Re: Questions you love/hate to have asked

[Raacc@aol.com]

I've been using the bookkeeping approach for several years now and it seems
to make life simpler (especially for students to organize their thoughts and
for me to evaluate them).  I require that my first quarter calculus physics
students create an i, j, (k) table with position, displacement, velocity, and
acceleration for an object's motion.  This really helps in relative motion.
 For forces, the sum of the column entries in a similar table give ma in the
respective column directions.  This also works well with vector products (and
in spreadsheet analysis).  Many students have resisted this technique since
it is not shown in the text.  However, other students have commented on how
it helps them collect their thoughts.  With momentum, I use a poker game
analogy between two card players to present the preliminary concept (again
bookkeeping).  Energy graphs are similar, if you create a table with the
different energy contributions and sum them to get the total energy.  Isn't
this what a physicist is?  A keeper of nature's books.

Bob Carlson

In a message dated 96-10-30 20:21:01 EST, you write:

<< >Seeing conservation of momentum and energy as consequences of the
> basic symmetries of nature is the truly elegant way to regard
> mechanics, but probably a bit sophisticated for young students? At
> that level, I usually discuss energy and momentum as book-keeping
> devices to keep track of work and impulse.  How do you feel about
> that approach, or do you think that the concept of force (see another
> ongoing thread!) is too vague at this level to sustain this approach?
 
 I think the bookkeeping metaphor is excellent, fully as good as the
 one I suggested. More on that later. I don't go into Noether's theorem
 (a PC thing to do nowadays, and thoroughly useless in teaching concepts
 in my view) when I discuss symmetry. The remark is an incentive to the
 interested student to explore deeper later on. We must remember in the
 introductory courses that not all of our students will go on to grad
 school in physics, but we must also remember that some of them will,
 and they do deserve attention to their needs. Still, I spend no more
 than a couple of minutes on alluding to the symmetries of Nature, but
 I do point out what they are.
 
 The bookkeeping analogy can be carried a bit further. No one can learn
 his net worth by merely looking in his bankbook. There are various
 equities to be appraised and added, and how about his share of the
 national debt? It's all relative; the only things that are absolute
 are the *differences* encountered when money is exchanged by members
 of the system, and they must balance.
 
 I applaud your metaphor; matter of fact, I'll steal it and use it
 myself from now on!
 
 Leigh
  >>