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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 SR71 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
surfacetoairmissile 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 SR71 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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 Spring '11
 SHEN
 Physics, Special Relativity

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