Re: [Phys-L] treating force as a vector ... consistently

[John Denker <jsd@av8n.com>]

On 08/20/2016 03:35 PM, Bob Sciamanda wrote:
> Scalars, Vectors and Tensors are MATHEMATICAL entities - used as
> calculational models of physical properties. There is a dangerous,
> but natural tendency to reify these MATHEMATICAL entities.  Fight
> it!

Agreed!

Continuing down that road, consider the contrast:

 ++ Physical reality is what it is and does what it does, quite
  independent of whatever models (if any) we build.

 -- We need models ... but we need to remember that all models
   are imperfect.

This is precisely why legalistic questions /about the model/ are
usually quite tricky.  Here's another contrast:

 ++ Q: Calculate the force on the tabletop under such-and-such
  conditions.  This is a question about the physics.

 -- Q: In such-and-such complicated situation, identify which
  force is equal-and-opposite to this other force.  This is
  probably intended as a question about the model.

     * As a question about the physics, this would be ambiguous,
      because there are lots of forces which can be shown to be
      equal and opposite, shown by various chains of reasoning.

     * If you intend it a legalistic question about the model,
      you get into all sorts of trouble.  For starters, you have
      to explain that it's a question about the model rather than
      about the physics, which is an unpleasant thing to explain.
      Then you find that it's hard to make the wording legally
      airtight enough to guarantee the answer you intend.

      More importantly, this is usually not worth the trouble,
      because the model was never entirely faithful to the real
      physics anyway!  Introductory physics is not the idolatrous
      worship of the Newtonian model.

I find that far too many Force Concept Inventory questions are
falsely advertised, because they are really Codeword Vocabulary
Inventory questions.  The attitude seems to be that the student
should (allegedly) recognize certain magic words and thereupon
analyze the situation using the third law to the exclusion of
all else.  Other magic words indicate that the situation should
(allegedly) be analyzed in terms of the second law to the exclusion
of all else.

These laws are just models.  I suppose it's nice to be able to
answer legalistic questions about the models, but that's nowhere
near as important as understanding the underlying physics.

Heller&Heller wrote a book about how to erect "fences" to "compel"
(their word) students to solve a given problem the desired way.
In contrast, I say education should empower the students, not
constrain them.  If the methods I am trying to teach are as
valuable as I claim they are, the students will /want/ to use
them, with almost no fences required.

   Occasionally I will set up temporary fences for safety,
   to keep beginners from falling into fatal traps, but
   that's a special case.

My style is to say:  Here is an important and interesting
question.  Solve it any way you like.  There are lots of
different correct answers.  Cue the barometer story.

==========

The third law has lots of interesting and important practical
applications.  Figuring out what happens to the earth when
acted upon by the gravitational field of a book is not very
high on the list.

Using this as a test of understanding of the third law seems
suboptimal.  Very often in physics class at all levels, and
in real life, it is traditional and reasonable to model the
earth as an infinite and immutable reservoir of momentum.
The effect of the book is negligible.

Similarly I've seen textbooks that say flat-out that the
gravitational field created by book-sized objects is negligible.

So we have models in conflict.  The third law says one thing,
while the immutable-earth model and the negligible-book model
say another.

On 08/19/2016 03:42 PM, Anthony Lapinski wrote:

> Nobody gets this right!

Indeed!  Is anybody here surprised that the students are
confused ... especially in a situation where a more-practical
and less-conflicted answer is available?

See also my previous note about test-item analysis.  Whenever
it is observed that "nobody gets this right" it behooves us
to figure out why.


On 08/20/2016 05:44 PM, Todd Pedlar wrote:
> As long as I never refer to actions or reactions (I actively oppose this
> the first day we talk about forces in my courses) and that I specify the
> following:
>
> 1) The two forces which constitute a Newton's Third Law Pair must act on
> different bodies
> 2) They must be of the same kind (friction, gravitation, contact forces,
> etc)

That's smart.  Those are nice points that clarify the model.

> really, it's not that hard

I disagree.  Maybe it's easy for you, but for the students it's not easy.

In particular, in real-world situations, there are lots of different
physical principles that apply, and figuring out which ones to apply,
and how to apply them, is nontrivial.  Conversely, in the introductory
classroom, designing a question that involves just one principle is a
very tricky business.  The result is likely to be either ambiguous or
super-unrealistic or both.