Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
4th Edition
ISBN: 9780133942651
Author: Randall D. Knight (Professor Emeritus)
Publisher: PEARSON
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Chapter 1, Problem 12EAP
A speed skater accelerates from rest and then keeps skating at a constant speed. Draw a complete motion diagram of the skater.
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Students have asked these similar questions
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
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
Ch. 1 - How many significant figures does each of the...Ch. 1 - How many significant figures does each of the...Ch. 1 - Is the particle in FIGURE Q1.3 speeding up?...Ch. 1 - Does the object represented in FIGURE Q1.4 have a...Ch. 1 - Does the object represented in FIGURE Q1.5 have a...Ch. 1 - Determine the signs (positive, negative, or zero)...Ch. 1 - Determine the signs (positive, negative, or zero)...Ch. 1 - Determine the signs (positive, negative, or zero)...Ch. 1 - A car skids to a halt to avoid hitting an object...Ch. 1 - Prob. 2EAP
Ch. 1 - You are watching a jet ski race. A racer speeds up...Ch. 1 - a. Write a paragraph describing the particle...Ch. 1 - You drop a soccer ball from your third-story...Ch. 1 - A baseball player starts running to the left to...Ch. 1 - A softball player slides into second base. Use the...Ch. 1 - a. FIGURE EX1.8 shows the first three points of a...Ch. 1 - FIGURE EX1.9 shows five points of a motion...Ch. 1 - FIGURE EX1.10 shows two dots of a motion diagram...Ch. 1 - FIGURE EX1.11 shows two dots of a motion diagram...Ch. 1 - A speed skater accelerates from rest and then...Ch. 1 - A car travels to the left at a steady speed for a...Ch. 1 - A goose flies toward a pond. It lands on the water...Ch. 1 - You use a long rubber band to launch a paper wad...Ch. 1 - A roof tile falls straight down from a two-story...Ch. 1 - Your roommate drops a tennis ball from a...Ch. 1 - 18. FIGURE EX1.18 shows the motion diagram of a...Ch. 1 - Prob. 19EAPCh. 1 - Prob. 20EAPCh. 1 - Draw a pictorial representation for the following...Ch. 1 - Draw a pictorial representation for the following...Ch. 1 - How many significant figures are there in the...Ch. 1 - Convert the following to SI units: a. 8.0 in b. 66...Ch. 1 - Convert the following to SI units: a. 75 in b....Ch. 1 - Using the approximate conversion factors in Table...Ch. 1 - Using the approximate conversion factors in Table...Ch. 1 - Prob. 28EAPCh. 1 - Prob. 29EAPCh. 1 - Prob. 30EAPCh. 1 - Estimate the height of a telephone pole. Give your...Ch. 1 - Estimate the average speed with which the hair on...Ch. 1 - Motor neurons in mammals transmit signals from the...Ch. 1 - For Problems 34 through 43, draw a complete...Ch. 1 - For Problems 34 through 43, draw a complete...Ch. 1 - For Problems 34 through 43, draw a complete...Ch. 1 - For Problems 34 through 43, draw a complete...Ch. 1 - For Problems 34 through 43, draw a complete...Ch. 1 -
For Problems 34 through 43, draw a complete...Ch. 1 - For Problems 34 through 43, draw a complete...Ch. 1 - For Problems 34 through 43, draw a complete...Ch. 1 - For Problems 34 through 43, draw a complete...Ch. 1 - For Problems 34 through 43, draw a complete...Ch. 1 - Problems 44 through 48 show a motion diagram. For...Ch. 1 - Problems 44 through 48 show a motion diagram. For...Ch. 1 - Problems 44 through 48 show a motion diagram. For...Ch. 1 - Problems 44 through 48 show a motion diagram. For...Ch. 1 - Problems 44 through 48 show a motion diagram. For...Ch. 1 - Problems 49 through 52 show a partial motion...Ch. 1 - Problems 49 through 52 show a partial motion...Ch. 1 - Problems 49 through 52 show a partial motion...Ch. 1 - Problems 49 through 52 show a partial motion...Ch. 1 - Prob. 53EAPCh. 1 - As an architect, you are designing a new house. A...Ch. 1 - 55. A 5.4-cm-diameter cylinder has a length of...Ch. 1 - An intravenous saline drip has 9.0 g of sodium...Ch. 1 - Prob. 57EAPCh. 1 - FIGURE P1.58 shows a motion diagram of a car...Ch. 1 - Write a short description of a real object for...Ch. 1 - Write a short description of a real object for...
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