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384_Physics ProblemsTechnical Physics

384_Physics ProblemsTechnical Physics - 386 P13.8 Universal...

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386 Universal Gravitation P13.8 Let θ represent the angle each cable makes with the vertical, L the cable length, x the distance each ball scrunches in, and d = 1 m the original distance between them. Then r d x = 2 is the separation of the balls. We have F y = 0: T mg cos θ = 0 F x = 0: T Gmm r sin θ = 2 0 FIG. P13.8 Then tan θ = Gmm r mg 2 x L x Gm g d x 2 2 2 2 = a f x d x Gm g L x = 2 2 2 2 a f . The factor Gm g is numerically small. There are two possibilities: either x is small or else d x 2 is small. Possibility one : We can ignore x in comparison to d and L , obtaining x 1 6 67 10 100 9 8 45 2 11 m N m kg kg m s m 2 2 2 a f e j b g e j = × . . x = × 3 06 10 8 . m. The separation distance is r = × = 1 2 3 06 10 1 000 61 3 8 m m m nm . . . e j . Possibility two : If d x 2 is small, x 0 5 . m and the equation becomes 0 5 6 67 10 100 9 8 45 0 5
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