Lecture_36

Lecture_36 - PHYS 342 Fall 2011 Lecture 36 Relativistic...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 non-relativistic 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?...
View Full Document

{[ snackBarMessage ]}

Page1 / 29

Lecture_36 - PHYS 342 Fall 2011 Lecture 36 Relativistic...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online