University Physics with Modern Physics with Mastering Physics (11th Edition)

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6.84: The arrow will acquire the energy that was used in drawing the bow ( i.e. , the work done by the archer), which will be the area under the curve that represents the force as a function of distance. One possible way of estimating this work is to approximate the F vs. x curve as a parabola which goes to zero at 0 = x and , 0 x x = and has a maximum of 0 F at , 2 0 x x = so that ). ( ) ( 0 4 2 0 0 x x x x F x F - = This may seem like a crude approximation to the figure, but it has the ultimate advantage of being easy to integrate;
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Unformatted text preview: . 3 2 3 2 4 ) ( 4 3 2 2 2 2 x F x x x x F dx x x x x F Fdx x x ∫ ∫ = -=-= With N 200 = F and J. 100 m, 75 . = = W x The speed of the arrow is then . s m 89 kg) (0.025 J) 100 ( 2 2 = = m W Other ways of finding the area under the curve in Fig. (6.28) should give similar results....
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