Fundamentals of Physics Extended
10th Edition
ISBN: 9781118230725
Author: David Halliday, Robert Resnick, Jearl Walker
Publisher: Wiley, John & Sons, Incorporated
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Chapter 1, Problem 28P
To determine
To find:
Number of moles of atoms in a large domestic cat.
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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
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)
none of the previous. Justify your answer.
f)
[5 marks]
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.
(b) Consider now the coordinate system x' (u, v, y, z) such that
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
Fv=AAμ.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
[5 marks]
(b)…
Chapter 1 Solutions
Fundamentals of Physics Extended
Ch. 1 - Prob. 1PCh. 1 - A gry is an old English measure for length,...Ch. 1 - The micrometer 1 m is often called the micron. a...Ch. 1 - Spacing in this book was generally done in units...Ch. 1 - SM WWW Horses are to race over a certain English...Ch. 1 - You can easily convert common units and measures...Ch. 1 - ILW Hydraulic engineers in the United States often...Ch. 1 - GO Harvard Bridge, which connects MIT with its...Ch. 1 - Antarctica is roughly semicircular, with a radius...Ch. 1 - Until 1883, every city and town in the United...
Ch. 1 - wor about 10 years after the French Revolution,...Ch. 1 - The fastest growing plant on record is a...Ch. 1 - GO Three digital clocks A, B, and C run at...Ch. 1 - A lecture period 50 mm is close to 1 microcentury....Ch. 1 - A fortnight is a charming English measure of time...Ch. 1 - Prob. 16PCh. 1 - SSM Five clocks are being tested in a laboratory....Ch. 1 - Because Earths rotation is gradually slowing, the...Ch. 1 - Suppose that, while lying on a beach near the...Ch. 1 - GO The record for the largest glass bottle was set...Ch. 1 - Earth has mass of 5.98 1024 kg. The average mass...Ch. 1 - Gold, which has a density of 19.32 g/cm3, is the...Ch. 1 - Prob. 23PCh. 1 - GO Grains of fine California beach sand are...Ch. 1 - During heavy rain, a section of a mountainside...Ch. 1 - Prob. 26PCh. 1 - Prob. 27PCh. 1 - Prob. 28PCh. 1 - On a spending spree in Malaysia, you buy an ox...Ch. 1 - Prob. 30PCh. 1 - Prob. 31PCh. 1 - Prob. 32PCh. 1 - SSM A ton is a measure of volume frequently used...Ch. 1 - Two types of barrel units were in use in the 1920s...Ch. 1 - An old English childrens rhyme states, Little Miss...Ch. 1 - Table 1-7 shows some old measures of liquid...Ch. 1 - A typical sugar cube has an edge length of 1 cm....Ch. 1 - An old manuscript reveals that a landowner in the...Ch. 1 - SSM A tourist purchases a car in England and ships...Ch. 1 - Prob. 40PCh. 1 - SSM A cord is a volume of cut wood equal to a...Ch. 1 - One molecule of water H2O contains two atoms of...Ch. 1 - A person on a diet might lose 2.3 kg per week....Ch. 1 - What mass of water fell on the town in Problem 7?...Ch. 1 - a A unit of time sometimes used in microscopic...Ch. 1 - A unit of area often used in measuring land areas...Ch. 1 - SSM An astronomical unit AU is the average...Ch. 1 - Prob. 48PCh. 1 - A traditional unit of length in Japan is the ken 1...Ch. 1 - You receive orders to sail due east for 24.5 mi to...Ch. 1 - The cubit is an ancient unit of length based on...Ch. 1 - As a contrast between the old and the modern and...Ch. 1 - SSM An astronomical unit AU is equal to the...Ch. 1 - The description for a certain brand of house paint...Ch. 1 - Strangely, the wine for a large wedding reception...Ch. 1 - The corn-hog ratio is a financial term used in the...Ch. 1 - You are to fix dinners for 400 people at a...Ch. 1 - A standard interior staircase has steps each with...Ch. 1 - In purchasing food for a political rally, you...Ch. 1 - An old English cookbook carries this recipe for...
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