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Mech8Sols - Physics 105B Problem Set 8 Jeff Schonert...

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Physics 105B Problem Set 8 May 27, 2008 Je ff Schonert: schonert (at) physics.ucsb.edu Taylor 15.17 a) Let Δ t denote the time of event 2 minus the time of event 1 (and similarly for Δ t ). The time interval in S is related to the time interval S by Δ t = γ Δ t - β c Δ x We are given that Δ t = 0 and Δ x = a , so plugging in gives Δ t = - γβ a/c . b) Now consider the same problem except in a frame S that is moving with a speed of the same magnitude of S but opposite direction. This means we only need to replace β with - β in the above formula ( γ stays the same). Then we have Δ t = γ Δ t + β c Δ x = γβ a c So in S the events are simultaneous, in S event 1 happens after event 2, and in S event 1 happens before event 2. Taylor 15.22 Since S is moving along the x -axis of S with velocity . 9 c , the two relevant velocity addition formulas are ( V = . 9 c ) v x = v x + V 1 + v x V/c 2 , v y = v y γ (1 + v x V/c 2 ) Now plug in V = . 9 c , v y = . 9 c , and v x = 0. Doing this gives v x = . 9 c and v y = . 392 c . The magnitude of the velocity vector is v = ( . 392 c ) 2 + ( . 9 c ) 2 = . 98 c The angle that this vector makes with the x -axis in S is θ = arctan v y v x = arctan . 19 = 23 . 6 1
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Taylor 15.48 a) According to (15.64),
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