College Physics For Ap® Courses
16th Edition
ISBN: 9781938168932
Author: Gregg Wolfe, Irina Lyublinskaya, Douglas Ingram
Publisher: OpenStax
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Chapter 5, Problem 18PE
A contestant in a winter sporting event pushes a 45.0-kg block of ice across a frozen lake as shown in Figure 5.23(a). (a) Calculate the minimum force F he must exert to get the block moving. (b) What is the magnitude of its acceleration once it starts to move, if that force is maintained?
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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
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ii)
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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 5 Solutions
College Physics For Ap® Courses
Ch. 5 - Define normal force. What is its relationship to...Ch. 5 - The glue on a piece of tape can exert forces. Can...Ch. 5 - When you learn to drive, you discover that you...Ch. 5 - When you push a piece of chalk across a...Ch. 5 - Athletes such as swimmers and bicyclists wear body...Ch. 5 - Two expressions were used for the drag force...Ch. 5 - As cars travel, oil and gasoline leaks onto the...Ch. 5 - Why can a squirrel jump from a tree branch to the...Ch. 5 - The elastic properties of the arteries are...Ch. 5 - What are you feeling when you feel your pulse?...
Ch. 5 - Examine different types of shoes, including sports...Ch. 5 - Would you expect your height to be different...Ch. 5 - Why can a squirrel from a tree branch to the...Ch. 5 - Explain why pregnant women often suffer from back...Ch. 5 - An old carpenter's trick to keep nails from...Ch. 5 - When a glass bottle full of vinegar warms up, both...Ch. 5 - A physics major is cooking breakfast when he...Ch. 5 - (a) When rebuilding her car's engine, a physics...Ch. 5 - (a) What is the maximum frictional force in the...Ch. 5 - Suppose you have a 120-kg wooden crate resting on...Ch. 5 - (a) If half of the weight of a small 1.00103 kg...Ch. 5 - A team of eight dogs pulls a sled with waxed wood...Ch. 5 - Consider the 65.0-kg ice skater being pushed by...Ch. 5 - Show that the acceleration of any object down a...Ch. 5 - Show that the acceleration of any object down an...Ch. 5 - Calculate the deceleration of a snow boarder going...Ch. 5 - (a) Calculate the acceleration of a skier heading...Ch. 5 - If an object is to rest on an incline without...Ch. 5 - Calculate the maximum deceleration of a car that...Ch. 5 - Calculate the maximum acceleration of a car that...Ch. 5 - Repeat Exercise 5.14 for a car with four-wheel...Ch. 5 - A freight train consists of two 8.00105 -kg...Ch. 5 - Consider the 52.0-kg mountain climber in Figure...Ch. 5 - A contestant in a winter sporting event pushes a...Ch. 5 - Repeat Exercise 5.18 with the contestant pulling...Ch. 5 - The terminal velocity of a person falling in air...Ch. 5 - A 60-kg and a go-kg skydiver jump from an airplane...Ch. 5 - A 560-g squirrel with a surface area of 930 cm2...Ch. 5 - To maintain a constant speed, the force provided...Ch. 5 - By what factor does the drag force on a car...Ch. 5 - Calculate the speed a spherical rain drop would...Ch. 5 - Using Stokes' law, verify that the units for...Ch. 5 - Find the terminal velocity of a spherical...Ch. 5 - Stokes' law describes sedimentation of particles...Ch. 5 - During a circus act, one performer swings upside...Ch. 5 - During a wrestling match, a 150 kg wrestler...Ch. 5 - (a) The "lead" in pencils is a graphite...Ch. 5 - TV broadcast antennas are the tallest artificial...Ch. 5 - (a) By how much does a 65.0-kg mountain climber...Ch. 5 - A 20.0-m tall hollow aluminum flagpole is...Ch. 5 - As an oil well is drilled, each new section of...Ch. 5 - Calculate the force a piano tuner applies to...Ch. 5 - A vertebra is subjected to a shearing force of 500...Ch. 5 - A disk between vertebrae in the spine is subjected...Ch. 5 - When using a pencil eraser, you exert a vertical...Ch. 5 - To consider the effect of wires hung on poles, we...Ch. 5 - A farmer making grape juice fills a glass bottle...Ch. 5 - (a) When water freezes, its volume increases by...Ch. 5 - This problem returns to the tightrope walker...Ch. 5 - The pole in Figure 5.24 is at a 90.0° bend in a...
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