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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Chapter 27, Problem 49EAP
To determine
The temperature of metal at which it has the resistance
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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 27 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Ch. 27 - Prob. 1CQCh. 27 - Prob. 2CQCh. 27 - The electron drift speed in a wire is exceedingly...Ch. 27 - Prob. 4CQCh. 27 - Prob. 5CQCh. 27 - All the wires in FIGURE Q27.6 are made of the same...Ch. 27 - Both batteries in FIGURE Q27.7 are ideal and...Ch. 27 - Both batteries in FIGURE Q27.8 are ideal and...Ch. 27 - The wire in FIGURE Q27.9 consists of two segments...Ch. 27 - Prob. 10CQ
Ch. 27 - ll. The wires in FIGURE Q27.11 are all made of the...Ch. 27 - Which, if any, of these statements are true? (More...Ch. 27 - Prob. 1EAPCh. 27 - Prob. 2EAPCh. 27 - .0 × 1016 electrons flow through a cross section...Ch. 27 - Prob. 4EAPCh. 27 - Prob. 5EAPCh. 27 - Prob. 6EAPCh. 27 - Prob. 7EAPCh. 27 - Prob. 8EAPCh. 27 - Prob. 9EAPCh. 27 - Prob. 10EAPCh. 27 - Prob. 11EAPCh. 27 - The current in an electric hair dryer is 10.0 A....Ch. 27 -
13. When a nerve cell fires, charge is...Ch. 27 - Prob. 14EAPCh. 27 - Prob. 15EAPCh. 27 - Prob. 16EAPCh. 27 - Prob. 17EAPCh. 27 - Prob. 18EAPCh. 27 - Prob. 19EAPCh. 27 - Prob. 20EAPCh. 27 - Prob. 21EAPCh. 27 - Prob. 22EAPCh. 27 - Prob. 23EAPCh. 27 - 24. The two segments of the wire in FIGURE EX27.24...Ch. 27 - A 1.5 V battery provides 0.50 A of current. a. At...Ch. 27 - Prob. 26EAPCh. 27 - Prob. 27EAPCh. 27 - Prob. 28EAPCh. 27 - Prob. 29EAPCh. 27 - Prob. 30EAPCh. 27 - Prob. 31EAPCh. 27 - Prob. 32EAPCh. 27 - Prob. 33EAPCh. 27 - Prob. 34EAPCh. 27 - Prob. 35EAPCh. 27 - Prob. 36EAPCh. 27 - Prob. 37EAPCh. 27 - Prob. 38EAPCh. 27 - Prob. 39EAPCh. 27 - Prob. 40EAPCh. 27 - Prob. 41EAPCh. 27 - Prob. 42EAPCh. 27 - Prob. 43EAPCh. 27 - Prob. 44EAPCh. 27 - Prob. 45EAPCh. 27 - Prob. 46EAPCh. 27 - Prob. 47EAPCh. 27 - Prob. 48EAPCh. 27 - Prob. 49EAPCh. 27 - Variations in the resistivity of blood can give...Ch. 27 - The conducting path between the right hand and the...Ch. 27 - The conductive tissues of the upper leg can be...Ch. 27 - The resistivity of a metal increases slightly with...Ch. 27 - Prob. 54EAPCh. 27 - You need to design a 1.0 A fuse that “blows” if...Ch. 27 - I A hollow metal cylinder has inner radius a....Ch. 27 - A hollow metal sphere has inner radius a, outer...Ch. 27 - The total amount of charge in coulombs that has...Ch. 27 - The total amount of charge that has entered a wire...Ch. 27 - The current in a wire at time t is given by the...Ch. 27 - The current supplied by a battery slowly decreases...Ch. 27 - The two wires in FIGURE P27.62 are made of the...Ch. 27 - What diameter should the nichrome wire in FIGURE...Ch. 27 - An aluminum wire consists of the three segments...Ch. 27 - A wire of radius R has a current density that...Ch. 27 - A 0.60 -mm-diameter wire made from an alloy (a...Ch. 27 - A 20 -cm-long hollow nichrome tube of inner...Ch. 27 - Prob. 68EAPCh. 27 - Prob. 69EAPCh. 27 - Prob. 70EAPCh. 27 - Prob. 71EAPCh. 27 - Prob. 72EAPCh. 27 - Prob. 73EAPCh. 27 - Prob. 74EAPCh. 27 - Prob. 75EAPCh. 27 - Prob. 76EAP
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