Re: positive and negative work

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Sun, 11 Nov 2001, Joe Heafner wrote:

> > From: John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>
> >
> > I remind the readership of phys-l once again that there are at
> > least seven distinct, useful, and regularly used definitions of
> > work.  We've been through these arguments so many times and they
>
> What are they? I only know of one definition. Of course, I'm
> not equating *work* and *pseudowork*. One is a transfer of
> energy and the other is not.

I don't know which one you are implying is which.  Both can be
shown to be related to different energy changes.

In answer to your question, here are a few items from the phys-l
archives going back a number of years that may be useful starting
places

 <http://mailgate.nau.edu/cgi-bin/wa?A2=ind9703&L=phys-l&P=R12675>

 <http://mailgate.nau.edu/cgi-bin/wa?A2=ind9710&L=phys-l&P=R9497>

 <http://mailgate.nau.edu/cgi-bin/wa?A2=ind9812&L=phys-l&P=R14282>

All of these make reference in one form or another to the paper I
have mentioned here many times over the years: "All About Work,"
Am. J. Phys., V60, 356-365, (1992).

For anyone who may be interested, I have placed a summary in the
form of two pages of excerpts from that paper at

 <http://www.csupomona.edu/~ajm/special/aaw_excerpts.pdf>

> >  "There is NO universally agreed upon definition of 'work.'"
>
> THIS is just as much a part of the problem as sloppy usage.
> The only correct definition of work that I'm aware of is *a
> process by which energy is transfered into or out of a system
> by application of a force*.

I've never heard work *defined* this way.  Work (in any of its
many forms) is conventionally *defined* as a product of some force
with some distance (or, more generally, as a sum of integrals of
infinitesimal such products.)  We can then go on to *prove* (using
Newton's Second Law) that the various definitions of work are
associated with various types of energy changes.  Such a
demonstration is called a "work-energy theorem."  It is important
to recognize that "work-energy theorems" make use of Newton's
second law and relate *separately* defined quantities
(specifically, "work" and "energy"); they are not themselves
*definitions*.

> There are of course other quantities that mathematically look
> like work, but because they do not correspond to any transfer
> of energy then we can't, and shouldn't, really call them work.
> Therefore, I find it logically inconsistent to say there are
> numerous correct defitions of work since there can really be
> only one correct definition.

I'm not sure I agree with this but in any event, as I said before,
there are at least seven different definitions of work that 1) CAN
be shown to be equal to some type of system energy change and that
2) ARE regularly used (often without the user even realizing that
he or she is using different definitions, as is regularly the case
in these phys-l threads.)

> Let's pick ONE SINGLE CORRECT defition and trash the rest.

That'll be very tough and not, IMO, a good idea since we make very
good use of many of them all the time.  I suggest instead that we
choose good names to *distinguish* them so that we begin to
recognize that we *do* use different definitions in different
circumstances.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm