Defining PE as the negative of the work done by weight
I don't think it is wise to "define" energy in terms of work. Energy
is the primary and fundamental quantity. Work is a secondary and
derived quantity. Work should be defined in terms of energy, not the
other way around.
I have no strong objection to !introducing! the subject of energy by
means of examples. You have to start somewhere. However, it must be
stressed that these examples (as always) constitute special cases, not
the general case. There is a big difference between a book and the
shadow of a book on the wall of your cave. http://faculty.washington.edu/smcohen/320/cave.htm
Even then, you want to choose your examples wisely. It seems
unnecessary and suboptimal to use work as a leading illustration of
energy. The alternatives are simpler and better. Try this:
-- An object on a high shelf has more energy than it would on a low
shelf. This is called gravitational potential energy. E_1 = m g h.
-- A object that in motion has more energy than it would at rest.
This is called kinetic energy. E_2 = .5 m v^2.
-- A spring that is compressed has more energy than it would when
relaxed.
-- An object that is hot has more energy than it would when cold.
-- There exist a few other forms of energy.
Energy cannot be created or destroyed, but it can be converted from
one form to another. A roller-coaster illustrates the conversion of
gravitational potential energy to kinetic energy and back again. A
pendulum (swing-set) is another good illustration.
Energy is a tremendously useful concept. For example, it allows you
to calculate the height-versus-speed tradeoff in a roller-coaster or a
swing-set quite easily. You don't need to talk about vectors or
forces or work. All you need is conservation of energy, plus the
assumption that KE and GPE are dominant, in the sense that very little
energy is converted to forms other than these two.
.... You get the idea. Energy is fundamental and primary.
There is something quite sweeping and quite grand about this. The
height-versus-speed result is INDEPENDENT OF MECHANISM. I don't care
what mechanism is used to convert GPE into KE. The roller-coaster
uses one mechanism, and the swing-set uses another. But the result is
the same, independent of mechanism.
To me, this is what physics is all about. This is the magic and
beauty of physics. Engineering is all about mechanism, but physics
can make grand sweeping statements that transcend mechanism.