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3063_Exam1_sp06

# 3063_Exam1_sp06 - PHY3063 Spring 2006 R D Field PHY 3063...

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PHY3063 Spring 2006 R. D. Field Exam 1 Page 1 of 8 January 31, 2006 PHY 3063 Exam 1 Name_____________________ Problem 1 (25 points): A rod with is at rest in the O-frame ( parallel to the x-axis ) with the left end of the rod ( L ) at x = 0 and right end ( R ) at x = R and a cart with rest length L 0 = 300 m is at rest in the O'-frame ( parallel to the x'-axis ) with the right end of the cart ( r ) at x' = 0 and left end (l) at x' = -L 0 . as shown in the figure . The O'-frame is moving to the right along the positive x-axis of the O-frame with velocity V = 0.8c and the origins of the two frames coincide at t = t' = 0 . (Note that c = 3×10 8 m/s.) Consider the following four events: Event Description A Right end of cart crosses left end of rod (Lr) B Right end of cart crosses right end of rod (Rr) C Left end of cart crosses left end of rod (Ll) D Left end of cart crosses right end of rod (Rl) In the O-frame event B and event C occur simultaneously ( i.e. 0 = = B C t t t ). Part A (10 points): Plot the four events A , B , C , and D on the space-time plots below and label the (ct, x) coordinates of each event in the O-frame and the (ct',x') coordinates of each event in the O'-frame . (Express the coordinates in terms of c, β , γ , and L 0 ). . O-frame x ct O'-frame x' ct' Part B (5 points): How long ( in microseconds ) does it take for the cart to cross over the rod according to an observer in the O-frame ( i.e. what is A D t t t = )?

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