Re: Apparent weight

["Bob Sciamanda" <trebor@velocity.net>]

-----Original Message-----
From: Tim Folkerts <Tim.Folkerts@valpo.edu>
To: phys-l@atlantis.uwf.edu <phys-l@atlantis.uwf.edu>
Date: Sunday, February 22, 1998 10:38 PM
Subject: Re: Apparent weight

> I am trying to interpret Newton's Laws for a beginnig student, and I
> recognize that my view may not be compatible with relativistic
> interpretations, but at a general physics level I think it works.
> . . .
> ---   Tim Folkerts


For what it's worth, here is a summary of how I present Newton's laws in
a first course:

1.) Newton believed in an absolute time and space.  To him it went
without saying that his physics would apply only to observations made by
an observer at rest; that there turned out to be a whole class of valid
frames was frosting on the cake, and is a conclusion - not an assumption.
(No need to confuse students with this right now.)

2.) Newton's goal was to describe the motion of objects in terms of
interactions (forces) between objects.  His paramount task was thus to
conceive a useful, quantitative definition of force.

3.) Since the idea is that the force on an object affects its motion,
force will be defined in terms of the change in some aspect of the
object's motion.  The first step will be to define what we want to mean
by ZERO (net) force.  What motion would be executed by an object free of
all mechanical influences (potentially lengthy discussion)?  Here Newton
sided with Galileo, against Aristotle and conventional wisdom.  Thus N1
defines the measure of zero (net) force.  In many ways this first step,
defining the state of motion of a force free object, is the crucial,
enabling assertion from which quite naturally follows:

4.) Since zero acceleration is to be the measure of zero force,  the
measure of the non zero net force on an object is naturally taken to be
the object's acceleration.  The simplest definition would be a linear
proportion: F = k a  (k would depend on units). If this works, there is
no need to get more complicated (it is interesting to explore the
implications of a quadratic function, for example).  (Given N1, this
comes easily, N1 is the crux.)

5.) But this would say that the same net force applied in turn to a
kiddie cart and a railroad car would produce the same acceleration.  But
our experience is that we have to exert a larger push on the more
"massive" object to get the same acceleration.  It would be useful to
incorporate this behavior into our definition of "force", so that the
notion might be usefully applied to our own mechanical exertions.  Thus
we are persuaded to incorporate the mass of the object being accelerated
into the measure of the net force on the object, so that we re-model: F =
ma.  (I think Newton did not feel the need to define mass; the notion was
in common use.  I take the view that after adding N3, we can use these
three "laws" as useful definitions of both F and m.)

6.) The third law recognizes that certain things never happen and seeks
an inherent property of force which accounts for these impossibilities.
If I had two objects A and B such that A repels B, but B experiences no
force from A, I could fasten them both to the floor of my kiddie cart and
it would accelerate forever.  At the root of all such impossibilities
Newton saw N3 acting: In two particle interactions F(Aon B) is equal to
F(BonA) and oppositely directed.

7.) The above is proposed as a useful definition of the force concept,
without specifying the mechanisms of any particular forces (the LHS of
F=ma).  Of course the definitions are sterile until specific forces are
identified in terms of measurable quantities and used to complete the
LHS, but we must begin with some such open definition. The progress of
Newtonian physics in completing the LHS is the falsifiable test of the
USEFULNESS of this definition.

8.) Masses can be quantitatively compared to a chosen standard mass by
causing them to interact with equal and opposite forces (eg. N3 operating
through a spring) and using m1/m2 =a2/a1 .

-Bob

Bob Sciamanda   sciamanda@edinboro.edu
Dept of Physics   trebor@velocity.net
Edinboro Univ of PA  http://www.edinboro.edu/~sciamanda/home.html
Edinboro, PA   (814)838-7185