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382_Physics ProblemsTechnical Physics

382_Physics ProblemsTechnical Physics - 384 P13.3 Universal...

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384 Universal Gravitation P13.3 (a) At the midpoint between the two objects, the forces exerted by the 200-kg and 500-kg objects are oppositely directed, and from F Gm m r g = 1 2 2 we have F G = = × 50 0 500 200 0 200 2 50 10 2 5 . . . kg kg kg m N b gb g a f toward the 500-kg object. (b) At a point between the two objects at a distance d from the 500-kg objects, the net force on the 50.0-kg object will be zero when G d G d 50 0 200 0 400 50 0 500 2 2 . . . kg kg m kg kg b gb g a f b gb g = or d = 0 245 . m P13.4 m m 1 2 5 00 + = . kg m m 2 1 5 00 = . kg F G m m r m m m m = × = × = × × = 1 2 2 8 11 1 1 2 1 1 2 8 11 1 00 10 6 67 10 5 00 0 200 5 00 1 00 10 0 040 0 6 67 10 6 00 . . . . . . . . . N N m kg kg m kg N m N m kg kg 2 2 2 2 2 2 e j b g a f b g e je j Thus, m m 1 2 1 5 00 6 00 0 + = . . kg kg b g or m m 1 1 3 00 2 00 0 = . . kg kg b gb g giving m m 1 2 3 00 2 00 = = . . kg, so kg . The answer m 1 2 00 = . kg and m 2 3 00 = . kg is physically equivalent. P13.5 The force exerted on the 4.00-kg mass by the 2.00-kg mass is
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