College Physics
1st Edition
ISBN: 9781938168000
Author: Paul Peter Urone, Roger Hinrichs
Publisher: OpenStax College
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Textbook Question
Chapter 4, Problem 5PE
In Figure 4.7, the net external force on the 24-kg mower is stated to be 51 N. If the
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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
College Physics
Ch. 4 - Propose a force standard different from the...Ch. 4 - What properties do forces have that allow us to...Ch. 4 - How are inertia and mass related?Ch. 4 - What is the relationship between weight and mass?...Ch. 4 - Which statement is correct? (a) Net force causes...Ch. 4 - Why can we neglect forces such as those holding a...Ch. 4 - Explain how the choice of the “Stem of interest”...Ch. 4 - Describe a situation in which the net external...Ch. 4 - A system can have a nonzero velocity while the net...Ch. 4 - A rock is thrown straight up. What is the net...
Ch. 4 - (a) Give an example of different net external...Ch. 4 - If the acceleration of a system is zero, are no...Ch. 4 - If a constant, nonzero force is applied to an...Ch. 4 - The gravitational force on the basketball in...Ch. 4 - When you take off in a jet aircraft, there is a...Ch. 4 - A device used since the 1940s to measure the kick...Ch. 4 - Describe a Situation in which one a force on and,...Ch. 4 - Why does an ordinary rifle recoil (kick backward)...Ch. 4 - An American football lineman reasons that it is...Ch. 4 - Newton's third law of motion tells us that forces...Ch. 4 - If a leg is suspended by a traction setup as shown...Ch. 4 - Ina traction setup a broken bone, with pulleys and...Ch. 4 - To simulate the apparent weightlessness of space...Ch. 4 - A cartoon shows the toupee coming off the head of...Ch. 4 - Explain, in terms of the properties of the four...Ch. 4 - What is the dominant force between astronomical...Ch. 4 - Give a detailed example of the exchange of a...Ch. 4 - A 63.0-kg sprinter starts a race with an...Ch. 4 - If the sprinter from the previous problem...Ch. 4 - A cleaner pushes a 4.50-kg laundry cart in such a...Ch. 4 - Since astronauts in orbit are apparently...Ch. 4 - In Figure 4.7, the net external force on the 24-kg...Ch. 4 - The same rocket sled drawn in Figure 4.31 is...Ch. 4 - (a) If the rocket sled shown in Figure 4.32 starts...Ch. 4 - What is the deceleration of the rocket sled if it...Ch. 4 - Suppose two children push horizontally, but in...Ch. 4 - A powerful motorcycle can produce an acceleration...Ch. 4 - The rocket sled shown in Figure 4.33 accelerates...Ch. 4 - Repeat the previous problem for the situation in...Ch. 4 - The weight of an astronaut plus his space suit on...Ch. 4 - Suppose the mass of a fully loaded module in which...Ch. 4 - What net external force is exerted on a 1100-kg...Ch. 4 - A brave but inadequate rugby player is being...Ch. 4 - Two teams of nine members each engage in a tug of...Ch. 4 - What force does a trampoline have to apply to a...Ch. 4 - (a) Calculate the tension in a vertical strand of...Ch. 4 - Suppose a 60.0-kg gymnast climbs a rope. (a) What...Ch. 4 - Show that, as stated in the text, a force F...Ch. 4 - Consider the baby being weighed in Figure 4.34....Ch. 4 - A 5.00105 -kg rocket is accelerating straight up....Ch. 4 - The wheels of a midsize car exert a force of 2100...Ch. 4 - Calculate the force a 70.0-kg high jumper must...Ch. 4 - When landing after a spectacular somersault, a...Ch. 4 - A freight train consists of two 8.00104 -kg...Ch. 4 - Commercial airplanes are sometimes pushed out of...Ch. 4 - A 1100-kg car pulls a boat on a trailer. (a) What...Ch. 4 - (a) Find the magnitudes of the forces F1 and F2...Ch. 4 - Two children pull a third child on a snow saucer...Ch. 4 - Suppose your car was mired deeply in the mud and...Ch. 4 - What force is exerted on the tooth in Figure 4.38...Ch. 4 - Figure 4.39 shows Superhero and Trusty Sidekick...Ch. 4 - A nurse pushes a cart by exerting a force on the...Ch. 4 - Construct Your Own Problem Consider the tension in...Ch. 4 - Construct Your Own Problem Consider people pushing...Ch. 4 - Unreasonable Results (a) Repeat Exercise 4.29, but...Ch. 4 -
Ch. 4 - A flea jumps by exerting a force of 1.20105 N...Ch. 4 - Two muscles in the back of the leg pull upward on...Ch. 4 - A 76.0-kg person is being pulled away from a...Ch. 4 - Integrated Concepts A 35.0-kg dolphin decelerates...Ch. 4 - Integrated Concepts When starting a foot race, a...Ch. 4 - Integrated Concepts A large rocket has a mass of...Ch. 4 - Integrated Concepts A basketball player jumps...Ch. 4 - Integrated Concepts A 2.50-kg fireworks shell is...Ch. 4 - Integrated Concepts Repeat Exercise 4.47 for a...Ch. 4 - Integrated Concepts An elevator filled with...Ch. 4 - Unreasonable Results (a) What is the final...Ch. 4 - Unreasonable Results A 75.0-kg man stands on a...Ch. 4 - (a) What is the strength of the weak nuclear force...Ch. 4 - (a) What is the ratio of the strength of the...Ch. 4 - What is the ratio of the strength of the strong...
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