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Work Done Against



Please excuse me if this is the second copy of this memo that you
received. I thought I posted it yesterday evening, but I never received a
copy so I am reposting it now.

Hi Gordon, you said!
If mechanical work is defined as equal to a force times the applied
distance, and since forces are supposed to always occur in pairs, work
might always be considered as being done by opposing the matching
force that's against it.

I am not sure what you mean when you say "work might always be considered
as being done by opposing the matching force that's against it." However,
consider the following.

As an object undergoes an upward displacement the gravitation force on it
does negative work, but the work done by the reaction force, which acts on
the planet, does no work. (I am assuming we are in a reference frame in
which the planet is stationary.) In this case the work done by the
matching force is zero..

As for applying that to an ambiguous case, consider:
a) a person lifts a weight in a stationary elevator 5 ft.
b) the elevator rises 5 ft and the person holds the weight against their
waist. The person applied force against the weight while it rose.
(They applied a force over a distance, right?)
c) the person "lifts" the weight 5ft while the elevator actually goes
down 5ft. The weight's actual altitude thusly did not change. A
camcorder fixed in the elevator would show the same view in a) or c).

In which case(s), a,b, & c, was work actually done and by whom or
what? Have you ever considered this situation or something equivalent?

I have considered such situations. To me, to understand the results it
seems helpful to realize that while the work done by a force is frame
dependent, the total work done by an action-reaction force pair is frame
independent, and so is a galilean invariant. This total work, which
equal's the negative of the system's potential-energy change, is non zero
only if there is a change in the configuration.

Gene Mosca


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Eugene (Gene) P. Mosca Phone 410-293-6659 (Fax 3729)
Physics Department 410-267-0144 Home
572 Holloway Road 610-683-3597 Summer
U.S.Naval Academy Mailstop 9C, Michelson Rm 339
Annapolis MD 21402 email: mosca@nadn.navy.mil
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