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9D Discussion Problem

# 9D Discussion Problem - 01 sec to make the trip At what...

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Some review and problems for discussion sections J. Gunion U.C. Davis 9D, Spring Quarter J. Gunion

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Discussion 1 1. Do you really understand the LT equations? Why GT equations don’t work Suppose x = x - vt , t = t (1) Can these GT relations be consistent with x = ct and x = ct (frame equivalence for light)? Answer is NO. Check. x = x - vt ct = ct - vt = ( c - v ) t = ( c - v ) t (2) is a contradiction. Try LT: x = γ ( x - vt ) , t = γ ( t - v c 2 x ) (3) J. Gunion 9D, Spring Quarter 1
and plug in x = ct and x = ct . ct = γ ( c - v ) t , ct = γ ( ct - v c ct ) = γ ( c - v ) t (4) means that the two equations are consistent. To get γ ( v ) must go through process given in class notes proof of LT. 2. The LA to SF bullet train. Suppose the distance as measured on the ground is 10 6 m (a thousand km). Suppose a passenger on the train claims it takes

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Unformatted text preview: . 01 sec to make the trip. At what speed was the train traveling? Answer: The passenger sees a length contracted distance of L = L/γ = 10 6 m/γ . Combine with his observation of trip time to conclude that . 01 sec = L v = L γv = 10 6 γv (5) J. Gunion 9D, Spring Quarter 2 or 10 6 m = 0 . 01 sec × γv = 0 . 01 sec × v q 1-v 2 c 2 . (6) Dividing out the . 01 and squaring, we get 10 16 m 2 /s 2 = v 2 1-v 2 c 2 (7) or 10 16-10 16 v 2 9 × 10 16 = v 2 (8) or 10 16 = v 2 (1 + 1 9 ) = v 2 10 9 (9) or v = 10 8 r 9 10 m/s = c √ 10 . (10) J. Gunion 9D, Spring Quarter 3...
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9D Discussion Problem - 01 sec to make the trip At what...

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