Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
4th Edition
ISBN: 9780134110684
Author: Randall D. Knight (Professor Emeritus)
Publisher: PEARSON
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Chapter 17, Problem 39EAP
Biologists think that some spiders “tune” strands of their web
to give enhanced response at frequencies corresponding to those at which desirable prey might struggle. Orb spider web silk has a typical diameter of
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ROTATIONAL DYNAMICS
Question 01
A solid circular cylinder and a solid spherical ball of the same mass and radius are rolling
together down the same inclined. Calculate the ratio of their kinetic energy. Assume pure
rolling motion Question 02
A sphere and cylinder of the same mass and radius start from ret at the same point and more
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Question 04
in 20
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]
Chapter 17 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Ch. 17 - Prob. 1CQCh. 17 - If you take snapshots of a standing wave on a...Ch. 17 - Prob. 3CQCh. 17 - Prob. 4CQCh. 17 - Prob. 5CQCh. 17 - Prob. 6CQCh. 17 - Prob. 7CQCh. 17 - Prob. 8CQCh. 17 - Prob. 9CQCh. 17 - 10. A trumpet player hears 5 beats per second when...
Ch. 17 - Prob. 1EAPCh. 17 - FIGURE EX17.2 is a snapshot graph at i = 0 s of...Ch. 17 - Prob. 3EAPCh. 17 - Prob. 4EAPCh. 17 - Prob. 5EAPCh. 17 - Prob. 6EAPCh. 17 - FIGURE EX17.7 shows a standing wave on a string...Ch. 17 - Prob. 8EAPCh. 17 - Prob. 9EAPCh. 17 - 10. The two highest-pitch strings on a violin are...Ch. 17 - A heavy piece of hanging sculpture is suspended by...Ch. 17 - Prob. 12EAPCh. 17 - Prob. 13EAPCh. 17 - What are the three longest wavelengths for...Ch. 17 - Prob. 15EAPCh. 17 - Prob. 16EAPCh. 17 - We can make a simple model of the human vocal...Ch. 17 - The lowest note on a grand piano has a frequency...Ch. 17 - A bass clarinet can be modeled as a 120cmlong...Ch. 17 - Prob. 20EAPCh. 17 - Prob. 21EAPCh. 17 - Prob. 22EAPCh. 17 - Two loudspeakers in a 20C room emit 686Hz sound...Ch. 17 - Prob. 24EAPCh. 17 - What is the thinnest film of MgF2(n1.39) on glass...Ch. 17 - Prob. 26EAPCh. 17 - I FIGURE EX17.27 shows the circular wave fronts...Ch. 17 - Prob. 28EAPCh. 17 - 29. Two in-phase loudspeakers, which emit sound...Ch. 17 - Two in-phase speakers 2.0m apart in a plane are...Ch. 17 - Prob. 31EAPCh. 17 - Prob. 32EAPCh. 17 - A flute player hears four beats per second when...Ch. 17 - Traditional Indonesian music uses an ensemble...Ch. 17 - Two microwave signals of nearly equal wavelengths...Ch. 17 - A 2.0mlong string vibrates at its second-harmonic...Ch. 17 - Prob. 37EAPCh. 17 - Prob. 38EAPCh. 17 - Biologists think that some spiders “tune” strands...Ch. 17 - Prob. 40EAPCh. 17 - Prob. 41EAPCh. 17 - Prob. 42EAPCh. 17 - Prob. 43EAPCh. 17 - A 75g bungee cord has an equilibrium length of...Ch. 17 - Prob. 45EAPCh. 17 - Prob. 46EAPCh. 17 - Prob. 47EAPCh. 17 - Prob. 48EAPCh. 17 - Prob. 49EAPCh. 17 - Prob. 50EAPCh. 17 - Prob. 51EAPCh. 17 - Prob. 52EAPCh. 17 - Prob. 53EAPCh. 17 - Prob. 54EAPCh. 17 - Prob. 55EAPCh. 17 - A 44-cm-diameter water tank is filled with 35 cm...Ch. 17 - Prob. 57EAPCh. 17 - Prob. 58EAPCh. 17 - Two in-phase loudspeakers emit identical 1000 Hz...Ch. 17 - Prob. 60EAPCh. 17 - Two loudspeakers emit sound waves of the same...Ch. 17 - Prob. 62EAPCh. 17 - Prob. 63EAPCh. 17 - Prob. 64EAPCh. 17 - Prob. 65EAPCh. 17 - Engineers are testing a new thin-film coating...Ch. 17 - Prob. 67EAPCh. 17 - Prob. 68EAPCh. 17 - Two loudspeakers in a plane, 5.0 m apart, are...Ch. 17 - Two identical loudspeakers separated by distance...Ch. 17 - Prob. 71EAPCh. 17 - Piano tuners tune pianos by listening to the beats...Ch. 17 - Prob. 73EAPCh. 17 - Prob. 74EAPCh. 17 - Prob. 75EAPCh. 17 - Two radio antennas are separated by 2.0 m. Both...Ch. 17 - Prob. 77EAPCh. 17 - Prob. 78EAPCh. 17 - Prob. 79EAPCh. 17 - Ultrasound has many medical applications, one of...Ch. 17 - Prob. 81EAP
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