It occurs to me that those who disdain the use of the CM Work/KE theorem
seem to feel free to use it in a thinly disguised form whenever they use
the conservation of mechanical energy in (purely mechanical) problems
involving conservative forces (eg: ideal roller coaster and free fall
problems). If a force is conservative (its line integral is independent
of path) then the work integral in the W/KE theorem can be evaluated
simply as the change in the value of a definable function of space, a
"potential energy" function. The W/KE theorem can then be manipulated
into a "constant of the motion" statement. The resulting "conservation of
kinetic plus potential energy" statement is simply a re-statement of the
CM Work/KE theorem applied to these special cases.
Note that this is not asserting the same conservation of energy, or energy
exchange, ideas asserted in the First Law of Thermodynamics. ( Although
pedagogically I always use this "conservation of mechanical energy" as a
speculation bridge to those ideas, and then re-visit it once those ideas
are on stage and it can be re-derived from the "exchange of a conserved
energy" model.)
Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net http://www.velocity.net/~trebor
----- Original Message -----
From: "Bob Sciamanda" <trebor@VELOCITY.NET>
To: <PHYS-L@lists.nau.edu>
Sent: Thursday, January 23, 2003 6:00 AM
Subject: There's work, and then there's work
| . . .
| Much confusion has resulted from using the word "work" to describe both
Fdx
| of (1) and Ydz of (2)
| Some have even written that the CM Work/KE theorem of (1) is invalid and
| should not be used because its Fdx work does not always describe an
energy
| transfer, as Ydz in (2) necessarily does by design. The CM Work/KE
theorem
| is a very useful calculational tool of Mechanics - it should not be
asked to
| do what it knows nothing of. Its work, Fdx, may in fact be useful in
the
| First Law of thermodynamics as a Ydz, evaluating an energy transfer; but
| this is a separate question and must be answered by an ad hoc energy
| transfer model of the phenomenon at hand.