Earth is approximately a sphere of radius \(6.37 \times 10^6 \ \mathrm{m}\). What are (a) its circumference in kilometers, (b) its surface area in square kilometers, and (c) its volume in cubic kilometers?
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Table of Contents
1
Measurement
1.1
Measuring Things, Including Lengths
1.2
Time
1.3
Mass
2
Motion Along a Straight Line
2.1
Position, Displacement, and Average Velocity
2.2
Instantaneous Velocity and Speed
2.3
Acceleration
2.4
Constant Acceleration
2.5
Free-Fall Acceleration
2.6
Graphical Integration In Motion Analysis
3
Vectors
3.1
Vectors and Their Components
3.2
Unit Vectors, Adding Vectors By Components
3.3
Multiplying Vectors
4
Motion in Two and Three Dimensions
4.1
Position and Displacement
4.2
Average Velocity and Instantaneous Velocity
4.3
Average Acceleration and Instantaneous Acceleration
4.4
Projectile Motion
4.5
Uniform Circular Motion
4.6
Relative Motion In One Dimension
4.7
Relative Motion In Two Dimensions
5
Force and Motion—I
5.1
Newton’s First and Second Laws
5.2
Some Particular Forces
5.3
Applying Newton’s Laws
6
Force and Motion—II
6.1
Friction
6.2
The Drag Force and Terminal Speed
6.3
Uniform Circular Motion
7
Kinetic Energy and Work
7.1
Kinetic Energy
7.2
Work and Kinetic Energy
7.3
Work Done By The Gravitational Force
7.4
Work Done By A Spring Force
7.5
Work Done By A General Variable Force
7.6
Power
8
Potential Energy and Conservation of Energy
8.1
Potential Energy
8.2
Conservation of Mechanical Energy
8.3
Reading A Potential Energy Curve
8.4
Work Done On A System By An External Force
8.5
Conservation of Energy
9
Center of Mass and Linear Momentum
9.1
Center of Mass
9.2
Newton’s Second Law For A System of Particles
9.3
Linear Momentum
9.4
Collision and Impulse
9.5
Conservation of Linear Momentum
9.6
Momentum and Kinetic Energy In Collisions
9.7
Elastic Collisions In One Dimension
9.8
Collisions In Two Dimensions
9.9
Systems With Varying Mass: A Rocket
10
Rotation
10.1
Rotational Variables
10.2
Rotation With Constant Angular Acceleration
10.3
Relating The Linear and Angular Variables
10.4
Kinetic Energy of Rotation
10.5
Calculating The Rotational Inertia
10.6
Torque
10.7
Newton’s Second Law For Rotation
10.8
Work and Rotational Kinetic Energy
11
Rolling, Torque, and Angular Momentum
11.1
Rolling As Translation and Rotation Combined
11.2
Forces and Kinetic Energy of Rolling
11.3
The Yo-Yo
11.4
Torque Revisited
11.5
Angular Momentum
11.6
Newton’s Second Law In Angular Form
11.7
Angular Momentum of A Rigid Body
11.8
Conservation of Angular Momentum
11.9
Precession of A Gyroscope
12
Equilibrium and Elasticity
12.1
Equilibrium
12.2
Some Examples of Static Equilibrium
12.3
Elasticity
13
Gravitation
13.1
Newton’s Law of Gravitation
13.2
Gravitation and The Principle of Superposition
13.3
Gravitation Near Earth’s Surface
13.4
Gravitation Inside Earth
13.5
Gravitational Potential Energy
13.6
Planets and Satellites: Kepler’s Laws
13.7
Satellites: Orbits and Energy
13.8
Einstein and Gravitation
14
Fluids
14.1
Fluids, Density, and Pressure
14.2
Fluids At Rest
14.3
Measuring Pressure
14.4
Pascal’s Principle
14.5
Archimedes’ Principle
14.6
The Equation of Continuity
14.7
Bernoulli’s Equation
15
Oscillations
15.1
Simple Harmonic Motion
15.2
Energy In Simple Harmonic Motion
15.3
An Angular Simple Harmonic Oscillator
15.4
Pendulums, Circular Motion
15.5
Damped Simple Harmonic Motion
15.6
Forced Oscillations and Resonance
16
Waves—I
16.1
Transverse Waves
16.2
Wave Speed On A Stretched String
16.3
Energy and Power of A Wave Traveling Along A String
16.4
The Wave Equation
16.5
Interference of Waves
16.6
Phasors
16.7
Standing Waves and Resonance
17
Waves—II
17.1
Speed of Sound
17.2
Traveling Sound Waves
17.3
Interference
17.4
Intensity and Sound Level
17.5
Sources of Musical Sound
17.6
Beats
17.7
The Doppler Effect
17.8
Supersonic Speeds, Shock Waves
18
Temperature, Heat, and the First Law of Thermodynamics
18.1
Temperature
18.2
The Celsius and Fahrenheit Scales
18.3
Thermal Expansion
18.4
Absorption of Heat
18.5
The First Law of Thermodynamics
18.6
Heat Transfer Mechanisms
19
The Kinetic Theory of Gases
19.1
Avogadro’s Number
19.2
Ideal Gases
19.3
Pressure, Temperature, and Rms Speed
19.4
Translational Kinetic Energy
19.5
Mean Free Path
19.6
The Distribution of Molecular Speeds
19.7
The Molar Specific Heats of An Ideal Gas
19.8
Degrees of Freedom and Molar Specific Heats
19.9
The Adiabatic Expansion of An Ideal Gas
20
Entropy and the Second Law of Thermodynamics
20.1
Entropy
20.2
Entropy In The Real World: Engines
20.3
Refrigerators and Real Engines
20.4
A Statistical View of Entropy
21
Coulomb’s Law
21.1
Coulomb’s Law
21.2
Charge is Quantized
21.3
Charge is Conserved
22
Electric Fields
22.1
The Electric Field
22.2
The Electric Field Due To A Charged Particle
22.3
The Electric Field Due To A Dipole
22.4
The Electric Field Due To A Line of Charge
22.5
The Electric Field Due To A Charged Disk
22.6
A Point Charge In An Electric Field
22.7
A Dipole In An Electric Field
23
Gauss’ Law
23.1
Electric Flux
23.2
Gauss’ Law
23.3
A Charged Isolated Conductor
23.4
Applying Gauss’ Law: Cylindrical Symmetry
23.5
Applying Gauss’ Law: Planar Symmetry
23.6
Applying Gauss’ Law: Spherical Symmetry
24
Electric Potential
24.1
Electric Potential
24.2
Equipotential Surfaces and The Electric Field
24.3
Potential Due To A Charged Particle
24.4
Potential Due To An Electric Dipole
24.5
Potential Due To A Continuous Charge Distribution
24.6
Calculating The Field From The Potential
24.7
Electric Potential Energy of A System of Charged Particles
24.8
Potential of A Charged Isolated Conductor
25
Capacitance
25.1
Capacitance
25.2
Calculating The Capacitance
25.3
Capacitors In Parallel and In Series
25.4
Energy Stored In An Electric Field
25.5
Capacitor With A Dielectric
25.6
Dielectrics and Gauss’ Law
26
Current and Resistance
26.1
Electric Current
26.2
Current Density
26.3
Resistance and Resistivity
26.4
Ohm’s Law
26.5
Power, Semiconductors, Superconductors
27
Circuits
27.1
Single-Loop Circuits
27.2
Multiloop Circuits
27.3
The Ammeter and The Voltmeter
27.4
Rc Circuits
28
Magnetic Fields
28.1
Magnetic Fields and The Definition of
28.2
Crossed Fields: Discovery of The Electron
28.3
Crossed Fields: The Hall Effect
28.4
A Circulating Charged Particle
28.5
Cyclotrons and Synchrotrons
28.6
Magnetic Force On A Current-Carrying Wire
28.7
Torque On A Current Loop
28.8
The Magnetic Dipole Moment
29
Magnetic Fields Due to Currents
29.1
Magnetic Field Due To A Current
29.2
Force Between Two Parallel Currents
29.3
Ampere’s Law
29.4
Solenoids and Toroids
29.5
A Current-Carrying Coil As A Magnetic Dipole
30
Induction and Inductance
30.1
Faraday’s Law and Lenz’s Law
30.2
Induction and Energy Transfers
30.3
Induced Electric Fields
30.4
Inductors and Inductance
30.5
Self-Induction
30.6
Rl Circuits
30.7
Energy Stored In A Magnetic Field
30.8
Energy Density of A Magnetic Field
30.9
Mutual Induction
31
Electromagnetic Oscillations and Alternating Current
31.1
LC Oscillations
31.2
Damped Oscillations In An Rlc Circuit
31.3
Forced Oscillations of Three Simple Circuits
31.4
The Series Rlc Circuit
31.5
Power In Alternating-Current Circuits
31.6
Transformers
32
Maxwell’s Equations; Magnetism of Matter
32.1
Gauss’ Law For Magnetic Fields
32.2
Induced Magnetic Fields
32.3
Displacement Current
32.4
Magnets
32.5
Magnetism and Electrons
32.6
Diamagnetism
32.7
Paramagnetism
32.8
Ferromagnetism
33
Electromagnetic Waves
33.1
Electromagnetic Waves
33.2
Energy Transport and The Poynting Vector
33.3
Radiation Pressure
33.4
Polarization
33.5
Reflection and Refraction
33.6
Total Internal Reflection
33.7
Polarization By Reflection
34
Images
34.1
Images and Plane Mirrors
34.2
Spherical Mirrors
34.3
Spherical Refracting Surfaces
34.4
Thin Lenses
34.5
Optical Instruments
34.6
Three Proofs
35
Interference
35.1
Light As A Wave
35.2
Young’s Interference Experiment
35.3
Interference and Double-Slit Intensity
35.4
Interference From Thin Films
35.5
Michelson’s Interferometer
36
Diffraction
36.1
Single-Slit Diffraction
36.2
Intensity In Single-Slit Diffraction
36.3
Diffraction By A Circular Aperture
36.4
Diffraction By A Double Slit
36.5
Diffraction Gratings
36.6
Gratings: Dispersion and Resolving Power
36.7
X-Ray Diffraction
37
Relativity
37.1
Simultaneity and Time Dilation
37.2
The Relativity of Length
37.3
The Lorentz Transformation
37.4
The Relativity of Velocities
37.5
Doppler Effect For Light
37.6
Momentum and Energy
Textbook Solutions for Fundamentals of Physics
Chapter 1.1 Problem 5
Question
Horses are to race over a certain English meadow for a distance of 4.0 furlongs. What is the race distance in
(a) rods and
(b) chains?
(1 furlong = 201.168 m, 1 rod = 5.0292 m, and 1 chain = 20.117 m.)
Solution
The first step in solving 1.1 problem number trying to solve the problem we have to refer to the textbook question: Horses are to race over a certain English meadow for a distance of 4.0 furlongs. What is the race distance in(a) rods and(b) chains?(1 furlong = 201.168 m, 1 rod = 5.0292 m, and 1 chain = 20.117 m.)
From the textbook chapter Measuring Things, Including Lengths you will find a few key concepts needed to solve this.
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full solution
Title
Fundamentals of Physics 12
Author
David Halliday, Robert Resnick, Jearl Walker
ISBN
9781119801122
Horses are to race over a certain English meadow for a distance of 4.0 furlongs. What is the race distance in (a) rods and (b) chains? (1 furlong = 201.168 m, 1 rod = 5.0292 m, and 1 chain = 20.117 m.)
Chapter 1.1 textbook questions
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Chapter 1: Problem 1 Fundamentals of Physics 12
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Chapter 1: Problem 2 Fundamentals of Physics 12
A gry is an old English measure for length, defined as 1/10 of a line, where line is another old English measure for length, defined as 1/12 inch. A common measure for length in the publishing business is a point, defined as 1/72 inch. What is an area of \(0.50 \ \mathrm{gry}^2\) in points squared (\(\text{points}^2\) )?
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Chapter 1: Problem 3 Fundamentals of Physics 12
The micrometer \(\left(1 \ \mu \mathrm{m}\right)\) is often called the micron. (a) How many microns make up 1.0 km? (b) What fraction of a centimeter equals \(1.0 \ \mu \mathrm{m}\)? (c) How many microns are in 1.0 yd?
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Chapter 1: Problem 4 Fundamentals of Physics 12
Spacing in this book was generally done in units of points and picas: 12 points = 1 pica, and 6 picas = 1 inch. If a figure was misplaced in the page proofs by 0.80 cm, what was the misplacement in (a) picas and (b) points?
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Chapter 1: Problem 5 Fundamentals of Physics 12
Horses are to race over a certain English meadow for a distance of 4.0 furlongs. What is the race distance in (a) rods and (b) chains? (1 furlong = 201.168 m, 1 rod = 5.0292 m, and 1 chain = 20.117 m.)
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Chapter 1: Problem 6 Fundamentals of Physics 12
You can easily convert common units and measures electronically, but you still should be able to use a conversion table, such as those in Appendix D. Table 1.1 is part of a conversion table for a system of volume measures once common in Spain; a volume of 1 fanega is equivalent to \(55.501 \ \mathrm{dm}^3\) (cubic decimeters). To complete the table, what numbers (to three significant figures) should be entered in (a) the cahiz column, (b) the fanega column, (c) the cuartilla column, and (d) the almude column, starting with the top blank? Express 7.00 almudes in (e) medios, (f) cahizes, and (g) cubic centimeters (\(\mathrm{cm}^3\) ).
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Chapter 1: Problem 7 Fundamentals of Physics 12
Hydraulic engineers in the United States often use, as a unit of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre of land to a depth of 1 ft. A severe thunderstorm dumped 2.0 in. of rain in 30 min on a town of area \(26 \ \mathrm{km}^2\) . What volume of water, in acre-feet, fell on the town?
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Chapter 1: Problem 8 Fundamentals of Physics 12
Harvard Bridge, which connects MIT with its fraternities across the Charles River, has a length of 364.4 Smoots plus one ear. The unit of one Smoot is based on the length of Oliver Reed Smoot, Jr., class of 1962, who was carried or dragged length by length across the bridge so that other pledge members of the Lambda Chi Alpha fraternity could mark off (with paint) 1-Smoot lengths along the bridge. The marks have been repainted biannually by fraternity pledges since the initial measurement, usually during times of traffic congestion so that the police cannot easily interfere. (Presumably, the police were originally upset because the Smoot is not an SI base unit, but these days they seem to have accepted the unit.) Figure 1.1 shows three parallel paths, measured in Smoots (S), Willies (W), and Zeldas (Z). What is the length of 50.0 Smoots in (a) Willies and (b) Zeldas?
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Chapter 1: Problem 9 Fundamentals of Physics 12
Antarctica is roughly semicircular, with a radius of 2000 km (Fig. 1.2). The average thickness of its ice cover is 3000 m. How many cubic centimeters of ice does Antarctica contain? (Ignore the curvature of Earth.)
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