Physics for Scientists and Engineers, Volume 1, Chapters 1-22
8th Edition
ISBN: 9781439048382
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Textbook Question
Chapter 1, Problem 1.9OQ
Newton’s second law of motion ((Chapter 5) says that the mass of an object times its acceleration is equal to the net force on the object. Which of the following gives the correct units for force? (a) kg·m/s2 (b) kg m2/s2 (c) kg/m·s2 (d) kg·m2/s (e) none of those answers
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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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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.]
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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,
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[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
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Question A2
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Suppose that A, is a covector field, and consider the object
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Chapter 1 Solutions
Physics for Scientists and Engineers, Volume 1, Chapters 1-22
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Ch. 1 - Prob. 1.8OQCh. 1 - Newtons second law of motion ((Chapter 5) says...Ch. 1 - A calculator displays a result as 1.365 218 0 X...Ch. 1 - Suppose the three fundamental standards of the...Ch. 1 - Why is the metric system of units considered...Ch. 1 - What natural phenomena could serve as alternative...Ch. 1 - Express the following quantities using the...Ch. 1 - Prob. 1.1PCh. 1 - The standard kilogram (Fig. 1.1a) is a...Ch. 1 - Prob. 1.3PCh. 1 - Prob. 1.4PCh. 1 - Prob. 1.5PCh. 1 - Prob. 1.6PCh. 1 - A crystalline solid consists of atoms stacked up...Ch. 1 - The mass of a copper atom is 1 06 10-25 kg, and...Ch. 1 - Prob. 1.9PCh. 1 - Figure P1.10 shows a frustum of a cone. Match each...Ch. 1 - Kinetic energy K (Chapter 7) has dimensions kg ...Ch. 1 - Prob. 1.12PCh. 1 - The position of a particle moving under uniform...Ch. 1 - (a) Assume the equation x = At3 + Bt describes the...Ch. 1 - A solid piece of lead has a mass of 23.94 g and a...Ch. 1 - An ore loader moves 1 200 tom/h from a mine to the...Ch. 1 - A rectangular building lot has a width of 75.0 ft...Ch. 1 - Suppose your hair grows at the rate 1/32 in. per...Ch. 1 - Why is the following situation impossible? A...Ch. 1 - A pyramid has a bright of 481 ft, and its base...Ch. 1 - The pyramid described in Problem 20 contains...Ch. 1 - Assume it takes 7.00 min to fill a 30.0-gal...Ch. 1 - A section of land has an area of 1 square mile and...Ch. 1 - A house is 50.0 ft long and 26 ft wide and has...Ch. 1 - Prob. 1.25PCh. 1 - Let AI represent the density of aluminum and Fe...Ch. 1 - One gallon of paint (volume = 3.78 103 m3) covers...Ch. 1 - Prob. 1.28PCh. 1 - Prob. 1.29PCh. 1 - Prob. 1.30PCh. 1 - Find the order of magnitude of the number of...Ch. 1 - (a) Compute the order of magnitude of the mass of...Ch. 1 - To an order of magnitude, how many piano tuners...Ch. 1 - Prob. 1.34PCh. 1 - A rectangular plate has a length of (21.310.2) cm...Ch. 1 - How many significant figures are in the following...Ch. 1 - The tropical year, the time interval from one...Ch. 1 - Carry out the arithmetic operations (a) the sum of...Ch. 1 - Review. In a community college parking lot, the...Ch. 1 - Review. While you arc on a trip to Europe, you...Ch. 1 - Review. A child is surprised that because of sales...Ch. 1 - Prob. 1.42PCh. 1 - Review. The ratio of the number of sparrows...Ch. 1 - Prob. 1.44PCh. 1 - Prob. 1.45PCh. 1 - Review. Prove that one solution of the equation...Ch. 1 - Prob. 1.47PCh. 1 - Review. A highway curve forms a section of a...Ch. 1 - Prob. 1.49PCh. 1 - Prob. 1.50PCh. 1 - Review. A student is supplied with a stack of copy...Ch. 1 - The radius of a uniform solid sphere is measured...Ch. 1 - A sidewalk is to be constructed around a swimming...Ch. 1 - Collectible coins are sometimes plated with gold...Ch. 1 - Prob. 1.55APCh. 1 - (a) What is the order of magnitude of the number...Ch. 1 - The diameter of our disk-shaped galaxy, the Milky...Ch. 1 - Why is the following situation impossible? In an...Ch. 1 - A high fountain of water is located at the center...Ch. 1 - A water fountain is at the center of a circular...Ch. 1 - The data in the following table represent...Ch. 1 - The distance from the Sun to the nearest star is...Ch. 1 - Assume there are 100 million passenger cars in the...Ch. 1 - A spherical shell has an outside radius of 2.60 cm...Ch. 1 - Bacteria and other prokaryotes are found deep...Ch. 1 - Air is blown into a spherical balloon so that,...Ch. 1 - A rod extending between x = 0 and x = 14.0 cm has...Ch. 1 - In physics, it is important to use mathematical...Ch. 1 - The consumption of natural gas by a company...Ch. 1 - A woman wishing to know the height of a mountain...Ch. 1 - Prob. 1.71APCh. 1 - Prob. 1.72APCh. 1 - You stand in a flat meadow and observe two cows...
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