PHYSICS:F/SCI.+ENGRS.(LL)-W/SINGLE CARD
10th Edition
ISBN: 9781337888547
Author: SERWAY
Publisher: CENGAGE L
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Chapter 14, Problem 25P
Review. Old Faithful Geyser in Yellowstone National Park erupts at approximately one-hour intervals, and the height of the water column reaches 40.0 m (Fig. P14.25). (a) Model the rising stream as a series of separate droplets. Analyze the free-fall motion of one of the droplets to determine the speed at which the water leaves the ground. (b) What If? Model the rising stream as an ideal fluid in streamline flow. Use Bernoulli’s equation to determine the speed of the water as it leaves ground level. (c) How does the answer from part (a) compare with the answer from part (b)? (d) What is the pressure (above atmospheric) in the heated underground chamber if its depth is 175 m? Assume the chamber is large compared with the geyser’s vent.
Figure P14.25
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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
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+
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 14 Solutions
PHYSICS:F/SCI.+ENGRS.(LL)-W/SINGLE CARD
Ch. 14.1 - Suppose you are standing directly behind someone...Ch. 14.2 - The pressure at the bottom of a filled glass of...Ch. 14.3 - Several common barometers are built, with a...Ch. 14.4 - You are shipwrecked and floating in the middle of...Ch. 14.6 - You observe two helium balloons floating next to...Ch. 14 - A large man sits on a four-legged chair with his...Ch. 14 - Prob. 2PCh. 14 - Estimate the total mass of the Earths atmosphere....Ch. 14 - Prob. 4PCh. 14 - What must be the contact area between a suction...
Ch. 14 - Prob. 6PCh. 14 - Review. A solid sphere of brass (bulk modulus of...Ch. 14 - The human brain and spinal cord are immersed in...Ch. 14 - Blaise Pascal duplicated Torricellis barometer...Ch. 14 - A tank with a flat bottom of area A and vertical...Ch. 14 - Prob. 11PCh. 14 - A 10.0-kg block of metal measuring 12.0 cm by 10.0...Ch. 14 - A plastic sphere floats in water with 50.0% of its...Ch. 14 - The weight of a rectangular block of low-density...Ch. 14 - A wooden block of volume 5.24 104 m3 floats in...Ch. 14 - A hydrometer is an instrument used to determine...Ch. 14 - Refer to Problem 16 and Figure P14.16. A...Ch. 14 - On October 21, 2001, Ian Ashpole of the United...Ch. 14 - Prob. 19PCh. 14 - Water flowing through a garden hose of diameter...Ch. 14 - Water falls over a dam of height h with a mass...Ch. 14 - A legendary Dutch boy saved Holland by plugging a...Ch. 14 - Water is pumped up from the Colorado River to...Ch. 14 - In ideal flow, a liquid of density 850 kg/m3 moves...Ch. 14 - Review. Old Faithful Geyser in Yellowstone...Ch. 14 - You are working as an expert witness for the owner...Ch. 14 - A thin 1.50-mm coating of glycerin has been placed...Ch. 14 - A hypodermic needle is 3.00 cm in length and 0.300...Ch. 14 - What radius needle should be used to inject a...Ch. 14 - An airplane has a mass of 1.60 104 kg, and each...Ch. 14 - Prob. 31PCh. 14 - Decades ago, it was thought that huge herbivorous...Ch. 14 - Prob. 33APCh. 14 - The true weight of an object can be measured in a...Ch. 14 - Prob. 35APCh. 14 - Review. Assume a certain liquid, with density 1...Ch. 14 - Evangelista Torricelli was the first person to...Ch. 14 - A common parameter that can be used to predict...Ch. 14 - In 1983, the United States began coining the...Ch. 14 - Review. With reference to the dam studied in...Ch. 14 - The spirit-in-glass thermometer, invented in...Ch. 14 - A woman is draining her fish tank by siphoning the...Ch. 14 - Prob. 43APCh. 14 - Prob. 44APCh. 14 - Prob. 45APCh. 14 - Review. In a water pistol, a piston drives water...Ch. 14 - Prob. 47APCh. 14 - The hull of an experimental boat is to be lifted...Ch. 14 - Show that the variation of atmospheric pressure...Ch. 14 - Why is the following situation impossible? A barge...
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