hw3 - at the exact middle of the rocket and the x’ axis...

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PHYS126 Spring 2011 Homework 3 Due Feb 25, beginning of lecture. 1. Beiser (textbook), Chapter 1, Exercise 21. 2. Lecture 3: Slide #28 We have shown that when measured at t’ = 0 in {s’}, length contraction results. We now decide to do this length measurement at some other t’, say, at t’= - γ V L o /c 2 . Show that the same length contraction is obtained (as it must be.) 3. Lecture 4: slide #7 Derive the velocity addition formula starting from the Lorentz transform. Note that even for motion along the x direction, even though y’ = y and z’ = z, u’ y and u’ z are NOT the same as u y and u z . Explain why. 4. Lecture 4: slide #12 Starting with Lorentz Transformation, show that the quantity c 2 ( t) 2 – ( x) 2 is an invariant, i.e., c 2 ( t) 2 – ( x) 2 = c 2 ( t’) 2 – ( x’) 2 5.A traveler in a rocket of length 2 l sets up a coordinate system S’ with origin O’ located
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Unformatted text preview: at the exact middle of the rocket and the x’ axis along the rocket’s length. At t’=0 he ignites a flashbulb at O’. (a) Write down the coordinates , and , for the arrival of the light at the front and back of the rocket. (b) Now consider the same experiment as observed in a frame S relative to which the rocket is traveling at speed v (with S and S’ arranged in the standard configuration). Use the Lorentz transformation to find the coordinates , and , of the arrival of the two signals. Explain clearly why the two times are not equal in frame S, although they were in S’. (This illustrates how two events that are simultaneous in S’ are not necessarily simultaneous in S.) 6. Beiser (textbook), Chapter 1, Exercise 16....
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