Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Textbook Question
Chapter 18, Problem 9P
The Trans-Alaska pipeline is 1 300 km long, reaching from Prudhoe Bay to the port of Valdez. It experiences temperatures from −73°C to +35°C. How much does the steel pipeline expand because of the difference in temperature? How can this expansion be compensated for?
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
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[2 marks]
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[3 marks]
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d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
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f)
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A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Page 2
SECTION A
Answer ALL questions in Section A
[Expect to use one single-sided A4 page for each Section-A sub question.]
Question A1
SPA6308 (2024)
Consider Minkowski spacetime in Cartesian coordinates th
=
(t, x, y, z), such that
ds² = dt² + dx² + dy² + dz².
(a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V.
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u =t-x,
v=t+x.
[2 marks]
Write down the line element, the metric, the Christoffel symbols and the Riemann curvature
tensor in the new coordinates. [See the Appendix of this document.]
[5 marks]
(c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify
explicitly that V. V is invariant under the coordinate transformation.
Question A2
[5 marks]
Suppose that A, is a covector field, and consider the object
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Chapter 18 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 18.1 - Prob. 18.1QQCh. 18.3 - Consider the following pairs of materials. Which...Ch. 18.4 - If you are asked to make a very sensitive glass...Ch. 18.4 - Prob. 18.4QQCh. 18.5 - A common material for cushioning objects in...Ch. 18.5 - On a winter day, you turn on your furnace and the...Ch. 18 - Prob. 1PCh. 18 - Prob. 2PCh. 18 - Prob. 3PCh. 18 - Liquid nitrogen has a boiling point of 195.81C at...
Ch. 18 - Prob. 5PCh. 18 - Prob. 6PCh. 18 - A copper telephone wire has essentially no sag...Ch. 18 - Prob. 8PCh. 18 - The Trans-Alaska pipeline is 1 300 km long,...Ch. 18 - Prob. 10PCh. 18 - Prob. 11PCh. 18 - Prob. 12PCh. 18 - Prob. 13PCh. 18 - Why is the following situation impossible? A thin...Ch. 18 - A volumetric flask made of Pyrex is calibrated at...Ch. 18 - Review. On a day that the temperature is 20.0C, a...Ch. 18 - Prob. 17PCh. 18 - Prob. 18PCh. 18 - An auditorium has dimensions 10.0 m 20.0 m 30.0...Ch. 18 - Prob. 20PCh. 18 - Prob. 21PCh. 18 - Prob. 22PCh. 18 - In state-of-the-art vacuum systems, pressures as...Ch. 18 - Prob. 24PCh. 18 - Prob. 25PCh. 18 - Prob. 26PCh. 18 - Prob. 27PCh. 18 - Prob. 28PCh. 18 - The pressure gauge on a cylinder of gas registers...Ch. 18 - Prob. 30APCh. 18 - Prob. 31APCh. 18 - Why is the following situation impossible? An...Ch. 18 - A student measures the length of a brass rod with...Ch. 18 - Prob. 34APCh. 18 - A liquid has a density . (a) Show that the...Ch. 18 - Prob. 36APCh. 18 - Prob. 37APCh. 18 - A bimetallic strip of length L is made of two...Ch. 18 - Prob. 39APCh. 18 - A vertical cylinder of cross-sectional area A is...Ch. 18 - Prob. 41APCh. 18 - Prob. 42APCh. 18 - Prob. 43APCh. 18 - Prob. 44CPCh. 18 - A 1.00-km steel railroad rail is fastened securely...Ch. 18 - Prob. 46CP
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