Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 19, Problem 19.3CQ
(a)
To determine
The prediction of
(b)
To determine
The condition for which the prediction of ideal
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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
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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
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Question 03
i)
Define the angular velocity of a rotating body and give its SI unit
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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 19 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
Ch. 19 - Prob. 19.1QQCh. 19 - Consider the following pairs of materials. Which...Ch. 19 - If you are asked to make a very sensitive glass...Ch. 19 - Two spheres are made of the same metal and have...Ch. 19 - A common material for cushioning objects in...Ch. 19 - On a winter day, you turn on your furnace and the...Ch. 19 - Markings to indicate length are placed on a steel...Ch. 19 - When a certain gas under a pressure of 5.00 106...Ch. 19 - If the volume of an ideal gas is doubled while its...Ch. 19 - The pendulum of a certain pendulum clock is made...
Ch. 19 - A temperature of 162F is equivalent to what...Ch. 19 - A cylinder with a piston holds 0.50 m3 of oxygen...Ch. 19 - What would happen if the glass of a thermometer...Ch. 19 - A cylinder with a piston contains a sample of a...Ch. 19 - Two cylinders A and B at the same temperature...Ch. 19 - A rubber balloon is filled with 1 L of air at 1...Ch. 19 - The average coefficient of linear expansion of...Ch. 19 - Suppose you empty a tray of ice cubes into a bowl...Ch. 19 - A hole is drilled in a metal plate. When the metal...Ch. 19 - On a very cold day in upstate New York, the...Ch. 19 - Common thermometers are made of a mercury column...Ch. 19 - A piece of copper is dropped into a beaker of...Ch. 19 - Prob. 19.3CQCh. 19 - Some picnickers stop at a convenience store to buy...Ch. 19 - Prob. 19.5CQCh. 19 - Prob. 19.6CQCh. 19 - An automobile radiator is filled to the brim with...Ch. 19 - When the metal ring and metal sphere in Figure...Ch. 19 - Prob. 19.9CQCh. 19 - Prob. 19.10CQCh. 19 - Prob. 19.1PCh. 19 - The temperature difference between the inside and...Ch. 19 - Prob. 19.3PCh. 19 - Prob. 19.4PCh. 19 - Liquid nitrogen has a boiling point of 195.81C at...Ch. 19 - Death Valley holds the record for the highest...Ch. 19 - Prob. 19.7PCh. 19 - The concrete sections of a certain superhighway...Ch. 19 - The active element of a certain laser is made of a...Ch. 19 - Prob. 19.10PCh. 19 - A copper telephone wire has essentially no sag...Ch. 19 - A pair of eyeglass frames is made of epoxy...Ch. 19 - The Trans-Alaska pipeline is 1 300 km long,...Ch. 19 - Prob. 19.14PCh. 19 - A square hole 8.00 cm along each side is cut in a...Ch. 19 - The average coefficient of volume expansion for...Ch. 19 - At 20.0C, an aluminum ring has an inner diameter...Ch. 19 - Why is the following situation impossible? A thin...Ch. 19 - A volumetric flask made of Pyrex is calibrated at...Ch. 19 - Review. On a day that the temperature is 20.0C, a...Ch. 19 - Prob. 19.21PCh. 19 - Review. The Golden Gate Bridge in San Francisco...Ch. 19 - Prob. 19.23PCh. 19 - A sample of a solid substance has a mass m and a...Ch. 19 - An underground gasoline lank can hold 1.00 103...Ch. 19 - A rigid lank contains 1.50 moles of an ideal gas....Ch. 19 - Prob. 19.27PCh. 19 - Your father and your younger brother are...Ch. 19 - Gas is contained in an 8.00-L vessel al a...Ch. 19 - A container in the shape of a cube 10.0 cm on each...Ch. 19 - An auditorium has dimensions 10.0 m 20.0 m 30.0...Ch. 19 - The pressure gauge on a lank registers the gauge...Ch. 19 - Prob. 19.33PCh. 19 - Prob. 19.34PCh. 19 - A popular brand of cola contains 6.50 g of carbon...Ch. 19 - In state-of-the-art vacuum systems, pressures as...Ch. 19 - An automobile tire is inflated with air originally...Ch. 19 - Review. To measure how far below the ocean surface...Ch. 19 - Review. The mass of a hot-air balloon and its...Ch. 19 - A room of volume V contains air having equivalent...Ch. 19 - Review. At 25.0 in below the surface of the sea,...Ch. 19 - Prob. 19.42PCh. 19 - A cook puts 9.00 g of water in a 2.00-L pressure...Ch. 19 - The pressure gauge on a cylinder of gas registers...Ch. 19 - Prob. 19.45APCh. 19 - A steel beam being used in the construction of a...Ch. 19 - A spherical steel ball bearing has a diameter of...Ch. 19 - A bicycle tire is inflated to a gauge pressure of...Ch. 19 - In a chemical processing plant, a reaction chamber...Ch. 19 - Why is the following situation impossible? An...Ch. 19 - A mercury thermometer is constructed as shown in...Ch. 19 - A liquid with a coefficient of volume expansion ...Ch. 19 - Prob. 19.53APCh. 19 - Two metal bars are made of invar and a third bar...Ch. 19 - A student measures the length of a brass rod with...Ch. 19 - The density of gasoline is 730 kg/m3 at 0C. Its...Ch. 19 - A liquid has a density . (a) Show that the...Ch. 19 - Prob. 19.58APCh. 19 - Review. A dock with a brass pendulum has a period...Ch. 19 - A bimetallic strip of length L is made of two...Ch. 19 - The rectangular plate shown in Figure P18.37 has...Ch. 19 - The measurement of the average coefficient of...Ch. 19 - Prob. 19.63APCh. 19 - A vertical cylinder of cross-sectional area A is...Ch. 19 - Review. Consider an object with any one of the...Ch. 19 - (a) Show that the density of an ideal gas...Ch. 19 - You are watching a new bridge being built near...Ch. 19 - You are watching a new bridge being built near...Ch. 19 - Review. (a) Derive an expression for the buoyant...Ch. 19 - Prob. 19.70APCh. 19 - Starting with Equation 18.11, show that the total...Ch. 19 - Review. A steel wire and a copper wire, each of...Ch. 19 - Review. A steel guitar string with a diameter of...Ch. 19 - A cylinder is closed by a piston connected to a...Ch. 19 - Prob. 19.75CPCh. 19 - A cylinder that has a 40.0-cm radius and is 50.0...Ch. 19 - Prob. 19.77CPCh. 19 - Review. A house roof is a perfectly flat plane...Ch. 19 - A 1.00-km steel railroad rail is fastened securely...
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