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Re: CONSERVATION OF ENERGY



REPOSTING AFTER CORRECTING TWO TYPING ERRORS. SORRY
In this morning message (see below) I forgot to specify that the book
was published by W.H. Freeman and Company, San Francisco, 1974. Its
ISBN reference is 0-7167-0357-2; it is likely to be out of print now.
Therefore let me describe some of its innovative formulations (after
the repeated text below).

Looking for a precedent for the "energy before work" way of teaching
elementary physics I found an intersting reference. It is a textbook
ENERGY AN INTRODUCTION TO PHYSICS BY R.H. ROMER; many of you know that
the author is the editor of AJP. He introduces kinetic and gravitational
forms of energy (operationally as m*v^2/2 and mgh) before the concept of
work. This is done in connection with the study of a pendulum. The author
wants students to discover that the sum of two quantities is conserved.

This approach can be implemented in at least two ways, depending on
the equipment available. One is to use a camcorder, another to use a
camera and a stroboscopic source of light. The goal is to collect data
on how the velocity, v, and the elevation, h, are related. You can also
collect data on free fall, for example, with a motion detector. Ask
students to plot v^2 versus h and discuss the significance of the the
straight line. What is the unit of the quantity represented by the
negative slope? Why is the slope so close to 19.6 (2*g)?

I will try this approach in the Fall.

1) The two forms of energy, see above, were introduced on page 86. Work
is introduced on page 117 (after F=m*a) "as a measure of energy transfer".
Here are some additional quotations. "If the kinetic energy of an object
is changing, its momentum and velocity vectors are changing and so there
must be a zero net force acting". Analysing the motion of a block on the
horizontal surface, under the influence of the net force F, and using
the second law, Romer shows (algebra) the change of kinetic energy must
be equal to F*distance. The name work is given to this quentity.

2) Page 119. "Work represents a way of *transferring* energy. Although
work and energy are closely related concepts, they are not the same.
They must have the same dimentions and must be measured in the same
units, as we can see from ...." Work and energy differ in the same
way that a bank *deposit* and a bank *balance* differ. .... In many
ways, the use of the word 'work' does not represent a happy choice,
for although the concept as defined here is related to the ordinary
meaning of the term, the correspondence is not perfect, as can be
seen from a couple of examples. Suppose that you are pusshing very
hard on a stalled car, but not hard enough to move it; ....."

3) An especially interresting result emerges if Equation 3.26 [work=dE]
is applied to the vertical motion of an object. ...." This leads to
the derivation (algebra) of what we call work-energy relation. The
work W, done by an external force, is equal to the change in the
mechanical energy (KE+GPE). The symbol GPE is used for the gravitational
potential energy introduced during the derivation. In the case of zero
work (a closed system) the mechanical energy must be conserved.

4) "The difficulty with Equation 4.2 [KE=GPE=const] is that it is often
incorrect. Two gliders interacting with each other on an air track ...
become slightly warmer after the collision than before. The law of
conservation of energy can be rescued by defining another form of
energy, *thermal* energy, (TE)." The need for distinguishing thermal
energy with a "nearly synonymous term" internal energy is stated in
the footnote. "

5) "..... we realize that energy can be transferred from a hot object to
a cooler one just by placing them next to each other, by a flow of heat
(symbolized by H). The "basic energy equation" is generalized at this
point by writing it as

W + H = d(KE + GPE + TE + Chemical Energy + Electric Energy + ...)

"Here H denotes the flow of heat, wheras W represents energy transfers
of all other types. Heat, like work, can be either positive or negative,
depending on .... For a closed system W=0 and H=0 so that dE=0. "The
total energy of a closed system is conserved."

6) "What happens when we you rub two sticks together? You are doing work,
transferring energy from your body to the sticks. The store of chemical
energy in your body decreases, and at the same time the thermal energy
of the sticks increases. If the system includes your body together with
the sticks and the surrounding air, the total energy is constant, but
energy is being converted from chemical energy to thermal energy and
being transferred from one part of the system to another, from your
body to the sticks." I suppose the conversion for chemical to thermal
should be called "warming" by phys-L-ers. The concept of elastic PE
is introduced in the analysis of bouncing.

7) Page 157. ".... Energy is being added to the house by the flow of heat,
H1, which increases the thermal energy of the house, an increase
reflected in an increase of temperature." The formal introduction of
the concept of temperature appears much later in the book. "Heating of
a house is precisely analgous to pouring water into a leaky bucket,
while the bucket [hole in the bottom] is partially submerged in a lake."

8) Page 202. After introducing temperature scales and emphasizing that
"temperature and heat are ... important concepts [which are] by no
means identical" Romer writes. "A more subtle distinction than that
between heat and temperature is the one between heat and thermal energy.
Thermal energy is a form of energy that an object has; the higher the
temperature the greater its thermal energy. The term heat should be used
only to refer to some sort of a process - a 'flow of heat'. Heat is
energy in transit from one place to another. In 3.4 we made a similar
distinction between work and energy. .... Work is a measure of energy
thransfer." ...."Thermal energy energies can be changed even when no
flow of heat occurs. Rub two sticks together, ..."

It is interesting that the unit of H, in connection with H=c*m*dT, is
calorie. Logically (in this sequence) this formula defines the heat
capacity "of any substance". The "equivalence between heat and work"
is introduced while discussing Joule's paddle-wheel experiment. "Heat
is not work but heat and work are equivalen in that the energy of a
system can be increased either by" W or by H. This is followed by a
comment on units and by 1 cal=4.186 J. "Calories and joules are both
still used, even though one of the two could be dispensed with."
I like this, using calories for a while and then dropping them is
much more pedagogical than skipping them alltogether.

9) Chapter on the First law (pages 202 to 238), will read later.
10 Chapter on the Second law (p 240 to 270), will read later.

Ludwik Kowalski