College Physics
OER 2016 Edition
ISBN: 9781947172173
Author: OpenStax
Publisher: OpenStax College
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Textbook Question
Chapter 9, Problem 4CQ
A wrecking ball is being used to knock down a building. One tall unsupported concrete wall remains standing. If the wrecking ball hits the wall near the top, is the wall more likely to fall over by rotating at its base or by falling straight down? Explain your answer. How is it most likely to fall if it is struck with the same force at its base? Note that this depends on how firmly the wall is attached at its base.
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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.
(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
Fv=AAμ.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
[5 marks]
(b)…
Chapter 9 Solutions
College Physics
Ch. 9 - What can you say about the velocity of a moving...Ch. 9 - Under what conditions can a rotating body be in...Ch. 9 - What three factors affect the torque created by a...Ch. 9 - A wrecking ball is being used to knock down a...Ch. 9 - Mechanics put a length of Pipe over the handle of...Ch. 9 - Prob. 6CQCh. 9 - Explain the need for tall towers on a suspension...Ch. 9 - When visiting some countries, you may see a person...Ch. 9 - Prob. 9CQCh. 9 - Prob. 10CQ
Ch. 9 - Why are the forces exerted on the outside world by...Ch. 9 - Explain why the forces in our joints are several...Ch. 9 - Why are the forces exerted on the outside world by...Ch. 9 - Explain why the forces in our joints are several...Ch. 9 - Certain of dinosaurs were bipedal (walked on two...Ch. 9 - Swimmers and athletes during competition need to...Ch. 9 - If the maximum force the biceps muscle can exert...Ch. 9 - Suppose the biceps muscle was attached through...Ch. 9 - Explain one of the reasons why pregnant women...Ch. 9 - (a) When opening a door, you push on it...Ch. 9 - When tightening a bolt, you push perpendicularly...Ch. 9 - Two children push on opposite sides of a door...Ch. 9 - Use the second condition for equilibrium (net =0 )...Ch. 9 - Repeat the seesaw problem in Example 9.1 with the...Ch. 9 - Prob. 6PECh. 9 - Two children of mass 20.0 kg and 30.0 kg sit...Ch. 9 - Prob. 8PECh. 9 - A person carries a plank of wood 2.00 m long with...Ch. 9 - Prob. 10PECh. 9 - Prob. 11PECh. 9 - Prob. 12PECh. 9 - Prob. 13PECh. 9 - Prob. 14PECh. 9 - Prob. 15PECh. 9 - Prob. 16PECh. 9 - To get up on the roof, a person (mass 70.0 kg)...Ch. 9 - Prob. 18PECh. 9 - Prob. 19PECh. 9 - Suppose you needed to raise a 250-kg mower a...Ch. 9 - Prob. 21PECh. 9 - Prob. 22PECh. 9 - Prob. 23PECh. 9 - Prob. 24PECh. 9 - Prob. 25PECh. 9 - Prob. 26PECh. 9 - Prob. 27PECh. 9 - Prob. 28PECh. 9 - Prob. 29PECh. 9 - Prob. 30PECh. 9 - Prob. 31PECh. 9 - Prob. 32PECh. 9 - Prob. 33PECh. 9 - Prob. 34PECh. 9 - Prob. 35PECh. 9 - Integrated Concepts Suppose we replace the 4.0-kg...Ch. 9 - Prob. 37PECh. 9 - You have just planted a sturdy 2-m-tall palm tree...Ch. 9 - Unreasonable Results Suppose two children are...Ch. 9 - Construct Your Own Problem Consider a method for...Ch. 9 - Prob. 1TPCh. 9 - Prob. 2TPCh. 9 - Prob. 3TPCh. 9 - Prob. 4TPCh. 9 - Prob. 5TPCh. 9 - Prob. 6TPCh. 9 - Prob. 7TPCh. 9 - Prob. 8TPCh. 9 - Prob. 9TPCh. 9 - Prob. 10TPCh. 9 - Prob. 11TP
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