University Physics Volume 2
18th Edition
ISBN: 9781938168161
Author: OpenStax
Publisher: OpenStax
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Textbook Question
Chapter 15, Problem 13CQ
Why are the primary and secondary coils of a transformer wrapped around the same closed loop of iron?
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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 15 Solutions
University Physics Volume 2
Ch. 15 - Check Your Understanding If a European ac voltage...Ch. 15 - Check Your Understanding Repeat Example 15.1 for...Ch. 15 - Check Your Understanding Find the voltages across...Ch. 15 - Check Your Understanding An ac voltmeter attached...Ch. 15 - Check Your Understanding Show that the tins...Ch. 15 - Check Your Understanding In the circuit of Figure...Ch. 15 - Check Your Understanding What happens to the...Ch. 15 - Check Your Understanding The resonant angular...Ch. 15 - Check Your Understanding A transformer steps the...Ch. 15 - What is the relationship between frequency and...
Ch. 15 - Explain why at high frequencies a capacitor acts...Ch. 15 - In an RLC series circuit, can the voltage measured...Ch. 15 - For what value of the phase angle between the...Ch. 15 - Discuss the differences between average power and...Ch. 15 - The average ac current delivered to a circuit is...Ch. 15 - Can the instantaneous power output of an ac source...Ch. 15 - The power rating of a resistor used in ac circuits...Ch. 15 - Why do transmission lines operate at very hig1...Ch. 15 - How can you distinguish the primary winding from...Ch. 15 - Battery packs in some electronic devices are...Ch. 15 - Will a transformer work if the input is a dc...Ch. 15 - Why are the primary and secondary coils of a...Ch. 15 - Write an expression for the output voltage of an...Ch. 15 - Calculate the reactance of a 5.0F capacitor at (a)...Ch. 15 - What is the capacitance of a capacitor whose...Ch. 15 - Calculate the reactance of a 5.0-mH inductor at...Ch. 15 - What is the self-inductance of a coil whose...Ch. 15 - At s1iat frequency is the reactance of a 20F...Ch. 15 - At 1000 Hz, the reactance of a 5.0-mH inductor is...Ch. 15 - A 50resistor is connected across the emf...Ch. 15 - A 25F capacitor is connected to an emf given by...Ch. 15 - A 100-mH inductor is connected across the emf of...Ch. 15 - What is the impedance of a series combination of a...Ch. 15 - A resistor and capacitor are connected in series...Ch. 15 - A resistor and inductor are connected in series...Ch. 15 - In an RLC series circuit, the voltage amplitude...Ch. 15 - An PLC series circuit with R=600 , L = 30 mH. and...Ch. 15 - For the cucu3t shown below, what are (a) the total...Ch. 15 - The emf of an ac source is given by v(t)=v0sint....Ch. 15 - Calculate the rms currents for an ac source is...Ch. 15 - A 40-mH inductor is connected to a 60-Hz AC source...Ch. 15 - For an RLC series circuit, the voltage amplitude...Ch. 15 - An ac source of voltage amplitude 10 V delivers...Ch. 15 - An RLC series circuit has an impedance of 60 and a...Ch. 15 - Calculate the resonant angular freqency of an RLC...Ch. 15 - The resonant frequency of RLC series circuits is...Ch. 15 - (a) What is the resonant frequency of an RLC...Ch. 15 - For an RLC series circuit, R=100 , L = 150 mH, and...Ch. 15 - An ac source of voltage amplitude 100 V and...Ch. 15 - (a) What is the resonant frequency of a resistor,...Ch. 15 - Suppose a coil has a self-inductance of 20.0 H and...Ch. 15 - An ac generator is connected to a device whose...Ch. 15 - A step-up transformer is designed so that the...Ch. 15 - A step-up transformer connected to a 100-V line U...Ch. 15 - An ac source of emf delivers 5.0 mW of power at an...Ch. 15 - A transformer is used to down 110 V from a wall...Ch. 15 - A transformer is used to supply a 12-V model train...Ch. 15 - The emf of an ac source is given by v(t)=V0sint,...Ch. 15 - A 700-pF capacitor is connected across an ac...Ch. 15 - A 20-mH inductor is connected across an AC source...Ch. 15 - A 30F capacitor is connected across a 60-Hz ac...Ch. 15 - A 7.0-mH induct is connected across a 60-Hz ac...Ch. 15 - What is the impedance of an RLC series circuit at...Ch. 15 - What is the resistance R in the circuit shown...Ch. 15 - An ac source of voltage amplitude 100 V and...Ch. 15 - In an RLC series circuit, R=200,L=1.0H ,...Ch. 15 - A power plant generator produces 100 A at 15 kV...Ch. 15 - Consider a power plant located 25 km outside a...Ch. 15 - Neon signs require 12-kV for their operation. A...Ch. 15 - The 335-kV ac electricity from a power...Ch. 15 - A 1.5k resistor and 30-mH inductor are connected...Ch. 15 - A 20 resistor, 50F capacitor, and 30-mH inductor...Ch. 15 - A 200- resistor, 150- F capacitor, and 23-H...Ch. 15 - Find the reactances of the following capacitors...Ch. 15 - An output impedance of an audio amplifier has an...Ch. 15 - Show that the SI unit for capacitive reactance is...Ch. 15 - A coil with a self-inductance of 16 mH and a...Ch. 15 - An RLC series circuit consists of a 50 resistor, a...Ch. 15 - An RLC series circuit consists of a 10 resistor,...Ch. 15 - Shown below are two circuits that act as crude...Ch. 15 - The two circuits shown below act as crude low-pass...
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