Re: Work/Energy Theorem

[SCIAMANDA@edinboro.edu]

> On Thu, 13 Mar 1997 SCIAMANDA@edinboro.edu wrote:

> > The word "work" is defined as the left hand side of the Work-Energy 
> > theorem (at least for me).

> Doesn't this strip a work-energy theorem of its physical import?  I always
> emphasize to students that the *definitions* of work and energy have NO
> physical content--they are *merely* definitions; substitutions of single
> symbols in place of mathematical combinations of other quantities. 

> A work-energy theorem, on the other hand, is a statement of the physical
> equality between some sum of well-defined works performed on a system and
> the change in some well-defined form of energy; it is a law of nature. 
> place is the fact that nature enforces these particular relationships. 
>  A. John Mallinckrodt      email:  mallinckrodt@csupomona.edu

I think you mis-read me, John.  The Work Energy theorem is a numerical 
equality which speaks of previously defined quantities (F,m dr,. .).
The W.E. theorem itself is NOT a definition.  But, when we give the name 
"work" to the left hand side of this equation, THEN we are defining the meaning 
of the word "work"; just as we define the phrase "kinetic energy" as 
the quantity whose change is the right hand side of the theorem. From  
then on the word "work" should refer to the LHS of the W.E. theorem.

Concerning your using "many forms" of the work-energy theorem, and many 
different meanings to the word "work", I simply don't think that adding 
this complexity makes anything any more understandable. 

I think it muddles the situation which I think is of paramount 
importance to the model of reality which physics is building:
The Work-Energy theorem (as I have previously quoted it) is a "law 
of nature" whose truth value rests soley on Newton's laws of motion. 
The conservation of energy, on the other hand, has a wider (universal) 
scope and rests upon our presumed ability to appropriately and 
consistently widen the definition of "energy" to make it ever so.

The W.E. theorem is a purely mechanical statement and is a closed 
book (within Newtonian mechanics);  statements of the conservation 
of energy will always remain open to a wider, yet to be defined model.

I think it is important not to lose this distinction between the 
work energy theorem (a numerical equality forced by Newton's three 
laws of motion) and the conservation of energy (a highly desirable 
and thus far successful) conceptual interpretation of the  
whole of reality.

I think that is why we have the First Law of Thermodynamics 
IN ADDITION TO the W.E. theorem.

Bob Sciamanda           sciamanda@edinboro.edu
Dept of Physics
Edinboro Univ of PA     http://www.edinboro.edu/~sciamanda/home.html