Thanks for constructive criticism. The corrected draft
about Model 1 and MODEL 2 is shown below. Let me repeat
that IT IS NOT an attempt to find the best possible sequence
for energy related topics for an introductory physics course.
What I would like to find is a sequence of energy related
topics, AND THE ASSOCIATED VOCABULARY, which is
not wrong. Keep in mind that I am referring to an elementary
physics course. If we can agree on what is acceptable here then
we can use it as a reference in future debates. Perhaps some
old disagreements will evaporate when we agree on how the
words should be used, at least on this list.
If we agree on the meaning of a word (such as force, work,
heat or energy) then the meaning of that word should not
be contradicted in more advanced considerations. Advanced
considerations are likely to provide more depth but they
should not be in conflict with what has already been accepted
in a given model. In other words, physical concepts should
not be made "context dependent", a new concept should be
assigned a new name. Will we be able to agree on a sequence
of well defined and non-contradictory words for concepts
used in the first physics course? I am not sure. Model 3 must
respect concepts introduced in Models 1 and 2. We will see.
Please cooperate constructively; do not derail the attempt by
focusing on topics which belong to advanced courses."
Let me summarize what I hope is acceptable so far:
1) It is not wrong to introduce "work done by a force" as a
dot product of F and s. In a calculus based physics course
"work" would be introduced as an integral of F*ds, etc. The
unit of W is Joule. KE is introduced as work done by a net
force acting on a particle (via kinematics and Newton’s
second law). It refers to an object moving in 3D space.
Note that work describes the effect of F on a particle
(or on a rigid body pushed or pulled through its center of
mass). Forces also have effects on objects with internal
degrees of freedom but I do not want to discuss this topic
here. [Why is it important to show that KE=0.5*p^2/m?]
2) It is not wrong to begin with a highly unrealistic Model 1
in which there are only two conservative forces: weight (mg)
and elasticity (k*x). This simple model allows us to introduce
PEgrv as work done against weight and PEspr as work done
against elasticity. It is not a good idea to elaborate on electric
or magnetic energy before the corresponding forces are
discussed in the second part of the course.
3) The law of conservation of mechanical energy,
Emech=KE+PEgrv+PEspr, is a useful idealization. It is
confirmed by experimental data when friction and air
resistance are negligible. We can use this law to solve
problems which were already solved via the analysis of
forces and get identical results. A spring plunger, a falling
rock, a ballistic pendulum are well known setups in which
experimental data are in reasonable agreement with
theoretical predictions based on the law of conservation
of Emech.
MODEL 2
If it was up to me I would introduce calorimetry at the very
beginning of the course and would not hesitate to use the
word "amount of caloric" for the quantity H. With this
concept, and its operationally defined unit, "calorie" we
can rate fuels and make reliable predictions about changes
of temperature. Then I would emphasize that attempts to
assign mass to caloric failed. Following the historical
approach seems to be useful in this case. I would use the
word "heat" as a synonym for caloric and would say that
a more appropriate name for the amount of caloric is
thermal energy, Eth.
4) After Model 1 I would say that friction is always present
in mechanical setups. We can often minimize friction but
we can not eliminate it entirely. In the real world the
mechanical energy Emech, as defined above, does not remain
constant, it usually decreases by the amount proportional
to work done by frictional forces. Even a swinging
pendulum, or a new bouncing ball, will come to rest,
sooner or later.
What happens to mechanical energy when it gradually
disappears? To answer this question one must be aware
that frictional forces are often associated with increases
of temperature. Experiments performed by Count Rumford,
and those performed by Joule, would be used to establish
the mechanical equivalent of heat. Then I would say that
caloric is not a substance, it is a form of energy. To
emphasize this we will start expressing H in Joules
and refer to this physical quantity as thermal energy, the
energy an object has by virtue of its temperature.
Experiments performed by Joule, and by others, demonstrated
that although Emech is decreasing the sum of Emech+Eth
remains constant. Referring to a sliding box I would invent
a new name for the above sum, for example, mtenergy.
Then I would generalize by saying that mtenergy is conserved
in many real experiments. That is the essence of Model 2.
Numerical examples would play an essential role in my
presentation.
I see no harm from a possible extrapolation in which the
Etot is introduced. There is nothing wrong with telling students
about "coming attractions." On the other hand a teacher
may decide to wait with broad generalizations till two or
three more forms of energy are introduced. In either case
the Feynman’s story of "Dennis the Menace" can be very
useful as an illustration what the energy "really is".
Let me emphasize that the terms "work" and "heat" are
now defined. Work done on a particle is a dot product
(F*ds), heat is thermal energy, Eth. In other words,
unlike heat, work is not a form of energy. Note that in
Model 2 heat generated through friction, H, is always
positive. This offers an opportunity to introduce entropy
(dS=H/T) whose unit is J/K. One can declare that S=0
at T=0 (an arbitrary reference level, like for PEgrv) and
observe that S is always positive. The natural tendency
of S to increase can be illustrated with numerous examples
without making a reference to the idea of non-reversibility
of dissipative processes. The entropy of the universe is
increasing, even when chemical reactions are ignored.
MORE ON MODEL 2
The kinetic theory of gasses provides us with the first
glimpse of the true nature of caloric. It shows that for a
simple case of an ideal gas (mono-atomic molecules)
Eth can be calculated as 1.5*N*R*T, where N is the
number of moles, R is the universal gas constant and
T is the absolute temperature. In the first physics course
this is usually generalized by saying that the amount of
thermal energy present in any object is directly
proportional to its absolute temperature.
The kinetic theory of gasses is a gigantic step toward
the understanding of the true nature of heat. But this
should not prevent me from associating this theory with
the Model 2. It is the central theoretical part of that model.
Solid substances can be viewed as molecules connected
with springs; the true nature of springs can be announced
but not explained until electric forces are discussed. The
amount of thermal energy contained in a solid is determined
by random motions of interacting molecules about their
equilibrium positions. The term "random molecular energy"
can be used but, in my opinion, it is not needed. Thermal
energy is the same thing as random molecular energy; it is
partially kinetic and partially potential.
Likewise a distinction between the "sub-microscopic" and
"macroscopic" energies is useful but not essential. The
term "internal energy" was often debated on this list. I do
not remember who said what but the opinion I formed was
that the internal energy can be both macroscopic and sub-
microscopic. To illustrate this I would refer to a mechanism
with spinning wheels (at a non-zero T). Is this acceptable?
Ludwik Kowalski