Fundamentals of Physics Extended
10th Edition
ISBN: 9781118230725
Author: David Halliday, Robert Resnick, Jearl Walker
Publisher: Wiley, John & Sons, Incorporated
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Chapter 15, Problem 39P
SSM WWW The balance wheel of an old-fashioned watch oscillates with angular amplitude π rad and period 0.500 s. Find (a) the maximum angular speed of the wheel, (b) the angular speed at displacement π/2 rad, and (c) the magnitude of the
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ROTATIONAL DYNAMICS
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A solid circular cylinder and a solid spherical ball of the same mass and radius are rolling
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rolling motion Question 02
A sphere and cylinder of the same mass and radius start from ret at the same point and more
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Question 03
i)
Define the angular velocity of a rotating body and give its SI unit
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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
Fundamentals of Physics Extended
Ch. 15 - Which of the following describe for the SHM of...Ch. 15 - The velocity vt of a particle undergoing SHM is...Ch. 15 - The acceleration at of a particle undergoing SHM...Ch. 15 - Which of the following relationships between the...Ch. 15 - You are to complete Fig. 15-22a so that it is a...Ch. 15 - You are to complete Fig. 15-23a so that it is a...Ch. 15 - Figure 15-24 shows the xt curves for three...Ch. 15 - Figure 15-25 shows plots of the kinetic energy K...Ch. 15 - Figure 15-26 shows three physical pendulums...Ch. 15 - You are to build the oscillation transfer device...
Ch. 15 - In Fig. 15-28, a springblock system is put into...Ch. 15 - Figure 15-29 gives, for three situations, the...Ch. 15 - An object undergoing simple harmonic motion takes...Ch. 15 - A 0.12 kg body undergoes simple harmonic motion of...Ch. 15 - What is the maximum acceleration of a platform...Ch. 15 - An automobile can be considered to be mounted on...Ch. 15 - SSM In an electric shaver, the blade moves back...Ch. 15 - A particle with a mass of 1.00 1020 kg is...Ch. 15 - SSM A loudspeaker produces a musical sound by...Ch. 15 - What is the phase constant for the harmonic...Ch. 15 - The position function x = 6.0 m cos3 rad/st /3...Ch. 15 - An oscillating blockspring system takes 0.75 s to...Ch. 15 - In Fig. 15-31, two identical springs of spring...Ch. 15 - What is the phase constant for the harmonic...Ch. 15 - SSM An oscillator consists of a block of mass...Ch. 15 - A simple harmonic oscillator consists of a block...Ch. 15 - SSM Two particles oscillate in simple harmonic...Ch. 15 - Two particles execute simple harmonic motion of...Ch. 15 - ILW An oscillator consists of a block attached to...Ch. 15 - GO At a certain harbor, the tides cause the ocean...Ch. 15 - A block rides on a piston a squat cylindrical...Ch. 15 - GO Figure 15-33a is a partial graph of the...Ch. 15 - ILW In Fig. 15-31, two springs are attached to a...Ch. 15 - GO Figure 15-34 shows block 1 of mass 0.200 kg...Ch. 15 - SSM WWW A block is on a horizontal surface a shake...Ch. 15 - In Fig. 15-35, two springs are joined and...Ch. 15 - GO In Fig. 15-36, a block weighing 14.0 N, which...Ch. 15 - GO In Fig. 15-37, two blocks m = 1.8 kg and M = 10...Ch. 15 - SSM When the displacement in SHM is one-half the...Ch. 15 - Figure 15-38 gives the one-dimensional potential...Ch. 15 - SSM Find the mechanical energy of a blockspring...Ch. 15 - An oscillating blockspring system has a mechanical...Ch. 15 - ILW A 5.00 kg object on a horizontal frictionless...Ch. 15 - Figure 15-39 shows the kinetic energy K of a...Ch. 15 - GO A block of mass M = 5.4 kg, at rest on a...Ch. 15 - GO In Fig. 15-41, block 2 of mass 2.0 kg...Ch. 15 - A 10 g particle undergoes SHM with an amplitude of...Ch. 15 - If the phase angle for a blockspring system in SHM...Ch. 15 - GO A massless spring hangs from the ceiling with a...Ch. 15 - A 95 kg solid sphere with a 15 cm radius is...Ch. 15 - SSM WWW The balance wheel of an old-fashioned...Ch. 15 - ILW A physical pendulum consists of a meter stick...Ch. 15 - SSM In Fig. 15-42, the pendulum consists of a...Ch. 15 - Suppose that a simple pendulum consists of a small...Ch. 15 - a If the physical pendulum of Fig. 15-13 and the...Ch. 15 - A physical pendulum consists of two meter-long...Ch. 15 - A performer seated on a trapeze is swinging back...Ch. 15 - A physical pendulum has a center of oscillation at...Ch. 15 - In Fig. 15-44, a physical pendulum consists of a...Ch. 15 - GO A rectangular block, with face lengths a = 35...Ch. 15 - GO The angle of the pendulum of Fig. 15-11b is...Ch. 15 - Prob. 50PCh. 15 - GO In Fig. 15-46, a stick of length L = 1.85 m...Ch. 15 - GO The 3.00 kg cube in Fig. 15-47 has edge lengths...Ch. 15 - SSM ILW In the overhead view of Fig. 15-48, a long...Ch. 15 - Prob. 54PCh. 15 - GO A pendulum is formed by pivoting a long thin...Ch. 15 - In Fig. 15-50: a 2.50 kg disk of diameter D = 42.0...Ch. 15 - The amplitude of a lightly damped oscillator...Ch. 15 - For the damped oscillator system shown in Fig....Ch. 15 - SSM WWW For the damped oscillator system shown in...Ch. 15 - The suspension system of a 2000 kg automobile sags...Ch. 15 - For Eq. 15-45, suppose the amplitude xm is given...Ch. 15 - Hanging from a horizontal beam are nine simple...Ch. 15 - A. 1000 kg car carrying four 82 kg people travels...Ch. 15 - Although California is known for earthquakes, is...Ch. 15 - A loudspeaker diaphragm is oscillating in simple...Ch. 15 - A uniform spring with k = 8600 N/m is cut into...Ch. 15 - GO In Fig. 15-51, three 10, 000 kg ore cars are...Ch. 15 - A 2.00 kg block hangs from a spring. A 300 g body...Ch. 15 - SSM In the engine of a locomotive, a cylindrical...Ch. 15 - GO A wheel is free to rotate about its fixed axle....Ch. 15 - A 50.0 g stone is attached to the bottom of a...Ch. 15 - A uniform circular disk: whose radius R is 12.6 cm...Ch. 15 - SSM A vertical spring stretches 9.6 cm when a 1.3...Ch. 15 - A massless spring with spring constant 19 N/m...Ch. 15 - A 4.00 kg block is suspended from a spring with k...Ch. 15 - A 55.0 g block oscillates in SHM on the end of a...Ch. 15 - Figure 15-53 gives the position of a 20 g block...Ch. 15 - Figure 15-53 gives the position xt of a block...Ch. 15 - Figure 15-54 shows the kinetic energy K of a...Ch. 15 - A block is in SHM on the end of a spring, with...Ch. 15 - A simple harmonic oscillator consists of a 0.50 kg...Ch. 15 - A simple pendulum of length 20 cm and mass 5.0 g...Ch. 15 - The scale of a spring balance that reads from 0 to...Ch. 15 - A 0.10 kg block oscillates back and forth along a...Ch. 15 - The end point of a spring oscillates with a period...Ch. 15 - The tip of one prong of a tuning fork undergoes...Ch. 15 - Prob. 87PCh. 15 - A block weighing 20 N oscillates at one end of a...Ch. 15 - A 3.0 kg particle is in simple harmonic motion in...Ch. 15 - A particle executes linear SHM with frequency 0.25...Ch. 15 - SSM What is the frequency of a simple pendulum 2.0...Ch. 15 - A grandfather clock has a pendulum that consists...Ch. 15 - A 4.00 kg block hangs from a spring, extending it...Ch. 15 - What is the phase constant for SMH with at given...Ch. 15 - An engineer has an odd-shaped 10 kg object and...Ch. 15 - A spider can tell when its web has captured, say,...Ch. 15 - A torsion pendulum consists of a metal disk with a...Ch. 15 - When a 20 N can is hung from the bottom of a...Ch. 15 - For a simple pendulum, find the angular amplitude...Ch. 15 - In Fig. 15-59, a solid cylinder attached to a...Ch. 15 - SSM A 1.2 kg block sliding on a horizontal...Ch. 15 - A simple harmonic oscillator consists of an 0.80...Ch. 15 - A block sliding on a horizontal frictionless...Ch. 15 - A damped harmonic oscillator consists of a block m...Ch. 15 - A block weighing 10.0 N is attached to the lower...Ch. 15 - A simple harmonic oscillator consists of a block...Ch. 15 - The vibration frequencies of atoms in solids at...Ch. 15 - Figure 15-61 shows that if we hang a block on the...Ch. 15 - The physical pendulum in Fig. 15-62 has two...Ch. 15 - A common device for entertaining a toddler is a...Ch. 15 - A 2.0 kg block executes SHM while attached to a...Ch. 15 - In Fig. 15-64, a 2500 kg demolition ball swings...Ch. 15 - The center of oscillation of a physical pendulum...Ch. 15 - A hypothetical large slingshot is stretched 2.30 m...Ch. 15 - What is the length of a simple pendulum whose full...Ch. 15 - A 2.0 kg block is attached to the end of a spring...
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