Re: Doubt : Newton's Second Law


"WonderingWanderer" <Litterally.Speaking@xxxxxxxxx> wrote in message
news:1156137277.504271.26000@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| Hi,
|
| I am a non-physicist and am (privately) studying the epistemology of
| Classical Physics. I have a doubt regarding how Newton came about his
| Second Law.
|
| I understand that Galileo got the initial intuition that it was
| acceleration, and not velocity, that Force on a body changes. However,
| how did Newton formulate his F = m*a equation ? Through some thought,
| one might argue that since acceleration 'a' depends on lenght and time
| ( lenght/time^2 ), one gets the intuition that constant of
| proportionality should be the third fundamental dimension of mass. This
| can also be qualititatively observed - heavy objects move slower than
| lighter ones, under the apparently same force applied.
|
| However, I want to know if Newton derived his Law ( the mathematical
| expression of it ) through a mathematical argument or emperical
| validation ?
|
| Thanks,
| Dry Wick !


AXIOMS, OR LAWS OF MOTION.

--------------------------------------------------------------------------------

LAW I.
Every body perseveres in its state of rest, or of uniform motion in a right
line, unless it is compelled to change that state by forces impressed
thereon.

PROJECTILES persevere in their motions, so far as they are not retarded by
the resistance of the air, or impelled downwards by the force of gravity. A
top, whose parts by their cohesion are perpetually drawn aside from
rectilinear motions, does not cease its rotation, otherwise than as it is
retarded by the air. The greater bodies of the planets and comets, meeting
with less resistance in more free spaces, preserve their motions both
progressive and circular for a much longer time.

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.

LAW III.
To every action there is always opposed an equal reaction; or the mutual
actions of two bodies upon each other are always equal, and directed to
contrary parts.

Whatever draws or presses another is as much drawn or pressed by that other.
If you press a stone with your finger, the finger is also pressed by the
stone. If a horse draws a stone tied to a rope, the horse (if I may so say)
will be equally drawn back towards the stone: for the distended rope, by the
same endeavour to relax or unbend itself, will draw the horse as much
towards the stone as it does the stone towards the horse, and will obstruct
the progress of the one as much as it advances that of the other.

If a body impinges upon another, and by its force change the motion of the
other, that body also (became of the quality of, the mutual pressure) will
undergo an equal change, in its own motion, towards the contrary part. The
changes made by these actions are equal, not in the velocities but in the
motions of bodies; that is to say, if the bodies are not hindered by any
other impediments. For, because the motions are equally changed, the changes
of the velocities made towards contrary parts are reciprocally proportional
to the bodies. This law takes place also in attractions, as will be proved
in the next scholium.


.

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