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Full Proof of the Work

# Full Proof of the Work - Full Proof of the Work-Energy...

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Full Proof of the Work-Energy Theorem Though a calculus based proof of the Work-Energy theorem is not completely necessary for the comprehension of our material, it allows us to both work with calculus in a physics context, and to gain a greater understanding of exactly how the Work-Energy Theorem works. Using that equation, the equation we derived for work done by a variable force, we can manipulate it to yield the work-energy theorem. First we must manipulate our expression for the force acting on a given object: F net = ma = m = m = mv Now we plug in our expression for force into our work equation: W net = F net dx = mv dx = mvdv Integrating from v o to v f : W net = mvdv = mv f 2 - mv o 2 This result is precisely the Work-Energy theorem. Since we have proven it with calculus, this theorem holds for constant and nonconstant forces alike. As such, it is a powerful and universal equation which, in conjunction with our study of energy in the next topic , will yield powerful results.

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Full Proof of the Work - Full Proof of the Work-Energy...

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