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
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 SHEN
 Physics, Particle Physics, Electron, Special Relativity, sea level, Darth Vader, Muon

Click to edit the document details