Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
4th Edition
ISBN: 9780134110684
Author: Randall D. Knight (Professor Emeritus)
Publisher: PEARSON
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Chapter 4, Problem 58EAP
A javelin thrower standing at rest holds the center of the javelin behind her head, then accelerates it through a distance of 70 cm as she throws. She releases the javelin 2.0 m above the ground traveling at an angle of 300 above the horizontal. Top-rated javelin throwers do throw at about a 30° angle, not the 45° you might have expected. because the biomechanics of the arm allow them to throw the javelin much faster at 30° than they would be able to at 45°. In this throw, the javelin hits the ground 62 m away. What was the acceleration of the javelin during the throw? Assume that it has a constant acceleration.
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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 4 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Ch. 4 - a. At this instant, is the particle in FIGURE Q4.1...Ch. 4 - a. At this instant, is the particle in FIGURE Q4.2...Ch. 4 - Tarzan swings through the jungle by hanging from a...Ch. 4 - A projectile is launched at an angle of 30°. a. Is...Ch. 4 - For a projectile, which of the following...Ch. 4 - A cart that is rolling at constant velocity on a...Ch. 4 - A rock is thrown from a bridge at an angle 30°...Ch. 4 - Anita is running to the right at 5 m/s in FIGURE...Ch. 4 - An electromagnet on the ceiling of an airplane...Ch. 4 - Zack is driving past his house in FIGURE Q4.1O. He...
Ch. 4 - II. In FIGURE Q4.11. Yvette and Zack are driving...Ch. 4 - In uniform circular motion, which of the following...Ch. 4 - FIGURE Q4.13 shows three points on a steadily...Ch. 4 - FIGURE Q4.14 shows four rotating wheels. For each,...Ch. 4 - FIGURE Q4.15 shows a pendulum at one end point of...Ch. 4 - Problems I and 2 show a partial motion diagram....Ch. 4 - Prob. 2EAPCh. 4 - Answer Problems 3 through 5 by choosing one of the...Ch. 4 - Answer Problems 3 through 5 by choosing one of the...Ch. 4 - Answer Problems 3 through 5 by choosing one of the...Ch. 4 - A rocket-powered hockey puck moves on a horizontal...Ch. 4 - A rocket-powered hockey puck moves on a horizontal...Ch. 4 - Prob. 8EAPCh. 4 - A particle moving in the xy- plane has velocity v...Ch. 4 - You have a remote-controlled car that has been...Ch. 4 - A ball thrown horizontally at 25 m/s travels a...Ch. 4 - A physics student on the Planet Exidor throws a...Ch. 4 - A supply plane needs to drop a package of food to...Ch. 4 - A rifle is aimed horizontally at a target 50 m...Ch. 4 - In the Olympic shotput event, an athlete throws...Ch. 4 - On the Apollo 14 mission to the moon, astronaut...Ch. 4 - A baseball player friend of yours wants to...Ch. 4 - A boat takes 3.0 hours to travel 30 km down a...Ch. 4 - When the moving sidewalk at the airport is broken,...Ch. 4 - Prob. 20EAPCh. 4 - A kayaker, needs to paddle north across a...Ch. 4 - Susan, driving north at 60 mph, and Trent, driving...Ch. 4 - FIGURE EX4.23 shows the...Ch. 4 - FIGURE EX4.24 shows the...Ch. 4 - FIGURE EX4.25 shows the...Ch. 4 - The earth’s radius is about 4000 miles. Kampala,...Ch. 4 - An old-fashioned single-play vinyl record rotates...Ch. 4 - As the earth mates, what is the speed of (a) a...Ch. 4 - How fast must a plane fly along the earth’s...Ch. 4 - A 3000-rn-high mountain is located on the equator....Ch. 4 - Peregrine falcons are known for their maneuvering...Ch. 4 - To withstand “g-forces” of up to 10 g’s, caused by...Ch. 4 - The radius of the earth’s very nearly circular...Ch. 4 - A speck of dust on a spinning DVD has a...Ch. 4 - Your roommate is working on his bicycle and has...Ch. 4 - I FIGURE EX4.36 shows the angular velocity graph...Ch. 4 - I FIGURE EX4.37 shows the angular acceleration...Ch. 4 - FIGURE EX4.38 shows the...Ch. 4 - A wheel initially rotating at 60 rpm experiences...Ch. 4 - A 5.0-rn-diameter merry-go-round is initially...Ch. 4 - An electric fan goes from rest to 1800 rpm in 4.0...Ch. 4 - A bicycle wheel is rotating at 50 rpm when the...Ch. 4 - Starting from rest, a DVD steadily accelerates to...Ch. 4 - A spaceship maneuvering near Planet Zeta is...Ch. 4 - equation reference goes here45. A particle moving...Ch. 4 - A projectile’s horizontal range over level ground...Ch. 4 - a. A projectile is launched with speed v0and angle...Ch. 4 - A projectile is launched from ground level at...Ch. 4 - A gray kangaroo can bound across level ground with...Ch. 4 - A ball is thrown toward a cliff of height h with a...Ch. 4 - A tennis player hits a ball 2.0 m above the...Ch. 4 - You are target shooting using a toy gun that fires...Ch. 4 - A 35 g steel ball is held by a ceiling-mounted...Ch. 4 - You are watching an archery tournament when you...Ch. 4 - You’re 6.0 m from one wall of the house seen in...Ch. 4 - Sand moves without slipping at 6.0 m/s down a...Ch. 4 - A stunt man drives a car at a speed of 20 m/s off...Ch. 4 - A javelin thrower standing at rest holds the...Ch. 4 - A rubber ball is dropped onto a ramp that is...Ch. 4 - You are asked to consult for the city’s research...Ch. 4 - Ships A and B leave port together. For the next...Ch. 4 - While driving north at 25 m/s during a rainstorm...Ch. 4 - You’ve been assigned the task of using a shaft...Ch. 4 - Prob. 64EAPCh. 4 - Prob. 65EAPCh. 4 - Astronauts use a centrifuge to simulate the...Ch. 4 - Communications satellites are placed in a circular...Ch. 4 - Prob. 68EAPCh. 4 - A high-speed drill rotating ccw at 2400 rpm comes...Ch. 4 - A turbine is spinning at 3800 rpm. Frication in...Ch. 4 - Prob. 71EAPCh. 4 - The angular velocity of a process control motor is...Ch. 4 - A Ferris wheel of radius R speeds up with angular...Ch. 4 - Prob. 74EAPCh. 4 - A painted tooth on a spinning gear has angular...Ch. 4 - A car starts from rest on a curve with radius of...Ch. 4 - Prob. 77EAPCh. 4 - In Problem 78 through 80 you are given the...Ch. 4 - Prob. 79EAPCh. 4 - In Problem 78 through 80 you are given the...Ch. 4 - In one contest at the country fair, seen in FIGURE...Ch. 4 - Prob. 82EAPCh. 4 - Prob. 83EAPCh. 4 - Prob. 84EAPCh. 4 - Prob. 85EAP
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