Physics:f/sci.+engrs.,ap Ed.
10th Edition
ISBN: 9781337553469
Author: Jewett, SERWAY
Publisher: Cengage
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Chapter 38, Problem 14P
You have an assistantship with a math professor in a future world where space travel is common and spacecraft regularly achieve near-light speeds. A spacecraft has taken of recently to carry individuals to colonize an Earth-like planet around a nearby star. Your professor, who remains on Earth, is teaching the students on the spacecraft via the future version of distance learning. It is time for the students on the spacecraft to take a math exam. The professor wishes the students to have a time interval Δtp = 2.00 h to complete the exam, so just as the spacecraft passes Earth on its last trip around the Sun at its constant cruising speed of 0.960c, she sends a signal to the proctor to have the students begin the exam. Knowing of your experience in physics courses, the professor asks you to determine the time interval through which she should wait before sending a radio signal to the departing spacecraft to tell the proctor to have the students stop working on the exam.
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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]
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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,
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[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 38 Solutions
Physics:f/sci.+engrs.,ap Ed.
Ch. 38.1 - Which observer in Figure 38.1 sees the balls...Ch. 38.1 - A baseball pitcher with a 90-mi/h fastball throws...Ch. 38.4 - Suppose the observer O on the train in Figure 38.6...Ch. 38.4 - A crew on a spacecraft watches a movie that is two...Ch. 38.4 - You are packing for a trip to another star. During...Ch. 38.4 - You are observing a spacecraft moving away from...Ch. 38.6 - You are driving on a freeway at a relativistic...Ch. 38.8 - The following pairs of energiesparticle 1: E, 2E;...Ch. 38 - In a laboratory frame of reference, an observer...Ch. 38 - Prob. 2P
Ch. 38 - A meterstick moving at 0.900c relative to the...Ch. 38 - A muon formed high in the Earths atmosphere is...Ch. 38 - A deep-space vehicle moves away from the Earth...Ch. 38 - An astronaut is traveling in a space vehicle...Ch. 38 - For what value of does = 1.010 0? Observe that...Ch. 38 - You have been hired as an expert witness for an...Ch. 38 - A spacecraft with a proper length of 300 m passes...Ch. 38 - A spacecraft with a proper length of Lp passes by...Ch. 38 - A light source recedes from an observer with a...Ch. 38 - A cube of steel has a volume of 1.00 cm3 and mass...Ch. 38 - Review. In 1963, astronaut Gordon Cooper orbited...Ch. 38 - You have an assistantship with a math professor in...Ch. 38 - Police radar detects the speed of a car (Fig....Ch. 38 - Shannon observes two light pulses to be emitted...Ch. 38 - A moving rod is observed to have a length of =...Ch. 38 - A rod moving with a speed v along the horizontal...Ch. 38 - A red light flashes at position xR = 3.00 m and...Ch. 38 - You have been hired as an expert witness in the...Ch. 38 - Figure P38.21 shows a jet of material (at the...Ch. 38 - A spacecraft is launched from the surface of the...Ch. 38 - Calculate the momentum of an electron moving with...Ch. 38 - Prob. 24PCh. 38 - Prob. 25PCh. 38 - Prob. 26PCh. 38 - An unstable particle at rest spontaneously breaks...Ch. 38 - (a) Find the kinetic energy of a 78.0-kg...Ch. 38 - Prob. 29PCh. 38 - Prob. 30PCh. 38 - Protons in an accelerator at the Fermi National...Ch. 38 - You are working for an alternative energy company....Ch. 38 - The total energy of a proton is twice its rest...Ch. 38 - When 1.00 g of hydrogen combines with 8.00 g of...Ch. 38 - The rest energy of an electron is 0.511 MeV. The...Ch. 38 - Prob. 36PCh. 38 - Prob. 37PCh. 38 - Prob. 38PCh. 38 - Prob. 39PCh. 38 - An unstable particle with mass m = 3.34 1027 kg...Ch. 38 - Review. A global positioning system (GPS)...Ch. 38 - Prob. 42APCh. 38 - An astronaut wishes to visit the Andromeda galaxy,...Ch. 38 - Prob. 44APCh. 38 - Prob. 45APCh. 38 - The motion of a transparent medium influences the...Ch. 38 - An object disintegrates into two fragments. One...Ch. 38 - Prob. 48APCh. 38 - Review. Around the core of a nuclear reactor...Ch. 38 - Prob. 50APCh. 38 - Prob. 51APCh. 38 - Prob. 52APCh. 38 - Prob. 53CPCh. 38 - A particle with electric charge q moves along a...Ch. 38 - Suppose our Sun is about to explode. In an effort...
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