning dynamics.  We tend to leap at F = m dv/dt right away, which is
 incomplete.  Newton's language was very cagey about this; better
 than most of our own textbooks. However, a distinct idea of P evolved 
 BEFORE F by some considerable time.  No co-evolution here, one distinctly
 precedes the other.
  >>

Dan,

I think the reason for using Fnet = ma is that it is less confusing (at the
level of mathematics that it is introduced).  Although, your stated equation
above is the correct one.  I find that most of my calculus physics students
do not really understand what derivatives or integrals really are.  I must
confess, that at that stage, I didn't either.  It wasn't until I started
using numerical methods that I fully understood the concepts.  As a side
comment, I wonder if Newton would have bothered with calculus if he'd had a
pc (or a Mac).  Maybe he still would have if it were a Mac. :-)

 rac
 
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