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

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10.58: a) From geometric consideration, the lever arm and the sine of the angle between r F and are both maximum if the string is attached at the end of the rod. b) In terms of the distance x where the string is attached, the magnitude of the torque is . 2 2 h x Fxh + This function attains its maximum at the boundary, where , h x = so the string should be attached at the right end of the rod. c) As a function of x , l and h , the torque has magnitude
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Unformatted text preview: . ) 2 ( 2 2 h l x xh F +-= τ This form shows that there are two aspects to increasing the torque; maximizing the lever arm l and maximizing sin . φ Differentiating with respect to x and setting equal to zero gives max x ). ) 2 ( 1 )( 2 ( 2 l h l + = This will be the point at which to attach the string unless h 2 > l , in which case the string should be attached at the furthest point to the right, . l x =...
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