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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Textbook Question
Chapter 4, Problem 4EAP
Answer Problems 3 through 5 by choosing one of the eight labeled acceleration vectors or selecting option I: =
3. At this instant, the particle has steady speed and is curving to the right. What is the direction of its acceleration?
4. At this instant, the particle is speeding up and curving upward. What is the direction of its acceleration?
5. At this instant, the particle is speeding up and curving downward. What is the direction of its acceleration?
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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]
Page 2
SECTION A
Answer ALL questions in Section A
[Expect to use one single-sided A4 page for each Section-A sub question.]
Question A1
SPA6308 (2024)
Consider Minkowski spacetime in Cartesian coordinates th
=
(t, x, y, z), such that
ds² = dt² + dx² + dy² + dz².
(a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V.
(b) Consider now the coordinate system x' (u, v, y, z) such that
u =t-x,
v=t+x.
[2 marks]
Write down the line element, the metric, the Christoffel symbols and the Riemann curvature
tensor in the new coordinates. [See the Appendix of this document.]
[5 marks]
(c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify
explicitly that V. V is invariant under the coordinate transformation.
Question A2
[5 marks]
Suppose that A, is a covector field, and consider the object
Fv=AAμ.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
[5 marks]
(b)…
Chapter 4 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Ch. 4 - a. At this instant, is the particle in FIGURE Q4.1...Ch. 4 - a. At this instant, is the particle in FIGURE Q4.2...Ch. 4 - Tarzan swings through the jungle by hanging from a...Ch. 4 - A projectile is launched at an angle of 30°. a. Is...Ch. 4 - For a projectile, which of the following...Ch. 4 - A cart that is rolling at constant velocity on a...Ch. 4 - A rock is thrown from a bridge at an angle 30°...Ch. 4 - Anita is running to the right at 5 m/s in FIGURE...Ch. 4 - An electromagnet on the ceiling of an airplane...Ch. 4 - Zack is driving past his house in FIGURE Q4.1O. He...
Ch. 4 - II. In FIGURE Q4.11. Yvette and Zack are driving...Ch. 4 - In uniform circular motion, which of the following...Ch. 4 - FIGURE Q4.13 shows three points on a steadily...Ch. 4 - FIGURE Q4.14 shows four rotating wheels. For each,...Ch. 4 - FIGURE Q4.15 shows a pendulum at one end point of...Ch. 4 - Problems I and 2 show a partial motion diagram....Ch. 4 - Prob. 2EAPCh. 4 - Answer Problems 3 through 5 by choosing one of the...Ch. 4 - Answer Problems 3 through 5 by choosing one of the...Ch. 4 - Answer Problems 3 through 5 by choosing one of the...Ch. 4 - A rocket-powered hockey puck moves on a horizontal...Ch. 4 - A rocket-powered hockey puck moves on a horizontal...Ch. 4 - Prob. 8EAPCh. 4 - A particle moving in the xy- plane has velocity v...Ch. 4 - You have a remote-controlled car that has been...Ch. 4 - A ball thrown horizontally at 25 m/s travels a...Ch. 4 - A physics student on the Planet Exidor throws a...Ch. 4 - A supply plane needs to drop a package of food to...Ch. 4 - A rifle is aimed horizontally at a target 50 m...Ch. 4 - In the Olympic shotput event, an athlete throws...Ch. 4 - On the Apollo 14 mission to the moon, astronaut...Ch. 4 - A baseball player friend of yours wants to...Ch. 4 - A boat takes 3.0 hours to travel 30 km down a...Ch. 4 - When the moving sidewalk at the airport is broken,...Ch. 4 - Prob. 20EAPCh. 4 - A kayaker, needs to paddle north across a...Ch. 4 - Susan, driving north at 60 mph, and Trent, driving...Ch. 4 - FIGURE EX4.23 shows the...Ch. 4 - FIGURE EX4.24 shows the...Ch. 4 - FIGURE EX4.25 shows the...Ch. 4 - The earth’s radius is about 4000 miles. Kampala,...Ch. 4 - An old-fashioned single-play vinyl record rotates...Ch. 4 - As the earth mates, what is the speed of (a) a...Ch. 4 - How fast must a plane fly along the earth’s...Ch. 4 - A 3000-rn-high mountain is located on the equator....Ch. 4 - Peregrine falcons are known for their maneuvering...Ch. 4 - To withstand “g-forces” of up to 10 g’s, caused by...Ch. 4 - The radius of the earth’s very nearly circular...Ch. 4 - A speck of dust on a spinning DVD has a...Ch. 4 - Your roommate is working on his bicycle and has...Ch. 4 - I FIGURE EX4.36 shows the angular velocity graph...Ch. 4 - I FIGURE EX4.37 shows the angular acceleration...Ch. 4 - FIGURE EX4.38 shows the...Ch. 4 - A wheel initially rotating at 60 rpm experiences...Ch. 4 - A 5.0-rn-diameter merry-go-round is initially...Ch. 4 - An electric fan goes from rest to 1800 rpm in 4.0...Ch. 4 - A bicycle wheel is rotating at 50 rpm when the...Ch. 4 - Starting from rest, a DVD steadily accelerates to...Ch. 4 - A spaceship maneuvering near Planet Zeta is...Ch. 4 - equation reference goes here45. A particle moving...Ch. 4 - A projectile’s horizontal range over level ground...Ch. 4 - a. A projectile is launched with speed v0and angle...Ch. 4 - A projectile is launched from ground level at...Ch. 4 - A gray kangaroo can bound across level ground with...Ch. 4 - A ball is thrown toward a cliff of height h with a...Ch. 4 - A tennis player hits a ball 2.0 m above the...Ch. 4 - You are target shooting using a toy gun that fires...Ch. 4 - A 35 g steel ball is held by a ceiling-mounted...Ch. 4 - You are watching an archery tournament when you...Ch. 4 - You’re 6.0 m from one wall of the house seen in...Ch. 4 - Sand moves without slipping at 6.0 m/s down a...Ch. 4 - A stunt man drives a car at a speed of 20 m/s off...Ch. 4 - A javelin thrower standing at rest holds the...Ch. 4 - A rubber ball is dropped onto a ramp that is...Ch. 4 - You are asked to consult for the city’s research...Ch. 4 - Ships A and B leave port together. For the next...Ch. 4 - While driving north at 25 m/s during a rainstorm...Ch. 4 - You’ve been assigned the task of using a shaft...Ch. 4 - Prob. 64EAPCh. 4 - Prob. 65EAPCh. 4 - Astronauts use a centrifuge to simulate the...Ch. 4 - Communications satellites are placed in a circular...Ch. 4 - Prob. 68EAPCh. 4 - A high-speed drill rotating ccw at 2400 rpm comes...Ch. 4 - A turbine is spinning at 3800 rpm. Frication in...Ch. 4 - Prob. 71EAPCh. 4 - The angular velocity of a process control motor is...Ch. 4 - A Ferris wheel of radius R speeds up with angular...Ch. 4 - Prob. 74EAPCh. 4 - A painted tooth on a spinning gear has angular...Ch. 4 - A car starts from rest on a curve with radius of...Ch. 4 - Prob. 77EAPCh. 4 - In Problem 78 through 80 you are given the...Ch. 4 - Prob. 79EAPCh. 4 - In Problem 78 through 80 you are given the...Ch. 4 - In one contest at the country fair, seen in FIGURE...Ch. 4 - Prob. 82EAPCh. 4 - Prob. 83EAPCh. 4 - Prob. 84EAPCh. 4 - Prob. 85EAP
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