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solutions_relativity

# solutions_relativity - PHY2061 R D Field Relativity...

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PHY2061 R. D. Field Solutions Relativity Page 1 of 6 Relativity Solutions Problem 1: A rod whose length at rest is 10 meters is moving to the right along the positive x-axis of the O-frame with velocity V = 0.8c . An observer riding on the rod ( i.e. in the O'-frame ) sets off two explosions simultaneously – so he says. If the rod is parallel to the x-axis how far apart are the two explosions ( in meters ) in the O-frame ? Is this length the same as the length of the rod as measured in the O-frame ? If your answer is no, then what is the length of the rod ( in meters ) as measured in the O-frame ? Answers: 16.67, no, 6 Solution: The two explosions occur simultaneously in the O'-frame which implies that t' = 0 and thus m m L t c x x 67 . 16 ) 10 )( 667 . 1 ( ) ( 0 = = = + = γ β γ where I used x' = L 0 . This is not the same as the length of the rod as measured in the O-frame . The length of the rod as measured in the O- frame corresponds to marking both ends of the rod simultaneously in the O- frame ( i.e. t = 0 ) as follows: L t c x L x γ β γ = = = ) ( 0 and m m L L 6 667 . 1 10 0 = = = γ . Problem 2: In the previous problem, what is the time interval ( in seconds ) between the two explosions as measured in the O-frame ? Which explosion occurred first in the O-frame , the one at the left or right end of the rod? Answers: 4.44x10 -8 , left one first Solution: The two explosions occur simultaneously in the O'-frame which implies that t' = 0 and thus m m L x t c t c 3 . 13 ) 10 )( 33 . 1 ( ) ( 0 = = = + = γβ β γ where I used x' = L 0 . This, y x z y’ z’ x’ V=0.8c O' O Explosions simultaneously in the O'-frame L 0

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