College Physics
1st Edition
ISBN: 9781938168000
Author: Paul Peter Urone, Roger Hinrichs
Publisher: OpenStax College
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Textbook Question
Chapter 11, Problem 15CQ
How do you convert pressure units like millimeters of mercury, centimeters of water, and inches of mercury into units like newtons per meter squared without resorting to a table of pressure conversion factors?
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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 11 Solutions
College Physics
Ch. 11 - What physical characteristic distinguishes a fluid...Ch. 11 - Which of the following substances are fluids at...Ch. 11 - Why are gases easier to compress than liquids and...Ch. 11 - How do gases differ from liquids?Ch. 11 - Approximately how does the density of air vary...Ch. 11 - Give an example in which density is used to...Ch. 11 - Figure 11.40 shows a glass of ice water filled to...Ch. 11 - How is pressure related to the sharpness of a...Ch. 11 - Why does a dull hypodermic needle hurt more than a...Ch. 11 - The outward force on one end of an air tank was...
Ch. 11 - Why is force exerted by static fluids always...Ch. 11 - In a remote location near the North Pole, an...Ch. 11 - How do jogging on soft ground and wearing padded...Ch. 11 - Toe dancing (as in ballet) is much harder on toes...Ch. 11 - How do you convert pressure units like millimeters...Ch. 11 - Atmospheric pressure exerts a large force (equal...Ch. 11 - Why does atmospheric pressure decrease more...Ch. 11 - What are two reasons why mercury rather than water...Ch. 11 - Figure 11.41 shows how sandbags placed around a...Ch. 11 - Why is it difficult to swim under water in the...Ch. 11 - Is there a net force on a due to atmospheric...Ch. 11 - Does atmospheric pressure add to the gas pressure...Ch. 11 - You can break a strong wine bottle by pounding a...Ch. 11 - Suppose the master cylinder in a hydraulic system...Ch. 11 - Explain why the fluid reaches equal levels on...Ch. 11 - Figure 11.17 shows how a common measurement of...Ch. 11 - Considering the magnitude of typical arterial...Ch. 11 - More force is required to pull the plug in a full...Ch. 11 - Do fluids exert buoyant forces in a "weightless"...Ch. 11 - Will the same ship float higher in salt water than...Ch. 11 - Marbles dropped into a partially filled bathtub...Ch. 11 - The density of oil is less than that of water, yet...Ch. 11 - Is surface tension due to cohesive or adhesive...Ch. 11 - Is capillary action due to cohesive or adhesive...Ch. 11 - Birds such as ducks, geese, and swans have greater...Ch. 11 - Water beads up on an oily sunbather, but not on...Ch. 11 - Could capillary action be used to move fluids in a...Ch. 11 - What effect does capillary action have on the...Ch. 11 - Pressure between the inside chest wall and the...Ch. 11 - Gold is sold by the troy ounce (31.103 g). What is...Ch. 11 - Mercury is commonly supplied in flasks containing...Ch. 11 - (a) What is the mass of a deep breath of air...Ch. 11 - A straightforward method of finding the density of...Ch. 11 - Suppose you have a coffee mug with a circular...Ch. 11 - (a) A rectangular gasoline tank can hold 50.0 kg...Ch. 11 - A trash compactor can reduce the volume of its...Ch. 11 - A 2.50-kg steel gasoline can holds 20.0 L of...Ch. 11 - What is the density of 18.0-karat gold that is a...Ch. 11 - There is relatively little empty space between...Ch. 11 - As a woman walks, her entire weight is momentarily...Ch. 11 - The pressure exerted by a phonograph needle on a...Ch. 11 - Nail tips exert tremendous pressures when they are...Ch. 11 - What depth of mercury creates a pressure of 1.00...Ch. 11 - The greatest ocean depths on the Earth are found...Ch. 11 - Verify that the SI unit of hpg is N/m2.Ch. 11 - Water towers store water above the level of...Ch. 11 - The aqueous humor in a person's eye is exerting a...Ch. 11 - How much force is exerted on one side of an 8.50...Ch. 11 - What pressure is exerted on the bottom of a...Ch. 11 - Calculate the average pressure exerted on the palm...Ch. 11 - The left side of the heart creates a pressure of...Ch. 11 - Show that the total force on a rectangular dam due...Ch. 11 - How much pressure is transmitted in the hydraulic...Ch. 11 - What force must be exerted on the master cylinder...Ch. 11 - A crass host pours the remnants of several bottles...Ch. 11 - A certain hydraulic system is designed to exert a...Ch. 11 - (a) Verify that work input equals work output for...Ch. 11 - Find the gauge and absolute pressures in the...Ch. 11 - (a) Convert normal blood pressure readings of 120...Ch. 11 - How tall must a water-filled manometer be to...Ch. 11 - Pressure cookers have been around for more than...Ch. 11 - Suppose you measure a standing person's blood...Ch. 11 - A submarine is stranded on the bottom of the ocean...Ch. 11 - Assuming bicycle tires are perfectly flexible and...Ch. 11 - What fraction of ice is submerged when it floats...Ch. 11 - Logs sometimes float vertically in a lake because...Ch. 11 - Find the density of a fluid in which a hydrometer...Ch. 11 - If your body has a density of 995 kg/m3, what...Ch. 11 - Bird bones have air pockets in them to reduce...Ch. 11 - A rock with a mass of 540 g in air is found to...Ch. 11 - Archimedes' principle can be used to calculate the...Ch. 11 - In an immersion measurement of a woman's density,...Ch. 11 - Some fish have a density slightly less than that...Ch. 11 - (a) Calculate the buoyant force on a 2.00-L helium...Ch. 11 - (a) What is the density of a woman who floats in...Ch. 11 - A certain man has a mass of 80 kg and a density of...Ch. 11 - A simple compass can be made by placing a small...Ch. 11 - What fraction of an iron anchor's weight will be...Ch. 11 - Scurrilous con artists have been known to...Ch. 11 - A twin-sized air mattress used for camping has...Ch. 11 - Referring to Figure 11.21, prove that the buoyant...Ch. 11 - (a) A 75.0-kg man floats in freshwater with 3.00%...Ch. 11 - What is the pressure inside an alveolus having a...Ch. 11 - (a) The pressure inside an alveolus with a 2.00104...Ch. 11 - What is the gauge pressure in millimeters of...Ch. 11 - Calculate the force on the slide wire in Figure...Ch. 11 - Figure 11.35(a) shows the effect of tube radius on...Ch. 11 - We stated in Example 11.12 that a xylem tube is of...Ch. 11 - What fluid is in the device shown in Figure 11.29...Ch. 11 - If the gauge pressure inside a rubber balloon with...Ch. 11 - Calculate the gauge pressures inside...Ch. 11 - Suppose water is raised by capillary action to a...Ch. 11 - Calculate the contact angle for olive oil if...Ch. 11 - When two soap bubbles touch, the larger is...Ch. 11 - Calculate the ratio of the heights to which water...Ch. 11 - What is the ratio of heights to which ethyl...Ch. 11 - During forced exhalation, such as when blowing up...Ch. 11 - You can chew through very tough objects with your...Ch. 11 - One way to force air into an unconscious person's...Ch. 11 - Heroes in movies hide beneath water and breathe...Ch. 11 - Gauge pressure in the fluid surrounding an...Ch. 11 - A full-term fetus typically has a mass of 3.50 kg....Ch. 11 - If the pressure in the esophagus is -2.00 mm Hg...Ch. 11 - Pressure in the spinal fluid is measured as shown...Ch. 11 - Calculate the maximum force in newtons exerted by...Ch. 11 - During heavy lifting, a disk between spinal...Ch. 11 - When a person sits erect, increasing the vertical...Ch. 11 - (a) How high will water rise in a glass capillary...Ch. 11 - A negative pressure of 25.0 atm can sometimes be...Ch. 11 - Suppose you hit a steel nail with a 0.500-kg...Ch. 11 - Calculate the pressure due to the ocean at the...Ch. 11 - The hydraulic system of a backhoe is used to lift...Ch. 11 - Some miners wish to remove water from a mine...Ch. 11 - You are pumping up a bicycle tire with a hand...Ch. 11 - Consider a group of people trying to stay afloat...Ch. 11 - The alveoli in emphysema victims are damaged and...
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