workenergy2 - Math 21a Supplement 2 on Work and Energy As...

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Math 21a Supplement 2 on Work and Energy As mentioned at the end of Section 5.1 in the text, the work done in moving a particle along a path γ in R 3 when a force vector F acts is defined to be w( γ ) γ F •d x (1) This is to say that term ‘work done in moving along γ ’ in physics has a specific meaning, the latter being the value of (1). (Presumably, this mathematical definition of work meshes well with our intuitive idea of work done.) Let me remind you (from the definition in the text) that the shorthand on the right side of (1) has the following meaning: Parameterize the path γ by choosing an interval, [a, b], on the line, and a vector valued function x (t) for a t b which traces out the path γ . With this done, then the right side of (1) is computed by the ordinary integral w( γ ) = a b F ( x (t))• x ´(t) dt . (2) Now, suppose that the path γ is the path that the particle would have travelled were its trajectory γ given by Newton’s law; thus
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workenergy2 - Math 21a Supplement 2 on Work and Energy As...

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