College Physics for AP Courses
1st Edition
ISBN: 9781630181871
Author: OpenStax, Ima Lyubkinskaya, Gregg Wolfe Douglas, Ingram, Liza Puiji, Sudhi Oberoi Nathan, Czuba
Publisher: OpenStax College.
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Textbook Question
Chapter 13, Problem 8CQ
Does it really help to run hot water over a tight metal lid on a glass jar before flying to open it? Explain your answer.
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Check out a sample textbook solutionStudents have asked these similar questions
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 13 Solutions
College Physics for AP Courses
Ch. 13 - What does it mean to say that two systems are in...Ch. 13 - Give an example of a physical property that varies...Ch. 13 - When a cold alcohol thermometer is placed in a hot...Ch. 13 - If you add boiling water to a cup at room...Ch. 13 - Thermal stresses caused by uneven cooling can...Ch. 13 - Water expands significantly when it freezes: a...Ch. 13 - One method at getting a tight fit, say of a metal...Ch. 13 - Does it really help to run hot water over a tight...Ch. 13 - Liquids and solids expand with increasing...Ch. 13 - Find out the human population of Earth. Is there a...
Ch. 13 - Under what circumstances would you expect a gas to...Ch. 13 - A constant-volume gas thermometer contains a fixed...Ch. 13 - How is momentum related to the pressure exerted by...Ch. 13 - A pressure cooker contains water and steam in...Ch. 13 - Why does condensation from most rapidly on the...Ch. 13 - What is the vapor pressure of solid carbon dioxide...Ch. 13 - Can carbon dioxide be liquefied at room...Ch. 13 - Oxygen cannot be liquefied at room temperature by...Ch. 13 - What is the distinction between gas and vapor?Ch. 13 - Because humidity depends only on water's vapor...Ch. 13 - Why does a beaker of 40.0C water placed in a...Ch. 13 - Why does rubbing alcohol evaporate much more...Ch. 13 - What is me Fahrenheit temperature of a person with...Ch. 13 - Frost damage to most plants occurs at temperatures...Ch. 13 - To conserve energy, room temperatures are kept at...Ch. 13 - A tungsten light bulb filament may operate a1 2900...Ch. 13 - The Surface temperature of the Sun is about 5750...Ch. 13 - One of the honest temperatures ever recorded on...Ch. 13 - (a) Suppose a cold front blows into your locale...Ch. 13 - (a) At what temperature do the Fahrenheit and...Ch. 13 - The height of the Washington Monument is measured...Ch. 13 - How much taller does me Eiffel Tower become at the...Ch. 13 - What is the change in length of a 3.00mlong column...Ch. 13 - How large an expansion gap should be left between...Ch. 13 - You are looking to purchase a small piece of land...Ch. 13 - Global warming will produce rising sea levels...Ch. 13 - Show that 60.0L of gasoline originally at 15.0C...Ch. 13 - (a) Suppose a meter Stick made of steel and one...Ch. 13 - (a) If a 500mL glass beaker is filled to the brim...Ch. 13 - Most automobiles have a coolant reservoir to catch...Ch. 13 - A physicist makes a cup of instant coffee and...Ch. 13 - (a) The density of water at 0C is very nearly...Ch. 13 - Show that 3, by calculating the change in volume V...Ch. 13 - The gauge pressure in your car tires is...Ch. 13 - Convert an absolute pressure of 7.00105N/m2 to...Ch. 13 - Suppose a gasfilled incandescent light bulb is...Ch. 13 - Large helium-filled balloons are used to lift...Ch. 13 - Confirm mat the units of nRT are those of energy...Ch. 13 - In the text, it was shown that N/V=2.681025m3 for...Ch. 13 - Calculate the number of moles in me 2.00L volume...Ch. 13 - An airplane passenger has 100cm3 of air in his...Ch. 13 - (a) What is me 1imlume (in km3) of Avogadro’s...Ch. 13 - An expensive vacuum System can achieve a pressure...Ch. 13 - The number density of gas atoms at a certain...Ch. 13 - A bicycle tire has a pressure of 7.00105N/m2 at a...Ch. 13 - A high—pressure gas cylinder contains 50.13L of...Ch. 13 - Find the number of moles in 2.00L of gas at 35.0C...Ch. 13 - Calculate the depth to which Avogadro's number of...Ch. 13 - (a) What is me gauge pressure in a 25.0C car tire...Ch. 13 - (a) In the deep space between galaxies, me density...Ch. 13 - Some incandescent light bulbs are filled with...Ch. 13 - Average atomic and molecular speeds (vrms) are...Ch. 13 - (a) What is the average kinetic energy in joules...Ch. 13 - The escape velocity of any object from Earth is...Ch. 13 - The escape velocity from the Moon is much smaller...Ch. 13 - Nuclear fusion, the energy source at the Sun,...Ch. 13 - Suppose that the average velocity (vrms) of carbon...Ch. 13 - Hydrogen molecules (molecular mass is equal to...Ch. 13 - Much of The 935 near the Sun is atomic hydrogen....Ch. 13 - There are two important isotopes of uranium 235U...Ch. 13 - Dry air is 78.1% nitrogen. What is the partial...Ch. 13 - (a) What is me vapor pressure of water at 20.0C ?...Ch. 13 - Pressure cookers increase cooking speed by raising...Ch. 13 - (a) At what temperature does water boil at an...Ch. 13 - What is the atmospheric pressure on top of Mt....Ch. 13 - At a spot in the high Andes, water boils at 80.0C,...Ch. 13 - What is the relative humidity on a 25.0C day when...Ch. 13 - What is the density of water vapor in g/m3 on a...Ch. 13 - A deepsea diver should breathe a gas mixture that...Ch. 13 - The vapor pressure of water at 40.0C is...Ch. 13 - Air in human lungs has a temperature of 37.0C and...Ch. 13 - If the relative humidity is 90.0% on a muggy...Ch. 13 - Late on an autumn day, the relative humidity is...Ch. 13 - Atmospheric pressure amp Mt. Everest is...Ch. 13 - What is the dew point (the temperature at which...Ch. 13 - On a certain day the temperature is 25.0C and the...Ch. 13 - Integrated Concepts The boiling point of water...Ch. 13 - Integrated Concepts (a) At what depth in fresh...Ch. 13 - Integrated Concepts To get an idea of the small...Ch. 13 - Integrated Concepts If you want to cook in water...Ch. 13 - Unreasonable Results (a) How many moles per cubic...Ch. 13 - Unreasonable Results (a) An automobile mechanic...Ch. 13 - Unreasonable Results The temperature inside a...Ch. 13 - Unreasonable Results Suppose the relative humidity...
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