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Re: positive and negative work



In Rick Tarara's recent message he specifically mentioned net work (emphasis
on net) and kinetic energy change (emphasis on kinetic). This example of
the work-energy theorem is one of the more clear cases.

Less-clear examples involve potential energy changes. If a person lifts a
box against gravity, the person does positive work and the gravitational
energy of the box increases. However, we can also discuss the work done by
the gravity force, and this would be negative.

In the text I am using (Tipler, 4-th edition) we find W(total) = delta-K (as
Rick mentions) and a few pages later we find W = minus-delta-U where the
work is the work of the gravity force and U is the gravitational potential
energy.

Likewise W = delta-U can be written for a spring if we are talking about the
work a person does to change the energy of a spring, but we need to write W
= minus-delta-U if we want to discuss the work of the spring force in
relation to the spring's energy.

There is a tendency for calculus-based textbooks to approach
work/potential-energy from the viewpoint that the work being calculated is
that of the conservative force that gives rise to that particular energy, so
these authors tend to write W = minus-delta-U. But I find students are more
comfortable viewing the work of the person or entity that is working against
the conservative force, so students would rather write W = delta-U. And, of
course, the net work in these cases can be zero (and therefore no change in
kinetic energy).

So I think the plus-minus problems arise more when viewing
work/potential-energy than when viewing the work/kinetic-energy that Rick
mentions.



Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817