I am glad that the apparent disagreement evaporated and that
our Model 1 is no longer controversial. This was an example
of a disagreement caused by simple misunderstanding. I was
referring to W as the dot product of F and s while JohnD
was referring to W from the first law. The same word should
never be used to represent two different concepts. Right?
It is time to move to Model 2. But before going ahead 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 dependant", 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. But it is
worth trying. Please cooperate constructively; do not derail
the attempt by focusing on topics belonging to more
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. 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).
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,
E=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 E.
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 Q.
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 the more appropriate name for the
amount of caloric, thermal energy, will be introduced later.
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 E, 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 always 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 Q in Joules and refer
to this physical quantity as a form energy. Experiments
performed by Joule, and by others, demonstrated that
although Q is decreasing the sum of E+Q remains constant.
Referring to a sliding box I would invent a new name for
the above sum, for example, mhenergy. Then I would
generalize by saying that mhenergy is conserved in real
experiments. That is the essence of Model 2.
At this stage I would avoid further generalizations, such as
chemical energy, nuclear energy, sound energy, etc. Telling
students what to expect is OK but elaborating on it would
violate the rule of not accepting things on faith. The
Feynman’s story of "Dennis the Menace" is worth sharing
at this stage.
Note that the terms "work" and "heat" are now defined.
Work done by a force is a dot product, heat generated in
a process is thermal energy. In other words, unlike heat,
work is not a form of energy. Note that in Model 2 deltaQ
is always positive (heat is generated). The model is not
sufficient to deal with processes in which deltaQ can be
either positive or negative. Is the traditional Model 2, as
described above, acceptable?
Ludwik Kowalski