College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 9, Problem 17P
Buoyant Forces and Archimedes’ Principle
A table-tennis ball has a diameter of 3.80 cm and average density of 0.084 0 g/cm3. What force is required to hold it completely submerged under water?
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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
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Chapter 9 Solutions
College Physics
Ch. 9.2 - Suppose you have one cubic meter of gold, two...Ch. 9.3 - The pressure at the bottom of a glass filled with...Ch. 9.4 - Several common barometers are built using a...Ch. 9.4 - Blood pressure is normally measured with the cuff...Ch. 9.5 - Atmospheric pressure varies from day to day. The...Ch. 9.5 - The density of lead is greater than iron, and both...Ch. 9.6 - You observe two helium balloons floating next to...Ch. 9 - The three containers in Figure CQ9.1 are filled...Ch. 9 - The density of air is 1.3 kg/m3 at sea level. From...Ch. 9 - Four solid, uniform objects are placed in a...
Ch. 9 - Figure CQ9.4 shows aerial views from directly...Ch. 9 - Prob. 5CQCh. 9 - Prob. 6CQCh. 9 - Water flows along a streamline down a river of...Ch. 9 - During inhalation, the pressure in the lungs is...Ch. 9 - The water supply for a city is often provided from...Ch. 9 - An ice cube is placed in a glass of water. What...Ch. 9 - Prob. 11CQCh. 9 - Will an ice cube float higher in water or in an...Ch. 9 - Prob. 13CQCh. 9 - Prob. 14CQCh. 9 - A person in a boat floating in a small pond throws...Ch. 9 - One of the predicted problems due to global...Ch. 9 - An 81.5kg man stands on a horizontal surface. (a)...Ch. 9 - The weight of Earths atmosphere exerts an average...Ch. 9 - Calculate the mass of a solid gold rectangular bar...Ch. 9 - Prob. 5PCh. 9 - Prob. 6PCh. 9 - Suppose a distant world with surface gravity of...Ch. 9 - Prob. 8PCh. 9 - (a) Calculate the absolute pressure at the bottom...Ch. 9 - Mercury is poured into a U-tube as shown in Figure...Ch. 9 - A collapsible plastic bag (Fig. F9.11) contains a...Ch. 9 - A hydraulic jack has an input piston of area 0.050...Ch. 9 - A container is filled to a depth of 20.0 cm with...Ch. 9 - Blaise Pascal duplicated Torricellis barometer...Ch. 9 - A sphygmomanometer is a device used to measure...Ch. 9 - Piston in Figure P9.16 has a diameter of 0.25...Ch. 9 - Buoyant Forces and Archimedes Principle A...Ch. 9 - Prob. 18PCh. 9 - A small ferryboat is 4.00 m wide and 6.00 m long....Ch. 9 - A 62.0-kg survivor of a cruise line disaster rests...Ch. 9 - A hot-air balloon consists of a basket banging...Ch. 9 - A large balloon of mass 226 kg is filled with...Ch. 9 - A spherical weather balloon is filled with...Ch. 9 - The average human has a density of 945 kg/m3 after...Ch. 9 - On October 21, 2001, Ian Ashpole of the United...Ch. 9 - The gravitational force exerted on a solid object...Ch. 9 - A cube of wood having an edge dimension of 20.0 cm...Ch. 9 - A light spring of force constant k = 160 N/m rests...Ch. 9 - A sample of an unknown material appears to weigh...Ch. 9 - An object weighing 300 N in air is immersed in...Ch. 9 - A 1.00-kg beaker containing 2.00 kg of oil...Ch. 9 - A horizontal pipe narrows from a radius of 0.250 m...Ch. 9 - A large water tank is 3.00 m high and filled lo...Ch. 9 - Wafer flowing through a garden hose of diameter...Ch. 9 - Prob. 35PCh. 9 - Prob. 36PCh. 9 - A hypodermic syringe contain a medicine with the...Ch. 9 - When a person inhales, air moves down the bronchus...Ch. 9 - A jet airplane in level flight has a mass of 8.66 ...Ch. 9 - A man attaches a divider to an outdoor faucet so...Ch. 9 - Prob. 41PCh. 9 - Prob. 42PCh. 9 - A jet of water squirts out horizontally from a...Ch. 9 - A large storage tank, open to the atmosphere at...Ch. 9 - The inside diameters of the larger portions of the...Ch. 9 - Water is pumped through a pipe of diameter 15.0 cm...Ch. 9 - Old Faithful geyser in Yellowstone Park erupts at...Ch. 9 - The Venturi tube shown in Figure P9.48 may be used...Ch. 9 - Prob. 49PCh. 9 - Prob. 50PCh. 9 - A certain fluid has a density of 1.080 kg/m3 and...Ch. 9 - Whole blood has a surface tension of 0.058 N/m and...Ch. 9 - Prob. 53PCh. 9 - Prob. 54PCh. 9 - Prob. 55PCh. 9 - Prob. 56PCh. 9 - Spherical panicles of a protein of density 1.8...Ch. 9 - A hypodermic needle is 3.0 era in length and 0.30...Ch. 9 - Prob. 59PCh. 9 - The aorta in humans has a diameter of about 2.0...Ch. 9 - Prob. 61PCh. 9 - Glycerin in water diffuses along a horizontal...Ch. 9 - Prob. 63PCh. 9 - Small spheres of diameter 1.00 mm fall through 20C...Ch. 9 - The Deformation of Solids 65. A 200.-kg load is...Ch. 9 - A 25.0-m long steel cable with a cross-sectional...Ch. 9 - A plank 2.00 cm thick and 15.0 cm wide is firmly...Ch. 9 - Artificial diamonds can be made using...Ch. 9 - For safety in climbing, a mountaineer uses a nylon...Ch. 9 - Assume that if the shear stress in steel exceeds...Ch. 9 - Bone has a Youngs modulus of 18 109 Pa. Under...Ch. 9 - A stainless-steel orthodontic: wire is applied to...Ch. 9 - A high-speed lifting mechanism supports an 800.-kg...Ch. 9 - The deepest point in the ocean is in the Mariana...Ch. 9 - Prob. 75PCh. 9 - The total cross-sectional area of the load-bearing...Ch. 9 - An iron block of volume 0.20 m5 is suspended from...Ch. 9 - Prob. 78APCh. 9 - In most species of clingfish (family...Ch. 9 - Prob. 80APCh. 9 - Prob. 81APCh. 9 - Superman attempts to drink water through a very...Ch. 9 - The human brain and spinal cord are immersed in...Ch. 9 - A Hydrometer is an instrument used to determine...Ch. 9 - Prob. 85APCh. 9 - A helium-filled balloon, whose envelope has a mass...Ch. 9 - A light spring of constant A = 90.0 N/m is...Ch. 9 - A U-tube open at both ends is partially filled...Ch. 9 - In about 1657. Otto von Guericke, inventor of the...Ch. 9 - Oil having a density of 930 kg/m3 floats on water....Ch. 9 - Prob. 91AP
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