Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
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ISBN: 9781305932302
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Textbook Question
Chapter 11, Problem 44AP
A light rope passes over a light, frictionless pulley. One end is fastened to a bunch of bananas of mass M, and a monkey of mass M clings to the other end (Fig. P11.32). The monkey climbs the rope in an attempt to reach the bananas. (a) Treating the system as consisting of the monkey, bananas, rope, and pulley, find the net torque on the system about the pulley axis. (b) Using the result of part (a), determine the total
Figure P11.32
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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
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
Ch. 11.1 - Which of the following statements about the...Ch. 11.2 - Recall the skater described at the beginning of...Ch. 11.3 - A solid sphere and a hollow sphere have the same...Ch. 11.4 - A competitive diver leaves the diving board and...Ch. 11 - Prob. 1OQCh. 11 - Prob. 2OQCh. 11 - Prob. 3OQCh. 11 - Prob. 4OQCh. 11 - Prob. 5OQCh. 11 - Prob. 6OQ
Ch. 11 - Prob. 7OQCh. 11 - Prob. 8OQCh. 11 - Prob. 1CQCh. 11 - Prob. 2CQCh. 11 - Prob. 3CQCh. 11 - Prob. 4CQCh. 11 - Prob. 5CQCh. 11 - In some motorcycle races, the riders drive over...Ch. 11 - Prob. 7CQCh. 11 - Prob. 8CQCh. 11 - Prob. 9CQCh. 11 - Prob. 10CQCh. 11 - Prob. 11CQCh. 11 - Prob. 1PCh. 11 - The displacement vectors 42.0 cm at 15.0 and 23.0...Ch. 11 - Prob. 3PCh. 11 - Prob. 4PCh. 11 - Prob. 5PCh. 11 - Prob. 6PCh. 11 - Prob. 7PCh. 11 - A particle is located at a point described by the...Ch. 11 - Two forces F1 and F2 act along the two sides of an...Ch. 11 - A student claims that he has found a vector A such...Ch. 11 - Prob. 11PCh. 11 - A 1.50-kg particle moves in the xy plane with a...Ch. 11 - Prob. 13PCh. 11 - Heading straight toward the summit of Pikes Peak,...Ch. 11 - Review. A projectile of mass m is launched with an...Ch. 11 - Prob. 16PCh. 11 - A particle of mass m moves in a circle of radius R...Ch. 11 - Prob. 18PCh. 11 - Prob. 19PCh. 11 - A 5.00-kg particle starts from the origin at time...Ch. 11 - A ball having mass m is fastened at the end of a...Ch. 11 - Prob. 22PCh. 11 - Prob. 23PCh. 11 - Show that the kinetic energy of an object rotating...Ch. 11 - A uniform solid disk of mass m = 3.00 kg and...Ch. 11 - Prob. 26PCh. 11 - Prob. 27PCh. 11 - Prob. 28PCh. 11 - Prob. 29PCh. 11 - Prob. 30PCh. 11 - Prob. 31PCh. 11 - Prob. 32PCh. 11 - A 60.0-kg woman stands at the western rim of a...Ch. 11 - Prob. 34PCh. 11 - A uniform cylindrical turntable of radius 1.90 m...Ch. 11 - Prob. 36PCh. 11 - A wooden block of mass M resting on a...Ch. 11 - Prob. 38PCh. 11 - A wad of sticky clay with mass m and velocity vi...Ch. 11 - Prob. 40PCh. 11 - Prob. 41PCh. 11 - Prob. 42PCh. 11 - The angular momentum vector of a precessing...Ch. 11 - A light rope passes over a light, frictionless...Ch. 11 - Prob. 45APCh. 11 - Prob. 46APCh. 11 - We have all complained that there arent enough...Ch. 11 - Prob. 48APCh. 11 - A rigid, massless rod has three particles with...Ch. 11 - Prob. 50APCh. 11 - Prob. 51APCh. 11 - Two children are playing on stools at a restaurant...Ch. 11 - Prob. 53APCh. 11 - Prob. 54APCh. 11 - Two astronauts (Fig. P11.39), each having a mass...Ch. 11 - Two astronauts (Fig. P11.39), each having a mass...Ch. 11 - Native people throughout North and South America...Ch. 11 - Prob. 58APCh. 11 - Global warming is a cause for concern because even...Ch. 11 - The puck in Figure P11.46 has a mass of 0.120 kg....Ch. 11 - Prob. 61CPCh. 11 - Prob. 62CPCh. 11 - Prob. 63CPCh. 11 - A solid cube of wood of side 2a and mass M is...
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