Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Textbook Question
Chapter 2, Problem 33P
Automotive engineers refer to the time rate of change of acceleration as the ‘‘jerk.” Assume an object moves in one dimension such that its jerk J is constant. (a) Determine expressions for its acceleration ax(t), velocity vx(t), and position x(t), given that its initial acceleration, velocity, and position are axi, vxi, and xi, respectively. (b) Show that ax2 = axi2 + 2J(vx − vxi).
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Question 04
in 20
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]
Chapter 2 Solutions
Physics for Scientists and Engineers
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Ch. 2 - An athlete leaves one end of a pool of length L at...Ch. 2 - A positiontime graph for a particle moving along...Ch. 2 - A car travels along a straight line at a constant...Ch. 2 - A person takes a trip, driving with a constant...Ch. 2 - A child rolls a marble on a bent track that is 100...Ch. 2 - Figure P2.9 shows a graph of vx versus t for the...Ch. 2 - (a) Use the data in Problem 3 to construct a...Ch. 2 - A particle starts from rest and accelerates as...Ch. 2 - Draw motion diagrams for (a) an object moving to...Ch. 2 - Each of the strobe photographs (a), (b), and (c)...Ch. 2 - An electron in a cathode-ray tube accelerates...Ch. 2 - A parcel of air moving in a straight tube with a...Ch. 2 - In Example 2.7, we investigated a jet landing on...Ch. 2 - An object moving with uniform acceleration has a...Ch. 2 - Solve Example 2.8 by a graphical method. On the...Ch. 2 - A glider of length moves through a stationary...Ch. 2 - Why is the following situation impossible?...Ch. 2 - A glider of length 12.4 cm moves on an air track...Ch. 2 - In the particle under constant acceleration model,...Ch. 2 - At t = 0, one toy car is set rolling on a straight...Ch. 2 - You are observing the poles along the side of the...Ch. 2 - Why is the following situation impossible? Emily...Ch. 2 - An attacker at the base of a castle wall 3.65 m...Ch. 2 - The height of a helicopter above the ground is...Ch. 2 - A ball is thrown upward from the ground with an...Ch. 2 - A student throws a set of keys vertically upward...Ch. 2 - At time t = 0, a student throws a set of keys...Ch. 2 - You have been hired by the prosecuting attorney as...Ch. 2 - A student drives a moped along a straight road as...Ch. 2 - Automotive engineers refer to the time rate of...Ch. 2 - In Figure 2.11b, the area under the velocitytime...Ch. 2 - The froghopper Philaenus spumarius is supposedly...Ch. 2 - A woman is reported to have fallen 144 ft from the...Ch. 2 - At t = 0, one athlete in a race running on a long,...Ch. 2 - Why is the following situation impossible? A...Ch. 2 - Hannah tests her new sports car by racing with...Ch. 2 - Two objects, A and B, are connected by hinges to a...Ch. 2 - Lisa rushes down onto a subway platform to find...Ch. 2 - Two thin rods are fastened to the inside of a...Ch. 2 - In a womens 100-m race, accelerating uniformly,...
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