Re: N1 special case of N2

["Dewey Dykstra, Jr." <dykstrad@EMAIL.BOISESTATE.EDU>]

Another "tangential" comment or two:

1.  While coming from the notion of the nature of force held in the
Newtonian view N1 can be seen to be a special case of N2, coming from the
typical students' initial notion of the nature of force it is not true that
N1 and N2 are true let alone one be a special case of the other.  Hence,
this relationship between N1 and N2 is of little pedagogical value until
students have made the conceptual leap (and it is a fairly large one) from
a person-on-the-street view of the nature of force to a more Newtonian one.
In fact an argument can be made that attempting to make a point with the
students on this issue before they have made the necessary conceptual leap
is an unnecessary distraction.

2.  While we are "fleshing out" the "situation" on force we would do well
to openly acknowledge that the role of force is as a construct and that
because it is a construct we:
        2a. do not actually directly measure force, (Instead we measure
effects we claim to be caused by this construct.  That is, we measure
motion and deformation of objects.) and
        2b. make this construct to "add up" in certain ways in situations
where we cannot measure all of the pertinent effects.  (That is, we assert
the equivalent of N1.  This is not to say we do not have a number of what
we consider to be powerful reasons for this assertion, but it is to say
that we do not "measure" it to be true.)

Along these general lines Max Jammer's book:  Concepts of Force, recently
republished on Dover is very interesting and potentially useful to those
serious about responsibly and effectively teaching about the nature of the
concept, force.

Dewey


> At 02:25 PM 9/14/00 -0400, Carl E. Mungan wrote:
> > Okay, what is N1, as distinct from a special case of N2?
>
> Let me try again to answer this.  Let's see if I can keep straight what N1
> stands for this time.
>
> IMHO it is quite an easy lemma to show that N1 is a special case of N2,
> namely the zero-acceleration case.  That suffices to answer Carl's question.
>
> ===============
>
> Tangential comments:
>
> 1) Just because it is a special case of another law, that doesn't mean it
> can't be considered a law itself.  The laws of electrostatics are a special
> case of the laws of electrodynamics.  Classical kinematics is a special
> case of relativistic kinematics.  Classical mechanics is a special case of
> quantum mechanics.  No problem.
>
> 2) There are several elements of what we normally consider "Newtonian
> mechanics" that are not captured by Newton's laws.  In particular, there
> are a bunch of "existence axioms":
>   -- we need to stipulate that reference frames exist, have certain
> properties, and can be constructed operationally, with good consistency
> and  reproducibility.
>   -- we need to stipulate that forces exist, have certain properties, and
> can be measured operationally, with good consistency and reproducibility.
>
> Many of these ideas go back to Galileo.
>
> So, when laying out the foundations of mechanics, one need not and should
> not pretend that Newton's laws are the whole story, or that they magically
> mean something beyond what the words say.



+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Dewey I. Dykstra, Jr.                 Phone: (208)426-3105
Professor of Physics                  Dept:  (208)426-3775
Department of Physics/MCF421/418      Fax: (208)426-4330
Boise State University            dykstrad@email.boisestate.edu
1910 University Drive                 Boise Highlanders
Boise, ID 83725-1570                  novice piper: GHB, Uilleann

"As a result of modern research in physics, the ambition and hope,
still cherished by most authorities of the last century, that physical
science could offer a photographic picture and true image of reality
had to be abandoned."  --M. Jammer in Concepts of Force, 1957.

"If what we regard as real depends on our theory, how can we make
reality the basis of our philosophy? ...But we cannot distinguish
what is real about the universe without a theory...it makes no sense
to ask if it corresponds to reality, because we do not know what
reality is independent of a theory."--S. Hawking in Black Holes
and Baby Universes, 1993.
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