Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 29, Problem 25PQ
(a)
To determine
Find the current flowing through bulb
(b)
To determine
Find the current flowing through bulb
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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]
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]
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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
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Chapter 29 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 29.1 - What are the SI units of ?Ch. 29.1 - Prob. 29.2CECh. 29.2 - Prob. 29.3CECh. 29.4 - Prob. 29.5CECh. 29.4 - Prob. 29.6CECh. 29.5 - Prob. 29.7CECh. 29 - Study the symbols in Table 29.2. Then, without...Ch. 29 - Prob. 2PQCh. 29 - Prob. 3PQCh. 29 - Suppose you need to measure the potential...
Ch. 29 - Prob. 5PQCh. 29 - Prob. 6PQCh. 29 - A real battery (modeled as an ideal emf device in...Ch. 29 - Prob. 8PQCh. 29 - Two circuits made up of identical ideal emf...Ch. 29 - Prob. 10PQCh. 29 - Prob. 11PQCh. 29 - Prob. 12PQCh. 29 - Eight real batteries, each with an emf of 5.00 V...Ch. 29 - Prob. 14PQCh. 29 - Prob. 15PQCh. 29 - Prob. 16PQCh. 29 - Prob. 17PQCh. 29 - Prob. 18PQCh. 29 - Prob. 19PQCh. 29 - An ideal emf device with emf is connected to two...Ch. 29 - Prob. 21PQCh. 29 - Prob. 22PQCh. 29 - Prob. 23PQCh. 29 - Prob. 24PQCh. 29 - Prob. 25PQCh. 29 - Prob. 26PQCh. 29 - Determine the currents through the resistors R2,...Ch. 29 - The emf devices in the circuits shown in Figure...Ch. 29 - Prob. 29PQCh. 29 - Prob. 30PQCh. 29 - Prob. 31PQCh. 29 - Prob. 32PQCh. 29 - Prob. 33PQCh. 29 - Prob. 34PQCh. 29 - A Figure P29.35 shows a combination of six...Ch. 29 - A Each resistor shown in Figure P29.36 has...Ch. 29 - Each resistor shown in Figure P29.36 has a...Ch. 29 - Prob. 38PQCh. 29 - Prob. 39PQCh. 29 - The emf in Figure P29.40 is 4.54 V. The...Ch. 29 - Figure P29.41 shows three resistors (R1 = 14.0 ,...Ch. 29 - Figure P29.42 shows five resistors and two...Ch. 29 - The emfs in Figure P29.43 are 1 = 6.00 V and 2 =...Ch. 29 - Prob. 44PQCh. 29 - Figure P29.45 shows five resistors connected...Ch. 29 - Figure P29.46 shows a circuit with a 12.0-V...Ch. 29 - Two ideal emf devices are connected to a set of...Ch. 29 - Two ideal emf devices are connected to a set of...Ch. 29 - Three resistors with resistances R1 = R/2 and R2 =...Ch. 29 - Prob. 51PQCh. 29 - Prob. 52PQCh. 29 - Prob. 53PQCh. 29 - Prob. 55PQCh. 29 - At time t = 0, an RC circuit consists of a 12.0-V...Ch. 29 - A 210.0- resistor and an initially uncharged...Ch. 29 - Prob. 58PQCh. 29 - A real battery with internal resistance 0.500 and...Ch. 29 - Figure P29.60 shows a simple RC circuit with a...Ch. 29 - Prob. 61PQCh. 29 - Prob. 62PQCh. 29 - Prob. 63PQCh. 29 - Ralph has three resistors, R1, R2, and R3,...Ch. 29 - Prob. 65PQCh. 29 - An ideal emf device is connected to a set of...Ch. 29 - Prob. 67PQCh. 29 - An ideal emf device (24.0 V) is connected to a set...Ch. 29 - Prob. 69PQCh. 29 - What is the equivalent resistance between points a...Ch. 29 - A capacitor with initial charge Q0 is connected...Ch. 29 - Prob. 73PQCh. 29 - Prob. 74PQCh. 29 - Prob. 75PQCh. 29 - Prob. 76PQCh. 29 - Figure P29.77 shows a circuit with two batteries...Ch. 29 - In the RC circuit shown in Figure P29.78, an ideal...Ch. 29 - Prob. 79PQCh. 29 - Calculate the equivalent resistance between points...Ch. 29 - In Figure P29.81, N real batteries, each with an...Ch. 29 - Prob. 82PQCh. 29 - Prob. 83PQCh. 29 - Prob. 84PQCh. 29 - Figure P29.84 shows a circuit that consists of two...Ch. 29 - Prob. 86PQCh. 29 - Prob. 87PQCh. 29 - Prob. 88PQCh. 29 - Prob. 89PQCh. 29 - Prob. 90PQCh. 29 - Prob. 91PQCh. 29 - Prob. 92PQCh. 29 - Prob. 93PQCh. 29 - Prob. 94PQCh. 29 - Prob. 95PQ
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