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[Phys-L] Re: A Third law question



It is sometimes asked on this list that I explain something.
I suppose that explaining things is a motivation for people who
want to be, or like being teachers.

They know, as I know, that the recipients of chalk and talk
"explain things to me" sessions are subject to a rather ineffective
learning mode.

All the same - I can convey a student view of the mystery
associated with some physical observables to which one tends
to grow numb with familiarity: gravity and inertia.

And I can present Newton's very first prefatory definitions:
mass then momentum then inertia then the relativity of velocity.

It is interesting to ponder Newton's observations on accurately
made pendulums for relating mass to weight. (Definition 1)
What could he be referring to here?
The variation of g with geographical location?
The small dependence of a pendulum's period on its weight?
Isn't the expression for period 2*pi *root ( L / g ) ?
You would need to read Principia to be sure, I expect.

There is a virtue in presenting learners with the works of the greats.
They often enough have ways of thinking that can be helpful.

There: is that explanation enough for now? :-)

Brian

At 10:04 PM 10/13/2005, Jack, you wrote:

Yes. But pls explain how all that is enlightening to modern
students.
Regards,
Jack

On Tue, 11 Oct 2005, Brian Whatcott wrote:

At 07:01 PM 10/11/2005, Cliff Parker, you wrote:
[Brian W]
In experiments, it is found that the force
in question is proportional to the object's mass, and to the
object's acceleration if "deep space"-like conditions are set up.
Near Earth, the force on the stationary mass is proportional
simply to its mass.

Ahh yes and what is this thing you speak of called mass?


Another writer pondering his order of presentation, decided to place
a definition of stuff, substance or mass first. He used several concrete
examples. Here is how he put it:


DEFINITIONS


DEFINITION I
The quantity of matter is the measure of the same, arising from its
density and bulk conjointly. Thus air of a double density, in a
double space, is quadruple in quantity; in a triple space,
sextuple in quantity. The same thing is to be understood of snow,
and fine dust or powders, that are condensed by compression or
liquefaction, and of all bodies that are by any causes whatever
differently condensed. I have no regard in this place to a medium,
if any such there is, that freely pervades the interstices between
the parts of bodies. It is this quantity that I mean hereafter
everywhere under the name of body or mass. And the same is
known by the weight of each body, for it is proportional to
the weight, as I have found by experiments on pendulums,
very accurately made, which shall be shown hereafter.


DEFINITION II
The quantity of motion is the measure of the same, arising
from the velocity and quantity of matter conjointly.
The motion of the whole is the sum of the motions of all
the parts; and therefore in a body double in quantity,
with equal velocity, the motion is double; with twice the
velocity, it is quadruple.


DEFINITION III
The vis insita, or innate force of matter, is a power of resisting,
by which every body, as much as in it lies, continues in its
present state, whether it be of rest, or of moving uniformly
forwards in a right line.
This force is always proportional to the body whose force
it is and differs nothing from the inactivity of the mass,
but in our manner of conceiving it. A body, from the inert
nature of matter, is not without difficulty put out of its state
of rest or motion. Upon which account, this vis insita may,
by a most significant name, be called inertia (vis inertiae)
or force of inactivity. But a body only exerts this force
when another force, impressed upon it, endeavors to change
its condition; and the exercise of this force may be considered
as both resistance and impulse; it is resistance so far as the
body, for maintaining its present state, opposes the force
impressed; it is impulse so far as the body, by not easily
giving way to the impressed force of another, endeavors to
change the state of that other. Resistance is usually ascribed
to bodies at rest, and impulse to those in motion; but motion
and rest, as commonly conceived, are only relatively
distinguished; nor are those bodies always truly at rest,
which commonly are taken to be so.

Newton Principia, 3rd ed. 1726. trans: A Motte, revised, F Cajori


Brian Whatcott Altus OK Eureka!