Re: [Phys-L] A Couple of Instances Where "Power" Is Not Power

[John Denker <jsd@av8n.com>]

On 12/01/2014 11:53 AM, Tom Sandin wrote:
> some wonder why students get so confused about the simplest things.

Indeed.

==========

Note that there are two kinds of conflicting meanings:

 1) One kind is the routine overloading of words, such as 
   -- "gravity" as in the seriousness of a grave situation.
   -- "gravity" as in physics.

  This sort of thing produces very little confusion,
  because the meanings are so dissimilar.  Students
  (and others) can sort it out based on context.

 2) Another kind concerns meanings that are close
  enough to be confusing, yet different enough to
  cause problems:
   -- "gravity" as in the acceleration of a free particle
    relative to some chosen frame.
   -- "gravity" as in the the law of universal gravitation,
    which is frame-independent.
       https://www.av8n.com/physics/weight.htm#sec-various-notions

  I consider this case (2) to be a much more grave 
  problem, compared to case (1).  Very commonly physics
  books switch back and forth between meanings in such
  a way that it is next to impossible to figure out the
  intended meaning.  You could figure it out by rederiving
  everything from scratch, but that's a lot of work, and
  greatly detracts from the value of the book.

  Conflicting meanings of the second kind make it difficult 
  to have an ordinary conversation.

  
  As an even simpler example, consider
   -- "acceleration" the scalar, as in increase of speed, the
    opposite of deceleration.
   -- "acceleration" the vector, as in change of velocity.

  Everybody, and I mean everybody including physicists, freely
  uses both of these terms.  The trick is to figure out which
  meaning makes sense in a given context.  Students are often
  slow to catch on.  I find it helps to use the two-word
  phrase "vector acceleration" as often as possible when
  talking to introductory-level students.

> the "power" of a lens (in diopters) and the "chromatic resolving
> power" (no unit) of a diffraction grating

To that list you could add things like political power and 
military power.  However, these things don't worry me.  I
put them in category (1) i.e. routine overloading.

I am much more worried about things like "thermal power" which
has dimensions of watts.  That is in category (2) because there
is tremendous overlap with the alleged F•dx definition.  It is
similar enough to be confusing, yet different enough to cause
problems.

Is thermal power part of "the" power or not?

=======================

The distinction between (1) and (2) is not always clear-cut.

It takes students a while to come to terms with the fact
that the physics force is different from vernacular force.

Many of the vernacular meanings of force are associated 
with causation, where as the physics definition is not.
F is numerically equal to ma, but F does not /cause/ ma 
... not by any reasonable definition of causation.  A lot
of students get this wrong.  (More than a few professional
physicists get it wrong, too.)

Many of the FCI questions are IMHO little more than word 
games, designed to trick students into answering in terms
of vernacular force (as in causation) rather than mechanical
force (as in Newton's laws).  The "right" answer is obvious
to physicists, because we spend all day in physics context.
However, students could reasonably read the question in 
another context.  I'm not even willing to call the typical 
student answers wrong, because the FCI is so grossly context-
dependent.  It focuses on the /word/ force rather than any 
operational consequences of the concept.  So really it 
should be called FVI:  Force Vocabulary Inventory.

To make it more clear what I am talking about:  Consider
the one about the truck colliding with a car.  It would
be difficult to define what you really mean by "the"
force in such a situation.  There are lots of different
forces during a collision, and it would be ridiculously 
difficult to measure them operationally.

  This stands in contrast to real-world applications of
  force, such as a truck using a rope to tow a car.  There
  you can talk about the tension in the rope.  This can 
  be measured operationally.  It has direct practical 
  significance in numerous ways, including the possibility
  of breaking the rope if the force is too large.

To be blunt:  I am skeptical of the FCI.  I worry about
the _construct validity_ (or lack thereof) of some of the
questions.  It's OK for vocabulary words to have more than
one meaning.  You can't force students to believe that
there's only one definition of "force".