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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Textbook Question
Chapter 5, Problem 17CQ
Describe two examples in which the
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Check out a sample textbook solutionStudents have asked these similar questions
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 5 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
Ch. 5.2 - Which of the following statements is correct? (a)...Ch. 5.4 - An object experiences no acceleration. Which of...Ch. 5.4 - You push an object, initially at rest, across a...Ch. 5.5 - Suppose you are talking by interplanetary...Ch. 5.6 - (i) If a fly collides with the windshield of a...Ch. 5.8 - You press your physics textbook flat against a...Ch. 5.8 - Prob. 5.7QQCh. 5 - The driver of a speeding empty truck slams on the...Ch. 5 - In Figure OQ5.2, a locomotive has broken through...Ch. 5 - Prob. 3OQ
Ch. 5 - Prob. 4OQCh. 5 - Prob. 5OQCh. 5 - The manager of a department store is pushing...Ch. 5 - Two objects are connected by a string that passes...Ch. 5 - Prob. 8OQCh. 5 - A truck loaded with sand accelerates along a...Ch. 5 - A large crate of mass m is place on the flatbed of...Ch. 5 - If an object is in equilibrium, which of the...Ch. 5 - A crate remains stationary after it has been...Ch. 5 - An object of mass m moves with acceleration a down...Ch. 5 - Prob. 1CQCh. 5 - Your hands are wet, and the restroom towel...Ch. 5 - In the motion picture It Happened One Night...Ch. 5 - If a car is traveling due westward with a constant...Ch. 5 - A passenger sitting in the rear of a bus claims...Ch. 5 - A child tosses a ball straight up. She says that...Ch. 5 - A person holds a ball in her hand. (a) Identify...Ch. 5 - Prob. 8CQCh. 5 - Prob. 9CQCh. 5 - Twenty people participate in a tug-of-war. The two...Ch. 5 - Prob. 11CQCh. 5 - Prob. 12CQCh. 5 - A weightlifter stands on a bathroom scale. He...Ch. 5 - Prob. 14CQCh. 5 - Suppose you are driving a classic car. Why should...Ch. 5 - Prob. 16CQCh. 5 - Describe two examples in which the force of...Ch. 5 - The mayor of a city reprimands some city employees...Ch. 5 - Give reasons for the answers to each of the...Ch. 5 - Prob. 20CQCh. 5 - Identify actionreaction pairs in the following...Ch. 5 - Prob. 22CQCh. 5 - Prob. 23CQCh. 5 - A certain orthodontist uses a wire brace to align...Ch. 5 - If a man weighs 900 N on the Earth, what would he...Ch. 5 - A 3.00-kg object undergoes an acceleration given...Ch. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - The average speed of a nitrogen molecule in air is...Ch. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - Review. The gravitational force exerted on a...Ch. 5 - Review. The gravitational force exerted on a...Ch. 5 - Review. An electron of mass 9. 11 1031 kg has an...Ch. 5 - Prob. 12PCh. 5 - One or more external forces, large enough to be...Ch. 5 - A brick of mass M has been placed on a rubber...Ch. 5 - Two forces, F1=(6.00i4.00j)N and...Ch. 5 - Prob. 16PCh. 5 - Prob. 17PCh. 5 - Prob. 18PCh. 5 - Prob. 19PCh. 5 - You stand on the seat of a chair and then hop off....Ch. 5 - Prob. 21PCh. 5 - Review. Three forces acting on an object are given...Ch. 5 - Prob. 23PCh. 5 - Prob. 24PCh. 5 - Review. Figure P5.15 shows a worker poling a boata...Ch. 5 - An iron bolt of mass 65.0 g hangs from a string...Ch. 5 - Prob. 27PCh. 5 - The systems shown in Figure P5.28 are in...Ch. 5 - Prob. 29PCh. 5 - A block slides down a frictionless plane having an...Ch. 5 - The distance between two telephone poles is 50.0...Ch. 5 - A 3.00-kg object is moving in a plane, with its x...Ch. 5 - A bag of cement weighing 325 N hangs in...Ch. 5 - A bag of cement whose weight is Fg hangs in...Ch. 5 - Prob. 35PCh. 5 - Prob. 36PCh. 5 - An object of mass m = 1.00 kg is observed to have...Ch. 5 - Prob. 38PCh. 5 - Prob. 39PCh. 5 - An object of mass m1 = 5.00 kg placed on a...Ch. 5 - Prob. 41PCh. 5 - Two objects are connected by a light string that...Ch. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - In the system shown in Figure P5.23, a horizontal...Ch. 5 - An object of mass m1 hangs from a string that...Ch. 5 - A block is given an initial velocity of 5.00 m/s...Ch. 5 - A car is stuck in the mud. A tow truck pulls on...Ch. 5 - Prob. 49PCh. 5 - Prob. 50PCh. 5 - In Example 5.8, we investigated the apparent...Ch. 5 - Consider a large truck carrying a heavy load, such...Ch. 5 - Prob. 53PCh. 5 - Prob. 54PCh. 5 - A 25.0-kg block is initially at rest on a...Ch. 5 - Why is the following situation impassible? Your...Ch. 5 - Prob. 57PCh. 5 - Before 1960m people believed that the maximum...Ch. 5 - Prob. 59PCh. 5 - A woman at an airport is towing her 20.0-kg...Ch. 5 - Review. A 3.00-kg block starts from rest at the...Ch. 5 - The person in Figure P5.30 weighs 170 lb. As seen...Ch. 5 - A 9.00-kg hanging object is connected by a light,...Ch. 5 - Three objects are connected on a table as shown in...Ch. 5 - Prob. 65PCh. 5 - A block of mass 3.00 kg is pushed up against a...Ch. 5 - Prob. 67PCh. 5 - Prob. 68PCh. 5 - Prob. 69PCh. 5 - A 5.00-kg block is placed on top of a 10.0-kg...Ch. 5 - Prob. 71PCh. 5 - A black aluminum glider floats on a film of air...Ch. 5 - Prob. 73APCh. 5 - Why is the following situation impossible? A book...Ch. 5 - Prob. 75APCh. 5 - A 1.00-kg glider on a horizontal air track is...Ch. 5 - Prob. 77APCh. 5 - Prob. 78APCh. 5 - Two blocks of masses m1 and m2, are placed on a...Ch. 5 - Prob. 80APCh. 5 - An inventive child named Nick wants to reach an...Ch. 5 - Prob. 82APCh. 5 - Prob. 83APCh. 5 - An aluminum block of mass m1 = 2.00 kg and a...Ch. 5 - Prob. 85APCh. 5 - Prob. 86APCh. 5 - Prob. 87APCh. 5 - Prob. 88APCh. 5 - A crate of weight Fg is pushed by a force P on a...Ch. 5 - Prob. 90APCh. 5 - A flat cushion of mass m is released from rest at...Ch. 5 - In Figure P5.46, the pulleys and pulleys the cord...Ch. 5 - What horizontal force must be applied to a large...Ch. 5 - Prob. 94APCh. 5 - A car accelerates down a hill (Fig. P5.95), going...Ch. 5 - Prob. 96CPCh. 5 - Prob. 97CPCh. 5 - Initially, the system of objects shown in Figure...Ch. 5 - A block of mass 2.20 kg is accelerated across a...Ch. 5 - Prob. 100CPCh. 5 - Prob. 101CPCh. 5 - In Figure P5.55, the incline has mass M and is...Ch. 5 - Prob. 103CPCh. 5 - Prob. 104CP
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