Pearson eText for College Physics: Explore and Apply -- Instant Access (Pearson+)
2nd Edition
ISBN: 9780137443000
Author: Eugenia Etkina, Gorazd Planinsic
Publisher: PEARSON+
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Textbook Question
Chapter 10, Problem 43P
* Pendulum on Mars The frequency of a pendulum is
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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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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
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Chapter 10 Solutions
Pearson eText for College Physics: Explore and Apply -- Instant Access (Pearson+)
Ch. 10 - Review Question 10.1 Can we say that the period of...Ch. 10 - Review Question 10.2 The velocity of an object...Ch. 10 - Review Question 10.3
What will happen to the...Ch. 10 - Review Question 10.4 The period of vibration of a...Ch. 10 - Review Question 10.5 Your grandfathers pendulum...Ch. 10 - Why was it important to assume that the springs...Ch. 10 - Review Question 10.7 What features of damped...Ch. 10 - Review Question 10.8 Describe the phenomenon of...Ch. 10 - 1. What are the features that make vibrational...Ch. 10 - 2. What does it mean if the amplitude of an...
Ch. 10 - 3. What does it mean if the period of an object’s...Ch. 10 - 4. What is the period of the kinetic or the...Ch. 10 - 5. A cart undergoing simple harmonic motion has a...Ch. 10 - The period of the object attached to a spring is...Ch. 10 - You have a simple harmonic oscillator. Where is...Ch. 10 - You have a simple harmonic oscillator. Where is...Ch. 10 - Which of the following arguments can be used to...Ch. 10 - 10. (a) Give three common examples of vibrational...Ch. 10 - An object of known mass hangs at the end of a...Ch. 10 - Describe two different ways to estimate the spring...Ch. 10 - You have a small metal ball attached to a 1.0-m...Ch. 10 - 14. A pendulum clock is running too fast. Explain...Ch. 10 - What simplifications were used to derive the...Ch. 10 - A pendulum clock is moved from the Mississippi...Ch. 10 - 17. Oil is often found in a geological structure...Ch. 10 - A pendulum and a block hanging at the end of a...Ch. 10 - Will me frequency of vibration of a swing when you...Ch. 10 - The amplitude of vibration of a swing slowly...Ch. 10 - 23. If you walk with your arms hanging down, they...Ch. 10 - You have a pendulum with a 1-m string. What is the...Ch. 10 - 1. A low-friction cart is placed between two...Ch. 10 - * You have a ball bearing ano a bowl. You let the...Ch. 10 - 3. Draw a sketch of a pendulum indicate the...Ch. 10 - Draw a graph showing the position-versus-time...Ch. 10 - Suppose that at time zero the can attached to the...Ch. 10 - * (a) Sketch a motion diagram and a...Ch. 10 - * Devise a position-versus-time function that...Ch. 10 - * The position of a vibrating object changes as a...Ch. 10 - * The velocity of a vibrating object changes as a...Ch. 10 - 11. * A cart at the end of a spring undergoes...Ch. 10 - 12. ** Refer to the situation in Problem 10.1. (a)...Ch. 10 - You exert a 100-N pull on the end of a spring....Ch. 10 - Metronome You want to make a metronome for music...Ch. 10 - Determine the frequency of vibration of the cart...Ch. 10 - 16. * A spring with a cart at its end vibrates at...Ch. 10 - 17. A cart with mass m vibrating at the end of a...Ch. 10 - 18. * A 300-g apple is placed on a horizontal...Ch. 10 - ** A 2.0-kg cart vibrates at the end of an 18-N/m...Ch. 10 - * What were the main ideas that we used to derive...Ch. 10 - 21. * A spring with a spring constant of 1200 N/m...Ch. 10 - 22. * A person exerts a 15-N force on a cart...Ch. 10 - 23. A spring with spring constant has a 1.4-kg...Ch. 10 - * Proportional reasoning By what factor must we...Ch. 10 - Proportional reasoning By what factor must we...Ch. 10 - 26. Monkey trick at zoo A monkey has a cart with a...Ch. 10 - 27. * A frictionless cart attached to a spring...Ch. 10 - A 2.0-kg cart attached to a spring undergoes...Ch. 10 - 29 * The motion of a cart attached to a horizontal...Ch. 10 - 30. Pendulum clock Shawn wants to build a clock...Ch. 10 - Show that the expression for the frequency of a...Ch. 10 - A pendulum swings with amplitude 0.020 m and...Ch. 10 - 33. * Proportional reasoning You are designing a...Ch. 10 - 34. * Building demolition A 500-kg ball at the end...Ch. 10 - 35. * You have a pendulum with a long string whose...Ch. 10 - * Variations in g The frequency of a person's...Ch. 10 - 37. EST A graph of position versus time for an...Ch. 10 - Determine the period of a 1.3-m-long pendulum on...Ch. 10 - * You have a simple pendulum that consists of a...Ch. 10 - * Equation Jeopardy The following expression...Ch. 10 - 41. * Trampoline vibration When a 60-kg boy sits...Ch. 10 - * Proportional reasoning if you double the...Ch. 10 - 43. * Pendulum on Mars The frequency of a pendulum...Ch. 10 - 44. * bio EST Annoying sound low-frequency...Ch. 10 - 45.** A 1.2-kg block sliding at 6.0 m/s on a...Ch. 10 - 108 kg. The tower sways back and forth at a...Ch. 10 - ** You shoot a 0.050-kg arrow into a 0.50-kg...Ch. 10 - 48. * You have a pendulum whose length is 1.3 m...Ch. 10 - * You hang a 0.10-kg block from a spring, causing...Ch. 10 - 50. * imagine that you have a cart on a spring...Ch. 10 - 51. Describe one situation from everyday life in...Ch. 10 - EST twins on a swing How frequently do you need to...Ch. 10 - 53. (a) Determine the maximum speed of a girl on a...Ch. 10 - Prob. 54PCh. 10 - 55. * Feeling road vibrations in a car if the...Ch. 10 - 57. A spring oscillator and a simple pendulum have...Ch. 10 - * You attach a block (mass m) to a spring (spring...Ch. 10 - * You attach a 1.6-kg object to a spring, pull it...Ch. 10 - 60. * Traveling through Earth A hole is drilled...Ch. 10 - 61. * EST Estimate the effective spring constant...Ch. 10 - *Galileos pendulum The length L of a pendulum is...Ch. 10 - 63. * A 0.5-kg low-friction cart is moving at...Ch. 10 - 103N/m. Determine (a) by how much the ball...Ch. 10 - 67. * A 5.0-g bullet traveling horizontally at an...Ch. 10 - at the start of the swinging. (a) Determine an...Ch. 10 - 70. ** Foucault's pendulum in 1851, the French...Ch. 10 - pushed to the left with initial speed v0....Ch. 10 - Prob. 72RPPCh. 10 - Prob. 73RPPCh. 10 - Prob. 74RPPCh. 10 - Prob. 75RPPCh. 10 - Prob. 76RPPCh. 10 - Prob. 77RPPCh. 10 - BIO Resonance vibration transfer and the ear When...Ch. 10 - BIO Resonance vibration transfer and the ear When...Ch. 10 - BIO Resonance vibration transfer and the ear When...Ch. 10 - BIO Resonance vibration transfer and the ear When...Ch. 10 - BIO Resonance vibration transfer and the ear When...
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