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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Textbook Question
Chapter 11, Problem 29P
A newly proposed device for generating electricity from the sun is a
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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 11 Solutions
College Physics: A Strategic Approach (3rd Edition)
Ch. 11 - Rub your hands together vigorously. What happens?...Ch. 11 - Describe the energy transfers and transformations...Ch. 11 - According to Table 11.4, cycling at 15 km/h...Ch. 11 - Prob. 4CQCh. 11 - For most automobiles, the number of miles per...Ch. 11 - A glassblower heats up a blob of glass in a...Ch. 11 - When the space shuttle returns to earth, its...Ch. 11 - Prob. 8CQCh. 11 - Prob. 9CQCh. 11 - A 20 kg block of steel at 23C and a 150 g piece of...
Ch. 11 - Prob. 11CQCh. 11 - For Questions 12 through 17, give a specific...Ch. 11 - For Questions 12 through 17, give a specific...Ch. 11 - For Questions 12 through 17, give a specific...Ch. 11 - For Questions 12 through 17, give a specific...Ch. 11 - For Questions 12 through 17, give a specific...Ch. 11 - For Questions 12 through 17, give a specific...Ch. 11 - A fire pistonan impressive physics...Ch. 11 - Prob. 19CQCh. 11 - A drop of green ink falls into a beaker of clear...Ch. 11 - Prob. 21CQCh. 11 - Prob. 22CQCh. 11 - According to the second law of thermodynamics, it...Ch. 11 - Assuming improved materials and better processes,...Ch. 11 - Electric vehicles increase speed by using an...Ch. 11 - When the suns light hits the earth, the...Ch. 11 - When you put an ice cube tray filled with liquid...Ch. 11 - Prob. 28CQCh. 11 - A person is walking on level ground at constant...Ch. 11 - A person walks 1 km, turns around, and runs back...Ch. 11 - Prob. 31MCQCh. 11 - 200 J of heat is added to two gases, each in a...Ch. 11 - An inventor approaches you with a device that he...Ch. 11 - Prob. 34MCQCh. 11 - Prob. 35MCQCh. 11 - A refrigerators freezer compartment is set at 10C;...Ch. 11 - A 10% efficient engine accelerates a 1500 kg car...Ch. 11 - Prob. 2PCh. 11 - A typical photovoltaic cell delivers 4.0 103 W of...Ch. 11 - Prob. 4PCh. 11 - A fast-food hamburger (with cheese and bacon)...Ch. 11 - In an average human, basic life processes require...Ch. 11 - An energy bar contains 6.0 g of fat. How much...Ch. 11 - An energy bar contains 22 g of carbohydrates. How...Ch. 11 - Prob. 9PCh. 11 - An energy bar contains 22 g of carbohydrates. If...Ch. 11 - Suppose your body was able to use the chemical...Ch. 11 - The label on a candy bar says 400 Calories....Ch. 11 - A weightlifter curls a 30 kg bar, raising it each...Ch. 11 - Prob. 14PCh. 11 - Prob. 15PCh. 11 - The planet Mercurys surface temperature varies...Ch. 11 - A piece of metal at 100C has its Celsius...Ch. 11 - Prob. 18PCh. 11 - 500 J of work are done on a system in a process...Ch. 11 - 600 J of heat energy are transferred to a system...Ch. 11 - 300 J of energy are transferred to a system in the...Ch. 11 - 10 J of heat are removed from a gas sample while...Ch. 11 - A heat engine extracts 55 kJ from the hot...Ch. 11 - A heat engine does 20 J of work while exhausting...Ch. 11 - A heat engine does 200 J of work while exhausting...Ch. 11 - A heat engine with an efficiency of 40% does 100 J...Ch. 11 - A power plant running at 35% efficiency generates...Ch. 11 - A heat engine operating between energy reservoirs...Ch. 11 - A newly proposed device for generating electricity...Ch. 11 - Converting sunlight to electricity with solar...Ch. 11 - A refrigerator takes in 20 J of work and exhausts...Ch. 11 - Air conditioners are rated by their coefficient of...Ch. 11 - 50 J of work are done on a refrigerator with a...Ch. 11 - Find the maximum possible coefficient of...Ch. 11 - Which, if any, of the heat engines in Figure...Ch. 11 - Which, if any, of the refrigerators in Figure...Ch. 11 - Prob. 37PCh. 11 - Prob. 38GPCh. 11 - Prob. 39GPCh. 11 - For how long would a 68 kg athlete have to swim at...Ch. 11 - a. How much metabolic energy is required for a 68...Ch. 11 - Prob. 42GPCh. 11 - Prob. 43GPCh. 11 - The record time for a Tour de France cyclist to...Ch. 11 - Championship swimmers take about 22 s and about 30...Ch. 11 - A 68 kg hiker walks at 5.0 km/h up a 7% slope....Ch. 11 - A 70 kg student consumes 2500 Cal each day and...Ch. 11 - To make your workouts more productive, you can get...Ch. 11 - The resistance of an exercise bike is often...Ch. 11 - Prob. 50GPCh. 11 - Prob. 51GPCh. 11 - A large horse can perform work at a steady rate of...Ch. 11 - A heat engine with a high-temperature reservoir at...Ch. 11 - An engine does 10 J of work and exhausts 15 J of...Ch. 11 - The heat exhausted to the cold reservoir of an...Ch. 11 - An engine operating at maximum theoretical...Ch. 11 - Some heat engines can run on very small...Ch. 11 - The coefficient of performance of a refrigerator...Ch. 11 - An engineer claims to have measured the...Ch. 11 - A 32% efficient electric power plant produces 900...Ch. 11 - A typical coal-fired power plant burns 300 metric...Ch. 11 - Each second, a nuclear power plant generates 2000...Ch. 11 - Prob. 63GPCh. 11 - Prob. 64GPCh. 11 - Air conditioners sold in the United States are...Ch. 11 - The surface waters of tropical oceans are at a...Ch. 11 - The light energy that falls on a square meter of...Ch. 11 - MCAT-Style Passage Problems Kangaroo Locomotion...Ch. 11 - MCAT-Style Passage Problems Kangaroo Locomotion...Ch. 11 - MCAT-Style Passage Problems Kangaroo Locomotion...Ch. 11 - MCAT-Style Passage Problems Kangaroo Locomotion...Ch. 11 - MCAT-Style Passage Problems Kangaroo Locomotion...
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