English for physicists: методическое указание 9786010421837

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КАЗАХСКИЙ НАЦИОНАЛЬНЫЙ УНИВЕРСИТЕТ имени АЛЬ-ФАРАБИ

ENGLISH FOR PHYSICISTS Методическое указание

Алматы «Қазақ университеті» 2017

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УДК 811.111 (075.8) Е 56 Рекомендовано к изданию Ученым советом факультета филологии и мировых языков и РИСО КазНУ им.аль-Фараби (протокол №2 от 29.12.2016 г.) Рецензент к.ф.н., доцент кафедры иностранных языков А.А. Мулдагалиева Составители: Л.Е. Страутман, Ш.Б. Гумарова, Б.К. Исабаева, А.А. Нурмуханбетова

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English for physicists: методическое указание / сост.: Л.Е. Страутман, Ш.Б. Гумарова, Б. Исабаева, А.А. Нурмуханбетова. – Алматы: Қазақ университеті, 2017. – 122 с. ISBN 978-601-04-2183-7 Данное методическое указание предназначено для работы со студентамибакалаврами и преподавателями вузов, а также учителями школ. При составлении пособия авторы стремились максимально облегчить и ускорить процесс усвоения языкового материала, принимая во внимание уровень подготовки учащихся. В работе большое внимание уделено терминологии, что позволяет обучающимся легко извлекать основную идею текста. Подбор текстов по специальности способствует самостоятельной работе над профессионально-ориентированным чтением, что отвечает требованиям высшей школы. Издается в авторской редакции. The present teaching manual is designated for students, teachers of physics and physicists. The aim of the authors is to facilitate the process of mastering the language material taking into account the level of learners. Special attention is paid to terminology and glossary which enables the students to catch the main idea of the text. The choice of texts on speciality contributes to the work connected with professionally-oriented reading meeting the requirements of higher educational institution. Published in authorial release.

УДК 811.111 (075.8)

ISBN 978-601-04-2183-7

© Сост.: Страутман Л.Е., Гумарова Ш.Б., Исабаева Б., Нурмуханбетова А.А., 2017 © КазНУ имени аль-Фараби, 2017

CONTENTS Introduction .............................................................................................. 4 Unit 1. Scientific Notation ........................................................................ 5 Unit 2. Metric System ............................................................................... 9 Unit 3. Algebra and Trigonometry ............................................................ 13 Unit 4. Vectors and Scalars ....................................................................... 18 Unit 5. Kinematics .................................................................................... 23 Unit 6. Free Fall ........................................................................................ 29 Unit 7. Objects Launched Upward ............................................................ 34 Unit 8. Newton's 2nd Law of Motion ....................................................... 38 Unit 9. Law of Momentum Conservation ................................................. 43 Unit 10. Universal Gravitation .................................................................. 48 Unit 11. Gravitational Fields ..................................................................... 54 Unit 12. Orbits .......................................................................................... 59 Unit 13. Kepler's Laws of Planetary Motion ............................................. 62 Unit 14. Pressure ....................................................................................... 66 Supplementary Texts ................................................................................ 70 Lexical and grammatical tests ................................................................... 90 Text working technique ............................................................................ 101 Formulas and Symbols .............................................................................. 107 Bibliography .............................................................................................. 121

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INTRODUCTION The present teaching manual is designated for learners of PreIntermediate/Intermediate levels studying at higher educational institutions. The aim of the manual is to teach students how to extract information from the text, to understand its main content and to develop elementary skills of speaking on speciality. The teaching manual includes fourteen texts followed by exercises, texts for supplementary reading, lexical-grammar tests and description of the technique of working at texts. The work on vocabulary and phrases from the text assumes removal of some difficulties when working at the text. The way of introducing grammar makes it possible to facilitate the work at certain speech tasks. Other types of exercises include word formation, choice of synonyms and antonyms, substitution tables, filling the gaps, translation from English into Russian/Kazakh and from Russian/Kazakh into English and answering the questions. The purpose of primary reading is to understand the main content of the text, which develops some skills of a purposeful intelligent reading. It is not recommended to translate the text in details as sometimes it is not considered as one of the effective ways of working at the text. The work before reading the text and translation of some sentences considerably facilitate the process of mastering the language material. Control and choice of texts for independent work are carried out at a teacher’s discretion. At the final stage of work it is possible to speak on the topic chosen by learners or a teacher.

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UNIT

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Vocabulary notation n. to relate (to) v. solid a. measurement n. vary a. tremendously adv. to denote v. cumbersome a. scale n. insulating layer integrated circuits power n. lose track to deal with v. decimal significant digit /figure multiplied by value n. to convert v. in essence to add v.

– система представления чисел; – 1) устанавливать связь; (to, with – между чем-л.); 2) быть связанным; 3) относиться, иметь отношение; – 1) твердый, плотный; сплошной; n твердое тело; ~ solution твердый раствор; – измерение; – 1) менять; 2) меняться; 3) изменяться; – 1) очень сильно; 2) чрезвычайно; – обозначать; – громоздкий; трудоемкий; – масштаб; – изолирующий слой затвора; – интегральная схема; – мощность; производительность; степень; – потерять счет; – иметь дело (чем-л.; с кем-л.); – десятичный; – значащая цифра; – умножать на; – ценность; важность; полезность; значение; смысл; – преобразовать; – в сущности, по существу; – добавить; прибавить; суммировать;

I. Practice pronunciation of the following words: physics ['fɪzɪks ] mathematics [ 'mæθə'mætɪks ] efficiently [ɪ'fɪʃntlɪ] accurately ['ækjʊrɪtlɪ] measurement ['meʒəmənt ] cumbersome ['kʌmbəsəm ] circuit ['sɜ:kɪt] 5

decimal ['desɪməl ] equal ['i:kwəl ] convert [ kən'vɜ:t ] assume [ ə'sju:m ] digit ['dɪdʒɪt ] radius ['reɪdiəs ] significant [ sɪɡ'nɪfɪkənt ]

II. Read and translate the words having the same root Physics – physicists – physical, science – scientist – scientific, relate – relation – related, multiply – multiplied, move – movement, add – addition – added, thick – thickness, integrate – integrative – integrated, assume – assumption – assumed, equal – equality. III. Match the words in the left column with its antonym in the right column 1. efficiently 2. significant 3.cumbersome 4. power 5. complicated 6. value 7. measurement

a. incapacity b. plain c. disadvantage d. estimate e. ineffective f. meaningless g. feathery

IV. Find in the text the equivalents of the following word combinations and write them out. 1) тесно связаны 2) обозначения больших и маленьких чисел 3) значащие цифры 4) правильное значение 5) вернуться к исходному значению 6) записать это в научной системе представления чисел 7) умножить число на некоторую степень 8) использовать отрицательные степени 9) получить конечное значение 10) переместить десятичный знак V. Give the degrees of comparison of the following words Vary, difficult, high, large, long, useful, small, much, many, easy, little, significant, original, final.

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VI. Read and translate the text Scientific Notation Although physics and mathematics aren't the same thing, they are in many ways closely related. Just like English is the language of this content, mathematics is the language of physics. A solid understanding of a few simple math concepts will allow us to communicate and describe the physical world both efficiently and accurately. Because measurements of the physical world vary so tremendously in size (imagine trying to describe the distance across the United States in units of hair thicknesses), physicists often times use what is known as scientific notation to denote very large and very small numbers. These very large and very small numbers would become quite cumbersome to write out repeatedly. Imagine writing 4,000,000,000,000 over and over again. Your hand would get tired and your pen would rapidly run out of ink! Instead, it's much easier to write this number as 4×1012. See how much easier that is? Or on the smaller scale, the thickness of the insulating layer (known as a gate dielectric) in the integrated circuits that power our computers and other electronics can be less than 0.000000001 m. It's easy to lose track of how many zeros you have to deal with, so scientists instead would write this number as 1×10-9 m. See how much simpler life can be with scientific notation? Scientific notation follows these simple rules. Start by showing all the significant figures in the number you're describing, with the decimal point after the first significant digit. Then, show your number being multiplied by 10 to the appropriate power in order to give you the correct value. It sounds more complicated than it is. Let's say, for instance, you want to show the number 300,000,000 in scientific notation (a very useful number in physics), and let's assume we know this value to three significant digits. We would start by writing our three significant digits, with the decimal point after the first digit, as «3.00». Now, we need to multiply this number by 10 to some power in order to get back to our original value. In this case, we multiply 3.00 by 108, for an answer of 3.00×108. Interestingly, the power you raise the 10 to is exactly equal to the number of digits you moved the decimal to the left as you converted from standard to scientific notation. 7

Similarly, if you start in scientific notation, to convert to standard notation, all you have to do is remove the 108 power by moving the decimal point eight digits to the right. Now you are an expert in scientific notation! But, what do you do if the number is much smaller than one? The same basic idea… let's assume we're dealing with the approximate radius of an electron, which is 0.00000000000000282 m. It's easy to see how unwieldy this could become. We can write this in scientific notation by writing our three significant digits, with the decimal point after the first digit, as «2.82». Again, we multiply this number by some power to 10 in order to get back to our original value. Because our value is less than 1, we need to use negative powers of 10. If we raise 10 to the power -15, specifically, we get a final value of 2.82×10-15 m. In essence, for every digit we moved the decimal place, we add another power of 10. And if we start with scientific notation, all we do is move the decimal place left one digit for every negative power of (to) 10. VII. Answer the questions on the text 1. In what way are physics and mathematics related? 2. What is meant by scientific notation? 3. What rules does it follow? 4. How many positions do you need to show the numbers in scientific notation? 5. Express the number 0.000470 in scientific notation. Express the number 2,870,000 in scientific notation.

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UNIT

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Vocabulary to involve v. prediction n. phenomenon n. to communicate v. data n. to set v. to standardize v. to define v. 3) устанавливать; unit n. current n. to form the foundation to refer v. to focus v. to introduce v. length n. to divide (into) to make up wire n. paperclip n. to break up familiar adj. to be based on

– 1) вовлекать; включать в себя 2) быть связанным с ч-л.; – предположение; предсказание – явление; – 1) сообщаться; 2) держать связь; 3) сообщение; – данные, сведения – комплектовать; – стандартизировать; – 1) определять; 2) давать определение; – 1) единица (оборудования); 2) блок; 3) установка; – 1) ток (эл.); 2) a. современный; – образовывать основание; – 1) ссылаться (на), 2) упоминать; – концентрировать(ся), сосредоточивать(cя); – представлять; – 1) длина; 2) отрезок, кусок; – делить (на); – составлять; – проволока, провод; – скрепка для бумаг; – разбивать; разрушать – хорошо известный, знакомый – быть основанным на ч.-л.;

I. Practice pronunciation of the following words: analysis [ə'nalɪsɪs] specific [spə'sɪfɪk ] standarize ['stændərdaɪz] meter ['mi:tə] kilogram [ 'kɪləɡram ] second ['sɛk(ə)nd ]

approximately [ə'prɒksɪmətli] length [lɛŋθ] equivalent [ɪ'kwɪv(ə)l(ə)nt] cube [kju:b] microsecond ['mʌɪkrə(ʊ),sɛkənd] extremely [ɪk'stri:mli ] 9

ampere ['ampɛ:] roughly ['rʌfli]

valuable ['valjʊb(ə)l] chart [tʃɑ:t]

II. Read and translate the words having the same root communicate – communication, measure – measurement, define – definition, found – foundation, introduce – introduction – introduced, divide – division – divided, convert – conversion. III. Make the following nouns plural Phenomenon, basis, analysis, datum, thesis, ampere, radius, medium, index. IV. Complete the sentences with the following words given below 1. ___________is considered to be the most basic of the natural sciences. 2. It ____________ the fundamental constituents of matter and their interactions as well as the nature of atoms and the build-up of molecules and condensed matter. 3. Physics tries to give unified description of the behavior of matter as well as of radiation, covering as many types of ______________as possible. 4. Physics is the natural science that ____________ the study of matter and its motion and behavior. 5. The electric ____________is a quantity of electrons flowing in a circuit per second of time. 6. The metric system __________ powers of 10, allowing for easy conversion from one unit to another. 7. It is important to try to___________ energy. (Phenomena, physics, deals with, involve, current, save, be based on) V. Mind the explanation of the following terms The Metric system is a system using meters, kilograms, grams and liters to measure things. 10

Physics is the scientific study of things like heat, light and sound. Analysis is the process of carefully examining the different parts of something. Phenomenon is something that is impressive or extraordinary. Measurement is the size of something that is found by measuring. Ampere is the basic unit of electrical current in the International System of Units (IS). Current is a flow of electrical charge carriers, usually electrons or electron-deficient atoms. Radius is the length of a straight line from the centre of a circle to the outside. Wire is a long piece of very thin metal. Power is (no plural) the energy or strength that somebody or something has. VI. Find sentences in the Passive Voice and translate them VII. Read and translate the text Metric System Physics involves the study, prediction, and analysis of realworld phenomena. To communicate data accurately, we must set specific standards for our basic measurements. The physics community has standardized on what is known as the Système International (SI), which defines seven baseline measurements and their standard units, forming the foundation of what is called the metric system of measurement. The SI system is often referred to as the mks system, as the three most common measurement units are meters, kilograms, and seconds, which we'll focus on for the majority of this course. The fourth SI base unit we'll use in this course, the ampere, will be introduced in the current electricity section. The base unit of length in the metric system, the meter, is roughly equivalent to the English yard. For smaller measurements, the meter is divided up into 100 parts, known as centimeters, and each centimeter is made up of 10 millimeters. For larger measurements, the meter is grouped into larger units of 1000 meters, known as a kilometer. The 11

length of a baseball bat is approximately one meter, the radius of a U.S. quarter is approximately a centimeter, and the diameter of the metal in a wire paperclip is roughly one millimeter. The base unit of mass, the kilogram (kg), is roughly equivalent to two U.S. pounds. A cube of water 10cm × 10cm × 10cm has a mass of 1 kg. Kilograms can also be broken up into larger and smalller units, with commonly used measurements of grams (1/1000th of a kilogram) and milligrams (1/1000th of a gram). The mass of a textbook is approximately 2 to 3 kilograms, the mass of a baseball is approximately 145 grams, and the mass of a mosquito is 1 to 2 milligrams. The base unit of time, the second, is likely already familiar. Time can also be broken up into smaller units such as milliseconds (10-3 seconds), microseconds (10-6 seconds), and nanoseconds (10-9 seconds), or grouped into larger units such as minutes (60 seconds), hours (60 minutes), days (24 hours), and years (365.25 days). Prefix tera giga mega kilo deci centi milli micro nano pico

Prefixes for Powers of 10 Symbol Notation T 1012 G 109 M 106 k 103 d 10–1 c 10–2 m 10–3 µ 10–6 n 10–9 p 10–12

The metric system is based on powers of 10, allowing for easy conversion from one unit to another. A chart showing the meaning of commonly used metric prefixes and their notations can be extremely valuable in performing unit conversions. VIII. Answer the questions on the text 1. What does Physics deal with? 2. What is known by the Système International (SI)? 3. What is English yard equivalent to? 4. What is the metric system based on?

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Vocabulary convenient a. tool n. to convey v. behavior n. to describe v. therefore adv. fluent a. to fret v. to conjure up v. frustration n. to solve a problem to determine v. to substitute v. final equation to distill v. sine n. cosine n. adjacent a. to inverse v.

– удобный; – 1) инструмент; 2) станок; – 1) переправлять; 2) доставлять; – 1) поведение; 2) тех. режим (работы); – 1) описывать; 2) изображать; – 1) поэтому; 2) следовательно, таким образом – 1) плавный; 2) гладкий; 3) беглый; – беспокоить (ся); – 1) явиться как по волшебству; 2) включить воображение; – 1) расстройство; 2) срыв; – решить задачу; – 1) определять; 2) устанавливать; – заменять; замещать; – окончательное уравнение; – перегонять, дистиллировать, гнать, очищать; – синус; – косинус; – смежный; – быть противоположным ч.-л.;

I. Practice pronunciation of the following words: natural ['natʃ(ə)r(ə)l] algebra ['aldʒɪbrə] trigonometry ['trɪɡə,nɒmɪtri] knowledge ['nɒlɪdʒ] successfully [sək'sesfəli] range [reɪn(d)ʒ] majority [mə'dʒɒrɪti] conjure ['kʌndʒə]

strategy ['stratɪdʒi] diagram ['dʌɪəɡram] value ['valju:] equation [ɪ'kweɪʒ(ə)n] triangle ['trʌɪaŋɡ(ə)l] cosine ['kəʊsʌɪn] tangent ['tan(d)ʒ(ə)nt] adjacent [ə'dʒeɪs(ə)nt]

II. a. Match the synonyms 1) convenient a) issue 2) tool b) huge 13

3) function 4) basic 5) problem 6) vast 7) important 8) substitute 9) final 10) majority

c) significant d) ultimate e) main f) plurality g) instrument h) comfortable i) alternative j) operation

b. Match the antonyms 1) determine a) stop 2) range b) expand 3) make c) reverse 4) wide d) destroy 5) replace e) unsuitable 6) produce f) dislike 7) reduce g) commence 8) appropriate h) remain 9) require i) narrow 10) inverse j) domain III. Fill in the gaps with the words below convey

tool

determine

substitute

cosine

1. Physicists use ____________to measure things from speed to capacitance. 2. Scientists need a powerful device to _________ a molecule's form and function. 3. The ____________, with sine and tangent, is one of the three most common trigonometric functions. 4. It is not easy to find alternate ways _____________ physics concepts to non-physicists. 5. Scientists believe that nuclear power is necessary to __________the gas power. IV. Mind the explanation of the following terms algebra – (no plural) a type of mathematics in which letters and symbols are used to represent numbers. 14

trigonometry – branch of mathematics that studies relationships involving lengths and angles of triangles. sine – the ratio of the side opposite a given acute angle to the hypotenuse. cosine – the ratio of the side adjacent to a given angle to the hypotenuse. tangent – the ratio of the side opposite a given angle to the side adjacent to the angle. adjacent – lying near, close, or contiguous, adjoining, neighboring. hypotenuse – the side of a right triangle opposite the right angle. V. Read and translate the text Algebra and Trigonometry Just as we find the English language a convenient tool for conveying thoughts to each other, we need a convenient language for conveying our understanding of the world around us in order to understand its behavior. The language most commonly (and conveniently) used to describe the natural world is mathematics. Therefore, to understand physics, we need to be fluent in the mathematics of the topics we'll study in this course… specifically basic algebra and trigonometry. Now don't you fret or frown, for those whom the word «trig» conjures up feelings of pain, angst, and frustration, have no fear. We will need only the most basic of algebra and trigonometry knowledge in order to successfully solve a wide range of physics problems. A vast majority of problems requiring algebra can be solved using the same problem solving strategy. First, analyze the problem and write down what you know, what you need to find, and make a picture or 15

diagram to better understand the problem if it makes sense. Then, start your solution by searching for a path that will lead you from your givens to your finds. Once you've determined an appropriate pathway (and there may be more than one), solve your problem algebraically for your answer. Finally, as your last steps, substitute in any values with units into your final equation, and solve for your answer, with units. Our use of trigonometry, the study of right triangles, can be distilled down to the definitions of the three basic trigonometric functions. When you know the length of two sides of a right triangle, or the length of one side and a non-right angle, you can solve for all the angles and sides of the triangle. If you can use the definitions of the sine, cosine, and tangent, you'll be fine in this course.

Of course, if you need to solve for the angles themselves, you can use the inverse trigonometric functions.

VI. Arrange the expressions using the suitable words in the following two columns 1) to know 2) to understand 3) to determine 4) to use 5) a convenient

a) a diagram b) the natural world c) the length of a right triangle d) problems e) behavior 16

6) need 7) to study 8) make 9) to solve 10) to describe

f) an appropriate pathway g) knowledge h) functions i) basic algebra j) tool

VII. Answer the questions on the text 1. For what purpose do we need a special language for conveying our understanding of the world? 2. Why do we have to study basic of algebra and trigonometry? 3. How can the majority of problems requiring algebra be solved? 4. A car travels from the airport 14 miles east and 7 miles north to its destination. What direction should a helicopter fly from the airport to reach the same destination, traveling in a straight line?

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UNIT

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Vocabulary quantity n. to represent v. to include v. force n. velocity n. acceleration n. concept n. arrow n. to indicate v. magnitude n. space n. to reverse retain n. resultant n. to draw v.

– количество; – 1) представлять; 2) изображать; отражать; – включать; – 1) сила; 2) действие; – скорость; – ускорение; – 1) концепция; 2) понятие; – стрелка; – указывать; показывать; – 1) размеры; 2) важность; – 1) космос; 2) пространство; – поменять; поворачивать; – 1) покой, отдых; 2) остаток; – сумма двух векторов; – вытягивать, отодвигать, подтягивать, приближать;

I. Practice pronunciation of the following words: Vector ['vɛktə] Scalar ['skeɪlə] examine [ɪɡ'zamɪn] magnitude ['maɡnɪtju:d ] quantity ['kwɒntɪti] temperature ['tɛmp(ə)rətʃə] descriptive [dɪ'skrɪptɪv] force [fɔ:s]

velocity [vɪ'lɒsɪti] acceleration [əksɛlə'reɪʃ(ə)n] concept ['kɒnsɛpt ] arrow ['arəʊ] figure ['fɪɡə] straight [streɪt] touch [tʌtʃ] resultant [rɪ'zʌlt(ə)nt]

II. Read and translate the words having the same root representing – represented – representment – misrepresent; directional – indirection – misdirection– directions; acceleration – accelerated – accelerating; indicated – indication – indicative – 18

indicator; reversal – reversible – reversion – reversed – reverser – reversing. III. Match the following words (a, b, c...) with the statements (1, 2, 3...) a) confuse b) concept c) to represent d) magnitude e) arrow f) to line up g) to retain h) acceleration 1) the sign that shows where something is or where you should go 2) difficult to understand 3) to be an example or sign of something 4) to stay without changes 5) the size, extent, or importance of something 6) physical term, representing decreasing or increasing velocity by time 7) to stand in a line or make a line 8) picture in your mind IV. Insert prepositions: of, into, on, to, at 1. Mechanical engineering achieved a prominent position _______ the very beginning. 2. Energy can change from one type ________another. 3. Electrical engineering is subdivided ___________ two branches. 4. It is well known that personal experience depends _______ practical work. 5. ______ the 17th century, Galileo Galilee began a re-examination _______ the motion ________ falling bodies. 6. The ship was helpless against the power __________the storm. 19

V. Mind the explanation of the following terms Vector – a quantity possessing both magnitude and direction. Scalar – a quantity possessing only magnitude. quantity – how much of something there is. magnitude – size, extent, dimensions. resultant – resulting from the combination of two or more agents. force – to do something by using a lot of strength. velocity – rapidity of motion or operation. acceleration – a change in velocity. VI .Read and translate the text. Retell it in English Vectors and Scalars Quantities in physics are used to represent real-world measurements, and therefore physicists use these quantities as tools to better understand the world. In examining these quantities, there are times when just a number, with a unit, can completely describe a situation. These numbers, which have a magnitude, or size, only are known as scalars. Examples of scalars include quantities such as temperature, mass, and time. At other times, a quantity is more descriptive if it also includes a direction. These quantities which have both a magnitude and direction are known as vectors. Vector quantities you may be familiar with include force, velocity, and acceleration. Most students will be familiar with scalars, but to many, vectors may be a new and confusing concept. By learning just a few rules for dealing with vectors, though, you’ll find that they are a powerful tool for problem solving. A study of motion involves introduction of a variety of quantities that are used to describe the physical world. Examples of such quantities include distance, displacement, speed, velocity, acceleration, force, mass, momentum, energy, work, power, etc. All these quantities can by divided into two categories – vectors and scalars. A vector quantity is a quantity that is fully described by both magnitude and direction. On the other hand, a scalar quantity is a quantity that is fully described by its magnitude. The emphasis of 20

this unit is to understand some fundamentals about vectors and to apply the fundamentals in order to understand motion and forces that occur in two dimensions. Examples of vector quantities include displacement, velocity, acceleration, and force. Each of these quantities is unique in that a full description of the quantity demands that both a magnitude and a direction are listed. For example, suppose your teacher tells you, «A bag of gold is located outside the classroom. To find it, displace yourself 20 meters». This statement may provide you enough information to pique your interest; yet, there is not enough information included in the statement to find the bag of gold. The displacement required to find the bag of gold has not been fully described. On the other hand, suppose your teacher tells you, «A bag of gold is located outside the classroom. To find it, displace yourself from the center of the classroom door 20 meters in a direction 30 degrees to the west of north». This statement now provides a complete description of the displacement vector – it lists both magnitude (20 meters) and direction (30 degrees to the west of north) relative to a reference or starting position (the center of the classroom door). Vector quantities are not fully described unless both magnitude and direction are listed. Vectors are often represented as arrows, with the length of the arrow indicating the magnitude of the quantity, and the direction of the arrow indicating the direction of the vector. In the figure at right, vector B has a magnitude greater than that of vector A. Vectors A and B point in the same direction, however. It’s also important to note that vectors can be moved anywhere in space. The positions of A and B could be reversed, and the individual vectors would retain their values of magnitude and direction. This makes adding vectors very straight forward! To add vectors A and B, all we have to do is line them up so that the tip of the first vector touches the tail of the second vector. Then, to find the sum of the vectors, known as the resultant, all we have to do is draw a straight line from the start of the first vector to the end of the last vector. This method works with any number of vectors. Velocity and speed are very similar ideas, but velocity is a vector, and speed is not. Suppose we knew that someone was driving at thirty-five kilometers an hour (35 km/hr), but the direction wasn't given. How would you draw an arrow to represent a vector? You can't know how to draw the vector if you only have one value (either 21

amount or direction). In this example, you were never told about the direction. Physicists would say that the speed is thirty-five kilometers an hour (35 km/hr), but the velocity is unknown. On the other hand, if you're moving at 35 km/hr in a northern direction, then you would have an arrow pointing north with a length of 35. Physicists would say that the velocity is 35 km/hr north. Velocity is the rate of motion in a specific direction. I'm going that-a-way at 30 kilometers per hour. My velocity is 30 kilometers per hour that-a-way. Average speed is described as a measure of distance divided by time. Velocity can be constant, or it can change (acceleration). Speed with a direction is velocity. You will use a lot of vectors when you work with velocity. Our real world example of navigation on the ocean used velocity for every vector. Velocity is a vector measurement because it has an amount and a direction. Speed is only an amount (a scalar). Speed doesn't tell the whole story to a physicist. Think of it another way. If I tell you I'm driving north and ask you how long until we get to the city. You can't know the answer since you don't know my speed. You need both values. When velocity is changing, the word acceleration is used. Acceleration is also a vector. You speed up if the acceleration and velocity point in the same direction. You slow down (also referred to as decelerating) if the acceleration and velocity point in opposite directions. When you accelerate or decelerate, you change your velocity by a specific amount over a specific amount of time. Just as with velocity, there is something called instantaneous acceleration. Instantaneous means scientists measure your acceleration for a specific moment of time. That way they can say he was accelerating at exactly this amount at this point during his trip. VII. Answer the questions on the text 1. Why do physicists use quantities? 2. What do we mean by ‘scalars’? 3. What examples do scalars include? 4. A motorboat, which has a speed of 5.0 meters per second in still water, is headed east as it crosses a river flowing south at 3.3 meters per second. What is the magnitude of the boat's resultant velocity with respect to the starting point? 3.3 m/s 5.0 m/s 6.0 m/s 8.3 m/s

22

UNIT

5

Vocabulary earth n. source n. solar a. hydroelectric a. fossil n. fuel n. trace v. origin n. investigate v. motion n. to develop v. to expand v. ability a. capacity n. location n. to lead (led) v. major a. constraint n.

– Земля; – источник; – солнечная система; – гидроэлектрический; – ископаемое; – топливо; – оставить след; – 1) возникновение; 2) происхождение; – 1) исследовать; 2) расследовать; – движение; – 1) развивать, разрабатывать; создавать; 2) проявлять(фото); – расширять (ся); – способность; – 1) производительность; мощность; 2) способность; – местонахождение; – вести, возглавлять; приводить к чему-либо; – главный, основной; – ограничение;

I. Practice pronunciation of the following words: honors ['ɒnəz] energy ['ɛnədʒi] universe ['ju:nɪvə:s] Earth [ə:θ] fossil ['fɒs(ə)l] fuel ['fju:əl] eventually [ɪ'vɛntʃuəli] type [taɪp]

motion ['məʊʃ(ə)n] principle ['prɪnsɪp(ə)l] serve [sə:v] expand [ɪk'spand] capacity [kə'pasɪti ] position [pə'zɪʃ(ə)n] Greek [ɡri:k] dynamics [dʌɪ'namɪks]

II. Read and translate the words having the same root investigate – investigator – investigatory; varying – unvarying; serve – disserve – reserve – serving – server; expand – expanding – 23

expanded – expander; ability – capability – disability – durability; capacity – capacitance – incapacity – capacitor – high-capacity; major – majority; location – dislocation – relocation; change – changeable – changeful – changeless – changing – changer; develop – developer – development – developing – developable. III. Use adverbs to complete the sentences strongly loudly

electrically

rarely

dangerously randomly

1. The electrical phenomena show that there are two ions to the molecule, and that these ions are ___________ changed. 2. Atomic bomb reaches ground level as sticky, dark, __________radioactive weapon. 3. In a solid, atoms are ___________ attracted. 4. When a bomb explodes, it bursts____________ and with great force. 5. Molecules tend to move from places of high concentration to places of low concentration, just by moving ______________. 6. Atoms of gases are ____________ distributed. IV. Mind the explanation of the following terms Kinematics – the branch of mechanics which describes the motion of points, bodies. Earth – this world; the planet that we live on. Source – device that produces electricity. Energy – the power from electricity, gas, coal, etc .that is used to make machines work and to make heat and light. Kinetic – is energy of motion. Solar power – (no plural) the sun and the planets that move around it. Hydroelectric – using the power of water to produce electricity. Fossil fuels – a part of a dead plant or an animal that has been in the ground for a very long time and has turned into rock. Motion – (no plural) movement. Dynamics – the branch of mechanics which describes state of motion (movements of specific objects). 24

V. Read and translate the text. Retell it in English Kinematics

Motion always draws our attention. Motion itself can be beautiful, causing us to marvel at the forces needed to achieve spectacular motion, such as that of a dolphin jumping out of the water, or a pole vaulter, or the flight of a bird, or the orbit of a satellite. The study of motion is kinematics, but kinematics only describes the way objects move – their velocity and their acceleration. Dynamics considers the forces that affect the motion of moving objects and systems. Newton’s laws of motion are the foundation of dynamics. These laws provide an example of the breadth and simplicity of principles under which nature functions. They are also universal laws in that they apply to similar situations on Earth as well as in space. Issac Newton’s (1642–1727) laws of motion were just one part of the monumental work that has made him legendary. The development of Newton’s laws marks the transition from the Renaissance into the modern era. This transition was characterized by a revolutionary change in the way people thought about the physical universe. For many centuries natural philosophers had debated the nature of the universe based largely on certain rules of logic with great weight given to the thoughts of earlier classical philosophers such as Aristotle (384–322 BC). Among the many great thinkers who contributed to this change were Newton and Galileo. 25

Galileo was instrumental in establishing observation as the absolute determinant of truth, rather than «logical» argument. Galileo’s use of the telescope was his most notable achievement in demonstrating the importance of observation. He discovered moons orbiting Jupiter and made other observations that were inconsistent with certain ancient ideas and religious dogma. For this reason, and because of the manner in which he dealt with those in authority, Galileo was tried by the Inquisition and punished. He spent the final years of his life under a form of house arrest. Because others before Galileo had also made discoveries by observing the nature of the universe, and because repeated observations verified those of Galileo, his work could not be suppressed or denied. After his death, his work was verified by others, and his ideas were eventually accepted by the church and scientific communities. Galileo also contributed to the formation of what is now called Newton’s first law of motion. Newton made use of the work of his predecessors, which enabled him to develop laws of motion, discover the law of gravity, invent calculus, and make great contributions to the theories of light and color. It is amazing that many of these developments were made with Newton working alone, without the benefit of the usual interactions that take place among scientists today. It was not until the advent of modern physics early in the 20th century that it was discovered that Newton’s laws of motion produce a good approximation to motion only when the objects are moving at speeds much, much less than the speed of light and when those objects are larger than the size of most molecules (about 10−9 m in diameter). These constraints define the realm of classical mechanics, as discussed in Introduction to the Nature of Science and Physics. At the beginning of the 20th century, Albert Einstein (1879–1955) developed the theory of relativity and, along with many other scientists, developed quantum theory. This theory does not have the constraints present in classical physics. All of the situations we consider in this chapter, and all those preceding the introduction of relativity in Special Relativity, are in the realm of classical physics. Physics is a science about the energy in the universe, in all its various forms. Here on Earth, the source of our energy, directly or indirectly, is the sun. Solar power, wind power, hydroelectric power, 26

fossil fuels, we can eventually trace the origin of all energy on our planet back to our sun. So where do we start in our study of the universe? Theoretically, we could start by investigating any of these types of energy. In reality, however, by starting with energy of motion (kinetic energy), we can develop a set of analytical problem solving skills from basic principles that will serve us well as we expand into our study of other types of energy. For an object to have kinetic energy, it must be moving. Specifically: 1 KE  mv 2 2

If kinetic energy is energy of motion, and energy is the ability or capacity to do work (moving an object), then we can think of kinetic energy as the ability or capacity of a moving object to move another object. But what does it mean to be in motion? A moving object has a varying position… its location changes as a function of time. So to understand kinetic energy, we'll need to better understand position and how position changes. This will lead us into our first major unit, kinematics, from the Greek word kinein, meaning to move. Formally, kinematics is the branch of physics dealing with the description of an object's motion, leaving the study of the «why» of motion to our next major topic, dynamics. VI. Are the sentences true (T), false (F) or not given (NG) 1. Physics is a science studying kinetic energy. 2. The Sun is the source of our energy. 3. Due to the sun we can get solar power, wind power, hydroelectric power, and fossil fuels. 4. Energy that we get from the sun is expensive. 5. The object must not move to have kinetic energy. 6. A moving object’s location changes as a function of time. 7. The word kinematics is from the Greek word kinein, meaning to jump. 8. Kinematics is a branch of mathematics. 27

VII. Answer the questions on the text 1. What do you understand by Physics? 2. What sources of energy do you know? 3. What is the origin of the word ‘kinematics? 4. An astronaut drops a hammer from 2.0 meters above the surface of the Moon. If the acceleration due to gravity on the Moon is 1.62 meters per second2, how long will it take for the hammer to fall to the Moon’s surface?

28

UNIT

6

Vocabulary free a. to fall (fell, fallen) v. to believe v. due to prep. to drop v. simultaneously adv. to crumple v. to conclude v. resistance n. to neglect v. to execute v. strength n. surface n. to indicate v.

– свободный; ~ of charge бесплатный; – падать; понижаться; n. падение; – верить, полагать, считать; – из-за, благодаря, вследствие; – бросать, оставлять; ~ the idea перестать думать, отказаться от мысли; n капля; – одновременно; – мять (ся); комкать морщиться съеживаться; – 1) заключить; 2) прийти к выводу; – 1) сопротивление; 2) v. сопротивляться; оказывать сопротивление; – пренебрегать; – выполнять; executable a. – выполняемый; – прочность; ~ of materials сопротивление материалов; – 1) поверхность; 2) a. наружный; – показывать;

I. Practice pronunciation of the following words: massive ['masɪv] feather [ fɛðə] piece ['pi:s ] tight [tʌɪt] air [eə] purpose ['pə:pəs]

continuously ['kən,tɪnjʊəsli| ] gravitation [ɡravɪteɪʃ(ə)n] strength [streŋθ] analyze ['ænəlaɪz] local [ləʊk(ə)l] affect [ə'fɛkt]

II. Read and translate the words having the same root correct – correction – corrective – correctly – corrector – incorrect; conclude – concluding; prediction – predict – predictable – 29

predicted; affect – affected – affection – affective – affecting; perform – performance – performer – performing – performed; acceleration – accelerated – accelerating. III. Fill in the gaps with the words below resistance

drop

strength

surface

velocity

fall

1. The _________ of an object is the rate of change of its position with respect to a frame of reference and is a function of time. 2. ____________of metals decreases at low temperature. 3. Our planet belongs to planets of terrestrial group. It means that the Earth's _____________is firm. 4. Mechanical ____________ is defined by numerous testing machines. 5. If you ____________ a load, it will ___________ with high speed. IV. Mind the explanation of the following terms height – how far it is from the bottom to the top of somebody or something . hypothesis – theory that you then test through study and experimentation. experiment – a scientific test that you do to find out what will happen or to see if something is true. gravitation – force between masses in the universe. V. Translate the sentences paying attention to the Modal verbs: 1. There are times when graphing motion may not be the most efficient or effective way of understanding the motion of an object. 2. To assist in these situations, you can add a set of problem-solving equations to your physics toolbox, known as the kinematic equations. 3. The scientists must carry out the experiment at once. 30

4. The workers had to solve the problem yesterday. 5. The engineer should be perfectly familiar with the properties of materials. VI. Read the text and make up a summary Free Fall Examination of free-falling bodies dates back to the days of Aristotle. At that time Aristotle believed that more massive objects would fall faster than less massive objects. He believed this in large part due to the fact that when examining a rock and a feather falling from the same height it is clear that the rock hits the ground first. Upon further examination it is clear that Aristotle was incorrect in his hypothesis. As proof, take a basketball and a piece of paper. Drop them simultaneously from the same height… do they land at the same time? Probably not. Now take that piece of paper and crumple it up into a tight ball and repeat the experiment. Now what do you see happen? You should see that both the ball and the paper land at the same time. Therefore you can conclude that Aristotle’s predictions did not account for the effect of air resistance. For the purposes of this course, drag forces such as air resistance will be neglected. In the 17th century, Galileo Galilee began a re-examination of the motion of falling bodies. Galileo, recognizing that air resistance affects the motion of a falling body, executed his famous thought experiment in which he continuously asked what would happen if the effect of air resistance was removed. Commander David Scott of Apollo 15 performed this experiment while on the moon. He simultaneously dropped a hammer and a feather, and observed that they reached the ground at the same time. Since Galileo’s experiments, scientists have come to a better understanding of how the gravitational pull of the Earth accelerates free-falling bodies. Through experimentation it has been determined that the local gravitational field strength (g) on the surface of the Earth is 9.8 N/kg, which further indicates that all objects in free fall (neglecting air resistance) experience an equivalent acceleration of 9.8 m/s2 toward the center of the Earth. (NOTE: If you move off the surface of the Earth the local gravitational field strength, and therefore the acceleration due to gravity, changes.) 31

You can look at free-falling bodies as objects being dropped from some height or thrown vertically upward. In this examination you will analyze the motion of each condition. What is gravity? Gravity is the mysterious force that makes everything fall down towards the Earth. But what is it? It turns out that all objects have gravity. It's just that some objects, like the Earth and the Sun, have a lot more gravity than others. How much gravity an object has depends on how big it is. To be specific, how much mass it has. It also depends on how close you are to the object. The closer you are, the stronger the gravity. Why is gravity important? Gravity is very important to our everyday lives. Without Earth's gravity we would fly right off it. We'd all have to be strapped down. If you kicked a ball, it would fly off forever. While it might be fun to try for a few minutes, we certainly couldn't live without gravity. Gravity also is important on a larger scale. It is the Sun's gravity that keeps the Earth in orbit around the Sun. Life on Earth needs the Sun's light and warmth to survive. Gravity helps the Earth to stay just the right distance from the Sun, so it's not too hot or too cold. Who discovered gravity? The first person who dropped something heavy on their toe knew something was going on, but gravity was first mathematically described by the scientist Isaac Newton. His theory is called Newton's law of universal gravitation. Later, Albert Einstein would make some improvements on this theory in his theory of relativity. What is weight? Weight is the force of gravity on an object. Our weight on Earth is how much force the Earth's gravity has on us and how hard it is pulling us toward the surface. Do objects fall at the same speed? Yes, this is called the equivalence principle. Objects of different masses will fall to the Earth at the same speed. If you take two balls of different masses to the top of a building and drop them, they will hit the ground at the same time. There is actually a specific acceleration that all objects fall at called a standard gravity, or «g». It equals 9.807 meters per second squared (m/s2). VII. Are the sentences true (T), false (F) or not given (NG) 1. Less massive objects will fall faster than more massive objects. 2. Aristotle was incorrect in his hypothesis. 32

3. Galileo Galilei began a re-examination in the 18th century. 4. David Scott was as a commander of Apollo 20. 5. Examination of free-falling bodies dates back to the days of Aristotle. 6. Free-falling constant is 9.6. 7. In his experiment Aristotle used a rock and a pen. 8. Aristotle did a lot of failed experiments. 9. Aristotle’s predictions did not account for the effect of air resistance. 10. The crew of Apollo 20 represented Galileo’s experiment on the Earth. VIII. Answer the questions on the text 1. What did Aristotle suppose of free-falling bodies? 2. Did his predictions account for the effect of air resistance? 3. What experiment did Galileo Galilei make? 4. What was determined through the experiment? 5. What is the importance of Galileo’s experiment?

33

UNIT

7

Vocabulary motion n. – движение; to launch v. – запускать; to establish v. – устанавливать; to throw (thrеw) v.– бросать; кидать; solid а. – твердый (о веществе); velocity n. – скорость; быстрота; to increase v. – увеличивать (ся); (ant. to decrease – уменьшать (ся); to accelerate v. – ускорять (ся); to provide v. – обеспечивать; surface n. – поверхность; to occur v. – случаться; происходить; иметь место; to depend (on) v. – зависеть от чего-либо; due to prep. – 1) вследствие чего-либо; 2) благодаря; to cause v. – 1) являться причиной, поводом; 2) причинять; rate n. – 1) норма; 2) тема, скорость; 3) класс; altitude n. – высота (над уровнем моря); to pass (through) v. – 1) проходить сквозь; 2) посредством; to be equal (to) v. – 1) быть равным чему-либо; to assign v. – 1) назначать; 2) давать задание; to assist v. – помогать, оказывать помощь;

I. Practice pronunciation of the following words: launch [lɔ:n(t)ʃ] analysis [ə'nalɪsɪs] vertical ['və:tɪk(ə)l] occur [ə'kə:] earth [ə:θ]

cause [kɔ:z] altitude ['altɪtju:d] equal ['i:kw(ə)l] assume [ə'sju:m] conceptual [kən'sɛptjʊəl]

II. Read the translate the words having the same root establish – establishment; vertical – vertically; assign – assignment; assist – assistance – assistant; equal – equality; understand – 34

understanding; consider – consideration; declare – declaration; concept – conceptual – conception; simplify – simply; complete – completely; quantity – quantitative; involve – involvement. III. Read and translate the words paying attention to the plural datum – data; stratum – strata; spectrum – spectra; axis – axes; nucleus – nuclei; quantum – quanta; focus – foci; momentum – momenta; formula – formulas IV. Translate the sentence paying attention to the Modal Verbs 1. The acceleration can be either 9.8 m/s2 or -9.8 m/s2 at maximum altitude. 2. The velocity of the ball must be zero. 3. You can start by assigning the direction the ball begins to move as positive. 4. Newton’s 2nd low of motion may be the most important principle in all of modern – day physics. 5. In equation form it can be exF pressed as a  net . m V. Read the text and render its main idea Objects Launched Upward Examining the motion of an object launched vertically upward is done in much the same way you examined the motion of an object falling from rest. The major difference is that you have to look at two segments of its motion instead of one: both up and down. Before you get into establishing a frame of reference and working through the quantitative analysis, you must build a solid conceptual understanding of what is happening while the ball is in the air. Consider the ball being thrown vertically into the air as shown in the diagram. In order for the ball to move upwards its initial velocity must be greater than zero. As the ball rises, its velocity decreases until it reaches its maximum height, where it stops, and then begins to fall. 35

As the ball falls, its speed increases. In other words, the ball is accelerating the entire time it is in the air, both on the way up, at the instant it stops at its highest point, and on the way down. The cause of the ball’s acceleration is gravity. The entire time the ball is in the air, its acceleration is 9.8 m/s2 down provided this occurs on the surface of the Earth. Note that the acceleration can be either 9.8 m/s2 or -9.8 m/s2. The sign of the acceleration depends on the direction you declared as positive, but in all cases the direction of the acceleration due to gravity is down, toward the center of the Earth. You have already established the ball’s acceleration for the entire time it is in the air is 9.8 m/s2 down. This acceleration causes the ball’s velocity to decrease at a constant rate until it reaches maximum altitude, at which point it turns around and starts to fall. In order to turn around, the ball’s velocity must pass through zero. Therefore, at maximum altitude the velocity of the ball must be zero. Now that a conceptual understanding of the ball’s motion has been established, you can work toward a quantitative solution. Following the rule of thumb established previously, you can start by assigning the direction the ball begins to move as positive. Remember that assigning positive and negative directions are completely arbitrary. You have the freedom to assign them how you see fit. Once you assign them, however, don’t change them. Once this positive reference direction has been established, all other velocities and displacements are assigned accordingly. For example, if up is the positive direction, the acceleration due to gravity will be negative, because the acceleration due to gravity points down, toward the center of the Earth. At its highest point, the ball will have a positive displacement, and will have a zero displacement when it returns to its starting point. If the ball isn’t caught, but continues toward the Earth past its starting point, it will have a negative displacement. A «trick of the trade» to solving free fall problems involves symmetry. The time an object takes to reach its highest point is equal to the time it takes to return to the same vertical position. The speed with which the projectile begins its journey upward is equal to the 36

speed of the projectile when it returns to the same height (although, of course, its velocity is in the opposite direction). If you want to simplify the problem, vertically, at its highest point, the vertical velocity is 0. This added information can assist you in filling out your vertical motion table. If you cut the object’s motion in half, you can simplify your problem solving – but don’t forget that if you want the total time in the air, you must double the time it takes for the object to rise to its highest point. VI. Find in the text the equivalents of the following word combinations: 1) основное отличие в том, что… 2) количественный анализ 3) первоначальная скорость 4) иными словами 5) поверхность земли 6) зависит от 7) одинаковое ускорение 8) благодаря гравитации 9) вертикальное (горизонтальное) положение 10) упростить задачу 11) правило левой руки (для определения направления механической силы), или правило большого пальца VII. Answer the questions 1. 2. 3. 4.

What causes the ball’s acceleration? What does the sign of the acceleration depend on? What does the rule of thumb state? A ball thrown vertically upward reaches a maximum height of 30 meters above the surface of Earth. At its maximum height, the speed of the ball is ? 5. A basketball player jumped straight up to grab a rebound. If she was in the air for 0.80 seconds, how high did she jump?

37

UNIT

8

Vocabulary modern-day physics to explain v. force n. net force v. come into force v. to state v. to express v. equation n. to occur v. to cause v. rate n. to pass (through) v. to be equal (to) v. to assign v.

– современная физика; – объяснять, толковать; – сила; – равнодействующая сила; – вступать в силу; – заявить, утверждать; – выражать; – уравнение; – случаться; происходить; иметь место; – являться причиной, поводом; 2) причинять; – норма; 2) тема, скорость; 3) класс; – проходить сквозь; 2) посредством; – быть равным ч.-л.; – 1) назначать; 2) давать задание;

I. Practice the pronunciation of the following words law [lɔ: ] proportional [prə'pɔ:ʃ(ə)n(ə)l] equation [ɪ'kweɪʒ(ə)n] inversely [ɪn'və:sli] direction [|dɪ'rɛkʃ(ə)n] kinematics ['kɪnɪ,matɪks] average ['av(ə)rɪdʒ]

horizontal [hɒrɪ'zɒnt(ə)l] abbreviate [ə'bri:vɪeɪt] apply [ə'plʌɪ] perspective [pə'spɛktɪv] expression [ɪk'sprɛʃ(ə)n] weight [weɪt] surface ['sə:fɪs]

ІІ. Fill in the gaps with the words below velocity

depend (on)

arbitrary explain

net force

1. Remember that assigning positive and negative directions are completely ____________. 2. If you want to simplify the problem, vertically, at its highest point, the vertical _____________ is 0. 38

3. Newton’s 2nd law of motion – how an object’s velocity is changed by a ______________. 4. The sign of the acceleration ______________the directions you declared as positive. 5. The direction of the acceleration will be in same direction as the ______________. III. Match the words in the left column with its antonym in the right column slightly entirely frequently apper varying above increase

rarely below constant decrease lower partly greatly

IV. Translate the following words a) exact – exactly inverse – inversely direct – directly positive – positively constant – constantly entire – entirely b) an object’s velocity net force directly proportional produce an acceleration break up (into) solve the equation V. Read the text paying attention to the modal verbs Newton's 2nd Law of Motion Newton’s 2nd Law of Motion may be the most important principle in all of modern-day physics because it explains exactly how an 39

object’s velocity is changed by a net force. In words, Newton’s 2nd Law states that «the acceleration of an object is directly proportional to the net force applied, and inversely proportional to the object’s mass». In equation form, you can express Newton’s 2nd Law as:

a

Fnet . m

It’s important to remember that both force and acceleration are vectors. Therefore, the direction of the acceleration, or the change in velocity, will be in the same direction as the net force. You can also look at this equation from the opposite perspective. A net force applied to an object changes an object’s velocity (produces an acceleration), and is frequently written as: Fnet = ma. You can analyze many situations involving both balanced and unbalanced forces on an object using the same basic steps. 1. Draw a free body diagram. 2. For any forces that don’t line up with the x- or y-axes, break those forces up into components that do lie on the x- or y-axis. 3. Write expressions for the net force in x- and y- directions. Set the net force equal to ma, since Newton’s 2nd Law tells us that Fnet = ma. 4. Solve the resulting equations. There are many applications of Newton’s first law of motion. Consider some of your experiences in an automobile. Have you ever observed the behavior of coffee in a coffee cup filled to the rim while starting a car from rest or while bringing a car to rest from a state of motion? Coffee «keeps on doing what it is doing». When you accelerate a car from rest, the road provides an unbalanced force on the spinning wheels to push the car forward; yet the coffee (that was at rest) wants to stay at rest. While the car accelerates forward, the coffee remains in the same position; subsequently, the car accelerates out from under the coffee and the coffee spills in your lap. On the other hand, when breaking from a state of motion the coffee continues forward with the same speed and in the same direction, ultimately hitting the windshield or the dash. Coffee in motion stays in motion. 40

There are many more applications of Newton’s first law of motion. Several applications are listed below. Perhaps you could think about the law of inertia and provide explanations for each application. – Blood rushes from your head to your feet while quickly stopping when riding on a descending elevator. – The head of a hammer can be tightened onto the wooden handle by banging the bottom of the handle against a hard surface. – Brick is painlessly broken over the hand of a physics teacher by slamming it with a hammer. (CAUTION: do not attempt this at home!) – Headrests are placed in cars to prevent whiplash injuries during rear-end collisions. – While riding a skateboard (or wagon or bicycle), you fly forward off the board when hitting a curb or rock or other object that abruptly halts the motion of the skateboard. VI. Find in the text the equivalents of the following word combinations современная физика равнодействующая сила пропорционально массе в виде уравнения следовательно как …так и решить уравнение найти скорость средняя сила /ускорение VII. Answer the questions 1. Why is Newton’s 2nd Law of Motion one of the most important principles in a modern – day physics? 2. What does the law state? 3. A 0.15-kilogram baseball moving at 20 m/s is stopped by a catcher in 0.010 seconds. Find the average force stopping the ball. 4. Two forces, F1 and F2, are applied to a block on a frictionless, horizontal surface as shown below.

41

If the magnitude of the block’s acceleration is 2.0 meters per second2, what is the mass of the block?

42

UNIT

9

Vocabulary external adj. to conserve v. explosion n. outcome n. tool n. to identify v. to determine v. variable adj. to solve v. collision n. to come into collision approach to interact v.

– внешний; (ant. internal) – сохранять; – взрыв; – 1) результат, последствие; 2) выход; – инструмент, орудие; – устанавливать, тождество, отождествлять; – 1) определять, устанавливать; 2) обуславливать; – изменчивый, непостоянный; – решать, находить выход, объяснять; – столкновение, коллизия; – вступать в противоречие; – подход, подходить, приближаться; – 1) взаимодействовать; 2) влиять друг на друга;

I. Practice pronunciation of the following words: momentum [mə'mɛntəm ] explosion [ɪk'spləʊʒ(ə)n] identify [ʌɪ'dɛntɪfʌɪ ] variable ['vɛ:rɪəb(ə)l]

conservation [kɒnsə'veɪʃ(ə)n ] isolation [ʌɪsə'leɪʃ(ə)n] collision [kə'lɪʒ(ə)n ] emphasize ['ɛmfəsʌɪz ]

II. Pick up synonyms and translate them Example: essential – important impact, create, vary, a great deal, effect, due, a lot, cause, result, change, great, various, basic, influence, different, principal, affect, dependent, markedly, outcome. III. Read and translate the words having the same root conserve – conservation constant – constantly 43

equal – equality identify – identification interact – interaction apply – application- applicable create – creator – creation consistent – consistently collide – collision – collider IV. Translate the sentences paying attention to the Passive Voice 1. We can state that momentum is always conserved. 2. Momentum is conserved in any closed system 3. An explosion results when an object is broken up into two more fragments. V. Read the text and be ready to retell it close to the original Law of Momentum Conservation Now that we've talked about momentum in an isolated system, where no external forces act, we can state that momentum is always conserved. Put more simply, in any closed system, the total momentum of the system remains constant. In the case of a collision or explosion (an event), if you add up the individual momentum vectors of all of the objects before the event, you'll find they're equal to the sum of the momentum vectors of the objects after the event. Written mathematically: pinitial = pfinal. This is a direct outcome of Newton's 3rd Law. Momentum Tables In analyzing collisions and explosions, a momentum table can be a powerful tool for problem solving. To create a momentum table, follow these basic steps: 1. Identify all objects in the system. List them vertically down the left-hand column. 2. Determine the momenta of the objects before the event. Use variables for any unknowns. 3. Determine the momenta of the objects after the event. Use variables for any unknowns. 44

4. Add up all the momenta from before the event, and set them equal to the momenta after the event. Solve your resulting equation for any unknowns. Conservation of energy Ancient philosophers as far back as Thales of Miletus thought of the conservation of some underlying substance of which everything is made. However, there is no particular reason to identify this with what we know today as «mass-energy» conservation (for example, Thales thought it was water). Empedocles wrote that in his universal system, composed of four roots (earth, air, water, fire), «nothing comes to be or perishes», instead, these elements suffer continual rearrangement. In 1605, Simon Stevinus was able to solve a number of problems in statics based on the principle that perpetual motion was impossible. In 1638, Galileo published his analysis of several situations – including the celebrated «interrupted pendulum» – which can be described (in modern language) as conservative converting of potential energy to kinetic energy and back again. Essentially, he pointed out that the height a moving body rises is equal to the height from which it falls, and used this observation to infer the idea of inertia. The remarkable aspect of this observation is that the height that a moving body ascends to does not depend on the shape of the frictionless surface that the body is moving on. In 1669, Christian Huygens published his laws of collision. Among the quantities, he listed as being invariant before and after the collision of bodies, were both the sum of their linear momentums as well as the sum of their kinetic energies. However, the difference between elastic and inelastic collision was not understood at the time. This led to the dispute among later researchers as to which of these conserved quantities was the more fundamental. He gave a much more explicit and clearer statement regarding the height of ascent of a moving body, and connected this idea with the impossibility of a perpetual motion. Huygens' study of the dynamics of pendulum motion was based on a single principle: that the center of gravity of heavy objects cannot lift itself. The fact that kinetic energy is scalar, unlike linear momentum which is a vector and hence easier to work with, did not escape the 45

attention of Gottfried Wilhelm Leibniz. It was Leibniz who during 1676–1689 first attempted a mathematical formulation of the kind of energy, which is connected with motion (kinetic energy). A key stage in the development of the modern conservation principle was the demonstration of the mechanical equivalent of heat. The caloric theory maintained that heat could neither be created nor destroyed, whereas conservation of energy entails the contrary principle that heat and mechanical work are interchangeable. In the middle of the eighteenth century Mikhail Lomonosov, a Russian scientist, postulated his corpuscular-kinetic theory of heat, which rejected the idea of a caloric. Through the results of empirical studies, Lomonosov came to the conclusion that heat was not transferred through the particles of the caloric fluid. In 1798, Benjamin Thompson performed measurements of the frictional heat generated in boring cannons, and developed the idea that heat is a form of kinetic energy; his measurements refuted caloric theory, but were imprecise enough to leave room for doubt. Matter is composed of such things as atoms, electrons, neutrons, and protons. It has intrinsic or rest mass. In the limited range of recognized experience of the nineteenth century it was found that such rest mass is conserved. Einstein's 1905 theory of special relativity showed that it corresponds to an equivalent amount of rest energy. This means that it can be converted to or from equivalent amounts of other (non-material) forms of energy, for example kinetic energy, potential energy, and electromagnetic radiant energy. When this happens, as recognized in the twentieth century experience, the rest mass is not conserved, unlike the total mass or total energy. All forms of energy contribute to the total mass and total energy. For example, an electron and a positron each have rest mass. They can perish together, converting their combined rest energy into photons having electromagnetic radiant energy, but no rest mass. If this occurs within an isolated system that does not release the photons or their energy into the external surroundings, then neither the total mass nor the total energy of the system will change. The produced electromagnetic radiant energy contributes just as much to the inertia (and to any weight) of the system as did the rest mass of the electron and positron before their demise. Likewise, non-material forms of energy can perish into matter, which has rest mass. 46

VI. Find in the text the equivalents of the following word combination 1) инерция движущегося тела 2) внутренняя сила 3) остается постоянной 4) в случае столкновения 5) мощный инструмент 6) уравнение с неизвестными 7) в течение короткого промежутка времени 8) должно быть ровно 9) остается последовательным 10) происходит взрыв VII. Complete the sentences 1. In any closed system the total momentum of the system remains ____________. 2. A _____________can be a powerful tool for problem solving. 3. A ____________is an event in which two or more objects approach and interact for a short period of time. 4. The total momentum before the event must be __________to the total momentum after the event. 5. An explosion results when an object __________ into two or more fragments. VIII. Answer the questions 1. What does Newton’s 3rd Law state? 2. For what purpose can a momentum table be a powerful tool? 3. What is a collision? 4. A 2000-kg car traveling at 20 m/s collides with a 1000-kg car at rest at a stop sign. If the 2000-kg car has a velocity of 6.67 m/s after the collision, find the velocity of the 1000-kg car after the collision. 5. A 4-kilogram rifle fires a 20-gram bullet with a velocity of 300 m/s. Find the recoil velocity of the rifle.

47

UNIT

10

Vocabulary to attract v. to include v. relationship n. double v. double – acting similar adj. inverse adj. hint n. to take a hint to deal (with) v. to substitute v. to estimate v. to estimate tables complete adj. to complete v. completely adv. to make sure v. to make sense v. quantity n. to verify v.

– привлекать, притягивать; – включать, содержать в себе; – отношение, взаимоотношение, связь; – удваивать; – двойного действия (о механизме); – похожий, подобный; – противоположный; – намек, оттенок; – понять намек; – 1) иметь дело с чем-либо, быть связанным с чем-либо; 2) рассматривать (вопрос); – 1) заменять; 2) подставлять; – 1) оценивать, дать оценку; 2) подсчитать; – подстановочные таблицы; – полный, законченный; – закончить, завершить; – полностью, целиком; – убеждаться в чем -либо; – меть смысл; – количество, величина; – проверять, подтверждать;

I. Practice pronunciation of the following words: universal [ju:nɪ'və:s(ə)l] determine [dɪ'tə:mɪn] compare [kəm'pɛ:] asteroid ['astərɔɪd]

detail ['di:teɪl] substitute ['sʌbstɪtju:t] verify ['vɛrɪfʌɪ] separate ['seprət]

II. Translate the sentences focusing on either Participle I or Participle II 1. The magnitude of the force can be calculated using Newton’s low of universal gravitation. 48

2. Pay attention to some hints for problem solving dealing with the law. 3. This type of relationship called an inverse square law describes many phenomena in the natural world. III. Find in the text the equivalents of the following word combinations in the text 1) гравитационная сила 2) закон всемирного тяготения 3) притягивать (ся) друг друга 4) обратно пропорционально 5) определить расстояние 6) сравнивая с чем-либо 7) удостовериться в чем-либо IV. Translate the word combinations from the text 1) attract each other with a gravitational force 2) directly proportional 3) a «fudge factor» 4) an inverse square law 5) some hints for problem solving 6) the longer, the fewer 7) to find an answer 8) to estimate the order of magnitude V. Translate using the table few fewer little less

people rain molecules pressure interest words mistakes

мало дождей мало интереса меньше слов меньше людей меньше давления мало фактов мало ошибок меньше молекул

49

VI. Read the text and answer the questions following below Universal Gravitation All objects that have mass attract each other with a gravitational force. The magnitude of that force, Fg, can be calculated using Newton's Law of Universal Gravitation:

Fg  G

m1m 2 . r2

This law tells us that the force of gravity between two objects is proportional to each of the masses (m1 and m2) and inversely proportional to the square of the distance between them (r). The universal gravitational constant, G, is a «fudge factor», so to say, included in the equation so that your answers come out in SI units. G is given as G=6.67*10-11 Nm2/kg2 Let's look at this relationship in a bit more detail. Force is directly proportional to the masses of the two objects, therefore if either of the masses were doubled, the gravitational force would also double. In similar fashion, if the distance between the two objects, r, was doubled, the force of gravity would be quartered since the distance is squared in the denominator. This type of relationship is called an inverse square law, which describes many phenomena in the natural world. NOTE: the distance between the masses, r, is actually the distance between the centers of masses of the objects. For large objects, such as the Earth, for example, you must determine the distance to the center of the Earth, not to its surface. While Kepler's laws provided a suitable framework for describing the motion and paths of planets around the sun, there was no acceptable explanation for why such paths existed. The cause for how the planets moved as they did was never stated. Kepler could only suggest that there was some sort of interaction between the sun and the planets that provided the driving force for the planet's motion. To Kepler, the planets were somehow «magnetically» driven by the sun to orbit in their elliptical trajectories. There was however no interaction between the planets themselves. 50

Newton was troubled by the lack of explanation for the planet's orbits. To Newton, there had to be some cause for such elliptical motion. Even more troubling was the circular motion of the moon about the earth. Newton knew that there must be some sort of force that governed the heavens; for the motion of the moon in a circular path and of the planets in an elliptical path required that there was an inward component of force. Circular and elliptical motion were clearly deviations from the inertial paths (straight-line) of objects. And as such, these celestial motions required a cause in the form of an unbalanced force. Circular motion (as well as elliptical motion) requires a centripetal force. The nature of such a force – its cause and its origin – interested Newton for some time and was the fuel for much mental pondering. And according to legend, a breakthrough came at age 24 in an apple orchard in England. Newton never wrote of such an event, yet it is often claimed that the notion of gravity as the cause of all heavenly motion was instigated when he was struck in the head by an apple while lying under a tree in an orchard in England. Whether it is a myth or a reality, the fact is certain that it was Newton's ability to relate the cause for heavenly motion (the orbit of the moon about the earth) to the cause for Earthly motion (the falling of an apple to the Earth) that led him to his notion of universal gravitation. A survey of Newton's writings reveals an illustration of the motion of the moon as a projectile. Newton's reasoning proceeded as follows. Suppose a cannonball is fired horizontally from a very high mountain in a region devoid of air resistance. In the absence of gravity, the cannonball would travel in a straight-line, tangential path. Yet in the presence of gravity, the cannonball would drop below this straight-line path and eventually fall to Earth (as in path A). Now suppose that the cannonball is fired horizontally again, yet with a greater speed. In this case, the cannonball would still fall below its straight-line tangential path and eventually drop to earth. Only this time, the cannonball would travel further before striking the ground (as in path B). Now suppose that there is a speed at which the cannonball could be fired such that the trajectory of the falling cannonball matched the curvature of the earth. If such a speed could be obtained, then the cannonball would fall around the earth instead of into it. The cannonball would fall towards the Earth without ever 51

colliding into it and subsequently become a satellite orbiting in circular motion (as in path C). And then at even greater launch speeds, a cannonball would once more orbit the earth, but in an elliptical path (as in path D). The motion of the cannonball orbiting to the earth under the influence of gravity is analogous to the motion of the moon orbiting the Earth. And if the orbiting moon can be compared to the falling cannonball, it can even be compared to a falling apple. The same force that causes objects on Earth to fall to the earth also causes objects in the heavens to move along their circular and elliptical paths. Quite amazingly, the laws of mechanics that govern the motions of objects on Earth also govern the movement of objects in the heavens. The inverse square law proposed by Newton suggests that the force of gravity acting between any two objects is inversely proportional to the square of the separation distance between the object's centers. Altering the separation distance (d) results in an alteration in the force of gravity acting between the objects. Since the two quantities are inversely proportional, an increase in one quantity results in a decrease in the value of the other quantity. That is, an increase in the separation distance causes a decrease in the force of gravity and a decrease in the separation distance causes an increase in the force of gravity. Furthermore, the factor by which the force of gravity is changed is the square of the factor by which the separation distance is changed. So if the separation distance is doubled (increased by a factor of 2), then the force of gravity is decreased by a factor of four (2 raised to the second power). And if the separation distance is tripled (increased by a factor of 3), then the force of gravity is decreased by a factor of nine (3 raised to the second power). Thinking of the force-distance relationship in this way involves using a mathematical relationship as a guide to thinking about how an alteration in one variable affects the other variable. Equations can be more than recipes for algebraic problem solving; they can be guides to thinking. 1. What does Newton’s Law of Universal Gravitation state? 2. What is meant by the inverse square law? 3. What is the gravitational force of attraction between two asteroids in space, each with a mass of 50,000 kg, separated by a distance of 3800 m?

52

VII. Complete the sentences 1. All objects that have mass attract each other with a_______ force. 2. The universal gravitational constant, G, is a_________. 3. Force is ________to the masses of the two objects. 4. The inverse _______ describes many phenomena in the national world. 5. For large object you must ________the distance to the centre of the Earth. 6. The________you keep the formula in terms of variables, the _______opportunities for mistakes. 7. If your answer doesn’t ___________, check your work.

53

UNIT

11

Vocabulary to observe v. to come into contact envision n. to experience v. to attempt to picture v. strength n. hint n. test object dense adj. density n. definition n. weight n. to realize v. to simplify v. to divide v. unit n. to work out v. approximately adj. slightly adv.

– 1) наблюдать, замечать; 2) вести научные наблюдения; – выступать в контакт; – представление; – испытывать, знать по опыту; – пытаться, пробовать; – описывать, представить себе; – сила, сопротивление; – намек, оттенок; – тестируемый объект, объект, подвергающийся/ подвергаемый испытанию; – плотный, компактный; – плотность; – 1) определение; 2) ясность, четкость; – вес, масса; – 1) понимать; 2) представлять себе; 3) осуществлять; – упрощать; – делить (ся), разделять(ся); – единица, целое; единица измерения; – 1) решать (задачу); 2) составлять, выражать (ся); 3) разрабатывать (план); – приблизительно; – немного, незначительно, слегка;

I. Translate the sentences paying attention to the words 1. The closer other masses are to Earth, the more gravitational force they will experience. 2. The closer the object is to the Earth, the larger a force it will experience. 3. The denser the force vectors are, the stronger the force. II. Find the English equivalents of the following words 1) гравитационное поле 2) чем ближе…, тем больше… 54

3) тестируемый объект 4) становится слабее 5) рассчитать /вычислить силу гравитации 6) упростить выражение 7) расстояние от поверхности земли III. Fill in the gaps with words given and translate the sentences gravity

force

come

into

contact

calculate

1. The stronger the _______, the stronger the gravitational field. 2. We can the force of gravity on test mass using Newton’s Law of Universal Gravitation. 3._______ is a non-contact, or field force. 4. Its effects are observed without the two objects ______with each other. IV. Read the international words and guess their meanings Gravity, contact, object, construct, characterize, visual, vector, position, definition, dynamics, acceleration, equivalent, sphere. V. Match the words with their English equivalents mystery realize obviously experience definition to be equal acceleration

опыт; испытывать быть равным чему либо ускорение понимать, осознавать тайна очевидно определение

VI. Read the text and answer the questions below Gravitational Fields Gravity is a non-contact, or field, force. Its effects are observed without the two objects coming into contact with each other. Exactly 55

how this happens is a mystery to this day, but scientists have come up with a mental construct to help us understand how gravity works. Envision an object with a gravitational field, such as the planet Earth. The closer other masses are to the Earth, the more gravitational force they will experience. We can characterize this by calculating the amount of force the Earth will exert per unit mass at various distances from the Earth. Obviously, the closer the object is to the Earth, the larger a force it will experience, and the farther it is from the Earth, the smaller a force it will experience. Attempting to visualize this, picture the strength of the gravitational force on a test object represented by a vector at the position of the object. The denser the force vectors are, the stronger the force, the stronger the «gravitational field». As these field lines become less and less dense, the gravitational field gets weaker and weaker. To calculate the gravitational field strength at a given position, we can go back to our definition of the force of gravity on our test object, better known as its weight. We've been writing this as mg since we began our study of dynamics. But, realizing that this is the force of gravity acting on an object, we can also calculate the force of gravity on test mass using Newton's Law of Universal Gravitation. Putting these together we find that:

Fg  mg 

Gm1m2 . r2

Realizing that the mass on the left-hand side of the equation, the mass of our test object, is also one of the masses on the right-hand side of the equation, we can simplify our expression by dividing out the test mass.

g

Gm . r2

56

Therefore, the gravitational field strength, g, is equal to the universal gravitational constant, G, times the mass of the object, divided by the square of the distance between the objects. But wait, you might say... I thought g was the acceleration due to gravity on the surface of the Earth! And you would be right. Not only is g the gravitational field strength, it's also the acceleration due to gravity. The units even work out... the units of gravitational field strength, N/kg, are equivalent to the units for acceleration, m/s2! Isaac Newton's law of universal gravitation proposed that the gravitational attraction between any two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The constant of proportionality in this equation is G – the universal gravitation constant. The value of G was not experimentally determined until nearly a century later (1798) by Lord Henry Cavendish using a torsion balance. Cavendish's apparatus for experimentally determining the value of G involved a light, rigid rod about 2-feet long. Two small lead spheres were attached to the ends of the rod and the rod was suspended by a thin wire. When the rod becomes twisted, the torsion of the wire begins to exert a torsional force that is proportional to the angle of rotation of the rod. The more twist of the wire, the more the system pushes backwards to restore itself towards the original position. Cavendish had calibrated his instrument to determine the relationship between the angle of rotation and the amount of torsional force. A diagram of the apparatus is shown below.

57

Cavendish then brought two large lead spheres near the smaller spheres attached to the rod. Since all masses attract, the large spheres exerted a gravitational force upon the smaller spheres and twisted the rod a measurable amount. Once the torsional force balanced the gravitational force, the rod and spheres came to rest and Cavendish was able to determine the gravitational force of attraction between the masses. By measuring m1, m2, d and Fgrav, the value of G could be determined. Cavendish's measurements resulted in an experimentally determined value of 6.75 x 10-11 N m2/kg2. Today, the currently accepted value is 6.67259 x 10-11 N m2/kg2. The value of G is an extremely small numerical value. Its smallness accounts for the fact that the force of gravitational attraction is only appreciable for objects with large mass. While two students will indeed exert gravitational forces upon each other, these forces are too small to be noticeable. Yet if one of the students is replaced with a planet, then the gravitational force between the other student and the planet becomes noticeable. 1. What do we mean by gravity? 2. How does gravity work? 3. In what way can we calculate the force of gravity on test mass? 4. Calculate the gravitational field strength on the surface of the Earth, using the knowledge that the mass of the Earth is approximately 5.98*1024 kg, and the distance from the surface to the center of mass of the Earth (which varies slightly since the Earth isn't a perfect sphere) is approximately 6378 km in New York.

g

 6.67x10 g

11 N m 2

Gm r2 / kg 2

 5.98x10 kg  24

 6.378x10 m  6

2

g  9.81N / kg  9.81m / s2 .

58

UNIT

12

Vocabulary celestial body solar system Milky Way to explain v. to develop to imagine v. cannon n. to place v. above (ant.below) to neglect v. air resistance across prep. to reach the ground enough adv. to fall v.(ant. to rise) to curve away weightless n. far from it to pull v. substantial a. to obtain v. to mean v.

– небесное тело; – солнечная система; – Млечный путь; – испытывать, знать по опыту; – 1) развивать; 2) разработать; – воображать, представлять себе; – пушка, орудие; – помещать, размещать, класть; – над (ант. под); – пренебрегать, не обращать внимание; – сопротивление воздуха; – через; – достичь земли; – достаточно; – опускать (ся), ант. поднимать (ся); – 1) гнуть, сгибать; 2) изгибать (ся); – невесомый; – напротив; – 1) тянуть, тащить, натягивать; 2) растягивать; – 1) важный, существенный, значительный; 2) прочный, крепкий; – получать, добывать, приобретать; – означать, иметь в виду, подразумевать;

I. Translate the words of the same root Explain – explanation, develop – development, imagine – imagination, resist – resistance; horizontal – horizontally, project – projective, parabola – parabolic, describe – description – descriptive, weight – weightless, substantial – substantially, calculate – calculation, refer – reference, obtain – obtainable. II. Translate the following: A celestial body, above the atmosphere, air resistance, before reaching the ground, at the same rate, to calculate a force, to maintain an orbit, a tremendous speed. 59

III. Match the words with their English equivalents develop air resistance Substantial force gravitational field remain approximately follow

оставить, становиться значительная сила гравитационная сила воздушное сопротивление последовать разрабатывать приблизительно

IV. Find the English equivalents of the following word combinations and write them out 1) небесное тело 2) на вершине горы 3) поверхность земли 4) достаточно высоко 5) с существенной силой 6) космический корабль 7) равнодействующая сила V. Find in the text Conditional sentences and translate them Orbits How do celestial bodies orbit each other? The moon orbits the Earth. The Earth orbits the sun. Our solar system is in orbit in the Milky Way galaxy... but how does it all work? To explain orbits, Sir Isaac Newton developed a «thought experiment» in which he imagined a cannon placed on top of a very tall mountain, so tall, in fact, that the peak of the mountain was above the atmosphere (this is important because it allows us to neglect air resistance). If the cannon then launched a projectile horizontally, the projectile would follow a parabolic path to the surface of the Earth. 60

If the projectile was launched with a higher speed, however, it would travel farther across the surface of the Earth before reaching the ground. If its speed could be increased high enough, the projectile would fall at the same rate the Earth's surface curves away. The projectile would continue falling forever as it circled the Earth! This circular motion describes an orbit. Put it another way, the astronauts in the Space Shuttle aren't weightless. Far from it, actually, the Earth's gravity is still acting on them and pulling them toward the center of the Earth with a substantial force. We can even calculate that force. If the Space Shuttle orbits the Earth at an altitude of 380,000m, what is the gravitational field strength due to the Earth? VI. Complete the sentences 1. Our ________ is in orbit in the Milky Way galaxy. 2. To explain ________sir Isaac Newton a ‘thought experiment’. 3. We can ___________that force. 4. The astronauts in the space Shuttle aren’t_____________. 5. The space Shuttle ____________approximately 7680 m/s, more than 23 times the speed of _______at sea level! VII. Answer the questions 1. What did Isaac Newton develop to explain orbits? 2. Is it possible to calculate a force? 3. If the Space Shuttle orbits the Earth at an altitude of 380 km, what is the gravitational field strength due to the Earth?

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UNIT

13

Vocabulary to govern v. to state v. to draw a line to sweep out v. to move along v. ratio n. accurate adj. to note v. revolution n.

– 1) управлять; 2) влиять; 3) обуславливать; – констатировать, формулировать; – провести линию; – сметать, чистить, охватывать; – двигаться (вдоль); – порция, рацион; – точный, правильный; – отмечать, упоминать, обращать внимание; – вращение;

I. Read the international words and guess their meaning planetary, ellipse, line, orbiting, diagram, publish, period, ratio, cube, orbital, interval, distance, parabola, hyperbola II. Translate the sentences paying attention to comparisons 1. It’s not as bad as it looks. 2. Planets that are closer to the sun have much shorter periods than planets that are farther from the sun. 3. Mercury, that is closest to the sun, has an orbital period of 88 days. III. Read the text and make a summary Kepler's Laws of Planetary Motion In the early 1600s, most of the scientific world believed that the planets should have circular orbits, and many believed that the Earth was the center of the solar system. Using the data collected by Tycho Brahe, German astronomer Johannes Kepler developed three laws governing the motion of planetary bodies, which described their orbits as ellipses with the sun at one of the focal points (even though the orbits of many planets are nearly circular). These laws are known as Kepler’s Laws of Planetary Motion. 62

Kepler’s First Law of Planetary Motion states that the orbits of planetary bodies are ellipses with the sun at one of the two foci of the ellipse. Kepler’s Second Law of Planetary Motion states that if you were to draw a line from the sun to the orbiting body, the body would sweep out equal areas along the ellipse in equal amounts of time. This is easier to observe graphically. In the diagram, if the orbiting body moves from point 1 to point 2 in the same amount of time as it moves from point 3 to point 4, areas A1 and A2 must be equal.

Kepler’s Third Law of Planetary Motion, described several years after the first two laws were published, states that the ratio of the squares of the periods of two planets is equal to the ratio of the cubes of their semi-major axes. If this sounds confusing, don’t worry, once again it’s not as bad as it looks. The semi-major axis is the distance of the planet from the sun. What this is really saying, then, is that planets that are closer to the sun (with a smaller semi-major axis) have much shorter periods than planets that are farther from the sun. For example, the planet Mercury, closest to the sun, has an orbital period of 88 days. Neptune, which is 30 times farther from the sun than the Earth, has an orbital period of 165 Earth years. ______________________________ since – так как; according (to) – 1) в соответствии с чем-либо;

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IV. Answer the questions in writing 1. What do Kepler’s Laws of Planetary Motion state? 2. How do they describe their orbits? 3. Given the elliptical planetary orbit shown above, identify the interval during which the planet travels with the highest speed. 1. Interval P1 to P2 2. Interval P3 to P4 3. They are the same. 4. The shape of Mars’ orbit around the sun is most accurately described as a: 1. circle 2. ellipse 3. parabola 4. hyperbola 5. Which planet takes the longest amount of time to make one complete revolution around the sun? 1. Venus 2. Earth 3. Jupiter 4. Uranus

V. Match each of the following terms with its definition a) ellipse; b) circular; c) orbit; d) equal; e) ratio; f) axis; g) distance; ________________1) a path described by one body in its revolution about another ________________2) the relation in number, quantity or degree between things ________________3) of the same measure, quantity or quality ________________4) a straight line passing through a body that revolves upon it ________________5) having the form of a circle ________________6) measure of separation in space or time ________________7) a closed curve of oval shape VI. Fill in the gaps with the words below solar

system

govern

foci

amounts of time

distance

1. The semi-major axis is the _________________of the planet from the sun. 64

2. The body would sweep out equal areas along the ellipse in equal ____________. 3. Kepler developed three laws ______________ the motion of planetary bodies. 4. Most of the scientific world thought that the Earth was the center of the __________________. 5. The orbits of planetary bodies are ellipses with the sun at one of the two _________________ of the ellipse. VII. Make an outline of the text and render its main idea

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UNIT

14

Vocabulary pressure exert pressure under certain circumstances feel (felt, felt) to explore v. exploration n. to act (upon) matter n. to traverse v. fragile surface to spot v. odd adj. go up to design v. crust of snow find (found, found) v. to multiply v. to sink (into) v. to hold (held, held) v. inside (ant. outside) to cause v. a «popping» sensation to transfer v. sit flat to fall (fell, fallen) asleep

– давление; – вызывать давление; – при определенных обстоятельствах; – чувствовать; – исследовать, изучать; – исследование; – действовать на что-либо; – вещество; – пересекать, класть поперек; – хрупкая поверхность; – определить (местонахождение), обнаружить; – непарный, разрозненный; 2) лишний, добавочный; – поднимать (ся), ant.descend (to) 1) спускаться, снижаться; – предназначать(ся); 2) происходить; – корка снега; – находить; – умножить, (ant. to divide – делить); – опускать (ся); 2) погружать (ся); – держать, владеть, иметь; – внутри (ант. снаружи); – быть причиной, причинять; – закладывание в ушах; – переносить, перемещать, передавать; – слабо пересеченная местность; – заснуть;

I. Translate the following: science – scientist – scientific; define – definition; explore – explorer – exploration; apply – applied – application; mathematics – mathematician – mathematically; divide – division; traverse – traversing; design – designed – designer; direct – direction; connect – connection 66

II. Translate the sentences paying attention to Participles and Gerund 1. It is a scalar quantity calculated as the force applied per unit area. 2. When traversing fragile surfaces it’s important to spread your weight out. 3. They are designed to reduce the pressure applied to the top crust of snow. 4. You can walk more easily without sinking into snow drifts. III. Find in the text the sentences with the Passive Voice IV. Find the English equivalents of the following word combinations and write them out 1) при определенных обстоятельствах 2) сила, действующая на поверхность 3) равная силе гравитации 4) хрупкая поверхность 5) атмосфера земли 6) вследствие давления 7) приблизительно V. Read and translate the text Pressure Everyone’s been under pressure at one time or another, or in certain circumstances has really «felt the pressure». From a scientific perspective, however, pressure has a very specific definition, and its exploration leads to some very important applications. In physics, pressure is the effect of a force acting upon a surface. Mathematically, it is a scalar quantity calculated as the force applied per unit area, where the force applied is always perpendicular to the surface. The SI unit of pressure, a Pascal (Pa), is equivalent to a N/m2.

P

F . A

All states of matter can exert pressure. When you walk across an ice-covered lake, you are applying a pressure to the ice equal to the 67

force of gravity acting on your body (your weight) divided by the area over which you’re contacting the ice. This is why it is important to spread your weight out when traversing fragile surfaces. Your odds of breaking through the ice go up tremendously if you walk across the ice in high heels, as the small area contacting the ice leads to a high pressure. This is also the reason snow shoes have such a large area. They are designed to reduce the pressure applied to the top crust of snow so that you can walk more easily without sinking into snow drifts. Fluids, also, can exert pressure. All fluids exert outward pressure in all directions on the sides of any container holding the fluid. Even the Earth’s atmosphere exerts pressure, which you are experiencing right now. The pressures inside and outside your body are so well balanced, however, that you rarely notice the 101,325 Pascals due to the atmosphere (approximately 10N/cm2). If you ride in an airplane and change altitude (and therefore pressure) quickly, you may have experienced a «popping» sensation in your ears – this is due to the pressure inside your ear balancing the pressure outside your ear in a transfer of air through small tubes that connect your inner ear to your throat. The pressure that a fluid exerts on an object submerged in that fluid can be calculated almost as simply. If the object is submersed to a depth (h), the pressure is found by multiplying the density of the fluid by the depth submerged, all multiplied by the acceleration due to gravity. Pgauge=ρgh. This is known as the gauge pressure, because this is the reading you would observe on a pressure gauge. If there is also atmosphere above the fluid, such as in the situation here on earth, you can determine the absolute pressure, or total pressure, by adding in the 68

atmospheric pressure (P0), which is equal to approximately 100,000 Pascals. Pabsolute=P0+Pgauge= P0+ρgh. VI. Answer the questions in writing 1. Could you give the definition of pressure? 2. What can pressure be exerted by? 3. Air pressure is approximately 100,000 Pascals. What force is exerted on this book when it is lying flat on a desk? The area of the book’s cover is 0.035 m2. 4. A fisherman with a mass of 75kg falls asleep on his four-legged chair of mass 5 kg. If each leg of the chair has a surface area of 2.5×10-4 m2 in contact with the ground, what is the average pressure exerted by the fisherman and chair on the ground? 5. Samantha spots buried treasure while scuba diving on her Caribbean vacation. If she must descend to a depth of 40 meters to examine the pressure, what gauge pressure will she read on her scuba equipment? The density of sea water is 1025 kg/m3.

VII. Complete the sentences: 1. Pressure has a very specific ___________, and its exploration _____________to some very important applications. 2. It’s the effect of a _____________ acting upon a surface 3. The force applied is always _____________to the surface. 4. All states of matter can ______________ pressure. 5. The pressures _________ and _________ your body are so well balanced, that you can hardly notice the 101,325 Pascals ____________the atmosphere.

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SUPPLEMENTARY TEXTS Energy The concept of energy is one of the most important topics in science and engineering. In everyday life, we think of energy in terms of fuel for transportation and heating, electricity for lights and appliances, and foods for consumption. However, these ideas do not really define energy. They merely tell us that fuels are needed to do a job and that those fuels provide us with something we call energy. The definitions of quantities such as position, velocity, acceleration, and force and associated principles such as Newton’s second law have allowed us to solve a variety of problems. Some problems that could theoretically be solved with Newton’s laws, however, are very difficult in practice. These problems can be made much simpler with a different approach. We will investigate this new approach, which will include definitions of quantities that may not be familiar to you. Other quantities may sound familiar, but they may have more specific meanings in physics than in everyday life. We begin this discussion by exploring the notion of energy. Energy is present in the Universe in various forms. Every physical process that occurs in the Universe involves energy and energy transfers or transformations. Unfortunately, despite its extreme importance, energy cannot be easily defined. The notion of energy is more abstract, although we do have experiences with energy, such as running out of gasoline, or losing our electrical service if we forget to pay the utility bill. The concept of energy can be applied to the dynamics of a mechanical system without resorting to Newton’s laws. This «energy approach» to describing motion is especially useful when the force acting on a particle is not constant; in such a case, the acceleration is not constant, and we cannot apply the constant acceleration equations. Particles in nature are often subject to forces that vary with the particles’ positions. These forces include gravitational forces and the 70

force exerted on an object attached to a spring. We shall describe techniques for treating such situations with the help of an important concept called conservation of energy. This approach extends well beyond physics, and can be applied to biological organisms, technological systems, and engineering situations. Automobiles powered by gasoline engines are very inefficient machines. Even under ideal conditions, less than 15% of the chemical energy in the fuel is used to power the vehicle. The situation is much worse than this under stop-and-go driving conditions in a city. In this section, we use the concepts of energy, power, and friction to analyze automobile fuel consumption. Many mechanisms contribute to energy loss in an automobile. About 67% of the energy available from the fuel is lost in the engine. This energy ends up in the atmosphere, partly via the exhaust system and partly via the cooling system. Approximately 10% of the available energy is lost to friction in the transmission, drive shaft, wheel and axle bearings, and differential. Friction in other moving parts transforms approximately 6% of the energy to internal energy, and 4% of the energy is used to operate fuel and oil pumps and such accessories as power steering and air conditioning. This leaves a mere 13% of the available energy to propel the automobile! This energy is used mainly to balance the energy loss due to flexing of the tires and the friction caused by the air, which is more commonly referred to as air resistance. What are the different forms of energy? Energy has a number of different forms, all of which measure the ability of an object or system to do work on another object or system. In other words, there are different ways that an object or a system can possess energy. Here are the different basic forms of energy: Kinetic Energy Consider a baseball flying through the air. The ball is said to have «kinetic energy» by virtue of the fact that its in motion relative to the ground. You can see that it is has energy because it can do «work» on an object on the ground if it collides with it (either by pushing on it and/or damaging it during the collision). 71

Potential Energy Consider a book lying on a table. The book is said to have «potential energy» because if it is nudged off, gravity will accelerate the book, giving the book kinetic energy. Because the Earth's gravity is necessary to create this kinetic energy, and because this gravity depends on the Earth being present, we say that the «Earth-book system» is what really possesses this potential energy, and that this energy is converted into kinetic energy as the book falls. Thermal, or heat energy Consider a hot cup of coffee. The coffee is said to possess «thermal energy», or «heat energy» which is really the collective, microscopic, kinetic and potential energy of the molecules in the coffee (the molecules have kinetic energy because they are moving and vibrating, and they have potential energy due their mutual attraction for one another – much the same way that the book and the Earth have potential energy because they attract each other). Temperature is really a measure of how much thermal energy something has. The higher the temperature, the faster the molecules are moving around and/or vibrating, i.e. the more kinetic and potential energy the molecules have. Chemical Energy Consider the ability of your body to do work. The glucose (blood sugar) in your body is said to have «chemical energy» because the glucose releases energy when chemically reacted (combusted) with oxygen. Your muscles use this energy to generate mechanical force and also heat. Chemical energy is really a form of microscopic potential energy, which exists because of the electric and magnetic forces of attraction exerted between the different parts of each molecule – the same attractive forces involved in thermal vibrations. These parts get rearranged in chemical reactions, releasing or adding to this potential energy. Electrical Energy All matter is made up of atoms, and atoms are made up of smalller particles, called protons (which have positive charge), neutrons (which have neutral charge), and electrons (which are negatively 72

charged). Electrons orbit around the center, or nucleus, of atoms, just like the moon orbits the earth. The nucleus is made up of neutrons and protons. Some materials, particularly metals, have certain electrons that are only loosely attached to their atoms. They can easily be made to move from one atom to another if an electric field is applied to them. When those electrons move among the atoms of matter, a current of electricity is created. This is what happens in a piece of wire when an electric field, or voltage, is applied. The electrons pass from atom to atom, pushed by the electric field and by each other (they repel each other because like charges repel), thus creating the electrical current. The measure of how well something conducts electricity is called its conductivity, and the reciprocal of conductivity is called the resistance. Copper is used for many wires because it has a lower resistance than many other metals and is easy to use and obtain. Most of the wires in your house are made of copper. Some older homes still use aluminum wiring. The energy is really transferred by the chain of repulsive interactions between the electrons down the wire – not by the transfer of electrons per se. This is just like the way that water molecules can push on each other and transmit pressure (or force) through a pipe carrying water. At points where a strong resistance is encountered, it is harder for the electrons to flow – this creates a «back pressure» in a sense back to the source. This back pressure is what really transmits the energy from whatever is pushing the electrons through the wire. Of course, this applied «pressure» is the «voltage». As the electrons move through a «resistor» in the circuit, they interact with the atoms in the resistor very strongly, causing the resistor to heat up – hence delivering energy in the form of heat. Or, if the electrons are moving instead through the wound coils of a motor, they instead create a magnetic field, which interacts with other magnets in the motor, and hence turns the motor. In this case the «back pressure» on the electrons, which is necessary for there to be a transfer of energy from the applied voltage to the motor's shaft, is created by the magnetic fields of the other magnets (back) acting on the electrons – a perfect push-pull arrangement! 73

Electrochemical Energy Consider the energy stored in a battery. Like the example above involving blood sugar, the battery also stores energy in a chemical way. But electricity is also involved, so we say that the battery stores energy «electro-chemically». Another electron chemical device is a «fuel-cell». Electromagnetic Energy Consider the energy transmitted to the Earth from the Sun by light (or by any source of light). Light, which is also called «electromagnetic radiation». Why the fancy term? Because light really can be thought of as oscillating, coupled electric and magnetic fields that travel freely through space (without there having to be charged particles of some kind around). It turns out that light may also be thought of as little packets of energy called photons (that is, as particles, instead of waves). The word «photon» derives from the word «photo», which means «light». Photons are created when electrons jump to lower energy levels in atoms, and absorbed when electrons jump to higher levels. Photons are also created when a charged particle, such as an electron or proton, is accelerated, as for example happens in a radio transmitter antenna. But because light can also be described as waves, in addition to being a packet of energy, each photon also has a specific frequency and wavelength associated with it, which depends on how much energy the photon has (because of this weird duality – waves and particles at the same time – people sometimes call particles like photons «wavicles»). The lower the energy, the longer the wavelength and lower the frequency, and vice versa. The reason that sunlight can hurt your skin or your eyes is because it contains «ultraviolet light», which consists of high energy photons. These photons have short wavelength and high frequency, and pack enough energy in each photon to cause physical damage to your skin if they get past the outer layer of skin or the lens in your eye. Radio waves, and the radiant heat you feel at a distance from a campfire, for example, are also forms of electro-magnetic radiation, or light, except that they consist of low energy photons (long wavelength and high frequencies – in the infrared band and lower) that your eyes can't perceive. This 74

was a great discovery of the nineteenth century – that radio waves, x-rays, and gamma-rays, are just forms of light, and that light is electro-magnetic waves. Sound Energy Sound waves are compression waves associated with the potential and kinetic energy of air molecules. When an object moves quickly, for example the head of drum, it compresses the air nearby, giving that air potential energy. That air then expands, transforming the potential energy into kinetic energy (moving air). The moving air then pushes on and compresses other air, and so on down the chain. A nice way to think of sound waves is as «shimmering air». Nuclear Energy The Sun, nuclear reactors, and the interior of the Earth, all have «nuclear reactions» as the source of their energy, that is, reactions that involve changes in the structure of the nuclei of atoms. In the Sun, hydrogen nuclei fuse (combine) together to make helium nuclei, in a process called fusion, which releases energy. In a nuclear reactor, or in the interior of the Earth, Uranium nuclei (and certain other heavy elements in the Earth's interior) split apart, in a process called fission. If this didn't happen, the Earth's interior would have long gone cold! The energy released by fission and fusion is not just a product of the potential energy released by rearranging the nuclei. In fact, in both cases, fusion or fission, some of the matter making up the nuclei is actually converted into energy. How can this be? The answer is that matter itself is a form of energy! This concept involves one of the most famous formulas in physics, the formula, E=mc2. This formula was discovered by Einstein as part of his «Theory of Special Relativity». In simple words, this formula means The energy intrinsically stored in a piece of matter at rest equals its mass times the speed of light squared. When we plug numbers in this equation, we find that there is actually an incredibly huge amount of energy stored in even little 75

pieces of matter (the speed of light squared is a very large number!). For example, it would cost more than a million dollars to buy the energy intrinsically stored in a single penny at our current (relatively cheap!) electricity rates. To get some feeling for how much energy is really there, consider that nuclear weapons only release a small fraction of the «intrinsic» energy of their components. Thermodynamics We now direct our attention to the study of thermodynamics, which involves situations in which the temperature or state (solid, liquid, gas) of a system changes due to energy transfers. Thermodynamics is very successful in explaining the bulk properties of matter and the correlation between these properties and the mechanics of atoms and molecules. Historically, the development of thermodynamics paralleled the development of the atomic theory of matter. By the 1820s, chemical experiments had provided solid evidence for the existence of atoms. At that time, scientists recognized that a connection between thermodynamics and the structure of matter must exist. In 1827, the botanist Robert Brown reported that grains of pollen suspended in a liquid move erratically from one place to another, as if under constant agitation. In 1905, Albert Einstein used kinetic theory to explain the cause of this erratic motion, which today is known as Brownian motion. Einstein explained this phenomenon by assuming that the grains are under constant bombardment by «invisible» molecules in the liquid, which themselves move erratically. This explanation gave scientists insight into the concept of molecular motion and gave credence to the idea that matter is made up of atoms. A connection was thus forged between the everyday world and the tiny, invisible building blocks that make up this world. Thermodynamics also addresses more practical questions. Have you ever wondered how a refrigerator is able to cool its contents, what types of transformations occur in a power plant or in the engine of your automobile, or what happens to the kinetic energy of a moving object when the object comes to rest? The laws of thermodynamics can be used to provide explanations for these and other phenomena. 76

Temperature and the Zeroth Law of Thermodynamics We often associate the concept of temperature with how hot or cold an object feels when we touch it. Thus, our senses provide us with a qualitative indication of temperature. However, our senses are unreliable and often mislead us. For example, if we remove a metal ice tray and a cardboard box of frozen vegetables from the freezer, the ice tray feels colder than the box even though both are at the same temperature. The two objects feel different because metal transfers energy by heat at a higher rate than cardboard does. What we need is a reliable and reproducible method for measuring the relative hotness or coldness of objects rather than the rate of energy transfer. Scientists have developed a variety of thermometers for making such quantitative measurements. We are all familiar with the fact that two objects at different initial temperatures eventually reach some intermediate temperature when placed in contact with each other. For example, when hot water and cold water are mixed in a bathtub, the final temperature of the mixture is somewhere between the initial hot and cold temperatures. Likewise, when an ice cube is dropped into a cup of hot coffee, it melts and the coffee’s temperature decreases. To understand the concept of temperature, it is useful to define two often-used phrases: thermal contact and thermal equilibrium. To grasp the meaning of thermal contact, imagine that two objects are placed in an insulated container such that they interact with each other but not with the environment. If the objects are at different temperatures, energy is exchanged between them, even if they are initially not in physical contact with each other. For purposes of the current discussion, we assume that two objects are in thermal contact with each other if energy can be exchanged between them by these processes due to a temperature difference. Thermal equilibrium is a situation in which two objects would not exchange energy by heat or electromagnetic radiation if they were placed in thermal contact. Let us consider two objects A and B, which are not in thermal contact, and a third object C, which is our thermometer. We wish to determine whether A and B are in thermal equilibrium with each other. The thermometer (object C) is first placed in thermal contact with object A until thermal equilibrium is reached. From that moment on, the thermometer’s reading remains 77

constant, and we record this reading. The thermometer is then removed from object A and placed in thermal contact with object B. The reading is again recorded after thermal equilibrium is reached. If the two readings are the same, then object A and object B are in thermal equilibrium with each other. If they are placed in contact with each other, there is no exchange of energy between them. We can summarize these results in a statement known as the zeroth law of thermodynamics. This statement can easily be proved experimentally and is very important because it enables us to define temperature. We can think of temperature as the property that determines whether an object is in thermal equilibrium with other objects. Two objects in thermal equilibrium with each other are at the same temperature. Conversely, if two objects have different temperatures, then they are not in thermal equilibrium with each other. Relativity Our everyday experiences and observations have to do with objects that move at speeds much less than the speed of light. Newtonian mechanics was formulated by observing and describing the motion of such objects, and this formalism is very successful in describing a wide range of phenomena that occur at low speeds. However, it fails to describe properly the motion of objects whose speeds approach that of light. Experimentally, the predictions of Newtonian theory can be tested at high speeds by accelerating electrons or other charged particles through a large electric potential difference. For example, it is possible to accelerate an electron to a speed of 0.99c (where c is the speed of light) by using a potential difference of several million volts. According to Newtonian mechanics, if the potential difference is increased by a factor of 4, the electron’s kinetic energy is four times greater and its speed should double to 1.98c. However, experiments show that the speed of the electron – as well as the speed of any other object in the Universe – always remains less than the speed of light, regardless of the size of the accelerating voltage. Because it places no upper limit on speed, Newtonian mechanics is contrary to modern experimental results and is clearly a limited theory. 78

In 1905, at the age of only 26, Einstein published his special theory of relativity. Regarding the theory, Einstein wrote, «The relativity theory arose from necessity, from serious and deep contradictions in the old theory from which there seemed no escape. The strength of the new theory lies in the consistency and simplicity with which it solves all these difficulties ...». Although Einstein made many other important contributions to science, the special theory of relativity alone represents one of the greatest intellectual achievements of all time. With this theory, experimental observations can be correctly predicted over the range of speeds from v = 0 to speeds approaching the speed of light. At low speeds, Einstein’s theory reduces to Newtonian mechanics as a limiting situation. It is important to recognize that Einstein was working on electromagnetism when he developed the special theory of relativity. He was convinced that Maxwell’s equations were correct, and in order to reconcile them with one of his postulates, he was forced into the revolutionary notion of assuming that space and time are not absolute. The special theory covers phenomena such as the slowing down of moving clocks and the contraction of moving lengths. In addition to its well-known and essential role in theoretical physics, the special theory of relativity has practical applications, including the design of nuclear power plants and modern global positioning system (GPS) units. These devices do not work if designed in accordance with nonrelativistic principles. What is an atom composed of? Erwin Schredinger developed the probability function for the Hydrogen atom (and a few others). The probability function basically describes a cloud-like region where the electron is likely to be found. It cannot say with any certainty, where the electron actually is at any point in time, yet can describe where it ought to be. The model based on this probability equation can best be described as the cloud model. The cloud model describes where the electron has probably been and where it is likely to be going. Imagine, as the electron moves it leaves a trace of where it was. This collection of traces quickly begins to resemble a cloud. The probable locations of the electron predicted by Schredinger's equation happen to coincide with the locations specified in Bohr's model. 79

An atom is the smallest particle of any element that still retains the characteristics of that element. However, atoms consist of even smaller particles. Atoms consist of a central, dense nucleus that is surrounded by one or more lightweight negatively charged particles called electrons. The nucleus is made up of positively charged particles called protons and neutrons which are neutral. An atom is held together by forces of attraction between the electrons and the protons. The neutrons help to hold the protons together. Protons and neutrons are believed to be made up of even smaller particles called quarks. Niels Bohr was a Danish scientist who introduced the model of an atom in 1913. Bohr's model consists of a central nucleus surrounded by tiny particles called electrons that are orbiting the nucleus in a cloud. These electrons are spinning so fast around the nucleus of the atom that they would be just a blur if we could see particles that small. In our pictures and exercises the electron appears to orbit in the same path around the nucleus much like the planets orbit the Sun. But, please be aware that electrons do not really orbit in the same path. The electrons actually change their orbit with each revolution. Blackbody Radiation

The radiation emitted from a very hot object (known as blackbody radiation) didn't align with physicists' understanding of light as a wave. Specifically, very hot objects emitted radiation in a specific 80

spectrum of frequencies and intensities, which varied with the temperature of the object. Hotter objects had higher intensities at lower wavelengths (toward the blue/UV end of the spectrum), and cooler objects emitted more intensity at higher wavelengths (toward the red/infrared end of the spectrum). Physicists expected that at very short wavelengths the energy radiated would become very large, in contrast to observed spectra. This problem was known as the ultraviolet catastrophe. German physicist Max Planck solved this puzzle by proposing that atoms could only absorb or emit radiation in specific, non-continuous amounts, known as quanta. Energy, therefore, is quantized – it only exists in specific discrete amounts. For his work, Planck was awarded the Nobel Prize in Physics in 1918. Photoelectric Effect Further evidence that light behaves like a particle was proposed by Albert Einstein in 1905. Scientists had observed that when EM radiation struck a piece of metal, electrons could be emitted (known as photoelectrons). What was troubling was that not all EM radiation created photoelectrons. Regardless of what intensity of light was incident upon the metal, the only variable that effected the creation of photoelectrons was the frequency of the light. If energy exists only in specific, discrete amounts, EM radiation exists in specific discrete amounts, and we call these smallest possible «pieces» of EM radiation «photons». A photon has zero mass and zero charge, and because it is a type of EM radiation, its velocity in a vacuum is equal to c (3*108 m/s). The energy of each photon of light is therefore quantized, and is related to its frequency by the equation: hc E photon  hf  .



In this equation, the value of h, known as Planck's Constant, is given as 6.63*10-34 J•s, and is available from the Regents Physics Reference Table. Einstein proposed that the electrons in the metal object were held in an «energy well», and had to absorb at least enough energy to 81

pull the electron out of the well in order to emit a photoelectron. The electrons in the metal would not be released unless they absorbed a single photon with that minimum amount of energy, known as the work function of the metal. Any excess absorbed energy beyond that needed required to free the electron became kinetic energy for the photoelectron. The animation below demonstrates a high-energy photon of light being absorbed by an electron in an atom. Because the photon has an energy greater than the energy holding the electron to its nucleus, the electron absorbs the photon and is emitted as a photoelectron. The kinetic energy of the emitted photoelectron is exactly equal to the amount of energy holding the electron to the nucleus subtracted from the energy of the absorbed photon. Compton Effect Einstein continued to extend his theories around the interaction of photons and atomic particles, going so far as to hypothesize those photons could have momentum, also a particle property, even though they had no mass. In 1922, American physicist Arthur Compton shot an X-ray photon at a graphite target to observe the collision between the photon and one of the graphite atom's electrons. Compton observed that when the photon collided with an electron, a photoelectron was emitted, but the original X-ray was also scattered and emitted, but with a longer wavelength (indicating it had lost energy). Further, the longer wavelength also indicated that the photon must have lost momentum. A detailed analysis showed that the energy and momentum lost by the X-ray was exactly equal to the energy and momentum gained by the photoelectron. Compton therefore concluded that not only do photons have momentum, they also obey the laws of conservation of energy and conservation of momentum! In 1923, French physicist Louis De Broglie took Compton's finding one step further. He stated that if EM waves can behave as moving particles, it would only make sense that a moving particle should exhibit wave properties. De Broglie's hypothesis was confirmed by shooting electrons through a double slit, similar to Young's Double Slit Experiment, and observing a diffraction pattern. 82

The wavelength of a moving particle, now known as the De Broglie Wavelength, is given by:

h p

 . * Although Blackbody Radiation, the Compton Effect, and De Broglie Wavelengths are not specifically included in the Regents Physics curriculum, they are included here briefly for general knowledge and understanding. Mass-Energy Equivalence In 1905, in a paper titled «Does the Inertia of a Body Depend Upon Its Energy Content», Albert Einstein proposed the revolutionary concept that an object's mass is a measure of how much energy that object contains, opening a door to a host of world-changing developments, eventually leading us to the major understanding that the source of all energy in the universe is, ultimately, the conversion of mass into energy! Conservation Laws If mass is a measure of an object's energy, we need to re-evaluate our statements of the law of conservation of mass and the law of conservation of energy. Up to this point, we have thought of these as separate statements of fact in the universe. Based on Einstein's discovery, however, mass and energy are two concepts effectively describing the same thing, therefore we could more appropriately combine these two laws into a single law, the law of conservation of mass-energy, which states that mass-energy cannot be created nor destroyed. The concept of mass-energy is one that is often misunderstood and oftentimes argued in terms of semantics... for example, a popular argument states that the concept of mass-energy equivalence means that mass can be converted to energy, and energy can be converted to mass. Many would disagree that this can occur, countering that since mass and energy are effectively the same thing, you can't convert one to the other. For our purposes, we'll save these arguments for future courses of study, and instead focus on a basic conceptual understanding. 83

The universal conservation laws we have studied so far this course include: Conservation of Mass – Energy Conservation of Charge Conservation of Momentum

E=mc2 Einstein's famous formula, E=mc2, relates the amount of energy contained in matter to the mass times the speed of light in a vacuum (c=3*108 m/s) squared. Theoretically, then, we could determine the amount of energy represented by 1 kilogram of matter as follows: Question: What is the energy equivalent of 1 kilogram of matter?

Answer: E  mc 2 E  1 kg   3 108

m

/s 

2

E  9 1016 J

This is a very large amount of energy... to put it in perspective, the energy equivalent of a large pickup truck is in the same order of magnitude of the total annual energy consumption of the United States! More practically, however, it is not realistic to convert large quantities of mass completely into energy. Current practice revolves around converting small amounts of mass into energy in nuclear processes. Typically these masses are so small that measuring in units of kilograms isn't practical. Instead, scientists often work with the much 84

smaller universal mass unit (u), which is equal in mass to onetwelfth the mass of a single atom of Carbon-12. The mass of a proton and neutron, therefore, is close to 1u, and the mass of an electron is close to 5*10-4 u. In precise terms, 1u=1.66053886*10-27 kg. One universal mass unit (1u) completely converted to energy is equivalent to 931 MeV. Because mass and energy are different forms of the same thing, this could even be considered a unit conversion problem. If given a mass in universal mass units, you can use this equivalence directly to solve for the equivalent amount of energy, without having to convert into standard units and utilize the E=mc2 equation. Binding Energy The nucleus of an atom consists of positively charged protons and neutral neutrons. Collectively, these nuclear particles are known as nucleons. Protons repel each other electrically, so why doesn't the nucleus fly apart? There is another force which holds nucleons together, known as the strong nuclear force. This extremely strong force overcomes the electrical repulsion of the protons, but it is only effective over very small distances. Because nucleons are held together by the strong nuclear force, you must add energy to the system to break apart the nucleus. The energy required to break apart the nucleus is known as the binding energy of the nucleus. If measured carefully, we find that the mass of a stable nucleus is actually slightly less than the mass of its individual component nucleons. The difference in mass between the entire nucleus and the sum of its component parts is known as the mass defect (Δm). The binding energy of the nucleus, therefore, must be the energy equivalent of the mass defect due to the law of conservation of massenergy. Fission & Fusion Fission is the process in which a nucleus splits into two or more nuclei. For heavy (larger) nuclei such as Uranium-235, the mass of the original nucleus is greater than the sum of the mass of the fission products. Where did this mass go? It is released as energy! A commonly used fission reaction involves shooting a neutron at an 85

atom of Uranium-235, which briefly becomes Uranium-236, an unstable isotope. The Uranium-236 atom then fissions into a Barium-141 atom and a Krypton-92 atom, releasing its excess energy while also sending out three more neutrons to continue a chain reaction! This process is responsible for our nuclear power plants, and is also the basis (in an uncontrolled reaction) of atomic fission bombs. Fusion, on the other hand, is the process of combining two or more smaller nuclei into a larger nucleus. If this occurs with small nuclei, the product of the reaction may have a smaller mass its precursors, thereby releasing energy as part of the reaction. This is the basic nuclear reaction that fuels our sun and the stars as hydrogen atoms combine to form helium. This is also the basis of atomic hydrogen bombs. Nuclear fusion holds tremendous potential as a clean source of power with widely available source material (we can create hydrogen from water). The most promising fusion reaction for controlled energy production fuses two isotopes of hydrogen known as deuterium and tritium to form a helium nucleus and a neutron, as well as an extra neutron, while releasing a considerable amount of energy. Currently, creating a sustainable, controlled fusion reaction that outputs more energy than is required to start the reaction has not yet been demonstrated, but remains an area of focus for scientists and engineers. Matter and Antimatter As we've learned previously, the atom is the smallest part of an element (such as oxygen) that has the characteristics of the element. Atoms are made up of very small negatively charged electrons surrounding, surrounding the much larger nucleus. The nucleus is composed of positively charged protons and neutral neutrons. The positively charged protons exert a repelling electrical force upon each 86

other, but the strong nuclear force holds the protons and neutrons together in the nucleus. This completely summarized our understanding of atomic structure until the 1930s, when scientists began to discover evidence that there was more to the picture, and that protons and nucleons were made up of even smaller particles. This launched the particle physics movement, which, to this day, continues to challenge our understanding of the entire universe by exploring the structure of the atom. In addition to matter we're familiar with, researchers have discovered the existence of antimatter. Antimatter is matter made up of particles with the same mass as regular matter particles, but opposite charges and other characteristics. An antiproton is a particle with the same mass as a proton, but a negative (opposite) charge. A positron has the same mass as an electron, but a positive charge. An antineutron has the same mass as a neutron, but has other characteristics opposite that of the neutron. When a matter particle and its corresponding antimatter particle meet, the particles may combine to annihilate each other, resulting in the complete conversion of both particles into energy consistent with the mass-energy equivalence equation: E=mc2. Forces in the Universe We've dealt with many types of forces in this course, ranging from contact forces such as tensions and normal forces to field forces such as the electrical force and gravitational force. When observed from their most basic aspects, however, we can consolidate all observed forces in the universe into the following four known fundamental forces. They are, from strongest to weakest: 1. Strong Nuclear Force: holds protons and neutrons together in the nucleus 2. Electromagnetic Force: electrical and magnetic attraction and repulsion 3. Weak force: responsible for radioactive beta decay 4. Gravitational Force: attractive force between objects with mass 87

Understanding these forces remains a topic of scientific research, with current work exploring the possibility that forces are actually conveyed by an exchange of force-carrying particles such as photons, bosons, gluons, and gravitons. Classification of Matter The current model of sub-atomic structure used to understand matter is known as the Standard Model. Development of this model began in the late 1960s, and has continued through today with contributions from many scientists across the world. The Standard Model explains the interactions of the strong (nuclear), electromagnetic, and weak forces, but has yet to account for the gravitational force. The search for the theorized Higgs Boson at Fermilab and CERN is an attempt to better unify and strengthen the Standard Model.

Although the Standard Model itself is a very complicated theory, the basic structure of the model is fairly straightforward. According to the model, all matter is divided into two categories, known as hadrons and the much smaller leptons. All of the fundamental forces act on hadrons, which include particles such as protons and neutrons. In contrast, the strong nuclear forces doesn't act on leptons, so only three fundamental forces act on leptons such as electrons, positrons, muons, tau particles and neutrinos. Hadrons are further divided into baryons and mesons. Baryons such as protons and neutrons are composed of three smaller particles known as quarks. Charges of baryons are always whole numbers. 88

Mesons are composed of a quark and an anti-quark (for example, an up quark and an anti-down quark). Scientists have identified six types of quarks. For each of the six types of quarks, there also exists a corresponding anti-quark with an opposite charge. The quarks have rather interesting names: up quark, down quark, charm quark, strange quark, top quark, and bottom quark. Charges on each quark are either one third of an elementary charge, or two third of an elementary charge, positive or negative, and the quarks are symbolized by their first letter. For the associated anti-quark, the symbol is the first letter of the anti-quark's name, with a line over the name. For example, the symbol for the up quark is u. The symbol for the anti-up quark is u. Similarly, scientists have identified six types of leptons: the electron, the muon, the tau particle, and the electron neutrino, muon neutrino, and tau neutrino. Again, for each of these leptons there also exists an associated anti-lepton. The most familiar lepton, the electron, has a charge of -1e. Its anti-particle, the positive, has a charge of +1e. Since a proton is made up of three quarks, and has a positive charge, the sum of the charges on its constituent quarks must be equal to one elementary charge. A proton is actually comprised of two up quarks and one down quark.

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LEXICAL AND GRAMMATICAL TESTS Choose the right variant: 1. The ___________ of energy is one of the most important topics in science and engineering. A) condition B) result C) concept D) solution 2. Even under ideal conditions, less than 15% of the chemical energy in the fuel is used to power the ___________. A) container B) vehicle C) vessel D) substance 3. By the 1820s, chemical experiments had provided __________evidence for the existence of atoms. A) liquid B) gas C) plasma D) solid 4. In 1905, Albert Einstein used ___________to explain the cause of this erratic motion. A) kinetic energy B) kinetic theory C) kinetic sand D) kinetic friction 5. Newtonian ____________is contrary to modern experimental results and is clearly a limited theory. A) liquid B) fluids C) mechanics D) theory 6. An atom is held together by forces of __________between the electrons and the protons. A) nature

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B) attraction C) influence D) movement 7. A proton A) is a negatively charged subatomic particle B) is a subatomic particle rotating around the nucleus C) is the atom of an element with different numbers of neutrons D) is a subatomic particle found in the nucleus of every atom 8. A neutron A) is a subatomic particle contained in the atomic nucleus B) is a subatomic particle moving around the nucleus of every atom C) is a negatively charged subatomic particle D) is the atom of an element with different numbers of neutrons 9. An isotope A) is a subatomic particle contained in the atomic nucleus B) is a positively charged subatomic particle C) is a negatively charged subatomic particle D) is the atom of an element with a different number of neutrons 10. Find a different word 1. idea, conception, reality, notion 2. force, power, effort, hindrance 3. phenomena, concept, element, matter 4. particle, piece, atom, whole 5. energy, charge, power, strength 6. method, action, decrease, growth 7. fraction, system, complex, structure 8. function, inertia, activity, operation 9. analysis, exploration, ignorance, investigation 10. delay, velocity, acceleration, momentum 11. Problems that could theoretically ___________ with Newton’s laws, however, are very difficult in practice. A) solve B) be solving C) solving D) be solved 12. Automobiles powered _________ gasoline engines are very inefficient machines. A) in B) by C) with D) at

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13. We can summarize these results in a statement __________as the zeroth law of thermodynamics. A) know B) knowing C) known D) knew 14. Two objects _______thermal equilibrium _________ each other are at the same temperature. A) at/ in B) of/ with C) with /of D) in/ with 15. Electrons ____________so fast around the nucleus of the atom. A) spinning B) is spinning C) are spinning D) are being spinned 16. Further, the longer wavelength also indicated that the photon _______ momentum. A) must have lost B) must to have lost C) must lost D) must have lose 17. The mass of the original nucleus is _________than the sum of the masses of the fission products. A) great B) greater C) greatest D) the greater 18. The nucleus ______________of positively charged protons and neutral neutrons. A) composed B) are composed C) composes D) is composed 19. Scientists discovered that protons and nucleons ________________of even smaller particles. A) were made B) were made for C) were make D) made from

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20. Antimatter is matter made up ______ particles ______ the same mass as regular matter particles. A) at/ in B) of/ with C) with /of D) in/ with 21. Hadrons ___________further ____________ into baryons and mesons. A) are divided B) is divided C) have divided D) has divided 22. A positron has the same mass as an electron, ______ a positive charge. A) because B) although C) so D) but 23. A proton is a __________charged particle that resides within the atomic nucleus. A) constructively B) positively C) positivity D) aggressively 24. Scientists use the concepts of energy, power, and friction to analyze automobile fuel ______________. A) construction B) creation C) consumption D) expansion 25. Many mechanisms contribute to ______________loss in an automobile. A) impact B) energy C) lack D) inactivity 26. The laws of thermodynamics ______________to provide explanations for these and other phenomena. A) can use B) can to be used C) can used D) can be used

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27. We often associate the concept _________ temperature ________ how hot or cold an object feels when we touch it. A) of/ with B) at/ in C) in/ to D) for /to 28. ____________the objects are at different temperatures, energy is exchanged between them A) when B) if C) unless D) although 29. It is important to recognize that Einstein _______________ on electromagnetism when he developed the special theory of relativity. A) were working B) is working C) was working D) has been working 30. The special theory of relativity has practical applications, __________ the design of nuclear power plants and modern global positioning system (GPS) units. A) including B) included C) having include D) are including 31. Nucleons ___________together by the strong nuclear force. A) are holding B) held C) are held D) was held 32. Fusion, on the other hand, is the ___________of combining two or more smaller nuclei into a larger nucleus. A) process B) light C) fuel D) current 33. Every physical _______________ that occurs in the Universe involves energy. A) process B) flew

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C) veperation D) step 34. The concept of energy can be applied to the dynamics of a mechanical system _______________resorting to Newton’s laws. A) like B) without C) with D) besides 35. It is possible to accelerate an electron to a speed of 0.99c by _________ a potential difference of several million volts. A) to use B) being used C) having been used D) using 36. Protons and neutrons are believed _______________of even smaller particles called quarks. A) be made up B) made up C) to be made up D) to make up 37. ______________the Standard Model itself is a very complicated theory, the basic structure of the model is fairly straightforward. A) Although B) Despite C) In spite of D) However 38. More practically, ______________, it is not realistic to convert large quantities of mass completely into energy. A) although B) despite C) in spite of D) however 39. An atom is ____________particle of any element that still retains the characteristics of that element. A) smallest B) the smallest C) small D) smaller 40. Nucleus is the tiny _________ in which the positive charge is concentrated inside an atom. A) room

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B) vessel C) volume D) plant 41. Automobiles ______________by gasoline engines are very inefficient machines. A) powered B) powering C) power D) have powered 42. Every physical process that occurs in ______ Universe involves energy. A) a B) – C) an D) the 43. Unfortunately, _____________its extreme importance, energy cannot be easily defined. A) Although B) Despite C) In spite of D) However 44. Objects of different masses will fall to _______ Earth at ______ same speed. A) the /the B) the / a C) the / an D) an / – 45. Galileo’s use of ___________ telescope was his most notable achievement in demonstrating ____________ importance of observation. A) an / – B) the / a C) the / an D) the /the 46. Energy changes from one form to another. A) Law of Gravity B) Laws of Motion C) Law of Conservation D) Law of Inertia 47. _________Galileo’s experiments, scientists have come to a better understanding of how the gravitational pull of the Earth accelerates free-falling bodies. A) if

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B) since C) when D) or 48. Gravity helps the Earth to stay just the right distance from the Sun, ____________ it's not too hot or too cold. A) nor B) since C) so D) where 49. Life on Earth needs the Sun's light and warmth to__________. A) launch B) survive C) lost D) leave 50. Objects _______ different masses will fall ______ the Earth ______ the same speed. A) of /on /at B) of /on /in C) of /on /with D) for /to /by 51. The higher the temperature, the faster the _____ are moving around and/or vibrating. A) planets B) cars C) planes D) molecules 52. Electrons orbit around the center, or nucleus of atoms, just like the ___ orbits the earth. A) sun B) sky C) moon D) Mars 53. When the electrons move among the atoms of matter, a current of ____ is created. A) electricity B) gravitation C) relativity D) rotation 54. Photons are created when electrons jump to ____ energy levels in atoms. A) lower

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B) higher C) excited D) exciting 55. This was a great discovery of the nineteenth century – that radio waves, x-rays, and gamma-rays, are just forms of light, and that light is electromagnetic waves. A) solar B) electromagnetic C) radiant D) fluorescent 56. In the Sun, hydrogen nuclei fuse (combine) together to make helium nuclei, in a process called _______, which releases energy. A) fission B) fusion C) fusible D) fisile 57. The energy intrinsically stored in a piece of matter at rest equals its mass times the ____ of light squared. A) speed B) energy C) distance D) power 58. When an ice cube is dropped into a cup of hot coffee, it melts and the coffee’s temperature _____. A) increases B) decreases C) rises D) remains 59. Two objects in thermal equilibrium with each other are at the _____ temperature. A) different B) another C) same D) variable 60. Experiments show that the speed of the electron always remains ___ than the speed of light, regardless of the size of the accelerating voltage. A) same B) faster C) less D) fast

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61. An atom is the smallest _______ of any element that still has the characteristics of that element. A) mass B) particle C) dimension D) spread 62. Atoms consist of a central, dense nucleus that is surrounded by one or more lightweight ________ charged particles called electrons. A) positive B) negative C) negatively D) positively 63. An atom is held together by forces of _______ between the electrons and the protons. A) dispersion B) magnification C) restoration D) attraction 64. Protons and neutrons are believed _______ of even smaller particles called quarks. A) to be make up B) to made up C) to be made up D) to being made up 65. The ______ was standardized as the unit for length after the French revolution, and has since been adopted throughout most of the world. A) kilogram B) meter C) second D) newton 66. Galileo also contributed to the formation of _____ is now called Newton’s first law of motion. A) that B) what C) which D) hence 67. Here on Earth, the ______ of our energy, directly or indirectly, is the sun. A) source B) potential C) mass D) meaning

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68. Formally, ______is the branch of physics dealing with the description of an object's motion, leaving the study of the «why» of motion to our next major topic, dynamics. A) electricity B) kinematics C) optics D) sound 69. Aristotle believed that more massive objects would fall faster than _____ massive objects. A) too B) much C) more D) less 70. Since Galileo’s experiments, scientists have come to a better understanding of how the gravitational pull of the Earth _____ free-falling bodies. A) rotates B) accelerates C) decelerates D) removes

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TEXT WORKING TECHNIQUE Identifying a Topic Sentence As the name suggests, a topic sentence states the topic, or main idea of a paragraph. Usually the first sentence in a paragraph is the topic sentence. In some cases, however, the first sentence of a paragraph does not state the main idea, and the second or third sentence may be the topic sentence. The other sentences in a paragraph supply details that support the main idea. They are called supporting sentences. Some topic sentences try to cover more than can be developed in one paragraph. They try to tell everything in one sentence. A good topic sentence states a subject or idea that can be properly developed in one paragraph. Making Outlines An outline is one way to make notes on what you read. Making an outline is a good way to fix material in your mind. An outline also provides a quick way to review. You will find it helpful to prepare an outline for either an oral or a written report. In making an outline, you list ideas in order of importance. One pattern for an outline follows: 1. Main topic A. Subtopic 1. Points to develop 2. Subtopics The number of main topics, subtopics and development points will vary according to the material being outlined. Identifying Cause and Effect Identifying Cause and Effect relationships is very important for understanding. A cause is an event, person, or condition that makes something happen. An effect is the result or outcome of a cause. For example, the statements below show: 101

1) The cause – and – effect relationship between absolute location and climate in the Caribbean: Islands located between 10 and 27 N < = > warm climate all year; 2) The cause – and – effect relationship between resources and population that exists in the Caribbean region: Too many people and too few resources < = > Over population. Remember that an effect may have several causes. And a cause may have several effects. You, as a student of geography, should be able to identify the main geographic cause or main geographic effect in a situation. To identify cause and effect relationships, follow these guidelines: 1. Look for the clues. Writers often give clues that make it easy to uncover cause and effect relationships. Cause clues include led to, brought about, produced, because, and the reason why. Effect clues include as a consequence, dependent on, give rise to, and outcome. Sometimes you will have to «read between the lines» to identify cause and effect relationship. 2. Check for complex connections. Remember that there may be many causes and effects in a situation. After identifying the main ones, look for the other links between happenings. Climate is one of the most important geographic factors in the physical settings of the Caribbean Islands. In studying the region’s climate, you will note several cause - and - effect relationships. Study the excerpt below. Identify the cause and effect. Because the northeast trade winds sweep the islands, rain falls mostly on the northern sides of the islands. Your completed diagram should resemble the following one: Northeast trade winds Rain falls mostly on the northern sides of the islands. In this case, the word because is the clue that the sentence contains a cause and effect relationship. Composing an essay An essay is a short composition that deals with a specific topic. It should always contain three components – an introduction, a body of information, and a conclusion. 102

1. Select a topic. Unless a topic is assigned, you need to select a topic. Make sure the topic is broad enough to provide enough material for an assay but not broad to be dealt with in brief composition. 2. Organize your idea into an outline. Remember that an essay should have three parts. Organize your thoughts accordingly. 3. Compose your essay clearly state your topic in the introduction. Present your evidence and supporting details in the body. Your conclusion should briefly sum up what you have said in the assay. To practice the skill read and respond to the following directive: «Write an essay in which you describe the religious conflicts that plague the eastern Mediterranean area». Since the topic – religious conflicts that plague the eastern Mediterranean area has already been selected for you. The next step is to gather information and prepare an outline. Your outline should resemble the following one: I. Introduction II. Religious conflicts A. Greek Orthodox and Muslim on Cyprus B. Muslims and Christians in Lebanon C. Muslim conflicts – Shiites and Sunnites D. The problem of Israel E. Jerusalem – holy city for Christians, Jews, and Muslims III. Conclusion Summarizing information As you read, it is not important to remember every word: your mind identifies the main ideas. It then notes the supporting details. In short, your mind summarizes the information presented. You should follow the same steps in writing a summary. A summary highlights the main points about a certain topic. Minor points are usually excluded because the purpose of a summary is to bring out main points. Writing a summary 1. Identify main ideas. As you read material to be summarized, note the main ideas. Also note all important supporting evidence. 2. Use your own words. Restate the main ideas in your own words. Using your own words helps you understand the main ideas. (If you have trouble stating the ideas in your own words, rewrite the material until you feel you understand and can restate it.) 103

3. Recognize relationships. Think in broad terms. Write a list of the main ideas. Look for main ideas that are related and state that relationship as a broad topic. Link all the main ideas to broader topics. Identify a general idea that links all the main ideas and use this idea as your first sentence. Read the extract and write a short summary. Before the development of farming many early people were nomads always on the move hunting and gathering food that grew wild. These hunters and gatherers were at the mercy of nature. If the numbers became too large, or if the animals that they hunted and the wild foods that they gathered were in short supply, some starved. Once the food supply in one place was used up, the group had to move on or go hungry. About 10,000 years ago, in the Middle East, India, Southeast Asia, and China, people discovered that they could raise their own food by planting and cultivating the foods that they had previously gathered. As their knowledge of agriculture – the art and science of farming – increased, people found that they forced to search for food. This meant that they could build permanent settlements. Over hundreds of years these settlements developed into cities. The following paragraph is a summary of the extract. In it the underlined sentences have been restated. Before the development of farming, early people had to search for food. The move hunting and gathering food that grew wild. They moved whenever food sources got too low. About 10,000 years ago people discovered that they could control their food supplies by planting and cultivating plants. Because they no longer had to move in search of food, they could build permanent settlements. Expressing a viewpoint Being informed about and be able to express a point of view is important to a citizen in today’s society. You will be concerned with and may wish to express your viewpoint on a variety of issues. As a student you are also called upon to express your viewpoint – in class discussions, essay tests, and research projects. To effectively express your viewpoint, follow these guidelines: 104

1. Research the topic. Make sure you know what you are talking about. Find what the opposing viewpoints are. 2. Determine your position. Study the evidence and evaluate the situation. Collect data to support your position. 3. State your position clearly. Write an introduction that identifies the issue and states your viewpoint. 4. Support your position. Develop additional paragraphs that provide support for your point of view. End with a concluding paragraph in which you clearly restate your position and reasoning. Understanding Descriptions (a) High mountains and old volcanoes divide the plateau’s southern and into very densely populated basins. (b) Rugged, snowcapped mountains rise from the middle of the parched, semiarid grasslands. Geographers study the physical and cultural features of the earth. They observe and then describe those features. The excerpts above describe the physical setting of Mexico. In the first excerpt the adjectives such as high and old are used to describe around the Mexican Plateau. The verb divide is also used illustrate the effect these mountains have on the plateau’s surface. The adverbial phrase densely populated describes the areas basin. In the second excerpt adjectives such as rugged, snowcapped, parched and semiarid are used to help form a mental picture of the landscape. Many types of modifying words and phrases are used to describe physical and cultural features and actions using such words and phrases give you a clearer image of what is actually like. Understanding geographic descriptions 1. Read the description carefully. Identify basic information that the description contains. Note in general what basic landforms or cultural features are being described. 2. Identify the descriptive words. Note the adjectives, adverbs and other modifying words and phrases in the description. Link the descriptions to the physical settings they modify. If necessary, use a dictionary to define specific descriptive terms. 3. Form a mental picture of what is being described. Note how each descriptive word or phrase helps you bring the mental image of the geographic concept more sharply into focus. 105

Guessing the words In the following excerpt from «Memoirs 1950-1963», former U.S ambassador George Kennan describes the Soviet Union. As you read you come across the words mean out of the context. Notice the words in bold. Try to define the words as they are used. On a sheet of paper write the Russian equivalent or an English synonym for each word without using a dictionary. Then use a dictionary to check your understanding. How close were you t the correct meaning of these words? It was summer – the marvelous summer of central Russia, with its deep blue skies, its fields and ravines, its evergreens and birches and poplars, its straggling villages and onion-domed churches, its far horizons with always the dark dim line of distant forests. The common people, beginning now to recover to some extent from the horrors and privations of the war, and animated, in these final months of the Stalin era, by fear of all political involvement and revulsion to all thought and talk of internal politics, were their characteristics patient, irrepressible vitality – creating a life for themselves, such as they could, within the rigid limits prescribed the system. The collective farmers were permitted now to sell. At open outdoor markets, such surplus produces as they could grow on their own small private plots. The city sub urbanities had likewise their kitchen gardens and sometimes even an animal or two. These various private activities tended to merge; and in this way there was growing up, particularly on the outskirts of Moscow, a form of petty free enterprise – a free enterprise strictly limited but active, busy, and in its way hopeful. There was, therefore, something old – Russian about these suburban communities an atmosphere of health and simplicity and subdued hope. 2. What is the author’s general opinion of Russia and its people?

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FORMULAS AND SYMBOLS Powers х2 – x squared x3 – x cubed 5 3 – five to the third power, the third power of five, five cubed 5-4 – five to the minus fourth power, the minus power of five 52 – five to the second power, the second power of five, five squared 4  2 The square root of four is two The square root out of four is (equals) two 3 27  3 The cube root of twenty seven is three 4 16  2 The fourth root of sixteen is two The square root of a  3 The cube root of a  5

2

5



√ 3 n

7

The fifth root out of a square The fifth root out of a to the power seven square root (out) of [skwɛ: ru:t (aʊt) ɒv] корень квадратный из cube root (out) of [kju:b ru:t (aʊt) ɒv] корень кубический из n-th root (out) of корень n-й степени

Mathematical sings + plus [plʌs] 1.плюс; 2. знак плюс; 3. положительная величина; 4. добавочный, дополнительный minus [mʌinəs] 1. минус; без; 2. знак минус; 3. отрицательная величина; отрицательный plus or minus плюс минус ± minus or plus = ≠ ~ ≈

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1. sign of equality [sain ɒv i'kwɒliti] знак равенства; 2. equals, (is) equal to [' i:kw(ə)l], равняется, равно (is) not equal to неравно difference [' dif(ə)r(ə)ns] разность approximately equal [ə'prɒksimətli 'i:kw(ə)l] приблизительно равно approaches [ə'prəʊtʃiz] достигает значения similar to ['similə] подобный greater than ['ɡreitər] больше (чем) not greater than не больше (чем)

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