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Work Energy Theorem (4)

# Work Energy Theorem (4) - Development of the Work Energy...

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Development of the Work Energy Theorem in Mechanics C George Kapp 2002 Table of Contents Page 1. Introduction ...................................................................... 2 2. Prolog, In search of Vis Visa .............................................. 3 3. Work ................................................................................. 4 4. Work Done by Net Force, KE .............................................. 7 5. Interlude. Looking at the Big Picture ................................. 8 6. Gravitational Potential Energy ............................................ 9 7. Elastic Potential Energy .................................................... 11 8. Work – Energy Theorem .................................................... 12 9. Conservation of Energy ..................................................... 13 10. Application Example ......................................................... 14 G.Kapp, 2/20/04 1

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Introduction. 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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