Physics Demystified : A Self-Teaching Guide (Demystified)

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Transcript of Physics Demystified : A Self-Teaching Guide (Demystified)

STAN GIBILISCO • Astronomy Demystified RHONDA HUETTENMUELLER • Algebra Demystified STEVEN KRANTZ • Calculus Demystified
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DOI: 10.1036/0071412123
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CHAPTER 1 Equations, Formulas, and Vectors 3 Notation 3
One-Variable First-Order Equations 9
One-Variable Second-Order Equations 12
One-Variable Higher-Order Equations 18
CHAPTER 2 Scientific Notation 29 Subscripts and Superscripts 29
Power-of-10 Notation 31
Significant Figures 44
The Polar Plane 62
Triangles 86
Quadrilaterals 92
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CHAPTER 5 Logarithms, Exponentials, and Trigonometry 113 Logarithms 113
Trigonometric Functions 124
Trigonometric Identities 127
CHAPTER 6 Units and Constants 147 Systems of Units 147
Base Units in SI 148
Other Units 154
Prefix Multipliers 158
Force 175
Displacement 176
Speed 178
Velocity 181
Acceleration 183
CHAPTER 8 Momentum, Work, Energy, and Power 193 Momentum 193
Collisions 196
Work 202
Energy 204
Power 209
The Nucleus 219
Compounds 234
CHAPTER 10 Basic States of Matter 241 The Solid Phase 242
The Liquid Phase 251
The Gaseous Phase 258
CHAPTER 11 Temperature, Pressure, and Changes of State 265 What Is Heat? 265
Temperature 269
Temperature and States of Matter 278
Test: Part One 285
CHAPTER 12 Direct Current 297 What Does Electricity Do? 297
Electrical Diagrams 303
CHAPTER 13 Alternating Current 323 Definition of Alternating Current 323
Waveforms 325
Amplitude 332
Magnetic Force 347
Inductive Reactance 375
The Bipolar Transistor 405
CHAPTER 17 Wave Phenomena 437 Intangible Waves 438
Fundamental Properties 440
Wave Interaction 448
Wave Mysteries 455
ELF Fields 472
Rf Waves 474
Radioactivity 490
Lenses and Mirrors 507
Time Dilation 534
Spatial Distortion 539
Mass Distortion 541
General Relativity 544
Suggested Additional References 593
This book is for people who want to learn basic physics without taking a formal course. It can also serve as a supplemental text in a classroom, tutored, or home-schooling environment. I recommend that you start at the beginning of this book and go straight through, with the possible exception of Part Zero.
If you are confident about your math ability, you can skip Part Zero. But take the Part Zero test anyway, to see if you are actually ready to jump into Part One. If you get 90 percent of the answers correct, you’re ready. If you get 75 to 90 percent correct, skim through the text of Part Zero and take the chapter-ending quizzes. If you get less than three-quarters of the answers correct in the quizzes and the section-ending test, find a good desk and study Part Zero. It will be a drill, but it will get you “in shape” and make the rest of the book easy.
In order to learn physics, you must have some mathematical skill. Math is the language of physics. If I were to tell you otherwise, I’d be cheating you. Don’t get intimidated. None of the math in this book goes beyond the high school level.
This book contains an abundance of practice quiz, test, and exam questions. They are all multiple choice, and are similar to the sorts of questions used in standardized tests. There is a short quiz at the end of every chapter. The quizzes are “open-book.” You may (and should) refer to the chapter texts when taking them. When you think you’re ready, take the quiz, write down your answers, and then give your list of answers to a friend. Have the friend tell you your score, but not which questions you got wrong. The answers are listed in the back of the book. Stick with a chapter until you get most of the answers right.
This book is divided into three major sections after Part Zero. At the end of each section is a multiple choice test. Take these tests when you’re done with the respective sections and have taken all the chapter quizzes. The section tests are “closed-book.” Don’t look back at the text when taking them. The questions are not as difficult as those in the quizzes, and they don’t require that you memorize trivial things. A satisfactory score is three- quarters of the answers correct. Again, answers are in the back of the book.
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There is a final exam at the end of this course. The questions are practical, and are less mathematical than those in the quizzes. The final exam contains questions drawn from Parts One, Two, and Three. Take this exam when you have finished all the sections, all the section tests, and all of the chapter quizzes. A satisfactory score is at least 75 percent correct answers.
With the section tests and the final exam, as with the quizzes, have a friend tell you your score without letting you know which questions you missed. That way, you will not subconsciously memorize the answers. You might want to take each test, and the final exam, two or three times. When you have gotten a score that makes you happy, you can check to see where your knowledge is strong and where it is not so keen.
I recommend that you complete one chapter a week. An hour or two daily ought to be enough time for this. Don’t rush yourself; give your mind time to absorb the material. But don’t go too slowly either. Take it at a steady pace and keep it up. That way, you’ll complete the course in a few months. (As much as we all wish otherwise, there is no substitute for “good study habits.”) When you’re done with the course, you can use this book, with its comprehensive index, as a permanent reference.
Suggestions for future editions are welcome.
Stan Gibilisco
Illustrations in this book were generated with CorelDRAW. Some clip art is courtesy of Corel Corporation, 1600 Carling Avenue, Ottawa, Ontario, Canada K1Z 8R7.
I extend thanks to Mary Kaser, who helped with the technical editing of the manuscript for this book.
Part Zero
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Equations, Formulas, and Vectors
An equation is a mathematical expression containing two parts, one on the left-hand side of an equals sign () and the other on the right-hand side. A formula is an equation used for the purpose of deriving a certain value or solving some practical problem. A vector is a special type of quantity in which there are two components: magnitude and direction. Physics makes use of equations, formulas, and vectors. Let’s jump in and immerse our- selves in them. Why hesitate? You won’t drown in this stuff. All you need is a little old-fashioned perseverance.
Notation Equations and formulas can contain coefficients (specific numbers), con- stants (specific quantities represented by letters of the alphabet), and/or vari- ables (expressions that stand for numbers but are not specific). Any of the common arithmetic operations can be used in an equation or formula. These include addition, subtraction, multiplication, division, and raising to a power. Sometimes functions are also used, such as logarithmic functions, exponen- tial functions, trigonometric functions, or more sophisticated functions.
Addition is represented by the plus sign ( ). Subtraction is represented by the minus sign (). Multiplication of specific numbers is represented
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PART 0 A Review of Mathematics4
either by a plus sign rotated 45 degrees () or by enclosing the numerals in parentheses and writing them one after another. Multiplication involving a coefficient and one or more variables or constants is expressed by writing the coefficient followed by the variables or constants with no symbols in between. Division is represented by a forward slash (/) with the numerator on the left and the denominator on the right. In complicated expressions, a horizontal line is used to denote division, with the numerator on the top and the denominator on the bottom. Exponentiation (raising to a power) is expressed by writing the base value, followed by a superscript indicating the power to which the base is to be raised. Here are some examples:
Two plus three 2 3 Four minus seven 4 7 Two times five 2 5 or (2)(5) Two times x 2x Two times (x 4) 2(x 4) Two divided by x 2/x Two divided by (x 4) 2/(x 4) Three to the fourth power 34
x to the fourth power x4
(x 3) to the fourth power (x 3)4
SOME SIMPLE EQUATIONS Here are some simple equations containing only numbers. Note that these are true no matter what.
3 3
1,000,000 106
(20) 20
Once in a while you’ll see equations containing more than one equals sign and three or more parts. Examples are
3 5 4 4 10 2
1,000,000 1,000 1,000 103 103 106
(20) 1 (20) 20
CHAPTER 1 Equations, Formulas, and Vectors 5
All the foregoing equations are obviously true; you can check them eas- ily enough. Some equations, however, contain variables as well as num- bers. These equations are true only when the variables have certain values; sometimes such equations can never be true no matter what values the vari- ables attain. Here are some equations that contain variables:
x 5 8
x 2y 3
x2 2x 1 0
Variables usually are represented by italicized lowercase letters from near the end of the alphabet.
Constants can be mistaken for variables unless there is supporting text indicating what the symbol stands for and specifying the units involved. Letters from the first half of the alphabet often represent constants. A com- mon example is c, which stands for the speed of light in free space (approx- imately 299,792 if expressed in kilometers per second and 299,792,000 if expressed in meters per second). Another example is e, the exponential constant, whose value is approximately 2.71828.
SOME SIMPLE FORMULAS In formulas, we almost always place the quantity to be determined all by itself, as a variable, on the left-hand side of an equals sign and some mathematical expression on the right-hand side. When denoting a for- mula, it is important that every constant and variable be defined so that the reader knows what the formula is used for and what all the quantities represent.
One of the simplest and most well-known formulas is the formula for finding the area of a rectangle (Fig. 1-1). Let b represent the length (in meters) of the base of a rectangle, and let h represent the height (in meters) measured perpendicular to the base. Then the area A (in square meters) of the rectangle is
A bh
PART 0 A Review of Mathematics6
A similar formula lets us calculate the area of a triangle (Fig. 1-2). Let b represent the length (in meters) of the base of a triangle, and let h represent the height (in meters) measured perpendicular to the base. Then the area A (in square meters) of the triangle is
Fig. 1-1. A rectangle with base length b, height h, and area A.
Fig. 1-2. A triangle with base length b, height h, and area A.
A bh/2
Consider another formula involving distance traveled as a function of time and speed. Suppose that a car travels at a constant speed s (in meters per second) down a straight highway (Fig. 1-3). Let t be a specified length of time (in seconds). Then the distance d (in meters) that the car travels in that length of time is given by
CHAPTER 1 Equations, Formulas, and Vectors 7
d st
If you’re astute, you will notice something that all three of the preceding formulas have in common: All the units “agree” with each other. Distances are always given in meters, time is given in seconds, and speed is given in meters per second. The preceding formulas for area will not work as shown if A is expressed in square inches and d is expressed in feet. However, the formulas can be converted so that they are valid for those units. This involves the insertion of constants known as conversion factors.
CONVERSION FACTORS Refer again to Fig. 1-1. Suppose that you want to know the area A in square inches rather than in square meters. To derive this answer, you must know how many square inches comprise one square meter. There are about 1,550 square inches in one square meter. Thus we can restate the formula for Fig. 1-1 as follows: Let b represent the length (in meters) of the base of a rectangle, and let h represent the height (in meters) meas- ured perpendicular to the base. Then the area A (in square inches) of the rectangle is
A 1,550bh
Look again at Fig. 1-2. Suppose that you want to know the area in square inches when the base length and the height are expressed in feet. There are exactly 144 square inches in one square foot, so we can restate the formula for Fig. 1-2 this way: Let b represent the length (in feet) of the base of a tri- angle, and let h represent the height (in feet) measured perpendicular to the base. Then the area A (in square inches) of the triangle is
Fig. 1-3. A car traveling down a straight highway over distance d at constant speed s for a length of time t.
PART 0 A Review of Mathematics8
A 144bh/2
(144/2) bh
Give Fig. 1-3 another look. Suppose that you want to know how far the car has traveled in miles when its speed is given in feet per second and the time is given in hours. To figure this out, you must know the relationship between miles per hour and feet per second. To convert feet per second approximately to miles per hour, it is necessary to multiply by 0.6818. Then the units will be consistent with each other: The distance will be in miles, the speed will be in miles per hour, and the time will be in hours. The for- mula for Fig. 1-3 can be rewritten: Suppose that a car travels at a constant speed s (in feet per second) down a straight highway (see Fig. 1-3). Let t be a certain length of time (in hours). Then the distance d (in miles) that the car travels in that length of time is given by
d 0.6818st
You can derive these conversion factors easily. All you need to know is the number of inches in a meter, the number of inches in a foot, the num- ber of feet in a mile, and the number of seconds in an hour. As an exercise, you might want to go through the arithmetic for yourself. Maybe you’ll want to derive the factors to greater precision than is given here.
Conversion factors are not always straightforward. Fortunately, databases abound in which conversion factors of all kinds are listed in tabular form. You don’t have to memorize a lot of data. You can simply look up the conversion factors you need. The Internet is a great source of this kind of information. At the time of this writing, a comprehensive conversion database for physi- cal units was available at the following location on the Web:
If you’ve used the Web very much, you know that uniform resource loca- tors (URLs) are always changing. If the preceding URL does not guide you to conversion factors, point your browser to the National Institute of Standards and Technology (NIST) home page and search the site for tables of conversion factors:
If the manner in which units are expressed on academic Web sites seems unfathomable, don’t worry. As you work your way through this book, you will get used to scientific notation, and such expressions will evolve from arcane to mundane.
CHAPTER 1 Equations, Formulas, and Vectors 9
One-Variable First-Order Equations In algebra, it is customary to classify equations according to the highest exponent, that is, the highest power to which the variables are raised. A one-variable first-order equation, also called a first-order equation in one variable, can be written in the following standard form:
ax b 0
where a and…