Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics)
9th Edition
ISBN: 9781305116429
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Textbook Question
Chapter 5, Problem 5.78AP
A rope with mass mr is attached to a block with mass mb as in Figure P5.42. The block rests on a frictionless, horizontal surface. The rope does not stretch. The free end of the rope is pulled to the right with a horizontal force
Figure P5.42
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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.
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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
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Question A2
[5 marks]
Suppose that A, is a covector field, and consider the object
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Chapter 5 Solutions
Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics)
Ch. 5 - Which of the following statements is correct? (a)...Ch. 5 - An object experiences no acceleration. Which of...Ch. 5 - You push an object, initially at rest, across a...Ch. 5 - Suppose you are talking by interplanetary...Ch. 5 - (i) If a fly collides with the windshield of a...Ch. 5 - You press your physics textbook flat against a...Ch. 5 - Charlie is playing with his daughter Toney in the...Ch. 5 - The driver of a speeding empty truck slams on the...Ch. 5 - In Figure OQ5.2, a locomotive has broken through...Ch. 5 - The third graders are on one side of a schoolyard,...
Ch. 5 - The driver of a speeding truck slams on the brakes...Ch. 5 - An experiment is performed on a puck on a level...Ch. 5 - The manager of a department store is pushing...Ch. 5 - Two objects are connected by a siring that passes...Ch. 5 - An object of mass m is sliding with speed v, at...Ch. 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 - If you hold a horizontal metal bar several...Ch. 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 - A spherical rubber balloon inflated with air is...Ch. 5 - A rubber ball is dropped onto the floor. What...Ch. 5 - Twenty people participate in a tug-of-war. The two...Ch. 5 - Can an object exert a force on itself? Argue for...Ch. 5 - When you push on a box with a 200-N force instead...Ch. 5 - A weight lifter stands on a bathroom scale. He...Ch. 5 - An athlete grips a light rope that passes over a...Ch. 5 - Suppose you are driving a classic car. Why should...Ch. 5 - In Figure CQ5.16, the light, taut, unstretchable...Ch. 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 - Balancing carefully, three boys inch out onto a...Ch. 5 - Identity action-reaction pairs in the following...Ch. 5 - As shown in Figure CQ5.22, student A, a 55-kg...Ch. 5 - Prob. 5.23CQCh. 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 - A certain orthodontist uses a wire brace to align...Ch. 5 - A toy rocket engine is securely fastened to a...Ch. 5 - The average speed of a nitrogen molecule in air is...Ch. 5 - The distinction between mass and weight was...Ch. 5 - (a) A cat with a mass of 850 kg in moving to the...Ch. 5 - Review. The gravitational force exerted on a...Ch. 5 - Review. 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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 - Figure P5.27 shows the horizontal forces acting on...Ch. 5 - The systems shown in Figure P5.28 are in...Ch. 5 - Assume the three blocks portrayed in Figure P5.29...Ch. 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 - Two people pull as hard as they can on horizontal...Ch. 5 - Figure P5.36 shows loads hanging from the ceiling...Ch. 5 - An object of mass m = 1.00 kg is observed to have...Ch. 5 - A setup similar to the one shown in Figure P5.38...Ch. 5 - A simple accelerometer is constructed inside a car...Ch. 5 - An object of mass m1 = 5.00 kg placed on a...Ch. 5 - Figure P5.41 shows the speed of a persons body as...Ch. 5 - Two objects are connected by a light string that...Ch. 5 - Two blocks, each of mass m = 3.50 kg, are hung...Ch. 5 - Two blocks, each of mass m, are hung from the...Ch. 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. 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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 - Two blocks connected by a rope of negligible mass...Ch. 5 - A block of mass 3.00 kg is pushed up against a...Ch. 5 - Review. One side of the roof of a house slopes up...Ch. 5 - Review. A Chinook salmon can swim underwater at...Ch. 5 - Review. A magician pulls a tablecloth from under a...Ch. 5 - A 5.00-kg block is placed on top of a 10.0-kg...Ch. 5 - The system shown in Figure P5.49 has an...Ch. 5 - A black aluminum glider floats on a film of air...Ch. 5 - A young woman buys an inexpensive used car stock...Ch. 5 - Why is the following situation impossible? A book...Ch. 5 - Review. 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A...Ch. 5 - Review. A block of mass m = 2.00 kg is released...Ch. 5 - In Figure P5.55, the incline has mass M and is...Ch. 5 - A block of mass m = 2.00 kg rests on the left edge...Ch. 5 - A mobile is formed by supporting four metal...
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