Mech8Sols

Mech8Sols - Physics 105B Problem Set 8 May 27, 2008 Jeff...

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Physics 105B Problem Set 8 May 27, 2008 Jef 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 ² We are given that Δ t = 0 and Δ x = a , so plugging in gives Δ t ± = - γβa/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 ² = γβa 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 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 ± = ³ ( . 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 ² = arctan ´ . 19 µ = 23 . 6
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This note was uploaded on 07/15/2008 for the course PHYS 105 taught by Professor Martinis during the Spring '08 term at UCSB.

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Mech8Sols - Physics 105B Problem Set 8 May 27, 2008 Jeff...

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