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Unformatted text preview: PHYS 342 Fall 2011 Lecture 36: Relativistic Kinematics Ron Reifenberger Birck Nanotechnology Center Purdue University Newton’s Laws of Motion allow a particle to accelerate to ANY speed. Clearly this can not e How do we solve this problem? be. How do we solve this problem? Lecture 36 1 ee Appendix at end of this lecture to OVERVIEW 1. See Appendix at end of this lecture to review nonrelativistic aspects of collisions 2. Analyze a sequence of four experiments to learn about conservation of momentum in relativistic collisions . ummary of Important results: 3. Summary of Important results 2 o o m v p m v v 2 2 2 1 ( 1 ) o c K est energy m c c 2 2 2 2 : 1) o o o o Rest energy define total energy E m c K m c m c m c m c 2 2 2 4 2 2 ( ) o o o o o E m c p c energy momentum relatationship Space Billiards I: Both ships at rest t=0 time m m m u o u o Ship No. 2 Both ships have learned to launch entical alls with m m u o identical balls with an identical speed u o m u o Ship No. 1 3 Is Momentum Conserved? Component Brown ball Green ball SUM efore x Before y m (u o ) m ( + u o ) After x y m(+u o ) m (u o ) 4 Space Billiards II: Both ships moving at Newtonian speeds initial 2 final u 2 u 2 2 p m u v f <<c Ship No. 2 2 initial u 2 final u m 2 u u o initial nal 1 u 1 final u m u o 1 1 p m u 1 initial u 1 u rom a stationary Ship No. 1 v f <<c 1 final u From a stationary observer's viewpoint 5 Is Momentum Conserved? Component Brown ball Green ball SUM efore x m (v f ) m ( + v f ) Before y m (u o ) m ( + u o ) After x m (v f ) m ( + v f ) y m (+u o ) m (u o ) 6 What happens as v f approaches c? Require Relativistic Velocity Transformations ' x f u v u 2 1 ' x f x v u c 2 2 2 ' ' 1 1 ' 1 ' y y y f f x x u u u v v u u c 2 ' 1 ' z z z c c u u u v 2 2 1 ' 1 ' f f x x v v u u c c 7 Space Billiards III: Both ships move symmetrically at relativistic speeds oth hips are Lorentz contracted AND time runs slow on Ship No. 2 Both ships are Lorentz contracted AND time runs slow on both ships. As a result, the velocity u o must be modified as shown. Is momentum still conserved? ( label each mass separately to m 2 v f p keep track of the algebra ) 2 ' 1 u 2 initial u 2 final u 2 1 o u 2 2 ' 1 1 ' x y y o f x u u u v u c 1 initial u nal 2 1 u 1 final u m 1 v o As viewed from a stationary observer's viewpoint f Ship No. 1 8 Is Momentum Conserved?...
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 Fall '08
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 Kinetic Energy, Mass, Momentum

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