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Re: Work-Energy or Work-Kinetic Energy??



I just got into a discussio with a collegue on the interpretation of
the work-energy theorem, and we had quite different views on this basic
topic. Is it W(net) = Delta(E), or W(net) = Delta(KE)?

Consider a system consisting of a single mass being lifted:
View 1) You do work, so energy of the system increases. This shows up
as potential energy.
View 2) You do work, but gravity does equal negative work. The total
work done is zero, so KE stays the same.

This is a matter of bookkeeping. Both viewpoints can be useful, and
the trick is to teach students to use only one at a time and be
consistent.

Or consider the mechanical equivalent of heat, with the water as the
system.
View 1) You do work, so the energy of the system increases. This
shows up as a rise in temperature.
View 2) You do work, but friction does an equal and opposite work.
Thus the KE of the system is still the same.

Work done by "friction" in cases like this is very subtle and perhaps
best avoided altogether in an introductory course. See the article
by Mallinckrodt and Leff in the April 1992 AJP. Therefore I advise
sticking to viewpoint number 1.

Every introductory book I checked calls it "Work-Energy" (not
"Work-Kinetic Energy"), but they all write it as W(net) = Delta(K) (not
W(net) = Delta(E)).

I agree that this is very confusing. I'm teaching this stuff in a
calculus-based course right now and I'm still undecided over how
many of these subtleties to call to the students' attention. The
new edition of Halliday, Resnick, and Walker does say "work-kinetic
energy theorem", but it's rather odd because they *define* work as
a transfer of energy (at this stage an undefined term since we only
know about kinetic). Then they *derive* the usual definition of
work by assuming that the work done on a point particle equals the
increase in kinetic energy.

-dan