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Re: the energy




Most people (of all ages, not just students) have a hard
time visualizing anything in D=3. Therefore a detailed
accounting of the energy in a complicated arrangement of
charges will probably be very hard to visualize.


This is certainly true, but dyslexics are generally better at it than
"normal" people.

Beyond this Anton Lawson has found that concepts which correspond to things
that can not be "seen" are very difficult to grasp. He also has persuasive
evidence that there is a level of thinking above the formal operational
level that is necessary for easily grasping such concepts. Since energy is
precisely such a concept, it is very difficult for everyone below this
level, the "theoretical level". It becomes even more difficult as you go
down to the concrete operational level, and may actually be impossible for
such individuals.

However, the fluid analogy or picture may make such concepts much easier.
Incidentally, the modeling people have also done away with the word
"transformation" in regard to energy. They try to get the students to
visualize energy as something which resides in specific places. For example
elastic energy is in a spring or rubber band. Kinetic is in the moving
body, but gravitational or electrostatic would be in the field. Again, this
helps make the concept more understandable. Instead of transforming energy,
you merely move it to a new location.

Incidentally this brings up the common misconception that is even repeated
in textbooks that energy resides in "chemical bonds". If one thinks of them
as being like rubber bands, then the energy stored increases as they are
stretched. Then one should not say the bonds are broken, but merely they
are stretched until the force has become very small. There is a very real
difficulty here, that lower level students can not comprehend the idea that
potential energy may become negative when a bond is formed, so the energy
stored is negative energy. When one speaks of breaking the bonds, students
then think of what happens when a rubber band is broken. The energy is
released.

While there certainly can be problems with thinking of energy as residing
someplace, it seems to be very useful as a means of understanding energy
"transformations". This latter idea is what the general public and
non-scientists need to really understand, as was pointed out in a previous
post. In addition the whole idea of conservation is also difficult for many
students. When confronted with the necessity of using conservation
reasoning, they will rely on surface features of the problem instead of
thinking about how the quantity is changing.

John M. Clement
Houston, TX