Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
9th Edition
ISBN: 9781305932302
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 9, Problem 74AP
(a)
To determine
The complete statement of the problem, giving the data and identify the unknowns.
(b)
To determine
The values of
(c)
To determine
The kinetic energy that has been transformed in to kinetic energy of the system.
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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
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[5 marks]
(b)…
Chapter 9 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
Ch. 9.1 - Two objects have equal kinetic energies. How do...Ch. 9.1 - Your physical education teacher throws a baseball...Ch. 9.3 - Two objects are at rest on a frictionless surface....Ch. 9.3 - Rank an automobile dashboard, seat belt, and air...Ch. 9.4 - Prob. 9.5QQCh. 9.4 - A table-tennis ball is thrown at a stationary...Ch. 9.6 - A baseball bat of uniform density is cut at the...Ch. 9.7 - A cruise ship is moving at constant speed through...Ch. 9 - Prob. 1OQCh. 9 - Prob. 2OQ
Ch. 9 - Prob. 3OQCh. 9 - Prob. 4OQCh. 9 - Prob. 5OQCh. 9 - Prob. 6OQCh. 9 - The momentum of an object is increased by a factor...Ch. 9 - The kinetic energy of an object is increased by a...Ch. 9 - If two particles have equal momenta, are their...Ch. 9 - Prob. 10OQCh. 9 - Prob. 11OQCh. 9 - Two particles of different mass start from rest....Ch. 9 - Prob. 13OQCh. 9 - A basketball is tossed up into the air, falls...Ch. 9 - Prob. 15OQCh. 9 - Prob. 16OQCh. 9 - Prob. 17OQCh. 9 - Prob. 18OQCh. 9 - Prob. 1CQCh. 9 - Prob. 2CQCh. 9 - Prob. 3CQCh. 9 - While in motion, a pitched baseball carries...Ch. 9 - You are standing perfectly still and then take a...Ch. 9 - Prob. 6CQCh. 9 - Two students hold a large bed sheet vertically...Ch. 9 - A juggler juggles three balls in a continuous...Ch. 9 - Prob. 9CQCh. 9 - Does a larger net force exerted on an object...Ch. 9 - Does a larger net force always produce a larger...Ch. 9 - A bomb, initially at rest, explodes into several...Ch. 9 - A particle of mass m moves with momentum of...Ch. 9 - Prob. 2PCh. 9 - Prob. 3PCh. 9 - A 3.00-kg particle has a velocity of...Ch. 9 - A baseball approaches home plate at a speed of...Ch. 9 - Prob. 6PCh. 9 - Prob. 7PCh. 9 - A 65.0-kg boy and his 40.0-kg sister, both wearing...Ch. 9 - Prob. 9PCh. 9 - When you jump straight up as high as you can, what...Ch. 9 - Two blocks of masses m and 3m are placed on a...Ch. 9 - Prob. 12PCh. 9 - An estimated forcetime curve for a baseball struck...Ch. 9 - Prob. 14PCh. 9 - A glider of mass m is free to slide along a...Ch. 9 - Prob. 16PCh. 9 - The front 1.20 m of a 1 400-kg car Ls designed as...Ch. 9 - A tennis player receives a shot with the ball...Ch. 9 - The magnitude of the net force exerted in the x...Ch. 9 - Prob. 20PCh. 9 - Water falls without splashing at a rate of 0.250...Ch. 9 - A 1 200-kg car traveling initially at vCi = 25.0...Ch. 9 - Prob. 23PCh. 9 - A car of mass m moving at a speed v1 collides and...Ch. 9 - A railroad car of mass 2.50 104 kg is moving with...Ch. 9 - Prob. 26PCh. 9 - Prob. 27PCh. 9 - A 7.00-g bullet, when fired from a gun into a...Ch. 9 - A tennis ball of mass 57.0 g is held just above a...Ch. 9 - Prob. 30PCh. 9 - Prob. 31PCh. 9 - Prob. 32PCh. 9 - Prob. 33PCh. 9 - (a) Three carts of masses m1 = 4.00 kg, m2 = 10.0...Ch. 9 - Prob. 35PCh. 9 - Prob. 36PCh. 9 - Prob. 37PCh. 9 - Two shuffleboard disks of equal mass, one orange...Ch. 9 - Prob. 39PCh. 9 - A proton, moving with a velocity of vii, collides...Ch. 9 - Prob. 41PCh. 9 - A 90.0-kg fullback running east with a speed of...Ch. 9 - Prob. 43PCh. 9 - Prob. 44PCh. 9 - Prob. 45PCh. 9 - Prob. 46PCh. 9 - Explorers in the jungle find an ancient monument...Ch. 9 - A uniform piece of sheet metal is shaped as shown...Ch. 9 - A rod of length 30.0 cm has linear density (mass...Ch. 9 - Prob. 50PCh. 9 - Prob. 51PCh. 9 - Consider a system of two particles in the xy...Ch. 9 - Prob. 53PCh. 9 - The vector position of a 3.50-g particle moving in...Ch. 9 - Prob. 55PCh. 9 - Prob. 56PCh. 9 - Prob. 57PCh. 9 - Prob. 58PCh. 9 - Prob. 59PCh. 9 - Prob. 60PCh. 9 - A garden hose is held as shown in Figure P9.32....Ch. 9 - Prob. 62PCh. 9 - Prob. 63PCh. 9 - A rocket has total mass Mi = 360 kg, including...Ch. 9 - A ball of mass m is thrown straight up into the...Ch. 9 - Prob. 66APCh. 9 - A 3.00-kg steel ball strikes a wall with a speed...Ch. 9 - (a) Figure P9.36 shows three points in the...Ch. 9 - Review. A 60.0-kg person running at an initial...Ch. 9 - A cannon is rigidly attached to a carriage, which...Ch. 9 - A 1.25-kg wooden block rests on a table over a...Ch. 9 - A wooden block of mass M rests on a table over a...Ch. 9 - Prob. 73APCh. 9 - Prob. 74APCh. 9 - Two gliders are set in motion on a horizontal air...Ch. 9 - Why is the following situation impossible? An...Ch. 9 - Prob. 77APCh. 9 - Prob. 78APCh. 9 - Prob. 79APCh. 9 - A small block of mass m1 = 0.500 kg is released...Ch. 9 - Review. A bullet of mass m = 8.00 g is fired into...Ch. 9 - Review. A bullet of mass m is fired into a block...Ch. 9 - A 0.500-kg sphere moving with a velocity expressed...Ch. 9 - Prob. 84APCh. 9 - Prob. 85APCh. 9 - Prob. 86APCh. 9 - Review. A light spring of force constant 3.85 N/m...Ch. 9 - Prob. 88APCh. 9 - Prob. 89APCh. 9 - Prob. 90APCh. 9 - Prob. 91APCh. 9 - Prob. 92CPCh. 9 - Prob. 93CPCh. 9 - Sand from a stationary hopper falls onto a moving...Ch. 9 - On a horizontal air track, a glider of mass m...Ch. 9 - Prob. 96CP
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