Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
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Chapter 2, Problem 2.22P
To determine
To Prove:
Particle with mass greater than zero, always has speed less than c.
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Problem 2.27: Determine the velocity for which the discrepancy between the
classical expression for the kinetic energy and the true expression
from relativity differ by 0.01%; in other words, determine the
maximum velocity for which we can use the classical expression
for the kinetic energy and trust our results to within 0.01%
accuracy.
Problem 2:
(a) Since the four-velocity u = Yu (c, u) is a four-vector, you should immediately know what its transfor-
mation properties are. Write down the standard Lorentz boost for all four components of u. Use these to
derive the relativistic velocity transformation formulas.
(b) In non-relativistic mechanics, the energy E contains an arbitrary additive constant. That is, no
1
physics is changed by the replacement E → E + Eo for any constant Eo. Using the fact that the four-
momentum p = (E/c,p2,Py, Pz) must transform like a four-vector, show that this is NOT true in relativistic
mechanics.
2.9. (a) Solve the integral
...| (dx .dx3N)
3N
and use it to determine the "volume"
the relevant region of the phase space of an extreme
relativistic gas ( = pc) of 3N particles moving in one dimension. Determine, as well, the
number of ways of distributing a given energy E among this system of particles and show that,
asymptotically, w0 = h³N.
(b) Compare the thermodynamics of this system with that of the system considered in Problem 2.8.
Chapter 2 Solutions
Modern Physics For Scientists And Engineers
Ch. 2 - Prob. 2.1PCh. 2 - Prob. 2.2PCh. 2 - Prob. 2.3PCh. 2 - Prob. 2.4PCh. 2 - Prob. 2.5PCh. 2 - Prob. 2.6PCh. 2 - Prob. 2.7PCh. 2 - Prob. 2.8PCh. 2 - Prob. 2.9PCh. 2 - Prob. 2.10P
Ch. 2 - Prob. 2.11PCh. 2 - Prob. 2.12PCh. 2 - Prob. 2.13PCh. 2 - Prob. 2.14PCh. 2 - Prob. 2.15PCh. 2 - Prob. 2.16PCh. 2 - Prob. 2.17PCh. 2 - Prob. 2.18PCh. 2 - Prob. 2.19PCh. 2 - Prob. 2.20PCh. 2 - Prob. 2.21PCh. 2 - Prob. 2.22PCh. 2 - Prob. 2.23PCh. 2 - Prob. 2.24PCh. 2 - Prob. 2.25PCh. 2 - Prob. 2.26PCh. 2 - Prob. 2.27PCh. 2 - Prob. 2.28PCh. 2 - Prob. 2.29PCh. 2 - Prob. 2.30PCh. 2 - Prob. 2.31PCh. 2 - Prob. 2.32PCh. 2 - Prob. 2.33PCh. 2 - Prob. 2.34PCh. 2 - Prob. 2.35PCh. 2 - Prob. 2.36PCh. 2 - Prob. 2.37PCh. 2 - Prob. 2.38PCh. 2 - Prob. 2.39PCh. 2 - Prob. 2.40PCh. 2 - Prob. 2.41PCh. 2 - Prob. 2.42PCh. 2 - Prob. 2.43PCh. 2 - Prob. 2.44PCh. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - Prob. 2.47PCh. 2 - Prob. 2.48PCh. 2 - Prob. 2.49PCh. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - Prob. 2.52P
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