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HW10 - Physics 105 Mechanics Fall 2009 Homework 10 Due...

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Physics 105: Mechanics Fall 2009 Homework 10 Due Friday 11/20 Read sections 8.6-8.7, 9.1-9.6, and 10.1 - 10.6 the text. Do the following problems. 1. Do 8.P.24. 2. Do 8.P.26. 3. Do 8.P.28. 4. Do 8.P.30. 5. Do 8.P.22. 6. Do 9.RQ.14. 7. Do 9.P.20. 8. Consider two particles, 1 and 2, with masses m 1 and m 2 and velocities ~v 1 and ~v 2 . In this problem, you will prove that the kinetic energy of the system, by which we mean K 1 + K 2 , can in fact be written as K trans + K rel . Recall that K trans = (1 / 2)( m 1 + m 2 ) | ~v CM | 2 and K rel = (1 / 2) m 1 | ~v 1 ,rel | 2 + (1 / 2) m 2 | ~v 2 ,rel | 2 . (We are assuming that the speeds are non-relativistic.) (a) Write an expression for K sys = K 1 + K 2 , in terms of the masses and velocities. (b) Using the fact that the velocity of particle 1 relative to the center of mass is ~v 1 ,rel = ~v 1 - ~v CM , and similarly for particle 2, show that K 1 + K 2 = K trans + K rel . Some useful mathematical identities: | ~v | 2 = ~v · ~v | ~v + ~w | 2 = ( ~v + ~w ) · ( ~v + ~w ) = ~v · ~v + 2 ~v · ~w + ~w · ~w 9. A superball of mass m is held just above a basketball of mass M. The balls are released from rest simultaneously. Assume that all the collisions are elastic. Just before the basketball reaches the
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