An Introduction to Physical Science
14th Edition
ISBN: 9781305079137
Author: James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Publisher: Cengage Learning
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Chapter 1, Problem 1E
To determine
In one kilometer determine the number of centimeters.
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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]
Chapter 1 Solutions
An Introduction to Physical Science
Ch. 1.1 - What are the two major divisions of natural...Ch. 1.1 - What are the five major divisions of physical...Ch. 1.2 - What does the scientific method say about the...Ch. 1.2 - Do scientific laws and legal laws have anything in...Ch. 1.3 - Which two senses give us the most information...Ch. 1.3 - How may our senses be enhanced?Ch. 1.4 - Prob. 1PQCh. 1.4 - Prob. 2PQCh. 1.5 - What are the four most common metric prefixes?Ch. 1.5 - What is the difference between a cubic centimeter...
Ch. 1.6 - Prob. 1PQCh. 1.6 - Prob. 2PQCh. 1.6 - A sample of gold has the same mass as that of the...Ch. 1.6 - In a football game, you often hear the expression...Ch. 1.6 - Prob. 1.3CECh. 1.7 - What is the purpose of significant figures?Ch. 1.7 - Why are mathematical results rounded?Ch. 1.7 - Prob. 1.4CECh. 1 - KEY TERMS 1. science (1.1) 2. scientific method...Ch. 1 - KEY TERMS
science (1.1) scientific method...Ch. 1 - Prob. CMCh. 1 - Prob. DMCh. 1 - KEY TERMS 1. science (1.1) 2. scientific method...Ch. 1 - Prob. FMCh. 1 - Prob. GMCh. 1 - Prob. HMCh. 1 - Prob. IMCh. 1 - KEY TERMS 1. science (1.1) 2. scientific method...Ch. 1 - Prob. KMCh. 1 - KEY TERMS 1. science (1.1) 2. scientific method...Ch. 1 - Prob. MMCh. 1 - Prob. NMCh. 1 - Prob. OMCh. 1 - Prob. PMCh. 1 - Prob. QMCh. 1 - Prob. RMCh. 1 - KEY TERMS 1. science (1.1) 2. scientific method...Ch. 1 - Prob. TMCh. 1 - Prob. UMCh. 1 - Prob. VMCh. 1 - Prob. WMCh. 1 - Which is the most fundamental of the physical...Ch. 1 - Which of the following is a concise statement...Ch. 1 - Which human sense is second in supplying the most...Ch. 1 - Which is the standard unit of mass in the metric...Ch. 1 - Which of the following is not a fundamental...Ch. 1 - Which metric prefix means one-thousandth? (a)...Ch. 1 - Which metric prefix means thousand? (a) centi- (b)...Ch. 1 - Which of the following metric prefixes is the...Ch. 1 - Prob. 9MCCh. 1 - Prob. 10MCCh. 1 - What is the expression 1 in. = 2.54 cm properly...Ch. 1 - Prob. 12MCCh. 1 - Which of the following numbers has the greatest...Ch. 1 - Prob. 1FIBCh. 1 - A possible explanation of observations is called...Ch. 1 - According to the ___, no hypothesis or theory of...Ch. 1 - Prob. 4FIBCh. 1 - Prob. 5FIBCh. 1 - Prob. 6FIBCh. 1 - Prob. 7FIBCh. 1 - Unlike mass, weight is not a(n) ___ property....Ch. 1 - The standard unit of ___ is the same in all...Ch. 1 - Prob. 10FIBCh. 1 - A common nonstandard metric unit of fluid volume...Ch. 1 - If A is denser than B, then A contains more ___...Ch. 1 - Prob. 1SACh. 1 - What are the five major divisions of physical...Ch. 1 - What is the first element of the scientific...Ch. 1 - Which generally comes first in solving problems,...Ch. 1 - Prob. 5SACh. 1 - What does the controversy over the face on Mars...Ch. 1 - How do the five senses rank in importance in...Ch. 1 - The senses cannot be completely relied on. Why?Ch. 1 - Prob. 9SACh. 1 - Why are some quantities called fundamental?Ch. 1 - A standard unit must have what characteristics?Ch. 1 - What makes up a system of units?Ch. 1 - For a given speed limit, would the numerical value...Ch. 1 - Prob. 14SACh. 1 - What standard metric unit is referenced to an...Ch. 1 - Prob. 16SACh. 1 - Prob. 17SACh. 1 - How is the decimal base 10 of the metric system an...Ch. 1 - Prob. 19SACh. 1 - Prob. 20SACh. 1 - Prob. 21SACh. 1 - Prob. 22SACh. 1 - Prob. 23SACh. 1 - In general, when a derived unit becomes...Ch. 1 - Prob. 25SACh. 1 - Prob. 26SACh. 1 - Prob. 27SACh. 1 - Prob. 28SACh. 1 - If you multiplied 9874 m by 36 m, how many...Ch. 1 - Prob. 1VCCh. 1 - Prob. 1ECh. 1 - Prob. 2ECh. 1 - What is the volume of a liter in cubic...Ch. 1 - Show that 1 cubic meter contains 1000 L.Ch. 1 - Water is sold in half-liter bottles. What is the...Ch. 1 - A rectangular container measuring 10 cm 20 cm 25...Ch. 1 - Write the following quantities in standard units....Ch. 1 - Fill in the blanks with the correct numbers for...Ch. 1 - Compute, in centimeters and in meters, the height...Ch. 1 - If the DNA strand in a molecule could be stretched...Ch. 1 - Prob. 11ECh. 1 - If we changed our speed limit signs to metric,...Ch. 1 - Is the following statement reasonable? (Justify...Ch. 1 - Is the following statement reasonable? The area of...Ch. 1 - Prob. 15ECh. 1 - The Hoover Dam Bridge connecting Arizona and...Ch. 1 - A popular saying is Give him an inch, and hell...Ch. 1 - A metric ton is 1000 kg, and a British ton is 2000...Ch. 1 - Compute the density in g/cm3 of a piece of metal...Ch. 1 - What is the volume of a piece of iron ( = 7.9...Ch. 1 - Round the following numbers to two significant...Ch. 1 - Round the following numbers to three significant...Ch. 1 - Round the following numbers to three significant...Ch. 1 - Round the following numbers to four significant...Ch. 1 - What is the result of (3.15 m 1.53 m)/0.78 m with...Ch. 1 - The calculator result of multiplying 2.15 is...
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