College Physics
OER 2016 Edition
ISBN: 9781947172173
Author: OpenStax
Publisher: OpenStax College
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Textbook Question
Chapter 1, Problem 11PE
Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)?
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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
Ch. 1 - Models are particularly useful in relativity and...Ch. 1 - How does a model differ from a theory?Ch. 1 - If two different theories describe experimental...Ch. 1 - What determines the validity of a theory?Ch. 1 - Certain criteria must be satisfied if a...Ch. 1 - Can the validity of a model be limited, or must it...Ch. 1 - Classical physics is a good approximation to...Ch. 1 - When is it necessary to use relativistic quantum...Ch. 1 - Can classical physics be used to accurately...Ch. 1 - Identify some advantages of metric units.
Ch. 1 - What is the relationship between the accuracy and...Ch. 1 - Prescriptions for vision correction are given in...Ch. 1 - The speed limit on some interstate highways is...Ch. 1 - A car is traveling at a speed of 33 m/s. (a) What...Ch. 1 - Show that 1.0m/s=3.6Km/h. Hint: Show the explicit...Ch. 1 - American football is played on a 100-yd-long...Ch. 1 - Soccer fields vary in size. A large soccer field...Ch. 1 - What is the height in meters of a person who is 6...Ch. 1 - Mount Everest, at 29,028 feet, is the tallest...Ch. 1 - The speed of sound is measured to be 342 m/s on a...Ch. 1 - Tectonic plates are large segments of the Earth's...Ch. 1 - (a) Refer to Table 1.3 to determine the average...Ch. 1 - Suppose that your bathroom scale reads your mass...Ch. 1 - A good-quality measuring tape can be off by 0.50...Ch. 1 - (a) A car speedometer has a 5.0% uncertainty. What...Ch. 1 - An infant's pulse rate is measured to be 1305...Ch. 1 - (a) Suppose that a person has an average heart...Ch. 1 - A can contains 375 mL of soda. How much is left...Ch. 1 - State how many significant figures are proper in...Ch. 1 - (a) How many significant figures are in the...Ch. 1 - (a) If your speedometer has an uncertainty of 2.0...Ch. 1 - (a) A person's blood pressure is measured to be...Ch. 1 - A person measures his or her heart rate by...Ch. 1 - What is the area of a circle 3.102 cm in diameter?Ch. 1 - If a marathon runner averages 9.5 mi/h, how long...Ch. 1 - A marathon runner completes a 42.188-km course in...Ch. 1 - The sides of a small rectangular box are measured...Ch. 1 - When non-metric units were used in the United...Ch. 1 - The length and width of a rectangular room are...Ch. 1 - A car engine moves a piston with a circular cross...Ch. 1 - How many heartbeats are there in a lifetime?Ch. 1 - A generation is about one-third of a lifetime....Ch. 1 - How many times longer than the mean life of an...Ch. 1 - Calculate the approximate number of atoms in a...Ch. 1 - Approximately how many atoms thick is a cell...Ch. 1 - (a) What fraction of Earth's diameter is the...Ch. 1 - (a) Calculate the number of cells in a hummingbird...Ch. 1 - Assuming one nerve impulse must end before another...
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