COLLEGE PHYSICS (LL W/WEBASSIGN)
11th Edition
ISBN: 9781337741644
Author: SERWAY
Publisher: CENGAGE L
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Question
Chapter 1, Problem 78AP
(a)
To determine
The time duration in years.
(b)
To determine
The number of bills required to encircle the planet.
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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 1 Solutions
COLLEGE PHYSICS (LL W/WEBASSIGN)
Ch. 1.9 - The magnitudes of two vectors A and B are 12 units...Ch. 1.10 - Figure 1.19 shows two vectors lying in the...Ch. 1.10 - Which vector has an angle with respect to the...Ch. 1 - Estimate the order of magnitude of the length, in...Ch. 1 - What types of natural phenomena could serve as...Ch. 1 - Find the order of magnitude of your age in...Ch. 1 - An object with a mass of 1 kg weighs approximately...Ch. 1 - (a) Estimate the number of times your heart beats...Ch. 1 - Estimate the number of atoms in 1 cm5 of a solid....Ch. 1 - Lacking modern timepieces, early experimenters...
Ch. 1 - Prob. 8CQCh. 1 - Prob. 9CQCh. 1 - List some advantages of the metric system of units...Ch. 1 - Estimate the time duration of each of the...Ch. 1 - Suppose two quantities, A and B, have different...Ch. 1 - Answer each question yes or no. Must two...Ch. 1 - Two different measuring devices are used by...Ch. 1 - If B is added to A, under what conditions does the...Ch. 1 - Under what circumstances would a vector have...Ch. 1 - The period of a simple pendulum, defined as the...Ch. 1 - (a) Suppose the displacement of an object is...Ch. 1 - A shape that covers an area A and has a uniform...Ch. 1 - Each of the following equations was given by a...Ch. 1 - Prob. 5PCh. 1 - Kinetic energy KE (Topic 5) has dimensions kg ...Ch. 1 - A rectangular airstrip measures 32.30 in by 210 m,...Ch. 1 - Use the rules for significant figures to find the...Ch. 1 - A carpet is to be installed in a room of length...Ch. 1 - Prob. 10PCh. 1 - How many significant figures are there in (a) 78.9...Ch. 1 - The speed of light is now defined to be 2.997 924...Ch. 1 - A rectangle has a length of (2.0 0.2) m and a...Ch. 1 - The radius of a circle is measured to be (10.5 ...Ch. 1 - The edges of a shoebox are measured to be 11.4 cm,...Ch. 1 - Carry out the following arithmetic operations: (a)...Ch. 1 - The Roman cubitus is an ancient unit of measure...Ch. 1 - A house is advertised as having 1 420 square feet...Ch. 1 - A fathom is a unit of length, usually reserved for...Ch. 1 - A small turtle moves at a speed of 186 furlongs...Ch. 1 - A firkin is an old British unit of volume equal to...Ch. 1 - Find the height or length of these natural wonders...Ch. 1 - A car is traveling at a speed of 38.0 m/s on an...Ch. 1 - A certain car has a fuel efficiency of 25.0 miles...Ch. 1 - The diameter of a sphere is measured to be 5.36...Ch. 1 - Suppose your hair grows at the rate of 1/32 inch...Ch. 1 - The speed of light is about 3.00 108 m/s. Convert...Ch. 1 - A house is 50.0 ft long and 26 ft wide and has...Ch. 1 - The amount of water in reservoirs is often...Ch. 1 - The base of a pyramid covers an area of 13.0 acres...Ch. 1 - A quart container of ice cream is to be made in...Ch. 1 - Estimate the number of steps you would have to...Ch. 1 - Estimate the number of breaths taken by a human...Ch. 1 - Estimate the number of people in the world who are...Ch. 1 - The habitable part of Earths surface has been...Ch. 1 - Treat a cell in a human as a sphere of radius 1.0...Ch. 1 - An automobile tire is rated to last for 50 000...Ch. 1 - A study from the National Institutes of Health...Ch. 1 - A point is located in a polar coordinate system by...Ch. 1 - A certain corner of a room is selected as the...Ch. 1 - Express the location of the fly in Problem 40 in...Ch. 1 - Two points in a rectangular coordinate system have...Ch. 1 - Two points are given in polar coordinates by (r, )...Ch. 1 - Given points (r1, 1) and (r2, 2) in polar...Ch. 1 - For the triangle shown in Figure P1.45, what are...Ch. 1 - A ladder 9.00 m long leans against the side of a...Ch. 1 - A high fountain of water is located at the center...Ch. 1 - A right triangle has a hypotenuse of length 3.00...Ch. 1 - In Figure P1.49, find (a) the side opposite , (b)...Ch. 1 - In a certain right triangle, the two sides that...Ch. 1 - In Problem 50, what is the tangent of the angle...Ch. 1 - A woman measures the angle of elevation of a...Ch. 1 - A surveyor measures the distance across a straight...Ch. 1 - Vector A has a magnitude of 8.00 units and makes...Ch. 1 - Vector A has a magnitude of 29 units and points in...Ch. 1 - An airplane flies 2.00 102 km due west from city...Ch. 1 - Vector A is 3.00 units in length and points along...Ch. 1 - A force F1, of magnitude 6.00 units acts on an...Ch. 1 - A roller coaster moves 2.00 102 ft horizontally...Ch. 1 - Calculate (a) the x-component and (b) the...Ch. 1 - A vector A has components Ax = 5.00 m and Ay =...Ch. 1 - A person walks 25.0 north of east for 3.10 km. How...Ch. 1 - The magnitude of vector A is 35.0 units and points...Ch. 1 - A figure skater glides along a circular path of...Ch. 1 - A girl delivering newspapers covers her route by...Ch. 1 - A quarterback takes the ball from the line of...Ch. 1 - A vector has an x-component of 25.0 units and a...Ch. 1 - A map suggests that Atlanta is 730. miles in a...Ch. 1 - The eye of a hurricane passes over Grand Bahama...Ch. 1 - The helicopter view in Figure P1.70 shows two...Ch. 1 - A commuter airplane starts from an airport and...Ch. 1 - (a) Find a conversion factor to convert from miles...Ch. 1 - The displacement of an object moving under uniform...Ch. 1 - Assume it takes 7.00 minutes to fill a 30.0-gal...Ch. 1 - One gallon of paint (volume = 3.79 103 m3) covers...Ch. 1 - A sphere of radius r has surface area A = 4r2 and...Ch. 1 - Assume there are 100 million passenger can in the...Ch. 1 - Prob. 78APCh. 1 - An average person sneezes about three times per...Ch. 1 - The nearest neutron star (a collated star made...
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