Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
9th Edition
ISBN: 9781305932302
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 6, Problem 37AP
A car travels clockwise at constant speed around a circular section of a horizontal road as shown in the aerial view of Figure P6.24. Find the directions of its velocity and acceleration at (a) position Ⓐ and (b) position Ⓑ.
Figure P6.24
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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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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 6 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
Ch. 6.1 - You are riding on a Ferris wheel that is rotating...Ch. 6.2 - A bead slides at constant speed along a curved...Ch. 6.3 - Consider the passenger in the car making a left...Ch. 6.4 - A basketball and a 2-inch-diameter steel ball,...Ch. 6 - Prob. 1OQCh. 6 - Prob. 2OQCh. 6 - A door in a hospital has a pneumatic closer that...Ch. 6 - A pendulum consists of a small object called a bob...Ch. 6 - Prob. 5OQCh. 6 - An office door is given a sharp push and swings...
Ch. 6 - Prob. 7OQCh. 6 - Prob. 1CQCh. 6 - Prob. 2CQCh. 6 - An object executes circular motion with constant...Ch. 6 - Describe the path of a moving body in the event...Ch. 6 - Prob. 5CQCh. 6 - If someone told you that astronauts are weightless...Ch. 6 - Prob. 7CQCh. 6 - Prob. 8CQCh. 6 - Why does a pilot tend to black out when pulling...Ch. 6 - A pail of water can be whirled in a vertical path...Ch. 6 - Prob. 1PCh. 6 - Whenever two Apollo astronauts were on the surface...Ch. 6 - In the Bohr model of the hydrogen atom, an...Ch. 6 - A curve in a road forms part of a horizontal...Ch. 6 - In a cyclotron (one type of particle accelerator),...Ch. 6 - A car initially traveling eastward turns north by...Ch. 6 - Prob. 7PCh. 6 - Consider a conical pendulum (Fig. P6.8) with a bob...Ch. 6 - A coin placed 30.0 cm from the center of a...Ch. 6 - Why is the following situation impossible? The...Ch. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - A 40.0-kg child swings in a swing supported by two...Ch. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - A roller coaster at the Six Flags Great America...Ch. 6 - One end of a cord is fixed and a small 0.500-kg...Ch. 6 - An adventurous archeologist (m = 85.0 kg) tries to...Ch. 6 - An object of mass m = 5.00 kg, attached to a...Ch. 6 - Prob. 21PCh. 6 - Prob. 22PCh. 6 - A person stands on a scale in an elevator. As the...Ch. 6 - Review. A student, along with her backpack on the...Ch. 6 - A small container of water is placed on a...Ch. 6 - Prob. 26PCh. 6 - The mass of a sports car is 1 200 kg. The shape of...Ch. 6 - Prob. 28PCh. 6 - Prob. 29PCh. 6 - A small piece of Styrofoam packing material is...Ch. 6 - Prob. 31PCh. 6 - Prob. 32PCh. 6 - Assume the resistive force acting on a speed...Ch. 6 - Review. A window washer pulls a rubber squeegee...Ch. 6 - Prob. 35PCh. 6 - You can feel a force of air drag on your hand if...Ch. 6 - A car travels clockwise at constant speed around a...Ch. 6 - Prob. 38APCh. 6 - A string under a tension of 50.0 N is used to...Ch. 6 - Disturbed by speeding cars outside his workplace,...Ch. 6 - A car of mass m passes over a hump in a road that...Ch. 6 - A childs toy consists of a small wedge that has an...Ch. 6 - A seaplane of total mass m lands on a lake with...Ch. 6 - An object of mass m1 = 4.00 kg is tied to an...Ch. 6 - A ball of mass m = 0.275 kg swings in a vertical...Ch. 6 - Why is the following situation impossible? A...Ch. 6 - Prob. 47APCh. 6 - Prob. 48APCh. 6 - Prob. 49APCh. 6 - A basin surrounding a drain has the shape of a...Ch. 6 - A truck is moving with constant acceleration a up...Ch. 6 - The pilot of an airplane executes a loop-the-loop...Ch. 6 - Review. While learning to drive, you arc in a 1...Ch. 6 - A puck of mass m1 is tied to a string and allowed...Ch. 6 - Prob. 55APCh. 6 - Prob. 56APCh. 6 - Prob. 57APCh. 6 - Review. A piece of putty is initially located at...Ch. 6 - Prob. 59APCh. 6 - Members of a skydiving club were given the...Ch. 6 - A car rounds a banked curve as discussed in...Ch. 6 - Prob. 62APCh. 6 - A model airplane of mass 0.750 kg flies with a...Ch. 6 - Prob. 64APCh. 6 - A 9.00-kg object starting from rest falls through...Ch. 6 - For t 0, an object of mass m experiences no force...Ch. 6 - A golfer tees off from a location precisely at i =...Ch. 6 - A single bead can slide with negligible friction...Ch. 6 - Prob. 69CPCh. 6 - Prob. 70CP
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