University Physics Volume 1
18th Edition
ISBN: 9781938168277
Author: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher: OpenStax - Rice University
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Textbook Question
Chapter 5, Problem 17CQ
If a book is located on a table, how many forces should be shown in a free-body diagram of the book? Describe them.
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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 5 Solutions
University Physics Volume 1
Ch. 5 - Check Your Understanding Find the magnitude and...Ch. 5 - Check Your Understanding A skydiver opens his...Ch. 5 - Check Your Understanding At the time of its...Ch. 5 - Check Your Understanding A 550-kg sports car...Ch. 5 - Check Your Understanding A car gas forces acting...Ch. 5 - Check Your Understanding For Example 5.8, find the...Ch. 5 - Check Your Understanding Two blocks are at rest...Ch. 5 - Check Your Understanding A force of 1150 N acts...Ch. 5 - Check Your Understanding One end of a 3.0-m rope...Ch. 5 - Check Your Understanding (a) Draw the free-body...
Ch. 5 - What properties do forces have that allow us to...Ch. 5 - Taking a frame attached to Earth as inertial,...Ch. 5 - A woman was transporting an open box of cupcakes...Ch. 5 - Why can we neglect forces such as those holding a...Ch. 5 - A rock is thrown straight up. At the top of the...Ch. 5 - What is the relationship between weight and mass?...Ch. 5 - How much does a 70-kg astronaut weight in space,...Ch. 5 - Which of the following statements is accurate? (a)...Ch. 5 - When you stand on Earth, your feet push against it...Ch. 5 - How would you give the value of g in vector form?Ch. 5 - Newton’s Third Law Identity the action and...Ch. 5 - Suppose that you are holding a cup of coffee in...Ch. 5 - (a) Why does an ordinary rifle recoil (kick...Ch. 5 - Common Forces A table is placed on a rug. Then a...Ch. 5 - A particle is moving to the right. (a) Can the...Ch. 5 - Drawing Free-Body Diagrams In completing the...Ch. 5 - If a book is located on a table, how many forces...Ch. 5 - If the book in the previous question is in free...Ch. 5 - Two ropes are attached to a tree, and forces of...Ch. 5 - A telephone pole has three cables pulling as shown...Ch. 5 - Two teenagers are pulling on ropes attached to a...Ch. 5 - Two forces of and act on an object. Find the third...Ch. 5 - While sliding a couch across a floor, Andrea and...Ch. 5 - Newton’s Second Law Andrea, a 63.0-kg sprinter,...Ch. 5 - If the sprinter from the previous problem...Ch. 5 - A cleaner pushes a 4.50-kg laundry cart in such a...Ch. 5 - Astronauts in orbit are apparently weightless....Ch. 5 - In Figure 5.12, the net external force on the...Ch. 5 - The rocket sled shown below decelerates at a rate...Ch. 5 - If the rocket sled shown in the previous problem...Ch. 5 - What is the deceleration of the rocket sled if it...Ch. 5 - Suppose two children push horizontally, but in...Ch. 5 - A powerful motorcycle can produce an acceleration...Ch. 5 - A car with a mass of 1000.0 kg accelerates from 0...Ch. 5 - The driver in the previous problem applies the...Ch. 5 - An 80.0-kg passenger in an SUV traveling at...Ch. 5 - A particle of mass 2.0 kg is acted on by a single...Ch. 5 - Suppose that the particle of the previous problem...Ch. 5 - Find the acceleration of the body of mass 5.0 kg...Ch. 5 - In the following figure, the horizontal surface on...Ch. 5 - Mass and Weight The weight of an astronaut plus...Ch. 5 - Suppose the mass of a fully loaded module in which...Ch. 5 - A rocket sled accelerates at a rate of 49.0m/s2 ....Ch. 5 - Repeat the previous problem for a situation in...Ch. 5 - A body of mass 2.00 kg is pushed straight upward...Ch. 5 - A car weighing 12,500 N stalls from rest and...Ch. 5 - A body with a mass of 10.0 kg is assumed to be in...Ch. 5 - A fireman has mass m ; he hears the fire alarm and...Ch. 5 - A baseball catcher is performing a stunt for a...Ch. 5 - When the Moon is directly overhead at sunset, the...Ch. 5 - (a) What net external force is exerted on a...Ch. 5 - A brave but inadequate rugby player is being...Ch. 5 - A history book is lying on top of a physics book...Ch. 5 - A truck collides with a car, and during the...Ch. 5 - Common Forces A leg is suspended in a traction...Ch. 5 - Suppose the shinbone in the preceding image was a...Ch. 5 - Two teams of nine members each engage in...Ch. 5 - What force does a trampoline have to apply to...Ch. 5 - (a) Calculate the tension in a vertical strand of...Ch. 5 - Suppose Kevin, a 60.0-kg gymnast, climbs a rope....Ch. 5 - Show that, as explained in the text, a force F...Ch. 5 - Consider Figure 5.28. The driver attempts to get...Ch. 5 - A bird has a mass of 26g and perches in the middle...Ch. 5 - -m rope is tied to a tree; the other end is tied...Ch. 5 - Consider the baby being weighed in the following...Ch. 5 - What force must be applied to a 100.0-kg crate on...Ch. 5 - A 2.0-kg block is on a perfectly smooth ramp that...Ch. 5 - Drawing Free-Body Diagrams A ball of mass m hangs...Ch. 5 - A car moves along a horizontal road. Draw a free-...Ch. 5 - A runner pushes against the track, as shown. (a)...Ch. 5 - The traffic light hangs from the cables as shown....Ch. 5 - Two small forces, F1=2.40i6.10tj N and...Ch. 5 - Two forces of 25 and 45 N act on an object. Their...Ch. 5 - A force of 1600 N acts parallel to a ramp to push...Ch. 5 - Draw a free-body diagram of a diver who has...Ch. 5 - For a swimmer who has just jumped off a diving...Ch. 5 - (a) Find an equation to determine the magnitude of...Ch. 5 - A sailboat has a mass of 1.50103kg and is acted on...Ch. 5 - Find the acceleration of the body of mass 10.0 kg...Ch. 5 - A body of mass 2.0 kg is moving along the x -axis...Ch. 5 - Force FBhas twice the magnitude of force FA. Find...Ch. 5 - Shown below is a body of mass 1.0 kg under the...Ch. 5 - A force acts on a car of mass m so that the speed...Ch. 5 - A 7.0-N force parallel to an incline is applied to...Ch. 5 - Two boxes, A and B, are at rest Box A is on level...Ch. 5 - A mass of 250.0 g is suspended from a spring...Ch. 5 - As shown below, two identical springs, each with...Ch. 5 - Shown below is a 30.0-kg block resting on a...Ch. 5 - In building a house, carpenters use nails from a...Ch. 5 - A force is applied to a block to move it up a 30...Ch. 5 - Two forces are applied to a 5.0-kg object, and it...Ch. 5 - The block on the tight shown below has more mass...Ch. 5 - If two tugboats pull on a disabled vessel, as...Ch. 5 - A 10.0-kg object is initially moving east at 15.0...Ch. 5 - On June 25, 1983, shot-putter Udo Beyer of East...Ch. 5 - A body of mass m moves in a horizontal direction...Ch. 5 - A body of mass m has initial velocity v0 in the...Ch. 5 - The velocities of a 3.0-kg object at and are and...Ch. 5 - A 120-kg astronaut is riding in a rocket sled that...Ch. 5 - Two forces are acting on a 5.0-kg object that...Ch. 5 - Suppose that you are viewing a soccer game from a...Ch. 5 - A 10.0-kg mass hangs from a spring that has the...Ch. 5 - A 0.0502-kg pair of fuzzy dice is attached to the...Ch. 5 - At a circus, a donkey pulls on a sled carrying a...Ch. 5 - Hanging from the ceiling over a baby bed, well out...Ch. 5 - A bullet shot from a rifle has mass of 10.0 g and...Ch. 5 - An object is acted on by three simultaneous...Ch. 5 - In a particle accelerator, a proton has mass...Ch. 5 - A drone is being directed across a frictionless...
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