Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
4th Edition
ISBN: 9780134110684
Author: Randall D. Knight (Professor Emeritus)
Publisher: PEARSON
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Textbook Question
Chapter 28, Problem 23EAP
What is the value of resistor R in FIGURE EX28.23?
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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
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(b)…
Chapter 28 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Ch. 28 - Rank in order, from largest to smallest, the...Ch. 28 - The tip of a flashlight bulb is touching the top...Ch. 28 - The wire is broken on the right side of the...Ch. 28 - The circuit of FIGURE Q28.4 has two resistors,...Ch. 28 - The circuit of FIGURE Q28.5 has two resistors,...Ch. 28 - Rank in order, from largest to smallest, the...Ch. 28 - Are the two resistors in FIGURE Q28.7 in series or...Ch. 28 - A battery with internal resistance r is connected...Ch. 28 - Initially bulbs A and B in FIGURE Q28.9 are...Ch. 28 - Bulbs A. B, and C in FIGURE Q28.1O axe identical,...
Ch. 28 - Bulbs A and B in FIGURE Q28.11 are identical, and...Ch. 28 - Prob. 12CQCh. 28 - FIGURE Q28.13 shows the voltage as a function of...Ch. 28 - Prob. 1EAPCh. 28 - Draw a circuit diagram for the circuit of FIGURE...Ch. 28 - Prob. 3EAPCh. 28 - Prob. 4EAPCh. 28 - a. What are the magnitude and direction of the...Ch. 28 - What is the magnitude of the potential difference...Ch. 28 - Prob. 7EAPCh. 28 - Prob. 8EAPCh. 28 - A 60 W lightbulb and a 100 W lightbulb are placed...Ch. 28 - Prob. 10EAPCh. 28 - The five identical bulbs in FIGURE EX2B.11 are all...Ch. 28 - Prob. 12EAPCh. 28 - Prob. 13EAPCh. 28 - A typical American family uses kWh of electricity...Ch. 28 - A waterbed heater uses 450 W of power. It is on 25...Ch. 28 - Prob. 16EAPCh. 28 - Prob. 17EAPCh. 28 - Prob. 18EAPCh. 28 - 19. The voltage across the terminals of a V...Ch. 28 - Prob. 20EAPCh. 28 - Prob. 21EAPCh. 28 - 22. Two of the three resistors in FIGURE EX28.22...Ch. 28 - What is the value of resistor R in FIGURE EX28.23?Ch. 28 - Prob. 24EAPCh. 28 - What is the equivalent resistance between points a...Ch. 28 - What is the equivalent resistance between points a...Ch. 28 - Prob. 27EAPCh. 28 - Prob. 28EAPCh. 28 - Prob. 29EAPCh. 28 - Prob. 30EAPCh. 28 - Prob. 31EAPCh. 28 - Prob. 32EAPCh. 28 - Prob. 33EAPCh. 28 - What is the time constant for the discharge of the...Ch. 28 - A 10F capacitor initially charged to 20C is...Ch. 28 - Prob. 36EAPCh. 28 - Prob. 37EAPCh. 28 - A capacitor is discharged through a resistor. The...Ch. 28 - Prob. 39EAPCh. 28 - 40. A refrigerator has a 1000 W compressor, but...Ch. 28 - Prob. 41EAPCh. 28 - An electric eel develops a potential difference...Ch. 28 - You have a resistor, a resistor, a resistor, and a...Ch. 28 - A 2.0 -m-long, 1.0 -mm-diameter wire has a...Ch. 28 - What is the equivalent resistance between points a...Ch. 28 - What are the emf and internal resistance of the...Ch. 28 - A string of holiday lights can be wired in series,...Ch. 28 - The circuit shown in FIGURE P28.48 is inside a 15...Ch. 28 - Suppose you have resistors 2.5,3.5, and 4.5 and a...Ch. 28 - A lightbulb is in series with a resistor. The...Ch. 28 - Prob. 51EAPCh. 28 - Prob. 52EAPCh. 28 - Prob. 53EAPCh. 28 - Prob. 54EAPCh. 28 - What are the battery current Ibatand the potential...Ch. 28 - A battery is a voltage source, always providing...Ch. 28 - A circuit you’re building needs an ammeter that...Ch. 28 - For the circuit shown in FIGURE P28.58, find the...Ch. 28 - For the circuit shown in FIGURE P28.59, find the...Ch. 28 - For the circuit shown in FIGURE P28.60, find the...Ch. 28 - What is the current through the 20 resistor in...Ch. 28 - For the circuit shown in FIGURE P28.62, find the...Ch. 28 - What is the current through the 10 resistor in...Ch. 28 - For what emf does the 200 resistor in FIGURE...Ch. 28 - Prob. 65EAPCh. 28 - Prob. 66EAPCh. 28 - Prob. 67EAPCh. 28 - II A circuit you're using discharges a 20F...Ch. 28 - A 150F defibrillator capacitor is charged to 1500V...Ch. 28 - Prob. 70EAPCh. 28 - A 0.25F capacitor is charged to 50 V. It is then...Ch. 28 - Prob. 72EAPCh. 28 - Prob. 73EAPCh. 28 - The capacitors in FIGURE P28.74 are charged and...Ch. 28 - Prob. 75EAPCh. 28 - Prob. 76EAPCh. 28 - Prob. 77EAPCh. 28 - Prob. 78EAPCh. 28 - Prob. 79EAPCh. 28 - Prob. 80EAPCh. 28 - Prob. 81EAPCh. 28 - Prob. 82EAP
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