Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 3, Problem 43SP
Compute algebraically the resultant of the following coplanar forces: 100 N at
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ROTATIONAL DYNAMICS
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A solid circular cylinder and a solid spherical ball of the same mass and radius are rolling
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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]
Chapter 3 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
Ch. 3 - 3.42 [I] Two forces act on a point object as...Ch. 3 - 3.43 [I] Compute algebraically the resultant of...Ch. 3 - 3.44 [I] Two forces, 80 N and 100 N, acting at...Ch. 3 - 3.45 [I] Find algebraically the (a) resultant...Ch. 3 - 3.46 [I] Having hauled it to the top of a...Ch. 3 - 3.47 [II] Repeat Problem 3.46 if the handle is...Ch. 3 - 3.48 [I] A force of 100 lb acting on a body...Ch. 3 - 3.49 [I] An unknown force acting on a 50.0-g...Ch. 3 - 3.50 [I] Once ignited, a small rocket motor on a...Ch. 3 - 3.51 [II] Typically, a bullet leaves a standard...
Ch. 3 - 3.52 [I] A force acts on a 2-kg mass and gives...Ch. 3 - 3.53 [I] An object has a mass of 300 g. (a)...Ch. 3 - 3.54 [I] A horizontal cable pulls a 200-kg cart...Ch. 3 - 3.55 [II] A 900-kg car is going 20 m/s along a...Ch. 3 - 3.56 [II] A 12.0-g bullet is accelerated from rest...Ch. 3 - 3.57 [II] A 20-kg crate hangs at the end of a long...Ch. 3 - 3.58 [II] A 5.0-kg mass hangs at the end of a...Ch. 3 - 3.59 [II] A 700-N man stands on a scale on the...Ch. 3 - 3.60 [II] Using the scale described in Problem...Ch. 3 - 3.61 [II] A cord passing over a frictionless,...Ch. 3 - 3.62 [II] An elevator starts from rest with a...Ch. 3 - 3.63 [II] Just as her parachute opens, a 60-kg...Ch. 3 - 3.64 [II] A 300-g mass hangs at the end of a...Ch. 3 - 3.65 [II] A 20-kg wagon is pulled along the level...Ch. 3 - 3.66 [II] A 12-kg box is released from the top of...Ch. 3 - 3.67 [I] A wooden crate weighing 1000 N is at...Ch. 3 - 3.68 [I] Someone wearing rubber-soled shoes is...Ch. 3 - 3.69 [I] A standing 580-N woman wearing climbing...Ch. 3 - 3.70 [II] For the situation outlined in Problem...Ch. 3 - 3.71 [II] An inclined plane makes an angle of ...Ch. 3 - 3.72 [II] A horizontal force F is exerted on a...Ch. 3 - 3.73 [II] An inclined plane making an angle of ...Ch. 3 - 3.74 [III] Repeat Problem 3.73 if the coefficient...Ch. 3 - 3.75 [III] A horizontal force of 200 N is required...Ch. 3 - 3.76 [II] Find the acceleration of the blocks in...Ch. 3 - 3.77 [III] Repeat Problem 3.76 if the coefficient...Ch. 3 - 3.78 [III] How large a force F is needed in Fig....Ch. 3 - 3.79 [III] In Fig. 3-28, how large a force F is...Ch. 3 - 3.80 [III] (a) What is the smallest force parallel...Ch. 3 - 3.81 [III] A 5.0-kg block rests on a incline. The...Ch. 3 - 3.82 [III] Three blocks with masses 6.0 kg, 9.0...Ch. 3 - 3.83 [I] Floating in space far from anything...Ch. 3 - 3.84 [I] Two cannonballs that each weigh 4.00...Ch. 3 - 3.85 [I] Imagine a planet and its moon...Ch. 3 - 3.86 [I] Two NASA vehicles separated by a...Ch. 3 - 3.87 [I] Suppose you are designing a small,...Ch. 3 - Prob. 88SPCh. 3 - Prob. 89SPCh. 3 - 3.90 [II] A space station that weighs 10.0 MN on...Ch. 3 - 3.91 [II] An object that weighs 2700 N on the...Ch. 3 - 3.92 [II] Imagine a planet having a mass twice...Ch. 3 - 3.93 [II] The Earth’s radius is about 6370 km. An...Ch. 3 - 3.94 [II] A man who weighs 1000 N on Earth stands...Ch. 3 - 3.95 [II] The radius of the Earth is about 6370...Ch. 3 - 3.96 [II] The fabled planet Dune has a diameter...Ch. 3 - 3.97 [III] An astronaut weighs 480 N on Earth. She...
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