Re: positive and negative work

["John S. Denker" <jsd@MONMOUTH.COM>]

I wrote:

> > Recommendation:  When in doubt, decompose the system into pointlike
> > elements and apply F dot ds to each element separately.  If you do
> > anything else, you're strictly on your own -- you shouldn't call it
> > "work", and whatever you call it you will have to explain what it is and
> > why we should care.

Then John Mallinckrodt wrote:

> This is, of course, precisely what is done in the paper you claim
>   to have read and not to have been persuaded by (and I am curious
>   what you found to be so unpersuasive.)  But as soon as you do
>   this, there are at least two questions that arise:

> 1. With respect to what will you measure your ds's?  An inertial
> frame, the frame of the system CM, an arbitrary frame?

Anything of physical significance can be calculated in a frame-independent
way.  Usually it may _also_ be calculated in innumerably many frame-dependent
ways also, but that doesn't change the physics.  Introducing a new reference
frame doesn't introduce a new concept;  it is just a new representation of the
same old concept.  It does not require a new mental model, and it does not
require conjuring up six or seven idiosyncratic names as if new concepts had
been created.

For example, any measurement of kinetic energy (plain old kinetic energy) will
depend on the reference frame, since some frames may be moving relative to
others.  But this does not change the physics of what happens on the pool
table, or anything else.  It doesn't require introducing a new concept of
kinetic energy, or a new name.

In an elementary course, do everything in the lab frame and don't worry about
it.  In a second course, pick a frame (any one frame) and stick to it.  The
third time around, figure out how to compare one frame's measurements with
another's.

> 2. Which forces will you consider on each particle?  Both external
> and internal forces?  Only the external ones?  Only the internal
> ones?

If we decompose the system into pointlike elements with no internal degrees of
freedom, as seemed to be the consensus a moment ago, then such questions do
not arise.  By definition the pointlike elements cannot have any internal
forces.