Re: F=ma

[Larry Cartwright <exit60@IA4U.NET>]

> Someone clever must have written about this. Anyone out there know a
> favorite read on the topic?

How about Newton himself?  Newton didn't really mention the role of mass
in his original statement of Law II.  What he did say at that point is
a=HF.  At whatever point F=ma or a=F/m came along, it wasn't in
Axiomata, Lex II of Principia.

"LEX II.  Mutationem motus proportionalem esse vi motrici impressae, &
fieri secundum lineam rectam qua vis illa imprimitur."

"LAW II.  The alteration of motion is ever proportional to the motive
force impressed; and is made in the direction of the right line in which
that force is impressed."

"If any force generates a motion, a double force will generate double
the motion, a triple force triple the motion, whether that force be
impressed altogether and at once, or gradually and successively. And
this motion (being always directed the same way with the generating
force), if the body moved before, is added to or subtracted from the
former motion, according as they directly conspire with or are directly
contrary to each other; or obliquely joined, when they are oblique, so
as to produce a new motion compounded from the determination of both."

Newton professed that forces do "generate" accelerations:  "Si vis
aliqua motum quemvis GENERET; dupla duplum, tripla triplum
GENERABIT...".  The text in Principia is driven by Newton's belief in
cause and effect.  It is full of cause and effect explanations, one of
the strongest being his "I will frame no hypotheses" essay in the
General Scholium at the very end of Principia:  "Hitherto we have
explained the phenomena of the heavens and of our sea by the power of
gravity, but have not yet assigned the cause of this power. This is
certain, that IT MUST PROCEED FROM A CAUSE that penetrates to the very
centres of the sun and planets, ..."

Above is from the 1792 Andrew Motte translation of the 1687 Principia.
Online you can see selections from the Motte translation at
<http://members.tripod.com/~gravitee/axioms.htm>.  Also see
<http://home.mira.net/~gaffcam/phil/newton.htm>.

\\//,

Larry
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Larry Cartwright  <exit60@ia4u.net>
Physics and Physical Science Teacher
Charlotte HS, Charlotte MI USA
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Leigh Palmer wrote:
> I've always looked at Newton's second law as being somehow incomplete.
> It does not include what I consider to be a causal element. Forces do
> cause accelerations, at least that is what my intuition tells me, or I
> was successfully brainwashed a long time ago. (This latter possibility
> is often referred to as "common sense".) Newton's law, especially
> written with a "coefficient of inertia", the mass, does not imply that
> forces cause acceleration. If one were to write it as a=HF, where
> H=1/m is the coefficient of compliance (or some other such name) it
> would look better to me.
>
> Someone clever must have written about this. Anyone out there know a
> favorite read on the topic?
>
> Leigh