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Development of the Work Energy Theorem in Mechanics
C
George Kapp
2002
Table of Contents
Page
1. Introduction.
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2
2. Prolog, In search of Vis Visa.
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3
3. Work.
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4
4. Work Done by Net Force, KE.
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7
5. Interlude.
Looking at the Big Picture.
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8
6. Gravitational Potential Energy.
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9
7. Elastic Potential Energy.
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11
8. Work – Energy Theorem.
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12
9. Conservation of Energy.
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13
10. Application Example.
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14
G.Kapp, 2/20/04
1
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View Full DocumentIntroduction.
The concepts of work and energy are introduced in
all beginning physics classes.
At that beginning level, the student has
attained a proficiency in algebra and trigonometry only, and as such,
many educators believe the student is unable to appreciate or
understand the development of the work energy theorem.
These
educators typically present work as force times displacement, kinetic
energy and potential energy as magic formulas, and spend much time
discussing how these energies transform from one form to the next.
Problems are authored and solved as if all problems can be solved by
“conservation of energy” and that it, energy, is
always
conserved.
Textbook sections entitled “
Optional 
Work done by a variable force.”
,
clearly set the tone of
lack of importance
of this situation,
for students
and instructors alike.
Some text book authors do address the idea that
work is an integral part of the energy concept, but fail to paint the big
picture of path independence or dependence, which ties all the work
energy components together in a logical fashion, favoring to create a
number of “special cases” that the student memorizes, but rarely
understands.
The fact that
it is not
necessary to know how the energy
transforms from form to form when solving problems
, the real power of the
work energy theorem, is totally missed.
This condemnation of physics education may in fact seem
somewhat harsh.
Textbook authors could use the afore noted lack of
math skill as argument to defend their approach to the work energy
omission.
Still, there is an understandable thread connecting work and
energy, path function, point function, and that story needs to be told
because it provides the foundation for understanding (or lack thereof) in
thermodynamics courses to follow.
In areas of physics, history will help convey a sense of the concept.
With force, we have but to look to Newton to see how this concept was
developed.
Newton’s laws are tightly packaged in a brief moment in
history.
Work energy, however, has no moment in history and no
founding father.
Work energy is similar to a meal in reverse, the dessert
served first, and lastly the meat and potatoes.
The work energy story
cannot be told in chronological order because it was not developed in any
logical order.
It simply evolved.
The goal of this paper is to present the work energy theorem to the
student of calculus based physics in an order that is logical, not
historical.
To show the beauty of the arrangement, the power of the
results, so that for the student, the Work Energy Theorem finally falls
together with crystal clarity.
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 Spring '10
 Kapp
 Physics, Energy, Force, Work, WorkEnergy Theorem

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