Energy before work

[LUDWIK KOWALSKI <kowalskil@alpha.montclair.edu>]

Messages posted several hours ago are arriving. My messages posted three
and two days ago did not appear on my screen. I will have to repost them.
Here is the last one, after some small changes.

A precedent for the energy-before-work way of teaching elementary physics? 
I found an intersting reference, a textbook ENERGY AN INTRODUCTION TO 
PHYSICS BY R.H. ROMER. It was published by W.H. Freeman and Company, San 
Francisco, 1974. The ISBN reference is 0-7167-0357-2; it is likely to be 
out of print now. 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 m*g*h) 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) that 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 pushing 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, used for the gravitational potential 
energy, is 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 of 'chemical to thermal' should be called 
'warming' by phys-L-ers. The concept of elastic PE is introduced in the 
analysis of an example with 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 transfer." ...."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