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273_Physics ProblemsTechnical Physics

273_Physics ProblemsTechnical Physics - Chapter 9*P9.59(a...

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Chapter 9 275 *P9.59 (a) Conservation of momentum: 0 5 2 3 1 1 5 1 2 3 0 5 1 3 8 1 5 0 5 1 5 4 0 5 1 5 4 1 5 0 2 2 . ± ± ± . ± ± ± . ± ± ± . . ± . ± ± . ± . ± ± . kg m s kg m s kg m s kg kg m s kg m s kg i j k i j k i j k v v i j k i j k + + + = + + = + + + = e j e j e j e j e j f f The original kinetic energy is 1 2 0 5 2 3 1 1 2 1 5 1 2 3 14 0 2 2 2 2 2 2 . . . kg m s kg m s J 2 2 2 2 + + + + + = e j e j The final kinetic energy is 1 2 0 5 1 3 8 0 18 5 2 2 2 . . kg m s J 2 2 + + + = e j different from the original energy so the collision is inelastic . (b) We follow the same steps as in part (a): + = + + = + + + = + 0 5 1 5 4 0 5 0 25 0 75 2 1 5 0 5 1 5 4 0 125 0 375 1 1 5 0 250 0 750 2 00 2 2 . ± . ± ± . . ± . ± ± . . ± . ± ± . ± . ± ± . . ± . ± . ± i j k i j k v v i j k i j k i j k e j e j e j e j e j kg m s kg m s kg kg m s kg m s kg m s f f We see v v 2 1 f f = , so the collision is perfectly inelastic . (c) Conservation of momentum: + = + + + = + + = 0 5 1 5 4 0 5 1 3 1 5 0 5 1 5 4 0 5 1 5 0 5 1 5 2 67 0 333 2 2 . ± . ± ± . ± ± ± . . ± . ± ± . ± . ± . ± . . . ± i j k i j k v v i j k i j k k e j e j e j e j a f kg m s kg m s kg kg m s kg m s kg m s a a a f f Conservation of energy:
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