College Physics: A Strategic Approach (3rd Edition)
3rd Edition
ISBN: 9780321879721
Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher: PEARSON
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Chapter P.7, Problem 15P
To determine
To explain: The type of
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ROTATIONAL DYNAMICS
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
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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]
Chapter P Solutions
College Physics: A Strategic Approach (3rd Edition)
Ch. P.1 - Prob. 1PCh. P.1 - The following questions are related to the passage...Ch. P.1 - The following questions are related to the passage...Ch. P.1 - Prob. 4PCh. P.1 - Animal Athletes Different animals have very...Ch. P.1 - Animal Athletes Different animals have very...Ch. P.1 - Animal Athletes Different animals have very...Ch. P.1 - Animal Athletes Different animals have very...Ch. P.1 - Animal Athletes Different animals have very...Ch. P.1 - The drag force on an object moving in a liquid is...
Ch. P.1 - The drag force on an object moving in a liquid is...Ch. P.1 - Sticky Liquids BIO The drag force on an object...Ch. P.1 - The drag force on an object moving in a liquid is...Ch. P.1 - Pulling Out of a Dive Falcons are excellent fliers...Ch. P.1 - Pulling Out of a Dive Falcons are excellent fliers...Ch. P.1 - Pulling Out of a Dive Falcons are excellent fliers...Ch. P.1 - Bending Beams If you bend a rod down, it...Ch. P.1 - Bending Beams If you bend a rod down, it...Ch. P.1 - Bending Beams If you bend a rod down, it...Ch. P.1 - Additional Integrated Problems 20. You go to the...Ch. P.1 - If you stand on a scale at the equator, the scale...Ch. P.1 - Additional Integrated Problems Dolphins and other...Ch. P.2 - Prob. 1PCh. P.2 - Prob. 2PCh. P.2 - Prob. 3PCh. P.2 - Prob. 4PCh. P.2 - The following passages and associated questions...Ch. P.2 - The following passages and associated questions...Ch. P.2 - The following passages and associated questions...Ch. P.2 - The following passages and associated questions...Ch. P.2 - The following passages and associated questions...Ch. P.2 - Testing Tennis Balls Tennis balls are tested by...Ch. P.2 - Testing Tennis Balls Tennis balls are tested by...Ch. P.2 - Testing Tennis Balls Tennis balls are tested by...Ch. P.2 - Squid Propulsion Squid usually move by using their...Ch. P.2 - Squid Propulsion Squid usually move by using their...Ch. P.2 - Squid Propulsion Squid usually move by using their...Ch. P.2 - Squid Propulsion Squid usually move by using their...Ch. P.2 - Teeing Off A golf club has a lightweight flexible...Ch. P.2 - Teeing Off A golf club has a lightweight flexible...Ch. P.2 - Teeing Off A golf club has a lightweight flexible...Ch. P.2 - Teeing Off A golf club has a lightweight flexible...Ch. P.2 - Additional Integrated Problems Football players...Ch. P.2 - Additional Integrated Problems The unit of...Ch. P.2 - Additional Integrated Problems A 100 kg football...Ch. P.2 - Additional Integrated Problems A swift blow with...Ch. P.2 - Additional Integrated Problems A childs sled has...Ch. P.3 - Size and Life Physicists look for simple models...Ch. P.3 - Size and Life Physicists look for simple models...Ch. P.3 - Size and Life Physicists look for simple models...Ch. P.3 - Size and Life Physicists look for simple models...Ch. P.3 - Prob. 6PCh. P.3 - Prob. 7PCh. P.3 - Prob. 8PCh. P.3 - Prob. 9PCh. P.3 - Prob. 10PCh. P.3 - Prob. 11PCh. P.3 - Prob. 12PCh. P.3 - Prob. 13PCh. P.3 - Prob. 14PCh. P.3 - Passenger Balloons Long-distance balloon flights...Ch. P.3 - Passenger Balloons Long-distance balloon flights...Ch. P.3 - Passenger Balloons Long-distance balloon flights...Ch. P.3 - Prob. 18PCh. P.3 - Prob. 19PCh. P.3 - Prob. 20PCh. P.3 - Prob. 21PCh. P.4 - Waves in the Earth and the Ocean In December 2004,...Ch. P.4 - Waves in the Earth and the Ocean In December 2004,...Ch. P.4 - Waves in the Earth and the Ocean In December 2004,...Ch. P.4 - Waves in the Earth and the Ocean In December 2004,...Ch. P.4 - Waves in the Earth and the Ocean In December 2004,...Ch. P.4 - Prob. 6PCh. P.4 - Prob. 7PCh. P.4 - Prob. 8PCh. P.4 - Prob. 9PCh. P.4 - Prob. 10PCh. P.4 - Prob. 11PCh. P.4 - Prob. 12PCh. P.4 - Prob. 13PCh. P.4 - Prob. 14PCh. P.4 - Prob. 15PCh. P.4 - Prob. 16PCh. P.4 - In the Swing A rope swing is hung from a tree...Ch. P.4 - In the Swing A rope swing is hung from a tree...Ch. P.4 - In the Swing A rope swing is hung from a tree...Ch. P.4 - Additional Integrated Problems The jumping gait of...Ch. P.4 - Prob. 21PCh. P.5 - Scanning Confocal Microscopy Although modern...Ch. P.5 - If, because of a poor-quality objective, the light...Ch. P.5 - The resolution of a scanning confocal microscope...Ch. P.5 - Prob. 4PCh. P.5 - In a horses eye, the image of a close object will...Ch. P.5 - Prob. 6PCh. P.5 - A horse is looking straight ahead at a person who...Ch. P.5 - Prob. 8PCh. 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