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problem12_50

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

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12.50: Denote the 25-kg sphere by a subscript 1 and the 100-kg sphere by a subscript 2. a) Linear momentum is conserved because we are ignoring all other forces, that is, the net external force on the system is zero. Hence, . 2 2 1 1 v m v m = This relationship is useful in solving part (b) of this problem. b)From the work- energy theorem, ( 29 2 2 2 2 1 1 i f 2 1 2 1 1 1 v m m m r r m Gm + = - and from conservation of momentum the speeds are related by . 2 2 1 1 v m v m = Using the conservation of momentum relation to eliminate 2 v in favor of 1 v and simplifying yields , 1 1 2 i f 2 1 2 2 2 1 - + = r r m m Gm v with a similar expression for 2 v
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Unformatted text preview: s. m 10 08 . 4 s, m 10 63 . 1 6 2 5 1--× = × = v v The magnitude of the relative velocity is the sum of the speeds, s. m 10 04 . 2 5-× c) The distance the centers of the spheres travel ( 29 2 1 and x x is proportional to their acceleration, and . 4 or , 2 1 1 2 2 1 2 1 x x m m a a x x = = = When the spheres finally make contact, their centers will be a distance of m, 40 2 or apart, 2 2 1 = + + R x x R m. 40 2 4 or 2 2 = + + R x x Thus, . 6 . 1 m 32 and , 4 . m 8 1 2 R x R x-=-=...
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