College Physics For Ap® Courses
16th Edition
ISBN: 9781938168932
Author: Gregg Wolfe, Irina Lyublinskaya, Douglas Ingram
Publisher: OpenStax
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Chapter 11, Problem 52PE
Referring to Figure 11.21, prove that the buoyant force on the cylinder is equal to the weight of the fluid displaced (Archimedes' principle). You may assume that the buoyant force is
Figure 11.21 (a) An object submerged in a fluid experiences a buoyant force FB. If FB is greater than the weight of the object, the object will rise. It FB is less than the weight of the object, the object will sink. (b) If the object is removed, it is replaced by fluid having weight Wf1. Since this weight is supported by surrounding fluid, the buoyant force must equal the weight of the fluid displaced. That is, FB=wfl, a statement of Archimedes' principle.
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ROTATIONAL DYNAMICS
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A sphere and cylinder of the same mass and radius start from ret at the same point and more
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Question 03
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Question 04
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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)
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f)
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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
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[2 marks]
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[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
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e)
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Chapter 11 Solutions
College Physics For Ap® Courses
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