Chapter1_5 - Momentum Conservation: In O-Frame In O'-Frame...

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PHY3063 R. D. Field Department of Physics Chapter1_5.doc University of Florida Conservation of Linear Momentum ( Classical ) y x z y' z' x' V O O' m 1 m 2 Before Collision y x z y' z' x' V O O' M 1 M 2 After Collision Consider two frames of reference the O-frame (label events according to t,x,y,z) and the O'-frame (label events according to t',x',y',z') moving at a constant velocity V, with respect to each other at let the origins coincide at t = t' = 0. Particles 1 and 2 with initial velocities 1 v and 2 v , respectively, collide head-on. After the collision the two particles have velocities 1 v and 2 v , respectively. All velocities lie along the x-axis.
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Unformatted text preview: Momentum Conservation: In O-Frame In O'-Frame 2 1 2 1 p p p p + = + 2 1 2 1 p p p p + = + 2 2 1 1 2 2 1 1 v M v M v m v m + = + 2 2 1 1 2 2 1 1 v M v M v m v m + = + Now transform from the O'-frame to the O-frame as follows: ) ( ) ( ) ( ) ( 2 2 1 1 2 2 1 1 V v M V v M V v m V v m + = + Thus, ) ( 2 1 2 1 2 2 1 1 2 2 1 1 M M m m V v M v M v m v m + + + = + and Galilean invariance implies m 1 +m 2 = M 1 +M 2 . Galilean invariance implies conservation of mass! Does not allow + + + + e e ! Galilean Transformation...
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.

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