Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Question
Chapter 6, Problem 21P
(a)
To determine
The value of the constant
(b)
To determine
The time required to reach a velocity of
(c)
To determine
The value of resistive force at the terminal speed.
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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)
The angular acceleration
iii)
The tangential linear acceleration of a point on the rim of the wheel
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 6 Solutions
Physics for Scientists and Engineers
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 - In the Bohr model of the hydrogen atom, an...Ch. 6 - Whenever two Apollo astronauts were on the surface...Ch. 6 - A car initially traveling eastward turns north by...Ch. 6 - A curve in a road forms part of a horizontal...Ch. 6 - In a cyclotron (one type of particle accelerator),...Ch. 6 - Why is the following situation impossible? The...
Ch. 6 - You are working during your summer break as an...Ch. 6 - A driver is suing the state highway department...Ch. 6 - A hawk flies in a horizontal arc of radius 12.0 m...Ch. 6 - A 40.0-kg child swings in a swing supported by two...Ch. 6 - A child of mass m swings in a swing supported by...Ch. 6 - One end of a cord is fixed and a small 0.500-kg...Ch. 6 - A roller coaster at the Six Flags Great America...Ch. 6 - An object of mass m = 5.00 kg, attached to a...Ch. 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 - The mass of a sports car is 1 200 kg. The shape of...Ch. 6 - Review. A window washer pulls a rubber squeegee...Ch. 6 - A small piece of Styrofoam packing material is...Ch. 6 - Prob. 21PCh. 6 - Assume the resistive force acting on a speed...Ch. 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 - 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 - The pilot of an airplane executes a loop-the-loop...Ch. 6 - A basin surrounding a drain has the shape of a...Ch. 6 - Review. While learning to drive, you arc in a 1...Ch. 6 - A truck is moving with constant acceleration a up...Ch. 6 - Because the Earth rotates about its axis, a point...Ch. 6 - A puck of mass m1 is tied to a string and allowed...Ch. 6 - Galileo thought about whether acceleration should...Ch. 6 - Members of a skydiving club were given the...Ch. 6 - A car rounds a banked curve as discussed in...Ch. 6 - In Example 6.5, we investigated the forces a child...Ch. 6 - Review. A piece of putty is initially located at...Ch. 6 - A model airplane of mass 0.750 kg flies with a...Ch. 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 - Because of the Earths rotation, a plumb bob does...Ch. 6 - You have a great job working at a major league...
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