EBK PHYSICS FOR SCIENTISTS AND ENGINEER
10th Edition
ISBN: 8220106906149
Author: Jewett
Publisher: Cengage Learning US
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Textbook Question
Chapter 5, Problem 17P
A block slides down a frictionless plane having an inclination of θ − 15.0º. The block starts from rest at the top. and the length of the incline is 2.00 m. (a) Draw a free-body diagram of the block. Find (b) the acceleration of the block and (c) its speed when it reaches the bottom of the incline.
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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
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
Ch. 5.2 - Which of the following statements is correct? (a)...Ch. 5.4 - An object experiences no acceleration. Which of...Ch. 5.4 - You push an object, initially at rest, across a...Ch. 5.5 - Suppose you are talking by interplanetary...Ch. 5.6 - (i) If a fly collides with the windshield of a...Ch. 5.8 - You press your physics textbook flat against a...Ch. 5.8 - Charlie is playing with his daughter Toney in the...Ch. 5 - A certain orthodontist uses a wire brace to align...Ch. 5 - One or more external forces, large enough to be...Ch. 5 - A 3.00-kg object undergoes an acceleration given...
Ch. 5 - The average speed of a nitrogen molecule in air is...Ch. 5 - Two forces, F1=(6.00i4.00j)N and...Ch. 5 - The force exerted by the wind on the sails of a...Ch. 5 - Review. Three forces acting on an object are given...Ch. 5 - If a single constant force acts on an object that...Ch. 5 - Review. The gravitational force exerted on a...Ch. 5 - Review. The gravitational force exerted on a...Ch. 5 - Review. An electron of mass 9. 11 1031 kg has an...Ch. 5 - If a man weighs 900 N on the Earth, what would he...Ch. 5 - You stand on the seat of a chair and then hop off....Ch. 5 - A brick of mass M has been placed on a rubber...Ch. 5 - Review. Figure P5.15 shows a worker poling a boata...Ch. 5 - An iron bolt of mass 65.0 g hangs from a string...Ch. 5 - A block slides down a frictionless plane having an...Ch. 5 - A bag of cement whose weight is Fg hangs in...Ch. 5 - The distance between two telephone poles is 50.0...Ch. 5 - An object of mass m = 1.00 kg is observed to have...Ch. 5 - A simple accelerometer is constructed inside a car...Ch. 5 - An object of mass m1 = 5.00 kg placed on a...Ch. 5 - In the system shown in Figure P5.23, a horizontal...Ch. 5 - A car is stuck in the mud. A tow truck pulls on...Ch. 5 - An object of mass m1 hangs from a string that...Ch. 5 - Why is the following situation impassible? Your...Ch. 5 - Consider a large truck carrying a heavy load, such...Ch. 5 - Before 1960m people believed that the maximum...Ch. 5 - A 9.00-kg hanging object is connected by a light,...Ch. 5 - The person in Figure P5.30 weighs 170 lb. As seen...Ch. 5 - Three objects are connected on a table as shown in...Ch. 5 - You are working as a letter sorter in a U.S Post...Ch. 5 - You have been called as an expert witness for a...Ch. 5 - A block of mass 3.00 kg is pushed up against a...Ch. 5 - Review. A Chinook salmon can swim underwater at...Ch. 5 - A 5.00-kg block is placed on top of a 10.0-kg...Ch. 5 - A black aluminum glider floats on a film of air...Ch. 5 - Why is the following situation impossible? A book...Ch. 5 - Two blocks of masses m1 and m2, are placed on a...Ch. 5 - A 1.00-kg glider on a horizontal air track is...Ch. 5 - An inventive child named Nick wants to reach an...Ch. 5 - A rope with mass mr is attached to a block with...Ch. 5 - In Example 5.7, we pushed on two blocks on a...Ch. 5 - In the situation described in Problem 41 and...Ch. 5 - A crate of weight Fg is pushed by a force P on a...Ch. 5 - In Figure P5.46, the pulleys and pulleys the cord...Ch. 5 - You are working as an expert witness for the...Ch. 5 - A flat cushion of mass m is released from rest at...Ch. 5 - What horizontal force must be applied to a large...Ch. 5 - An 8.40-kg object slides down a fixed,...Ch. 5 - A block of mass 2.20 kg is accelerated across a...Ch. 5 - Why is the following situation impossible? A...Ch. 5 - Initially, the system of objects shown in Figure...Ch. 5 - A mobile is formed by supporting four metal...Ch. 5 - In Figure P5.55, the incline has mass M and is...
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Drawing Free-Body Diagrams With Examples; Author: The Physics Classroom;https://www.youtube.com/watch?v=3rZR7FSSidc;License: Standard Youtube License