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Re: ENERGY BEFORE Q (was Displacement)

Defining PE as the negative of the work done by weight
was included in my outline. The idea that m*g is weight
was introduced in Chapter 4. That is why it is OK to
lean on it in Chapter 5.

By the way, perhaps you want to know that my screen
shows equal signs at the end of many lines of your message.
I suppose I am not the only one to see them. Something to
do with automatic wrapping, I suppose. But why the equal
signs? Is it "my fault" or is it "your fault"?
Ludwik Kowalski

Joseph Bellina wrote:

I think, Ludwik, that the choice to not use the force by the person t=
o
calculate the change is potential energy is that the force by the per=
son=20
is not conservative...ie the work done is not path independent, where=
as
the work done by the gravitational force, or the electric force, for
another example, is. Since you need path independence to imagine a
function only dependent on displacement, a potential energy, you have=
to=20
use the naturally occuring force.
Another spin would be, while you might claim that the force by my han=
d
on a book and the force by the earth on a book have the same magnitud=
e
when I raise the book at a constant velocity, those are not the same
forces conceptually. I would have to define the potential energy cha=
nge=20
in terms of the work done by the force by the earth, and then conclud=
e
that it might be the same, and use that as a computational scheme...b=
ut
a computational trick is not an identity. Further, on a rotating ear=
th,=20
the force by my hand is not the same magnitude as the force by the
earth.

cheers,

joe

On Thu, 11 Oct 2001, Ludwik Kowalski wrote:

It is annoying to see two question marks to appear instead of
minuses in two places. Somebody may be confused. Let me
try to correct this. Perhaps I did press wrong keys last night.
***********************************************
=20
I appreciate Joe=92s confirmation that something is not right
with displacements in Chapter 5 of Serway and Faughn.
IS THIS MESS REPEATED IN THE CALCULUS
BASED VERSION OF THEIR BOOK?
=20
Let me again pretend I am a critically thinking student trying
to outline how energy is introduced in this chapter. Comments
and questions are inserted in capital letters.
=20
a) First "work done by a force", and its unit J, are introduced.
This definition is "natural"; a longer path calls for more effort.
WORK COULD HAVE BEEN DEFINED AS (F*S)/2, FOR
EXAMPLE, BUT A SIMPLE DEFINITION IS PREFERRED.
Work can be positive or negative, depending on relative
orientations of vectors F and S. An example of negative W?
Yes, suppose somebody pushes a box toward me. I am
trying to stop it with a force F1 which is smaller than the force
F2 responsible for pushing. In this case the work done by my
force F1 is negative while the work done by F2 is positive.
IS IT OK TO SAY "WORK DONE BY A FORCE" INSTEAD
OF "WORK DONE BY ME OR YOU?" I THINK SO.
=20
b) It is shown that work done by a net force is always equal
to a change in (m*v^2)/2. We give this changing quantity a
name (kinetic energy). We are not free to define KE in any
other way, it can not be m*v^2, for example, or (m*v^2)/3,
etc., unless the definition of work is changed, or unless
kinetic energy is introduced before work.
=20
c) So what is kinetic energy? It is a quantity whose change
(positive or negative) tells us how much work was done by
a net force. Can a work done by a net force be negative?
Yes, for example, when it is used to slow down a box which
would otherwise continue to move with the same v. In this
case the net force does a work on the box whose KE is
decreasing. We are ready to generalize this observation by
saying energy is the "ability to do work". IS THIS OK?
WHOSE ABILITY? THE ABILITY OF THE NET FORCE.
WE ALREADY ACCEPTED THE IDEA THAT WORK IS
ALWAYS ATTRIBUTED TO A FORCE AND NOT TO
AN "AGENT." RIGHT ?
=20
d) At this stage we are familiar with only one kind of
energy, KE. What is potential energy? That is where
the textbook becomes messy and where the displacement
is defined as (initial - final). WHY DID THEY DO THIS?
=20
e) WHY DIDN'T THEY SAY THAT M*g*Y IS THE
WORK A PUSHING FORCE MUST DO TO BRING M
TO AN ELEVATION Y WITHOUT ACCELERATION?
IT IS SO OBVIOUS. THE PUSHING FORCE MUST
BE EQUAL AND OPPOSITE TO THE FORCE WE
CALL WEIGHT M*g. IN THIS CONTEXT PE CAN
BE DEFINED AS WORK DONE BY THE UPWARD
PUSHING FORCE OR AS minus WORK DONE BY
WEIGHT. THIS WOULD BE CONSISTENT WITH
OUR GENERAL DEFINITION OF ENERGY AS
THE "ABILITY OF A FORCE TO DO WORK". YES,
ABILITY IS AN ABSTRACT CONCEPT.
=20
f) What comes next? The authors are trying to prove
mathematically that the sum of KE+PE remains constant
when M moves vertically, either up or down. Their
"derivation" is not acceptable because they use (initial - final)
in one case and (final - initial) in another.
=20
g) I AM NOT SURE THAT IT IS CORRECT TO SAY
THE CONSERVATION OF ENERGY IS "DERIVED"
MATHEMATICALLY (IN THE SAME WAY AS THE
WORK-KINETIC ENERGY WAS DERIVED EARLIER IN
THE CHAPTER). THE LAW OF CONSERVATION OF
ENERGY, EVEN IN THIS TRIVIAL CASE, SHOULD BE
PRESENTED AS AN EXPERIMENTAL FACT. IN OTHER
WORDS, WE SHOULD NOT TRY TO PROVE THAT THE
(KE+PE=3DCONST) IS A MATHEMATICAL CONSEQUENCE
OF SOMETHIBG ELSE. WOULD YOU AGREE?
Ludwik Kowalski
=20

Joseph J. Bellina, Jr. 219-284-4662
Associate Professor of Physics =20
Saint Mary's College
Notre Dame, IN 46556