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

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11.95: Assume that the center of gravity of the loaded girder is at , 2 L and that the cable is attached a distance x to the right of the pivot. The sine of the angle between the lever arm and the cable is then , ) ) 2 (( 2 2 x L h h - + and the tension is obtained from balancing torques about the pivot; , 2 ) ) 2 (( 2 2 L w x L h hx T = - + where w is the total load (the exact value of w and the position of the center of gravity do not matter for the purposes of this problem). The minimum tension will
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Unformatted text preview: occur when the term in square brackets is a maximum; differentiating and setting the derviative equal to zero gives a maximum, and hence a minimum tension, at ). 2 ( ) ( 2 min L L h x + = However, if , 2 if occurs which , min L h L x the cable must be attached at L , the furthest point to the right....
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