College Physics: A Strategic Approach (3rd Edition)
3rd Edition
ISBN: 9780321879721
Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher: PEARSON
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Textbook Question
Chapter 7, Problem 6CQ
A screwdriver with a very thick handle requires less force to operate than one with a very skinny handle. Explain why this is so.
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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
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ii)
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iii)
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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 7 Solutions
College Physics: A Strategic Approach (3rd Edition)
Ch. 7 - The batter in a baseball game hits a home run. As...Ch. 7 - Viewed from somewhere in space above the north...Ch. 7 - Figure Q7.3 shows four pulleys, each with a heavy...Ch. 7 - If you are using a wrench to loosen a very...Ch. 7 - If you are using a wrench to loosen a very...Ch. 7 - A screwdriver with a very thick handle requires...Ch. 7 - If you have ever driven a truck, you likely found...Ch. 7 - A common type of door stop is a wedge made of...Ch. 7 - A student gives a steady push to a ball at the end...Ch. 7 - Prob. 10CQ
Ch. 7 - Prob. 11CQCh. 7 - If you grasp a hammer by its lightweight handle...Ch. 7 - Suppose you have two identical-looking metal...Ch. 7 - The moment of inertia of a uniform rod about an...Ch. 7 - The wheel in Figure Q7.15 is rolling to the right...Ch. 7 - With care, its possible to walk on top of a barrel...Ch. 7 - A nut needs to be tightened with a wrench. Which...Ch. 7 - Suppose a bolt on your car engine needs to be...Ch. 7 - Prob. 19MCQCh. 7 - A typical compact disk has a mass of 15 g and a...Ch. 7 - Suppose manufacturers increase the size of compact...Ch. 7 - Two horizontal rods are each held up by vertical...Ch. 7 - Prob. 23MCQCh. 7 - A particle undergoing circular motion in the...Ch. 7 - Questions 25 through 27 concern a classic...Ch. 7 - Questions 25 through 27 concern a classic...Ch. 7 - Questions 25 through 27 concern a classic...Ch. 7 - What is the angular position in radians of the...Ch. 7 - A child on a merry-go-round takes 3.0 s to go...Ch. 7 - What is the angular speed of the tip of the minute...Ch. 7 - An old-fashioned vinyl record rotates on a...Ch. 7 - The earths radius is about 4000 miles. Kampala,...Ch. 7 - A Ferris wheel rotates at an angular velocity of...Ch. 7 - A turntable rotates counterclockwise at 78 rpm. A...Ch. 7 - A fast-moving superhero in a comic book runs...Ch. 7 - Figure P7.9 shows the angular position of a...Ch. 7 - The angular velocity (in rpm) of the blade of a...Ch. 7 - The 1.00-cm-long second hand on a watch rotates...Ch. 7 - The earths radius is 6.37 106 m; it rotates once...Ch. 7 - To throw a discus, the thrower holds it with a...Ch. 7 - A computer hard disk starts from rest, then speeds...Ch. 7 - The crankshaft in a race car goes from rest to...Ch. 7 - Reconsider the situation in Example 7.10. If Luis...Ch. 7 - Balls are attached to light rods and can move in...Ch. 7 - Six forces, each of magnitude either F or 2F, are...Ch. 7 - What is the net torque about the axle on the...Ch. 7 - The tune-up specifications of a car call for the...Ch. 7 - A professors office door is 0.91 m wide, 2.0 m...Ch. 7 - In Figure P7.22, force F2, acts half as far from...Ch. 7 - Tom and Jerry both push on the 3.00-m-diameter...Ch. 7 - What is the net torque on the bar shown in Figure...Ch. 7 - What is the net torque on the bar shown in Figure...Ch. 7 - What is the net torque on the bar shown in Figure...Ch. 7 - Prob. 27PCh. 7 - Prob. 28PCh. 7 - Hold your arm outstretched so that it is...Ch. 7 - Prob. 30PCh. 7 - The 2.0 kg, uniform, horizontal rod in Figure...Ch. 7 - A 4.00-m-long, 500 kg steel beam extends...Ch. 7 - An athlete at the gym holds a 3.0 kg steel ball in...Ch. 7 - The 2.0-m-long, 15 kg beam in Figure P7.34 is...Ch. 7 - Two thin beams are joined end-to-end as shown in...Ch. 7 - Figure P7.36 shows two thin beams joined at right...Ch. 7 - A regulation table tennis ball is a thin spherical...Ch. 7 - Three pairs of balls are connected by very light...Ch. 7 - A playground toy has four seats, each 5.0 kg,...Ch. 7 - A solid cylinder with a radius of 4.0 cm has the...Ch. 7 - A bicycle rim has a diameter of 0.65 m and a...Ch. 7 - a. What is the moment of inertia of the door in...Ch. 7 - A small grinding wheel has a moment of inertia of...Ch. 7 - While sitting in a swivel chair, you push against...Ch. 7 - An objects moment of inertia is 2.0 kg m2. Its...Ch. 7 - A 200 g, 20-cm-diameter plastic disk is spun on an...Ch. 7 - The 2.5 kg object shown in Figure P7.47 has a...Ch. 7 - A frictionless pulley, which can be modeled as a...Ch. 7 - If you lift the front wheel of a poorly maintained...Ch. 7 - On page 207 there is a photograph of a girl...Ch. 7 - A toy top with a spool of diameter 5.0 cm has a...Ch. 7 - A bicycle with 0.80-m-diameter tires is coasting...Ch. 7 - Figure P7.55 shows the angular...Ch. 7 - The grap in Figure P7.56 shows the angular...Ch. 7 - A car with 58-cm-diameter tires accelerates...Ch. 7 - The cable lifting an elevator is wrapped around a...Ch. 7 - The 20-cm-diameter disk in Figure P7.59 can rotate...Ch. 7 - A combination lock has a 1.0-cm-diameter knob that...Ch. 7 - A 70 kg mans arm, including the hand, can be...Ch. 7 - The three masses shown in Figure P7.62 are...Ch. 7 - A reasonable estimate of the moment of inertia of...Ch. 7 - Starting from rest, a 12-cm-diameter compact disk...Ch. 7 - The ropes in Figure P7.65 are each wrapped around...Ch. 7 - Flywheels are large, massive wheels used to store...Ch. 7 - A 1.0 kg ball and a 2.0 kg ball are connected by a...Ch. 7 - A 1.5 kg block is connected by a rope across a...Ch. 7 - The two blocks in Figure P7.69 are connected by a...Ch. 7 - The 2.0 kg, 30-cm-diameter disk in Figure P7.70 is...Ch. 7 - A tradesman sharpens a knife by pushing it with a...Ch. 7 - MCAT-Style Passage Problems The Bunchberry The...Ch. 7 - The Bunchberry The bunchberry flower has the...Ch. 7 - The Bunchberry The bunchberry flower has the...Ch. 7 - The Bunchberry The bunchberry flower has the...Ch. 7 - Prob. 76MSPPCh. 7 - Prob. 77MSPPCh. 7 - Prob. 78MSPP
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