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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Chapter 13, Problem 46PE
Hydrogen molecules (molecular mass is equal to
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ROTATIONAL DYNAMICS
Question 01
A solid circular cylinder and a solid spherical ball of the same mass and radius are rolling
together down the same inclined. Calculate the ratio of their kinetic energy. Assume pure
rolling motion Question 02
A sphere and cylinder of the same mass and radius start from ret at the same point and more
down the same plane inclined at 30° to the horizontal
Which body gets the bottom first and what is its acceleration
b) What angle of inclination of the plane is needed to give the slower body the same
acceleration
Question 03
i)
Define the angular velocity of a rotating body and give its SI unit
A car wheel has its angular velocity changing from 2rads to 30 rads
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ii)
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Question 04
in 20
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 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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