College Physics: A Strategic Approach (3rd Edition)
3rd Edition
ISBN: 9780321879721
Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher: PEARSON
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Textbook Question
Chapter 27, Problem 19P
At what speed relative to a laboratory does a clock tick at half the rate of an identical clock at rest in the laboratory? Give your answer as a fraction of c.
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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]
Chapter 27 Solutions
College Physics: A Strategic Approach (3rd Edition)
Ch. 27 - Prob. 1CQCh. 27 - Frame S moves relative to frame S as shown in...Ch. 27 - a. Two balls move as shown in Figure Q27.3. What...Ch. 27 - A lighthouse beacon alerts ships to the danger of...Ch. 27 - As a racket passes the earth at 0.75c, it fires a...Ch. 27 - At the instant that a clock standing next to you...Ch. 27 - Prob. 7CQCh. 27 - Firecrackers 1 and 2 are 600 m apart. You are...Ch. 27 - Your clocks and calendars are synchronized with...Ch. 27 - Two trees are 600 m apart. You are standing...
Ch. 27 - Figure Q27.11 shows Peggy standing at the center...Ch. 27 - In Figure Q27.12, clocks C1 and C2, in frame S are...Ch. 27 - A meter stick passes you at a speed of 0.5c....Ch. 27 - Youre passing a car on the highway. You want to...Ch. 27 - Prob. 15CQCh. 27 - Prob. 16CQCh. 27 - The rocket speeds shown in Figure Q27.18 are...Ch. 27 - Can a particle of mass m have total energy less...Ch. 27 - In your chemistry classes, you have probably...Ch. 27 - Lee and Leigh are twins. At their first birthday...Ch. 27 - A space cowboy wants to eject from his spacecraft...Ch. 27 - A lamp flashes at the origin. Then, 1 s later, a...Ch. 27 - Prob. 24MCQCh. 27 - A particle moving at speed 0.40c has momentum p0....Ch. 27 - A particle moving at speed 0.40c has kinetic...Ch. 27 - A sprinter crosses the finish line of a race. The...Ch. 27 - A baseball pitcher can throw a ball with a speed...Ch. 27 - A boy on a skateboard coasts along at 5 m/s. He...Ch. 27 - A boat takes 3.0 hours to travel 30 km down a...Ch. 27 - When the moving sidewalk at the airport is broken,...Ch. 27 - Prob. 6PCh. 27 - An out-of-control alien spacecraft is diving into...Ch. 27 - A starship blasts past the earth at 2.0 103 m/s....Ch. 27 - You are flying at 0.99c with respect to Kara. At...Ch. 27 - You are standing at the point x = 300 m, y = 400 m...Ch. 27 - Prob. 11PCh. 27 - Bianca is standing at x = 600 m. Firecracker 1, at...Ch. 27 - You are standing at x = 9.0 km Lightning bolt 1...Ch. 27 - A light flashes at position x = 0 m. One...Ch. 27 - Jose is baking to the east. Lightning bolt 1...Ch. 27 - Your 1000-m-long starship has warning lights at...Ch. 27 - There is a lightbulb exactly halfway between the...Ch. 27 - A cosmic ray travels 60 km through the earths...Ch. 27 - At what speed relative to a laboratory does a...Ch. 27 - An astronaut travels to a star system 4.5 ly away...Ch. 27 - Prob. 21PCh. 27 - At what speed as a fraction of c, will a moving...Ch. 27 - Jill claims that her new rocket is 100 m long. As...Ch. 27 - A muon travels 60 km through the atmosphere at a...Ch. 27 - The Stanford Linear Accelerator (SLAC) accelerates...Ch. 27 - Our Milky Way galaxy is 100,000 ly in diameter. A...Ch. 27 - The X-15 rocket-powered plane holds the record for...Ch. 27 - A rocket cruising past earth at 0.800c shoots a...Ch. 27 - A base on Planet X fires a missile toward an...Ch. 27 - A solar flare blowing out from the sun at 0.90c is...Ch. 27 - Prob. 31PCh. 27 - Prob. 32PCh. 27 - Prob. 33PCh. 27 - Prob. 34PCh. 27 - What are the kinetic energy, the rest energy, and...Ch. 27 - A quarter-pound hamburger with all the fixings has...Ch. 27 - How fast much an electron move so that its total...Ch. 27 - At what speed is a particle's kinetic energy twice...Ch. 27 - A firecracker explodes at x = 0 m, t = 0 s. A...Ch. 27 - Youre standing on an asteroid when you see your...Ch. 27 - A subatomic particle moves through the laboratory...Ch. 27 - Prob. 42GPCh. 27 - A very fast-moving train car passes you, moving to...Ch. 27 - Two events in reference frame S occur 10 s apart...Ch. 27 - A spaceship heads directly toward an asteroid at a...Ch. 27 - Hill Two spaceships approach each other at speeds...Ch. 27 - A cube has a density of 2000 kg/m3 while at rest...Ch. 27 - A railroad car that is 20 m long when at rest...Ch. 27 - A spaceship flies past an experimenter who...Ch. 27 - Marissas spaceship approaches Josephs at a speed...Ch. 27 - At a speed of 0.90c, a spaceship travels to a star...Ch. 27 - Prob. 54GPCh. 27 - A rocket traveling at 0.500c sets out for the...Ch. 27 - A distant quasar is found to be moving away from...Ch. 27 - Two rockets approach each other. Each is traveling...Ch. 27 - A railcar has a velocity of 0.5c relative to the...Ch. 27 - James, Daniella, and Tara all possess identical...Ch. 27 - A space beacon on Planet Karma emits a pulse of...Ch. 27 - Two rockets, A and B, approach the earth from...Ch. 27 - What is the speed of an electron after being...Ch. 27 - What is the speed of a proton after being...Ch. 27 - Prob. 66GPCh. 27 - What is the momentum of a particle with speed...Ch. 27 - Prob. 68GPCh. 27 - What is the total energy, in MeV, of a. A proton...Ch. 27 - Prob. 70GPCh. 27 - At what speed is the kinetic energy of a particle...Ch. 27 - Prob. 72GPCh. 27 - The chemical energy of gasoline is 46 MJ/kg. If...Ch. 27 - A standard nuclear power plant generates 3.0 GW of...Ch. 27 - The sun radiates energy at the rate 3.8 1026 W....Ch. 27 - The radioactive element radium (Ra) decays by a...Ch. 27 - Prob. 77GPCh. 27 - MCAT-Style Passage Problems Pion Therapy Subatomic...Ch. 27 - MCAT-Style Passage Problems Pion Therapy Subatomic...Ch. 27 - MCAT-Style Passage Problems Pion Therapy Subatomic...Ch. 27 - MCAT-Style Passage Problems Pion Therapy Subatomic...
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