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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Chapter 39, Problem 8CQ
To determine
The momentum of the particle when the speed is doubled.
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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]
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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)
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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
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Chapter 39 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
Ch. 39.1 - Which observer in Figure 38.1 sees the balls...Ch. 39.1 - Prob. 39.2QQCh. 39.4 - Suppose the observer O on the train in Figure 38.6...Ch. 39.4 - Prob. 39.4QQCh. 39.4 - Prob. 39.5QQCh. 39.4 - Prob. 39.6QQCh. 39.4 - You are observing a spacecraft moving away from...Ch. 39.6 - You are driving on a freeway at a relativistic...Ch. 39.8 - Prob. 39.9QQCh. 39 - Prob. 1OQ
Ch. 39 - A spacecraft zooms past the Earth with a constant...Ch. 39 - Prob. 3OQCh. 39 - Prob. 4OQCh. 39 - Prob. 5OQCh. 39 - Prob. 6OQCh. 39 - Prob. 7OQCh. 39 - Prob. 8OQCh. 39 - Prob. 9OQCh. 39 - Prob. 10OQCh. 39 - Prob. 1CQCh. 39 - Prob. 2CQCh. 39 - Prob. 3CQCh. 39 - Prob. 4CQCh. 39 - Prob. 5CQCh. 39 - Prob. 6CQCh. 39 - Prob. 7CQCh. 39 - Prob. 8CQCh. 39 - Prob. 9CQCh. 39 - Prob. 10CQCh. 39 - Prob. 11CQCh. 39 - Prob. 12CQCh. 39 - Prob. 13CQCh. 39 - Prob. 14CQCh. 39 - Prob. 1PCh. 39 - In a laboratory frame of reference, an observer...Ch. 39 - The speed of the Earth in its orbit is 29.8 km/s....Ch. 39 - Prob. 4PCh. 39 - A star is 5.00 ly from the Earth. At what speed...Ch. 39 - Prob. 6PCh. 39 - Prob. 7PCh. 39 - Prob. 8PCh. 39 - Prob. 9PCh. 39 - An astronaut is traveling in a space vehicle...Ch. 39 - Prob. 11PCh. 39 - Prob. 12PCh. 39 - Prob. 13PCh. 39 - Prob. 14PCh. 39 - Prob. 15PCh. 39 - Prob. 16PCh. 39 - Prob. 17PCh. 39 - A cube of steel has a volume of 1.00 cm3 and mass...Ch. 39 - Prob. 19PCh. 39 - Prob. 20PCh. 39 - Prob. 21PCh. 39 - Review. In 1963, astronaut Gordon Cooper orbited...Ch. 39 - Prob. 23PCh. 39 - Prob. 24PCh. 39 - Prob. 25PCh. 39 - Prob. 26PCh. 39 - Prob. 27PCh. 39 - Prob. 28PCh. 39 - Prob. 29PCh. 39 - Prob. 30PCh. 39 - Prob. 31PCh. 39 - Prob. 32PCh. 39 - Prob. 33PCh. 39 - Prob. 34PCh. 39 - Prob. 35PCh. 39 - Prob. 36PCh. 39 - Prob. 37PCh. 39 - Prob. 38PCh. 39 - Prob. 39PCh. 39 - Prob. 40PCh. 39 - Prob. 41PCh. 39 - Prob. 42PCh. 39 - Prob. 43PCh. 39 - Prob. 44PCh. 39 - Prob. 45PCh. 39 - Prob. 46PCh. 39 - Prob. 47PCh. 39 - (a) Find the kinetic energy of a 78.0-kg...Ch. 39 - Prob. 49PCh. 39 - Prob. 50PCh. 39 - Prob. 51PCh. 39 - Consider electrons accelerated to a total energy...Ch. 39 - Prob. 53PCh. 39 - Prob. 54PCh. 39 - Prob. 55PCh. 39 - Prob. 56PCh. 39 - Prob. 57PCh. 39 - Prob. 58PCh. 39 - Prob. 59PCh. 39 - Prob. 60PCh. 39 - Prob. 61PCh. 39 - An unstable particle with mass m = 3.34 1027 kg...Ch. 39 - Prob. 63PCh. 39 - Prob. 64PCh. 39 - Prob. 65PCh. 39 - Prob. 66APCh. 39 - Prob. 67APCh. 39 - Prob. 68APCh. 39 - Prob. 69APCh. 39 - Prob. 70APCh. 39 - Prob. 71APCh. 39 - Prob. 72APCh. 39 - Prob. 73APCh. 39 - Prob. 74APCh. 39 - Prob. 75APCh. 39 - Prob. 76APCh. 39 - Prob. 77APCh. 39 - Prob. 78APCh. 39 - Prob. 79APCh. 39 - Prob. 80APCh. 39 - Prob. 81APCh. 39 - Prob. 82APCh. 39 - An alien spaceship traveling at 0.600c toward the...Ch. 39 - Prob. 84APCh. 39 - Prob. 85APCh. 39 - Prob. 86APCh. 39 - Prob. 87APCh. 39 - Prob. 88CPCh. 39 - The creation and study of new and very massive...Ch. 39 - Prob. 90CPCh. 39 - Owen and Dina are at rest in frame S, which is...
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