College Physics for AP Courses
1st Edition
ISBN: 9781630181871
Author: OpenStax, Ima Lyubkinskaya, Gregg Wolfe Douglas, Ingram, Liza Puiji, Sudhi Oberoi Nathan, Czuba
Publisher: OpenStax College.
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Textbook Question
Chapter 7, Problem 65PE
Unreasonable Results
A car advertisement claims that its 900-kg car accelerated from rest to 30.0 m/s and drove 100 km, gaining 3.00 km in altitude, on 1.0 gal of gasoline. The average
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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 7 Solutions
College Physics for AP Courses
Ch. 7 - Give an example of something think of as work in...Ch. 7 - Give an example of a situation in which there is a...Ch. 7 - Describe a situation in which a force is exerted...Ch. 7 - The person in Figure 7.33 does work on the lawn...Ch. 7 - Work done on a system puts energy into it Work...Ch. 7 - When solving for speed in Example 7.4, we kept...Ch. 7 - In Example 7.7, we calculated the final speed of a...Ch. 7 - Does the work you do on a book when you lift it...Ch. 7 - What is a conservative force?Ch. 7 - The force exerted by a diving board is...
Ch. 7 - Define mechanical energy. What is the relationship...Ch. 7 - What is the relationship of potential energy to...Ch. 7 - Consider the following scenario. A car for which...Ch. 7 - Describe the energy transfers and transformations...Ch. 7 - Do devices with efficiencies of less than one...Ch. 7 - List four different forms or types of energy. Give...Ch. 7 - List the energy conversions that occur when riding...Ch. 7 - Most electrical appliances are rated in watts....Ch. 7 - Explain, in terms of the definition of power, why...Ch. 7 - A spark of static electricity, such as that you...Ch. 7 - Explain why it is easier to climb a mountain on a...Ch. 7 - Do you do work on the outside world when you rub...Ch. 7 - Shivering is an involuntary response to lowered...Ch. 7 - Discuss the relative effectiveness of dieting and...Ch. 7 - What is the difference between energy conservation...Ch. 7 - If the efficiency of a coal-fired electrical...Ch. 7 - How much work does a supermarket checkout...Ch. 7 - A 75.0-kg person climbs stairs, gaining 2.50...Ch. 7 - (a) Calculate the work done on a 1500-kg elevator...Ch. 7 - Suppose a car travels 108 km at a speed of 30.0...Ch. 7 - Calculate the work done by an 85.0-kg man who...Ch. 7 - How much work is done by the boy pulling his...Ch. 7 - A shopper pushes a grocery cart 20.0 m at constant...Ch. 7 - Suppose the ski patrol lowers a rescue sled and...Ch. 7 - Compare the kinetic energy of a 20,000-kg truck...Ch. 7 - (a) How fast must a 3000-kg elephant move to have...Ch. 7 - Confirm the value given for the kinetic energy of...Ch. 7 - (a) Calculate the force needed to bring a 950-kg...Ch. 7 - A car's bumper is designed to withstand a 4.0-km/h...Ch. 7 - Boxing gloves are padded to lessen the force of a...Ch. 7 - Using energy considerations, calculate the average...Ch. 7 - A hydroelectric power facility (see Figure 7.38)...Ch. 7 - (a) How much gravitational potential energy...Ch. 7 - Suppose a 350-g kookaburra (a large kingfisher...Ch. 7 - In Example 7.7, we found that the speed of a...Ch. 7 - A 100-g toy car is propelled by a compressed...Ch. 7 - In a downhill ski race, surprisingly, little...Ch. 7 - A 5.00105 -kg subway train is brought to a stop...Ch. 7 - A pogo stick has a spring with a force constant of...Ch. 7 - A 60.0-kg skier with an initial speed of 12.0 m/s...Ch. 7 - (a) How high a hill can a car coast up (engine...Ch. 7 - Using values from Table 7.1, how many DNA...Ch. 7 - Using energy considerations and assuming...Ch. 7 - If the energy in fusion bombs were used to supply...Ch. 7 - (a) Use of hydrogen fusion to supply energy is a...Ch. 7 - The Crab Nebula (see Figure 7.41) pulsar is the...Ch. 7 - Suppose a star 1000 times brighter than our Sun...Ch. 7 - A person in good physical condition can put out...Ch. 7 - What is the cost of operating a 3.00-W electric...Ch. 7 - A large household air conditioner may consume 15.0...Ch. 7 - (a) What is the average power consumption in watts...Ch. 7 - (a) What is the average useful power output of a...Ch. 7 - A 500-kg dragster accelerates from rest to a final...Ch. 7 - (a) How long will it take an 850-kg car with a...Ch. 7 - (a) Find the useful power output of an elevator...Ch. 7 - (a) What is the available energy content, in...Ch. 7 - (a) How long would it takea 1.50105 -kg airplane...Ch. 7 - Calculate the power output needed for a 950-kg car...Ch. 7 - (a) Calculate the power per square meter reaching...Ch. 7 - (a) How long can you rapidly climb stairs...Ch. 7 - (a) What is the power output in watts and...Ch. 7 - Calculate the power output in watts and horsepower...Ch. 7 - (a) What is the efficiency of an out-of-condition...Ch. 7 - Energy that is not utilized for work or heat...Ch. 7 - Using data from Table 7.5, calculate the daily...Ch. 7 - What is the efficiency of a subject on a treadmill...Ch. 7 - Shoveling snow can be extremely taxing because the...Ch. 7 - Very large forces are produced in joints when a...Ch. 7 - Jogging on hard surfaces with insufficiently...Ch. 7 - (a) Calculate the energy in kJ used by a 55.0-kg...Ch. 7 - Kanellos Kanellopoulos flew 119 km from Crete to...Ch. 7 - The swimmer shown in Figure 7.44 exerts an average...Ch. 7 - Mountain climbers carry bottled oxygen when at...Ch. 7 - The awe-inspiring Great Pyramid of Cheops was...Ch. 7 - (a) How long can you play tennis on the 800 kJ...Ch. 7 - Integrated Concepts (a) Calculate the force the...Ch. 7 - Integrated Concepts A 75.0-kg cross-country skier...Ch. 7 - Integrated Concepts The 70.0-kg swimmer in Figure...Ch. 7 - Integrated Concepts A toy gun uses a spring with a...Ch. 7 - Integrated Concepts (a) What force must be...Ch. 7 - Unreasonable Results A car advertisement claims...Ch. 7 - Unreasonable Results Body fat is metabolized,...Ch. 7 - Construct Your Own Problem Consider a person...Ch. 7 - Construct Your Own Problem Consider humans...Ch. 7 - Integrated Concepts A 105-kg basketball player...
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