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Re: positive and negative work



On Sun, 11 Nov 2001, Brian Whatcott wrote:

Hmmmm...we agree that a car would accelerate down an incline,
if a force acting 'uphill' were not holding its speed steady.
We see that this retarding force varies with the throttle so we are
confident that the car is supplying this retarding force.

So the car exerts a force on itself?

We see that this force acts opposite the motion, so we say by convention
the work is negative.

The foregoing is a great illustration of the kind of trouble one
gets into when one is sloppy or negligent in specifying the
details of forces, motions, and works. Try out this recasting of
the previous sentence:

We see that the force exerted BY THE ROAD ON THE CAR acts
opposite the motion OF THE CAR RELATIVE TO THE ROAD, so we say
by convention the PSEUDOWORK done BY THE ROAD ON THE CAR in
the FRAME OF THE ROAD ITSELF is negative.

Note the careful specification 1) of the agent of the force in
question and the system on which the force in question acts, 2)
the frame within which the motion is observed, 3) the
specification of the work definition being used.

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
are always the result of using sloppy language. Usually, they
result from negligence in specifying the definition of work that
is being discussed and the work-energy relationship that is
applicable as a result. Despite the many reincarnations of this
thread, many of us still act as if there was a universally
agreed upon definition of "work." Repeat after me:

"There is NO universally agreed upon definition of 'work.'"

It may be O.K. to say in general that "work changes the energy of
a system" but to go any further you must be specific about which
definition of work you are using and, most importantly, you must
properly invoke the correct work-energy relationship--i.e., the
one that actually applies to the type of work you are talking
about.

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