PHYSICS 1250 PACKAGE >CI<
9th Edition
ISBN: 9781305000988
Author: SERWAY
Publisher: CENGAGE LEARNING (CUSTOM)
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Textbook Question
Chapter 2, Problem 2.65AP
A ball starts from rest and accelerates at 0.5(H) m/s2 while moving down an inclined plane 9.00 m long. When it reaches the bottom, the ball rolls up another plane, where it comes to rest after moving 15.0 m on that plane. (a) What is the speed of the ball at the bottom of the first plane? (b) During what lime interval does the ball roll down the first plane? (c) What is the acceleration along the second plane? (d) What is the ball’s speed 8.00 m along the second plane?
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ROTATIONAL DYNAMICS
Question 01
A solid circular cylinder and a solid spherical ball of the same mass and radius are rolling
together down the same inclined. Calculate the ratio of their kinetic energy. Assume pure
rolling motion Question 02
A sphere and cylinder of the same mass and radius start from ret at the same point and more
down the same plane inclined at 30° to the horizontal
Which body gets the bottom first and what is its acceleration
b) What angle of inclination of the plane is needed to give the slower body the same
acceleration
Question 03
i)
Define the angular velocity of a rotating body and give its SI unit
A car wheel has its angular velocity changing from 2rads to 30 rads
seconds. If the radius of the wheel is 400mm. calculate
ii)
The angular acceleration
iii)
The tangential linear acceleration of a point on the rim of the wheel
Question 04
in 20
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 2 Solutions
PHYSICS 1250 PACKAGE >CI<
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Emily...Ch. 2 - A baseball is hit so that it travels straight...Ch. 2 - It is possible to shoot an arrow at a speed as...Ch. 2 - The height of a helicopter above the ground is...Ch. 2 - Prob. 2.51PCh. 2 - A ball is thrown upward from the ground with an...Ch. 2 - A student throws a set of keys vertically upward...Ch. 2 - At time t = 0, a student throws a set of keys...Ch. 2 - A daring ranch hand sitting on a tree limb wishes...Ch. 2 - A package is dropped at time t = 0 from a...Ch. 2 - Automotive engineers refer to the time rate of...Ch. 2 - A student drives a moped along a straight road as...Ch. 2 - The speed of a bullet as it travels down the...Ch. 2 - A certain automobile manufacturer claims that its...Ch. 2 - The froghopper Philaenus spumarius is supposedly...Ch. 2 - An object is at x = 0 at t = 0 and moves along the...Ch. 2 - Ail inquisitive physics student and mountain...Ch. 2 - In Figure 2.11b, the area under the velocitytime...Ch. 2 - A ball starts from rest and accelerates at 0.5(H)...Ch. 2 - A woman is reported to have fallen 144 ft from the...Ch. 2 - An elevator moves downward in a tall building at a...Ch. 2 - Why is the following situation impossible? 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