ProblemSet2 - Problem Set 2 Physics 2216 : Due Tuesday,...

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Problem Set 2 Physics 2216 : Due Tuesday, 01/31/2012 1. Here we will develop a feeling for how the relativistic factor, γ = (1 - β 2 ) - 1 2 , varies as a function of speed, particularly at low velocities ( β = v c ). a) Perform a Taylor series expansion for γ in powers of β 2 , keeping only the first 3 terms (i.e., powers up to β 4 ). If you haven’t done this in a while, you may want to look up an old calculus textbook (here, we are assuming that β ± 1). b) The Lockheed SR-71 Blackbird spyplane was one of the fastest machines ever built. With a top speed over Mach 3 (three times the speed of sound), it could outrun a surface-to-air-missile and fly from Los Angeles to Washington DC in just about one hour. Calculate γ - 1 (i.e. the change of γ from when it is at rest) for an SR-71 flying top speed (relative to the ground). Feel free to use your calculation from (a). c) Calculate γ for values of β = 0.001 and 0.1, and compare the value computed
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ProblemSet2 - Problem Set 2 Physics 2216 : Due Tuesday,...

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