EBK PHYSICS FOR SCIENTISTS AND ENGINEER
9th Edition
ISBN: 8220100461262
Author: SERWAY
Publisher: Cengage Learning US
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Textbook Question
Chapter 11, Problem 11.33P
A 60.0-kg woman stands at the western rim of a horizontal turntable having a moment of inertia of 500 kg · m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth. Consider the woman–turntable system as motion begins. (a) Is the mechanical energy of the system constant? (b) Is the momentum of the system constant? (c) Is the
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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
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
Ch. 11 - Which of the following statements about the...Ch. 11 - Recall the skater described at the beginning of...Ch. 11 - A solid sphere and a hollow sphere have the same...Ch. 11 - A competitive diver leaves the diving board and...Ch. 11 - An ice skater starts a spin with her arms...Ch. 11 - A pet mouse sleeps near the eastern edge of a...Ch. 11 - Let us name three perpendicular directions as...Ch. 11 - Let the four compass directions north, east,...Ch. 11 - Answer yes or no 10 (he following questions, (a)...Ch. 11 - Prob. 11.6OQ
Ch. 11 - Two ponies of equal mass are initially at...Ch. 11 - Consider an isolated system moving through empty...Ch. 11 - Stars originate as large bodies of slowly rotating...Ch. 11 - A scientist arriving at a hotel asks a bellhop to...Ch. 11 - Prob. 11.3CQCh. 11 - Two children are playing with a roll of paper...Ch. 11 - Both torque and work are products of force and...Ch. 11 - In some motorcycle races, the riders drive over...Ch. 11 - If the torque acting on a particle about an axis...Ch. 11 - A ball is thrown in such a way that it does not...Ch. 11 - If global warming continues over the next one...Ch. 11 - A cat usually lands on its feet regardless of the...Ch. 11 - Prob. 11.11CQCh. 11 - Prob. 11.1PCh. 11 - The displacement vectors 42.0 cm at 15.0 and 23.0...Ch. 11 - Prob. 11.3PCh. 11 - Use the definition of the vector product and the...Ch. 11 - Calculate the net torque (magnitude and direction)...Ch. 11 - Prob. 11.6PCh. 11 - If AB=AB, what is the angle between A and B?Ch. 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 - Prob. 11.10PCh. 11 - A light, rigid rod of length l = 1.00 m joins two...Ch. 11 - A 1.50-kg particle moves in the xy plane with a...Ch. 11 - A particle of mass m moves in the xy plane with a...Ch. 11 - Heading straight toward the summit of Pikes Peak,...Ch. 11 - Review. A projectile of mass m is launched with an...Ch. 11 - Review. A conical pendulum consists of a bob of...Ch. 11 - A particle of mass m moves in a circle of radius R...Ch. 11 - A counterweight of mass m = 4.00 kg is attached to...Ch. 11 - The position vector of a particle of mass 2.00 kg...Ch. 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 - A uniform solid sphere of radius r = 0.500 m and...Ch. 11 - Big Ben (Fig. P10.27, page 281), the Parliament...Ch. 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 - Model the Earth as a uniform sphere. (a) Calculate...Ch. 11 - Prob. 11.27PCh. 11 - The distance between the centers of the wheels of...Ch. 11 - A space station is coast me ted in the shape of a...Ch. 11 - A disk with moment of inertia I1 rotates about a...Ch. 11 - A playground merry-go-round of radius R = 2.00 m...Ch. 11 - Prob. 11.32PCh. 11 - A 60.0-kg woman stands at the western rim of a...Ch. 11 - A student sits on a freely rotating stool holding...Ch. 11 - A uniform cylindrical turntable of radius 1.90 m...Ch. 11 - Prob. 11.36PCh. 11 - A wooden block of mass M resting on a...Ch. 11 - Review. A thin, uniform, rectangular signboard...Ch. 11 - A wad of sticky clay with mass m and velocity vi...Ch. 11 - Why is the following situation impossible? A space...Ch. 11 - A 0.005 00-kg bullet traveling horizontally with...Ch. 11 - Section 11.5 The Motion of Gyroscopes and Tops A...Ch. 11 - The angular momentum vector of a precessing...Ch. 11 - A light rope passes over a light, frictionless...Ch. 11 - Prob. 11.45APCh. 11 - Review. Two boys are sliding toward each other on...Ch. 11 - We have all complained that there arent enough...Ch. 11 - Prob. 11.48APCh. 11 - A rigid, massless rod has three particles with...Ch. 11 - Prob. 11.50APCh. 11 - A projectile of mass m moves to the right with a...Ch. 11 - Two children are playing on stools at a restaurant...Ch. 11 - Prob. 11.53APCh. 11 - Prob. 11.54APCh. 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 - A uniform rod of mass 300 g and length 50.0 cm...Ch. 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 - A uniform solid disk of radius R is set into...Ch. 11 - In Example 11.8, we investigated an elastic...Ch. 11 - Prob. 11.63CPCh. 11 - A solid cube of wood of side 2a and mass M is...
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