College Physics: A Strategic Approach (3rd Edition)
3rd Edition
ISBN: 9780321879721
Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher: PEARSON
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Textbook Question
Chapter 4, Problem 40P
A girl stands on a sofa. Identify all the action/reaction pairs of forces between the girl and the sofa.
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Students have asked these similar questions
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
College Physics: A Strategic Approach (3rd Edition)
Ch. 4 - If an object is not moving, does that mean that...Ch. 4 - An object moves in a straight line at a constant...Ch. 4 - If you know all of the forces acting on a moving...Ch. 4 - Three arrows are shot horizontally. They have left...Ch. 4 - A carpenter wishes to tighten the heavy head of...Ch. 4 - Internal injuries in vehicular acci-dents may be...Ch. 4 - Heres a great everyday use of the physics...Ch. 4 - Suppose you are an astronaut in deep space, far...Ch. 4 - Jonathan accelerates away from a stop sign. His...Ch. 4 - Normally, jet engines push air out the back of the...
Ch. 4 - If you are standing still, the upward normal force...Ch. 4 - Josh and Taylor, standing face-to-face on...Ch. 4 - A person sits on a sloped hillside. Is it ever...Ch. 4 - Walking without slipping requires a static...Ch. 4 - Figure 4.30 b showed a situation in which the...Ch. 4 - Alyssa pushes to the right on a filing cabinet;...Ch. 4 - A very smart three-year-old child is given a wagon...Ch. 4 - The tire on this drag racer is severely twisted:...Ch. 4 - Suppose that, while in a squatting position, you...Ch. 4 - A block has acceleration a when pulled by a...Ch. 4 - A 5.0 kg block has an acceleration of 0.20 m/s2...Ch. 4 - Tennis balls experience a large drag force. A...Ch. 4 - A group of students is making model cars that will...Ch. 4 - A person gives a box a shove so that it slides up...Ch. 4 - A person is pushing horizontally on a box with a...Ch. 4 - As shown in the chapter, scallops use jet...Ch. 4 - Dave pushes his four-year-old son Thomas across...Ch. 4 - Figure Q4.29 shows block A sitting on top of block...Ch. 4 - Whiplash injuries during an automobile accident...Ch. 4 - An automobile has a head-on collision. A passenger...Ch. 4 - In a head-on collision, an infant is much safer in...Ch. 4 - Problems 4 through 6 show two forces acting on an...Ch. 4 - Problems 4 through 6 show two forces acting on an...Ch. 4 - Problems 4 through 6 show two forces acting on an...Ch. 4 - A mountain climber is hanging from a vertical...Ch. 4 - You look up from your textbook and observe a...Ch. 4 - A baseball player is sliding into second base....Ch. 4 - A jet plane is speeding down the runway during...Ch. 4 - A skier is sliding down a 15 slope. Friction is...Ch. 4 - A falcon is hovering above the ground, then...Ch. 4 - Figure P4.13 shows an acceleration-versus-force...Ch. 4 - A constant force applied to object A causes it to...Ch. 4 - A compact car has a maximum acceleration of 4.0...Ch. 4 - A constant force is applied to an object, causing...Ch. 4 - A constant force is applied to an object, causing...Ch. 4 - A man pulling an empty wagon causes it to...Ch. 4 - A car has a maximum acceleration of 5.0 m/s2 What...Ch. 4 - Scallops eject water from their shells to provide...Ch. 4 - Figure P4.21 shows an objects...Ch. 4 - In t-ball, young players use a bat to hit a...Ch. 4 - Two children fight over a 200 g stuffed bear. The...Ch. 4 - A 1500 kg car is traveling along a straight road...Ch. 4 - The motion of a very massive object can be...Ch. 4 - Very small forces can have tremendous effects on...Ch. 4 - Problems 27 through 29 show a free-body diagram....Ch. 4 - Problems 27 through 29 show a free-body diagram....Ch. 4 - Problems 27 through 29 show a free-body diagram....Ch. 4 - Problems 30 through 38 describe a situation. For...Ch. 4 - Problems 30 through 38 describe a situation. For...Ch. 4 - Problems 30 through 38 describe a situation. For...Ch. 4 - Problems 30 through 38 describe a situation. For...Ch. 4 - Problems 30 through 38 describe a situation. For...Ch. 4 - Problems 30 through 38 describe a situation. For...Ch. 4 - Problems 30 through 38 describe a situation. For...Ch. 4 - Problems 30 through 38 describe a situation. For...Ch. 4 - Problems 30 through 38 describe a situation. For...Ch. 4 - Three ice skaters, numbered 1, 2, and 3, stand in...Ch. 4 - A girl stands on a sofa. Identify all the...Ch. 4 - A car is skidding to a stop on a level stretch of...Ch. 4 - Squid use jet propulsion for rapid escapes. A...Ch. 4 - Redraw the motion diagram shown in Figure P4.43,...Ch. 4 - Redraw the motion diagram shown in Figure P4.44,...Ch. 4 - Redraw the motion diagram shown in Figure P4.45,...Ch. 4 - Redraw the motion diagram shown in Figure P4.46,...Ch. 4 - A student draws the flawed free-body diagram shown...Ch. 4 - A student draws the flawed free-body diagram shown...Ch. 4 - Problems 49 through 61 describe a situation. For...Ch. 4 - Problems 49 through 61 describe a situation. For...Ch. 4 - Problems 49 through 61 describe a situation. For...Ch. 4 - Problems 49 through 61 describe a situation. For...Ch. 4 - Problems 49 through 61 describe a situation. For...Ch. 4 - Problems 49 through 61 describe a situation. For...Ch. 4 - Problems 49 through 61 describe a situation. For...Ch. 4 - Problems 49 through 61 describe a situation. For...Ch. 4 - Problems 49 through 61 describe a situation. For...Ch. 4 - Problems 49 through 61 describe a situation. For...Ch. 4 - Problems 49 through 61 describe a situation. For...Ch. 4 - Problems 49 through 61 describe a situation. For...Ch. 4 - A bag of groceries is on the back seat of your car...Ch. 4 - A car has a mass of 1500 kg. If the driver applies...Ch. 4 - A rubber ball bounces. Wed like to understand how...Ch. 4 - If a car stops suddenly, you feel thrown forward....Ch. 4 - The fastest pitched baseball was clocked at 46...Ch. 4 - The froghopper, champion leaper of the insect...Ch. 4 - A beach ball is thrown straight up, and some time...Ch. 4 - If your car is stuck in the mud and you dont have...Ch. 4 - If your car is stuck in the mud and you don't have...Ch. 4 - If your car is stuck in the mud and you don't have...Ch. 4 - If your car is stuck in the mud and you don't have...
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