EBK PHYSICS FOR SCIENTISTS AND ENGINEER
1st Edition
ISBN: 9780100546714
Author: Katz
Publisher: YUZU
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Chapter 8, Problem 64PQ
FIGURE 8.38 Comparison of a circular and an elliptical orbit. The semimajor axis of the ellipse is the radius of the circular orbit. At points I and J on the ellipse, the particle’s speed is the same as it would be on the circle. At perihelion P, the particle’s speed is too high to maintain a circular orbit, and at aphelion A, it is too low.
G Case Study Comet Hale-Bopp’s elliptical orbit is described in Problem 63. Draw an energy graph for the Sun–comet system. For points A, P, I, and J (Fig. 8.38, page 236), superimpose a bar chart on the energy graph.
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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 8 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
Ch. 8.1 - Comet Halleys Orbital Parameters Figure 8.1 shows...Ch. 8.2 - Prob. 8.2CECh. 8.2 - Prob. 8.3CECh. 8.3 - In Figure 8.11, a person launches a ball off of a...Ch. 8 - Case Study From Figure 8.1B for Comet Halley, is...Ch. 8 - Estimate the kinetic energy of the following: a....Ch. 8 - Prob. 3PQCh. 8 - Prob. 4PQCh. 8 - A 0.430-kg soccer ball is kicked at an initial...Ch. 8 - Prob. 6PQ
Ch. 8 - According to a scaled woman, a 67.7-kg man runs...Ch. 8 - Prob. 8PQCh. 8 - Prob. 9PQCh. 8 - Prob. 10PQCh. 8 - Prob. 11PQCh. 8 - Prob. 12PQCh. 8 - Prob. 13PQCh. 8 - In each situation shown in Figure P8.12, a ball...Ch. 8 - Prob. 15PQCh. 8 - Prob. 16PQCh. 8 - Prob. 17PQCh. 8 - Prob. 18PQCh. 8 - A ball of mass 0.40 kg hangs straight down on a...Ch. 8 - Prob. 20PQCh. 8 - Prob. 21PQCh. 8 - Prob. 22PQCh. 8 - One type of toy car contains a spring that is...Ch. 8 - A block is placed on top of a vertical spring, and...Ch. 8 - Rubber tends to be nonlinear as an elastic...Ch. 8 - A block is hung from a vertical spring. The spring...Ch. 8 - A spring of spring constant k lies along an...Ch. 8 - A block on a frictionless, horizontal surface is...Ch. 8 - A falcon is soaring over a prairie, flying at a...Ch. 8 - A stellar black hole may form when a massive star...Ch. 8 - A newly established colony on the Moon launches a...Ch. 8 - The Flybar high-tech pogo stick is advertised as...Ch. 8 - An uncrewed mission to the nearest star, Proxima...Ch. 8 - A small ball is tied to a string and hung as shown...Ch. 8 - Prob. 35PQCh. 8 - Prob. 36PQCh. 8 - Prob. 37PQCh. 8 - Prob. 38PQCh. 8 - Figure P8.39 shows two bar charts. In each, the...Ch. 8 - Prob. 40PQCh. 8 - If a spacecraft is launched from the Moon at the...Ch. 8 - A 1.50-kg box rests atop a massless vertical...Ch. 8 - A man unloads a 5.0-kg box from a moving van by...Ch. 8 - Starting at rest, Tina slides down a frictionless...Ch. 8 - Prob. 45PQCh. 8 - Karen and Randy are playing with a toy car and...Ch. 8 - An intrepid physics student decides to try bungee...Ch. 8 - A block of mass m = 1.50 kg attached to a...Ch. 8 - Prob. 49PQCh. 8 - A jack-in-the-box is actually a system that...Ch. 8 - A side view of a half-pipe at a skateboard park is...Ch. 8 - Prob. 52PQCh. 8 - Prob. 53PQCh. 8 - Prob. 54PQCh. 8 - A particle moves in one dimension under the action...Ch. 8 - Prob. 56PQCh. 8 - Prob. 57PQCh. 8 - Prob. 58PQCh. 8 - Prob. 59PQCh. 8 - Much of the mass of our Milky Way galaxy is...Ch. 8 - A stellar black hole may form when a massive star...Ch. 8 - Prob. 62PQCh. 8 - Prob. 63PQCh. 8 - FIGURE 8.38 Comparison of a circular and an...Ch. 8 - A 50.0-g toy car is released from rest on a...Ch. 8 - Prob. 66PQCh. 8 - The Earths perihelion distance (closest approach...Ch. 8 - After ripping the padding off a chair you are...Ch. 8 - A In a classic laboratory experiment, a cart of...Ch. 8 - A block is attached to a spring, and the block...Ch. 8 - At the start of a basketball game, a referee...Ch. 8 - At the start of a basketball game, a referee...Ch. 8 - Prob. 73PQCh. 8 - Prob. 74PQCh. 8 - At 220 m, the bungee jump at the Verzasca Dam in...Ch. 8 - Prob. 76PQCh. 8 - A block of mass m1 = 4.00 kg initially at rest on...Ch. 8 - A Eric is twirling a ball of mass m = 0.150 kg...Ch. 8 - Prob. 79PQCh. 8 - Prob. 80PQCh. 8 - Prob. 81PQCh. 8 - Prob. 82PQCh. 8 - Prob. 83PQCh. 8 - Prob. 84PQ
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