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Re: ENERGY BEFORE Q



Referring to JohnD (?)

I don't think it is wise to "define" energy in terms of work.
Energy is the primary and fundamental quantity. Work is a
secondary and derived quantity. Work should be defined in
terms of energy, not the other way around.

Jim wrote:

The concept of "energy" is an _invention_ (by Young) as is
the concept of "work". How can either be considered
"fundamental" and the other not?

1) I tried to follow the "first physics course" pretending to be
a student in order to identify conceptual barriers. This may
be a useful approach. The name of the thread was ENERGY
BEFORE Q. Let us stick to this for a while. First we should
ignore Q, and dissipative forces. We should address these
subjects a little later, just like students are expected to do.

2) There are several physical quantities whose unit is J.
Which quantity (W, KE, PEgrv or PEspr) is fundamental
depends on which one is introduced first. JohnD said
let us begin with PEgrv defined as m*g*h, where h is
an elevation with respect to a chosen reference level.
Why not? Let us follow this sequence. What is the
next step?

3) I suppose it is going to be the KE. So why is it defined
as (m*v^2)/2 and not, for example, as m*v^2? Because,
according to what we learn in kinematics, 0.5*m*v^2 is
always equal to PEgr in free fall. We are discovering the
very first manifestation of conservation of energy. Joules
are conserved in our very limited world of two energies.
The sum of PEgr and KE remains constant when an object
moves up or down vertically. This is interesting, changes
occur but the something (sum of two physical quantities)
remains the same. Is it really a discovery or is it a man-
made system made by manipulating definitions? I would
let philosophers to wander about this.

5) What is next? Consider a vertically positioned spring and
an object of mass m falling on it from a given elevation h.
The spring constant is k and the mass of the spring is
negligible in comparison with m. Is it easy to show (by
algebra) that m*g*h and 0.5*k*x^2 must be equal? Not
very easy because we have to deal with a situation in which
the net F, acting on m, is not constant. Keep in mind we are
only in the Week #5 of the very first physics course. Please
stay at this level, please do not spoil the game, by bringing
in ideas from more advanced courses. We will get there,
little by little. The main point is not to say what is correct
but how to teach it.

5) Show how to justify the PEspr=0.5*k*x^2 definition
without leaning on the definition of work. Do we need to
define work or should we go ahead without this concept.
Students already know how to add or subtract vectors but
not how to multiply them. Both Jim and JohnD seem to
agree that "work should be defined in terms of energy, not
the other way around." That what we should try to do.

SO I HAVE THREE QUESTIONS:

A) HOW TO JUSTIFY (k*x^2)/2 ?

B) HOW CAN WORK BE DEFINED IN TERMS OF
ENERGY IN THE WORLD OF TWO CONSERVATIVE
FORCES?

C) IS THE MODELING IDEA OF "ENERGY BEFORE WORK"
MORE DESIRABLE THAN TRADITIONAL APPROACHES IN
WHICH WORK IS ALWAYS USED TO DEFINE ENERGY?

Let me address the second question. Suppose we declare that, by
definition, work is the amount of energy converted from one form
into another. Why bother describing it in terms of two vectors?
Can physics be constructed without introducing the quantity called
work? Do we need to introduce it before entering the world of
frictional forces and changes of temperatures? I hope somebody
will take over and proceeds to the next thread, "Energy with Q."
How to make sure that general laws are perceived by students
as honest generalizations and not as ad hoc statements?
Ludwik Kowalski