The Work - W net = F net x f x o Using Newton's Second Law...

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The Work-Energy Theorem Now that we have a definition of work, we can apply the concept to kinematics . Just as force was related to acceleration through F = ma , so is work related to velocity through the Work-Energy Theorem. Derivation of the Work-Energy Theorem It would be easy to simply state the theorem mathematically. However, an examination of how the theorem was generated gives us a greater understanding of the concepts underlying the equation. Because a complete derivation requires calculus, we shall derive the theorem in the one-dimensional case with a constant force. Consider a particle acted upon by a force as it moves from x o to x f . Its velocity also increases from v o to v f . The net work on the particle is given by:
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Unformatted text preview: W net = F net ( x f- x o ) Using Newton's Second Law we can substitute for F: W net = ma ( x f- x o ) Given uniform acceleration, v f 2- v I 2 = 2 a ( x f- x o ) . Substituting for a ( x f- x o ) into our work equation, we find that: W net = mv f 2- mv o 2 This equation is one form of the work-energy equation, and gives us a direct relation between the net work done on a particle and that particle's velocity. Given an initial velocity and the amount of work done on a particle, we can calculate the final velocity. This is important for calculations within kinematics, but is even more important for the study of energy, which we shall see below....
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