Re: Work/Energy Theorem

[John Mallinckrodt <ajmallinckro@CSUPomona.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. 
Indeed, the only reason for having defined work and energy in the first
place is the fact that nature enforces these particular relationships. 

> When that theorem is applied to a single 
> particle, the work done by a force is the force integrated over the 
> displacement of the particle.  ...
>
> When the theorem is applied to a system of particles,  the 
> work done by a force is the force integrated over the displacement 
> of the C.M. of the particle system. ...

It may be OK to look at it this way, but I prefer to say that these you
are referring to two *different* work-energy theorems: 

#1: It is *always* the case that the total work done on a system by
external forces calculated with respect to an inertial frame is equal to
the total change in energy (bulk kinetic + random kinetic + internal
potential) of the system.  The first example is a highly special instance
of this general law in which the total energy is equal to the bulk kinetic
energy simply because the chosen system has no internal degrees of
freedom.

#2: It is also *always* the case that the total "pseudowork" done on a
system is equal to the change in the system's bulk kinetic energy.  The
second example is an instance of this general law. 

As I mentioned in a previous post, there are many useful work-energy
theorems.  Seven of them are detailed in my paper with Harvey Leff "All
About Work", AJP, 60, 356-365, 1992.)

John
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