Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
4th Edition
ISBN: 9780134110684
Author: Randall D. Knight (Professor Emeritus)
Publisher: PEARSON
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Chapter 26, Problem 30EAP
You need a capacitance of
have a
additional capacitor do you need to produce a total capacitance
of
series?
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ROTATIONAL DYNAMICS
Question 01
A solid circular cylinder and a solid spherical ball of the same mass and radius are rolling
together down the same inclined. Calculate the ratio of their kinetic energy. Assume pure
rolling motion Question 02
A sphere and cylinder of the same mass and radius start from ret at the same point and more
down the same plane inclined at 30° to the horizontal
Which body gets the bottom first and what is its acceleration
b) What angle of inclination of the plane is needed to give the slower body the same
acceleration
Question 03
i)
Define the angular velocity of a rotating body and give its SI unit
A car wheel has its angular velocity changing from 2rads to 30 rads
seconds. If the radius of the wheel is 400mm. calculate
ii)
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iii)
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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 26 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Ch. 26 - l. FIGURE Q26.1 shows the x-component of E as a...Ch. 26 - Prob. 2CQCh. 26 - a. Suppose that E =0 V/m throughout some region of...Ch. 26 - Estimate the electric fields and at points 1 and 2...Ch. 26 - Estimate the electric fields and E2 t points 1 and...Ch. 26 - Prob. 6CQCh. 26 - Prob. 7CQCh. 26 - FIGURE Q26.8 shows a negatively charged...Ch. 26 - Prob. 9CQCh. 26 - FIGURE Q26.10 shows a 3 V battery with metal wires...
Ch. 26 - The parallel-plate capacitor in FIGURE Q26.11 is...Ch. 26 - Rank in order, from largest to smallest, the...Ch. 26 - I. What is the potential difference between xi= 10...Ch. 26 - Il What is the potential difference between yi= —5...Ch. 26 - Il FIGURE EX26.3 is a graph of Ex. What is the...Ch. 26 - Il FIGURE EX26.4 is a graph of Ex The potential at...Ch. 26 - Prob. 5EAPCh. 26 - Prob. 6EAPCh. 26 - Prob. 7EAPCh. 26 - I What are the magnitude and direction of the...Ch. 26 - FIGURE EX26.9 shows a graph of V versus x in a...Ch. 26 - Prob. 10EAPCh. 26 - Prob. 11EAPCh. 26 - FIGURE EX26.12 is a graph of V versus x. Draw the...Ch. 26 - Prob. 13EAPCh. 26 - Prob. 14EAPCh. 26 - Prob. 15EAPCh. 26 - Prob. 16EAPCh. 26 - How much work does the charge escalator do to move...Ch. 26 - How much charge does a 9.0 V battery transfer from...Ch. 26 - How much work does the electric motor of a Van de...Ch. 26 - Prob. 20EAPCh. 26 - Two 3.0cm diameter aluminum electrodes are spaced...Ch. 26 - What is the capacitance of the two metal spheres...Ch. 26 - Prob. 23EAPCh. 26 - Prob. 24EAPCh. 26 - 25. A capacitor, a capacitor, and a capacitor
...Ch. 26 - Prob. 26EAPCh. 26 - What is the equivalent capacitance of the three...Ch. 26 - What is the equivalent capacitance of the three...Ch. 26 - You need a capacitance of 50F , but you don't...Ch. 26 - You need a capacitance of 50F , but you don't...Ch. 26 - To what potential should you charge a 1.0F...Ch. 26 - 50pJ of energy is stored in a 2.0cm2.0cm2.0cm...Ch. 26 - A 2.0-cm-diameter parallel-plate capacitor with a...Ch. 26 - The capacitor in a defibrillator unit supplies an...Ch. 26 - Prob. 35EAPCh. 26 - Prob. 36EAPCh. 26 - A typical cell has a layer of negative charge on...Ch. 26 - The electric field in a region of space is...Ch. 26 - Ill The electric field in a region of space is...Ch. 26 - An infinitely long cylinder of radius R has linear...Ch. 26 - Prob. 41EAPCh. 26 - Prob. 42EAPCh. 26 - a. Use the methods of Chapter 25 to find the...Ch. 26 - Prob. 44EAPCh. 26 - Engineers discover that the electric potential...Ch. 26 - The electric potential in a region of space is...Ch. 26 - Prob. 47EAPCh. 26 - Prob. 48EAPCh. 26 - Prob. 49EAPCh. 26 - Prob. 50EAPCh. 26 - Prob. 51EAPCh. 26 - Prob. 52EAPCh. 26 - Prob. 53EAPCh. 26 - Two 2.0 cm × 2.0 cm metal electrodes are spaced...Ch. 26 - Find expressions for the equivalent capacitance of...Ch. 26 - What are the charge on and the potential...Ch. 26 - What are the charge on and the potential...Ch. 26 - Prob. 58EAPCh. 26 - Prob. 59EAPCh. 26 - Six identical capacitors with capacitance C are...Ch. 26 - Prob. 61EAPCh. 26 - A battery with an emf of 60 V is connected to the...Ch. 26 - Prob. 63EAPCh. 26 - Prob. 64EAPCh. 26 - Prob. 65EAPCh. 26 - Prob. 66EAPCh. 26 - Prob. 67EAPCh. 26 - Prob. 68EAPCh. 26 - Prob. 69EAPCh. 26 - Prob. 70EAPCh. 26 - Prob. 71EAPCh. 26 - Prob. 72EAPCh. 26 - Prob. 73EAPCh. 26 - Prob. 74EAPCh. 26 - In Problems 75 through 77 you are given the...Ch. 26 - Prob. 76EAPCh. 26 - Prob. 77EAPCh. 26 -
78. Two 5.0-cm-diameter metal disks separated by...Ch. 26 - Prob. 79EAPCh. 26 - Charge is uniformly distributed with charge...Ch. 26 - Consider a uniformly charged sphere of radius R...Ch. 26 - Prob. 82EAPCh. 26 - Prob. 83EAP
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