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Elementary Knowledge of the Structure of Matter· Motion and "Forces· ·Pressu re of Fluids (Hydrostat i cs and Aerostatics)· Work and Power· En.ergy. Heat Phenomena· Heat Transfer and Work· Changes in the States of Aggregation o f Matter· Heat Engines· El ect ri c i ty· Structure of the Atom· ·E l ectr i c Current · I ts Strbngth , El ectr ic Pote nt ial and Res i stance· El ectric Power and Work Done by El ectr ic Curr ent· El ectromag net iC Phenomena· Junior AV. Peryshkin. N.A.Rodina Mir Publishers Moscow
Thermal Units 1 joule (1J) 1 kilojoule (1 kJ), 1 kJ=1000J Units of Specific Heat 1 joule per kilogram-degree Celcius (1 J/kg°C) Units of Heat of Combustion . Specific Heat of Melting, Specific Heat of Evaporation 1 joule per kilogram (1J/kg) Units of Current 1 ampere (1 A) 1 kiloampere (1 kA), 1kA= 1OOOA 1 milliampere (1mA), 1mA=0.001A 1 microampere {1~-tA),1~-tA=0.000001A Units of Voltage 1 volt (1 V) 1 kilovolt (1 kV), 1 kV=1 OOOV 1 millivolt (1 m V), 1mV=0.001V Units of Resistance 1 ohm (1n) 1 megoh m (:1 Mn), 1 Mn = ·1 ooo ooo n 1 kilohm (1kn),1kn=1000n
Uflits of Length 1 metre (m) 1 kilometre (1km),1km=1000m 1 decimetre (1 dm), 1 dm = 0.1 m 1 centimetre (1 cm), 1cm=0.01 m 1 millimetre (1 mm),1 mm=0.001m Units of Area 1 square metre (1m 2) 1 square kilometre (1km2),1km2=1 OOOOOOm2 1 hectare (1 ha), 1 ha= 10 000 m2 , 1 are =1 0Qm2 1 square decimetre (1dm 2),1dm2=0.01m2 1 square centimetre (1 cm2 ),1 cm2=0.0001 m2 1 square millimetre (1 mm2 ),1 mm2=0.000 001 m2 Units of Volume 1 cubic metre (1m3) 1 cubic kilometre (1km3 ),1 km3=1 OOOOOOOOOm3 1 cubic decimetre (1 drn3), 1 dm3= 0.001 m3 1 cubic centimetre (1 cm 3 ), 1cm 3=0.000 001m3 1 litre (11),11=1dm3 1 millilitre (1ml),1mi=0.0011=1cm3 Units of Speed 1 metre per second (1 m/s) 1 kilometre per hour (1 km/h),1 km/h=0.28m/s 1 cenfimetre per second (1 cm/s),1 cm/s=0.01m/s Units of Force 1 newton (1 N) 1 kilonewton (1 kN), 1kN ~1000N
Junior PHYSICS
A.B.TiepLIIIIKHH H.A.PoAHHa <JIHJHKa Yqe6HHK AJI.II 6-7 KJiaCCOB MocKBa "TipocsemeHHe" 1982
Junior AV Peryshkin N.A.Rodina Transla ted fr om th e Ru ss ia n by lr ene Aleksa n ova Mir Publishers Moscow
Fi~t published 1985 Revised from the 1982 Russian edition TO THE READER Mir Publishers would be grateful for your comments on the content, translation and design of this book. We would also be pleased to receive any other suggestions you may wish to make. Our address is: Mir Publishers 2 Pervy Rizhsky Pereulok 1-110, GSP, Moscow, 129820 USSR Printed in the Union of Soviet Socialist Republics ·Ha aHcAUUCKOM R3blKe © 11J.AaTeJibCTBO «flpOCBeJ.lleHHe», 1982 © English translation, Mir Publishers, 1985
Contents 1 Introduction I. Nature and Mankind 11 2. What Is Physics? 12 3. Body, Substance, Matter 13 4. Observations and Experiments 14 5. Physical Quantities . Measurement of Ph ys ica l Quantities 15 6. Physics, Technology, Nature 16 Elementary Knowledge of the Structure 22 of Matter 7. The Structure of Matter 22 8. Molecules 24 9. Diffusion in Gases, Liquids and Solids 26 10. The Speed of Molecular Motion and the Body Tempera- ture 27 I 1. Mutual Attraction and Repulsion of Molecules 28 I 2. Three States of Matter 30 I 3. The Difference in the Molecular Structure of Solids, Liquids and Gases 32 Motion and Forces 34 14. Mechanical Motion I 5. Uniform and Non uniform Motions I 6. The Speed of Uniform Motion . Units of Speed I 7. Average Speed of Non uniform Motion 18. Calculating the Path and the Time of Motion 19. Inertia 20. Inertia in Everyday Life and in Engineering 21. Interaction of Bodies 22. The Mass of a Body. Units of Mass 23. Defining the Mass of a Body by Balances 24. The Density of a Substance 25. Calculating the Mass and Volume of a Body Density from Its 26. Expressing the Density of a Substance in Terms of the Mass of a M olecule and the Number of Molecules in Unit Volume 34 36 37 39 40 42 44 45 47 49 51 53 54 5
27. The Force 56 28. The Grav itati on. Th e Force of Gravity 58 29. The Elas ti c Force. The Weight of a Body 59 30. Units of Force. T he Rel ation Between the Force of G ravit y and th e Mass of a Body 61 3 I. A Spring Balance 63 32. A Force Is a Vector Quantity 64 33. Addition of Two Forces Directed Along th e Same Straight Line. The Res ultan t of Forces 66 34. The Friction Force 35. Static Friction 36. Friction in Nature and Engineering 37. Intermolecular Forces. The Wetting Phenomenon 38. Pressure. Un its of Pressure 39. Press ure in Nature and Engin eerin g 69 71 72 74 76 78 40. Gas Pressure 81 Pressure of Fluids 84 (Hydrostatics and Aerostatics) 41. Transmission of Pressure by Fluids. Pascal's Law 84 42. Free Surface of a Liquid 87 43 . Pressure in F luids 88 44. Calculating the Pressure of a Liq uid on the Bottom and Walls of a Vessel 90 45. Comm unicating Vessels 92 46. The Weight of Air. Atmospheric P ressure 97 47. The Existence of an Air Envelope of the Earth 98 48. Measuring the Atmospheric Pressure. Torricelli's Exper- iment 100 49. The Aneroid Barometer I03 50. Atmospheric Press ure at Various Alt it udes 104 5 1. Manometers I 06 52. Piston Pumps 108 53. Hydraulic Press I09 54. How a Fluid Acts on a Body Immersed in It 113 55. Buoyancy. Archimedes' Principle 114 56. Flotation 117 57. Why Ships Keep Afloat 120 58. Aeronautics 122 Work and Power. Energy 125 59. Mechanical Work. Un its of Work 125 60. Power. Units of Power 127 6
61. Simple Mechanisms 131 62. A Lever. Equilibrium of Forces on a Lever 132 63. Levers in Engineering, in Nature and in Everyday Life 134 64. Application of the Lever Law to a Pulley 138 65. Equality of the Amounts of Work Done with the Use of Simple Mechanisms. The "Golden Rule" of Mechanics 140 66. The Efficiency of a Mechanism 142 67. Energy 143 68. Potential and. Kinetic Energies 144 69 . Transformation of One Kind of Mechanical Energy into Another 147 2 Heat Phenomena 150 Heat Transfer and Work 150 70. Thermal Motion 150 7 1. Internal Energy 151 72 . Means of Changing the Internal Energy of a Body 153 73. Heat Conduction 155 74. Heat Convection 157 75. Convection in Nature and Engineering 159 76. Heat Radiation 161 77. Examples of Heat Transfer 163 78. Quantity of Heat. Units of the Quantity of Heat 164 79. Specific Heat Capacity 166 80. Calculatin g the Heat Required to Raise the Temperature of a Body and That Given Off by a Cooling Body 167 8 1. Energy of F uel. Heat of Fuel Combustion 169 82. The Law of Conservation and Transformation of Energy {; Mechanical and Thermal Processes 171 Changes in the States of Aggregation 173 of Matter 83. States of Aggregation of Matter 173 84. Melting and Solidification of Crystalline Bodies 174 85. The Graph of Melting and Solidification of Crystalline Bodies 175 86. Melting and Solidification from the Point of View of Teaching on the Molecular Structure of Matter 176 87. Specific Heat of Melting 177 88. Energy Release in Solidification of a Substance 179 89. Evaporation and Condensation 180 90. Absorption of Energy in Evaporation of Liquids and Its Release in Vapour Condensation 182 91. Boiling 183 7
92. Specific Latent Heat of Vaporization and Condensation 184 93. How the Quantities of Heat Can Be Calculated 186 Heat Engines 188 94. Work Done by the Expanding Gas or Steam 188 95. The Internal Combustion Engine 189 96. The Steam Turbine 192 97. The Efficiency of a Heat Engine 194 Electricity 196 Structure of the Atom 196 98. Contact Electrization of Bodies. An Electric Charge 196 99. Two Kinds of Charges. Interaction of Charged Bodies 197 I 00. The Electroscope. Conductors and Nonconductors of Electricity 199 I 0 I. An Electric Field 200 I 02. Divisibility of an Electric Charge 201 I 03. Ioffe's and Millikan's Experiments. The Electron 203 I 04. Rutherford 's Experiment. The Nuclear Model of an Atom 205 105. Atomic Structure 207 I 06. The Electrization of Bodies Explained 209 Electric Current. Its Strength, Voltage and Resistance 212 107. Electric Current 212 I 08. Sources of Electric Current 213 I 09. An Electric Circuit and Its Components 216 110. Electric Current in Metals 217 Ill. Electric Current in an Electrolytic Solution 219 112. The Effects of Electric Current 220 113. The Direction of Electric Current 222 114. The Current. Units of Current 223 115. The Ammeter. Measuring the Current 225 116. The Voltage 227 117. Units of Voltage 228 118. The Voltmeter. Measuring the Voltage 230 119. The Relationship Between Current and Voltage 232 120. The Resistance of Conductors. Units of Resistance 234 121. Ohm's Law for a Part of a Circuit 235 122. Calculating the Resistance of a Conductor. Resistivity 239 123. Examples of Calculating the Resistances of Conductors, the Current, and the Voltage 241 124. Rheostats 242 8
125. Conductors Connected in Series 244 126. Conductors Connected in Parallel 24 7 Electric Power and Work Done by Electric Current 250 127. Electric Power 250 128. Work Done by Electric Current 251 129. Heating of Conductors by Electric Current. Joule's and Lenz's Law 253 130. An Incandescent Lamp. Electrical Heating Devices 255 131. A Short Circuit. Safety Devices 259 Electromagnetic Phenomena 262 132. A Magnetic Field 262 133. The Magnetic Field of a Direct Current. Lines of Magnetic Force 263 134. The Magnetic Field of a Coil with Current 265 135. Electromagnets and Their Application 266 136. Permanent Magnets. The Magnetic Field of Permanent Magnets 269 137. The Magnetic Field of the Earth 271 138. The Telephone 273 139. The Electric Motor 274 140. The Phenomenon of Electromagnetic Induction. Electric Current Generator 278 141. Use of Electric Power in the USSR 281 \ Laboratory Work Answers to the Exercises Material for Supplementary Reading Brownian Movement Weightlessness The Force of Gravity on Other Planets A Hydrostatic Paradox. Pascal's Experiment Pressure at the Bottom of Seas and Oceans. of Sea Depths Pneumatic Machines and Instruments The Discovery of Atmospheric Pressure A Legend about Archimedes 284 303 304 304 305 306 307 Investigation 309 311 312 313 9
The Energy of the Moving Water and Wind. Hydraulic and Wind Motors 3 14 Use of th e Solar Energy on th e Earth 316 Amorphous Bodies. Melting of Amorphous Bodies 3 17 Metal Casting 318 A Refrigerat or 3 19 Review Questions 320 Answers to the Review Questions 333 Index 334
1 Introduction 1. Nature and Mankind The en tire material world around us - the air, water, earth, human beings, plants, animals, the sun, the planets, and the universe - is called nature. Nature was not created by anyone ; it always ex isted and wi ll always exist. It va ries o r moves continuously. The planets and the stars are in motion. Rivers change their courses. Plants and animals grow and develop. Human beings also change nature continuously with their wits and labour. Over the centuries mankind has constructed towns, settlements, works, and factories, ploughed and sowed fields, invented various machines. As human knowledge of nature increased, scientists began to classify it into various branches of science. They found that all the alterations occurring in nature are regular, i.e., every phenomenon has a cause. For instance, various objects fall to the earth because they are attracted by the earth's gravity. Day is followed by night since the earth rotates about its axis (Fig. 1). Wind originates partly as the result of the nonuniform heating of the air. Natural sc iences study the laws of nature and apply them to meet human nl;!eds. The natural sciences develop constantly. As our understanding of natural phenomena improves, we find more and more practical applications for them. \ F ig. I 11
Lomonosov, (1711 - 1765) Mikhail Vasilyevich 2. What Is Physics? Physics is one of the natural sciences. The word physi<.:s originates from the Greek word for nature, fusis . Physics studies mechanical, thermal, electrical and light phenomena, all of which are known as physical phenomena. Melting ice, boiling water, a falling stone, a glowing filament in an electric lamp, and a flash of lightning are examples of physical phenomena. The other natural sciences-astronomy, chemistry, geography, botany, and zoology - all make use of the laws of physics. Geographers, for example, use physical laws to explain changes in the climate, the flow of the earth's rivers, or the origin of wind. The laws of physics are employed by zoologists to explain the movement of terrestrial animals and fish, the emission and perception of sounds by animals, and the structure of their organs of sight. Physics is one of the most oldest sciences. The first physicists were Greek scientists who lived hundreds of years before the birth of Christ. They were the first to offer explanations of the surrounding natural phenomena. The word "physics" was first introduced by the ancient scientist Aristotle (384-322 B. C.). The word first appeared in Russian in the work of the great Russian scientist M. V. Lomonosov. Progress in the field of physics is the result of research by <;cientists from many countries. Important discoveries in physics were made by Galileo Galilei, Isaac Newton, M. V. Lomonosov, Michael Faraday, D . I. Mendeleev, Pierre and Marie Curie, Ernest Rutherford, Albert Einstein, A. F. Ioffe, S.l. Vavilov, I. V. Kurchatov, and others. Mikhail Vasilyevich Lomonosov, the first Russian academician, is an outstanding figure in the history of Ru ssian science. The extremely diligent Lomonosov worked successfully in a number of scientific disciplines. The 12
eminent Russian writer A. S. Push kin wrote that the prodigious Lomonosov not only founded the first Russian university, but was himself "o ur first university". • ) 1. What is physics? 2. What does physics study? 3. Give examples of physical phenomena. 4. Why is physics regarded as one of the principal natural sciences? 5. Who introduced the word "physics" into science? 3. Body, Substance, Matte r In addition to an ordinary vocabulary, physics has a special vocabulary of terms to designate physical notions. Some of these terms, for instance, "electricity", "energy", "outer space", have gradually crept into everyday speech. Certain words from our spoken language acquire another meaning when used in physics. Thus, the word "body" normally refers to the body of a man or an animal. In physics, however, a phys1cal hud:. is used to denote not only those bodies but also a house, a tractor, the moon, a grain of sand, i.e., any object. Figure 2 shows several physical bodies: a pencil, a water tap, a drop of water, a balloon filled with air. Every body has a shape and occupies a certain volume. Figure 3 shows two bodies that are different in shape but equal in volume: a piece of plasticine and an elephant moulded from the same piece of plasticine. Figure 4 shows two spoons, bodies of different volumes but identical in shape. A physical body is made of physical material called a sub~tancc . Iron , water, salt, and hydrogen are all substances. Water is a substance, and a drop of water is a physical body. Aluminium is also a substance, and an aluminium spoon is a physical body. A substance is a kind of mattc1 . Scientists use the word "matter" to denote Fig. 2 Fig. 3 Fig. 4 13
everything that exists m objective reality, 1.e., independently of our consciousness. ? l. What d o the words " physical body" mean in physics? 2. What is a substance? Give examples of physical bodies and substances. 4. Observations and Experiments Everybody knows that ice melts in warm conditions, that water freezes in the cold, that a magnet attracts iron objects, and so on. Where do we get this knowledge? People obtain most of their knowledge by observation . Thus, we can all see that unattached bodies fall to the earth. We accumulate our knowledge about nature through observation. Scientists also obtain knowledge by observation, especially of particular controlled experiments that are always carefully planned in advance. To study falling bodies, for example, the Italian scientist Galileo Galilei dropped various balls from the leaning tower of Pisa (Fig. 5) and measured the time of their descent. With experiments of this kind, Galileo was able to describe the laws governing falling bodies. Fig. 5 14 Observation and experimentation are the sources of physical know ledge. To obtain scientific information about the world around us, we have to consider and explain our experimental results and find the causes of the phenomena we observe. We need various physical instruments to conduct experiments. Some of the instruments are very simple and intended for simple · measurements: a rule, a graduated cylinder (a measuring glass) used to measure the volume of liquids (Fig. 6), a weight suspended by a thread, which can serve as a plumb line (Fig. 7). More intricate instruments include ammeters, voltmeters (Fig. 8), stopwatches (Fig. 9), and thermometers (Fig. 10). Instruments became more exact and complicated with the development of physics and technol- ogy.
Fig. 9 Fig. 6 Fig. 8 Fig. 10 Modem physicists have very elaborate instruments at their disposal, which were developed jointly by scientists, engineers, technicians, and workers, and make it possible to study the structure of matter. Huge instruments, in fact, enormous and very intricate installations, have thus been built in the town of Dubna near Moscow, USSR. One of them, a proton synchrotron, is about 60 metres in diameter ; the magnets that make up the synchrotron contain 36 000 tons of steel. Scientists from various socialist countries are involved m research using this synchrotron. ? I. How do we obtain knowledge about natural phenomena? 2. What is the difference between observations and experiments? 3. What physical instruments do you know? 5. Physical Quantities. Measurement of Physical Quantities To obtain the most accurate knowledge about physical phenomena, we must make measurements in the course of ex periments. To know how the volume of water depends on temperature, for instance, it is necessary to measure both these quantities while heating the water. 15
Volume and temperature are examples of physical quantities. Length, area , time, speed, mass, and force are also physical quantities. A physical quantity can always be measured. A quantity is measured by comparing it with a similar quantity that is accepted as a unit ofmeasurement. To measure the length of a table, for instance, we must compare it with a length that is accepted as a unit length, say, with the metre. We will then know its numerica l value m conventionalunits. There are special units to measureevery physical quantity. Area, for example, can be measured in squaremetres. A time unit (I s) measurestime, and volume can be expressed in cubic metres. For the sake of convenience, nearly all the countries of the world have adopted the same units for measuring physical quantities. I . What does it mean to measure a quantity? 2. What units of length, area, and volume do you know? 3. Give exampl es of phys-ical quantiti es . 6. Phys ics, Technology, NatureThe second half of the twentieth century is the age of the scientific and technical revolution. Characteristic of this modern age is the wide and rapid introduction of discoveries made in physics, mathematics, chemistry, biol- ogy, geography, and other sciences into technology, industry, and every- day life. A television tower (Moscow, Ostankino)16
A passenger jet plane Physics is the foundation of modern technology, which means that various technical devices use the phenomena and laws of nature discovered and studied by physicists. Thus, internal combustion engines, for instance, which actuate cars, tractors, diesel locomotives, tanks, ships furrowing seas and rivers were produced as a result of studying various heat phenomena. Grain harvesting by a "Kolos" combine harvester 17 2 - 97 1
A "Kamaz" truck ER-200 electric train (develops a speed up to 200 kmjh) 18
Popov, Aleksandr Stepanovich Zhukovsky, Nikolai Egorovich (1859- 1906) (1847- 1921) Electricity was discovered several centuries before B. C., but it was applied only in the second half of the nineteenth century, when many electrical phenomena and laws were discovered and studied. Today, electric light, electrical heating devices, telegraph, radio, and television are permanent fea- tures of our everyday life. In factories, works, and mines, machine-tools and various devices are powered by electric engines. In metallurgy, high-grade steels and many kinds of precious metals are obtained in electric furnaces. Electricity fmds use in city transport and in railways, it is effectively employed in agriculture. Cinema and television are based on the knowledge of light and acoustic phenomena. We can cite many other examples of a pplying physical knowledge in engineering. In their turn, the scientists use the achievements of technology, perfect machinery and precise measuring instruments to make new discoveries in physics. Space exploration, for instance, would have been impossible without powerful rockets created by physicists. Science and engineering are closely interrelated. Discoveries made in science provide for further development of technology, and the development of engineering is .conducive to ever new achievements in science. Physics is of great importance for the understanding of many phenomena of organic and inorganic world. It was physics, for instance, that explained the nature of lightning and thunder, helped understand the structure of the Sun and stars, the origin of earthquakes and whirlwinds. X-rays discovered in physics allows us to observe the skeleton and the internal organs of man and animals. Ultrasound studied by physicists helps understand how bats find ~their bearings in darkness, how dolphins move in the sea, and many other things. The Soviet Union can boast of many eminent scientists who contributed much to the development of engineering as well as science. 19 2•
Vavilov, Sergei Ivanovich (1891 - 1951) Tsiolkovsky, Konstantin Eduardovich (1857- 1935) Radio, one of the most important means of modern communication, was invented by the Russian scientist Aleksandr Stepanovich Popov. On May 7, 1895 he read a communication concerning an invention of a device which could receive electric signals without conductors. That day went down in the history of world culture as the date of one of the outstanding inventions, the radio, which is now in such a wide use. Nikolai Egorovich Zhukovsky, whom Lenin called "the father of the Russian aviation", was a Russian scientist who contributed much to the development of aviation. Zhukovsky and his colleagues laid the foundations for aviation in the Soviet Union. Passenger airliners can fly at a speed of 900 km/h (250 m/s) and carry 350 passengers, while cargo airplanes take up to 40 tons of cargo on board. Electric light is to the credit of the Russian engineers Pave! Nikolaevich Yablochkov and Aleksandr Nikolaevich Lodygin. Daylight lamps became widely practised after they were perfected by Sergei lvanovich Vavilov. Konstant.in Eduardovich Tsiolkovsky wa s the first to study the laws of jet propulsion. He designed a flying apparatus, a rocket intended for flights from the earth to other planets of the solar system. Tsiolkovsky's research was used by scientists and engineers in preparing for space flights. The achievements of Soviet science and engineering are known far and wide. Our country was the first to construct an electric power station that operates on atomic energy and to launch a satellite of the earth. The world's first space rocket, which became a new planet of the solar system, was Soviet, and a Soviet rocket was the first to reach the moon. The first man in space was the Soviet cosmonaut, Yuri Alekseevich Gagarin. The exploration of outer space rapidly increases. Dockings of spacecraft are carried out, complicated research is performed on board the spaceships, flights became considerably longer. 20
Gagarin, Yuri Alekseevich (1934- 1968) Korolev, Sergei Pavlovich (1907- 1966) The Soviet scientist Sergei Pavlovich Korolev made a great contribution to the scientific and technica l elaboration of space flights . The development of atomic power engineering in our country is associated with the name of Igor Vasilyevich Kurchatov. Kurchatov headed the research concerned with the harnessing of nuclear ene rgy. As a result, the first Soviet uranium-graphite nuclear reactor was sta rted up in December 1946 ; the first atomic electric station in the world was constructed in the town of Obn insk in 1954, and that was the beginning of the use of a tomic energy for peaceful purposes. •) What does physics mean for engineering? for studying organic and inorganic world? Give examples to illustrate your answers. Kurcha tov, Igor Vasilyevich (1903- 1960) 21
Elementary Knowledge of the Structure of Matter 7. The Structure of Matter Physicists not only observe and describe phenomena and properties of bodies but also try to explain them. How would you explain, for instance, that water spilled on the smooth floor spreads over it instead of staying put? Why is it easy to compress gas and very difficult to do so with solids and liquids ? Why is it easier to bend or flatten out a piece of heated steel than a piece of cold steel? We can answer these and many other questions only if we know the structure of matter. Knowing the structure of matter we can not only explain many physical phenomena but also predict them, realize what can be done to accelerate or slow them down, i.e., to control natural phenomena. Having studied the structure of bodies, we can explain their properties and even create new substances possessing the necessary properties, such as hard and strong alloys, heat-resistant materials. Science helped to create such materials as plastics, artificial rubber, kapron, nylon. All of them have found wide application in engineering, medicine, everyday life. Certain phenomena and experiments enable us to form an opinion on the structure of matter. If we take a ball and compress it, the volume of the air in it will decrease. We can compress a piece of rubber or wax and thus decrease its volume. The volume of a body also changes upon heating or cooling. Figure 11 shows a glass flask whose neck is immersed in water. Upon heating, the air displaces the water from the neck of the flask and its bubbles begin to come out, and this means that the volume of the air increases upon heating (Fig. lla). When the flask is cooled, water enters it. This signifies that the volume of the air remaining in it has decreased (Fig. llb). Fig. 11 (b) Fig. 12 22
Fig. 13 (a) (b) A steel ball, which passes freely through a ring, will become larger upon heating and stick in the ring (Fig. 12). When the ball cools down, its volume will decrease and it will again pass through the ring. We can make a test with heating a liquid in a flask (Fig. 13) and make sure that it expands because its level in the neck of the flask rises. Thus, experiments show that the volumes of bodies can change, either increase or decrease. What is the cause of this phenomenon? We can explain this phenomenon assuming that substances con:;ist of -.~parate particles with spaces between them. When the particles move far apart, the volume of the body increases. When the particles move closer together, theirvo lume decreases. Assumptions of this kind are called hypotheses in science, and their validity is verified by means of experiments. Why do the substances, such as water, steel, wood, seem to be solid? The matter is that the particles forming the substances are so small that we cannot see them. The following experiment can give us an idea of the size of the particles. A small grain of paint is dissolved in a glass of water. Then, a certain amount of co loured water is poured off into another glass and the glass is filled up with pure water. The solution in the second glass is less coloured than in the first. A small amount of the solution is poured from the second glass into a third and the third glass is again filled up with pure water. The procedure is repeated several times and each time the solution becomes lighter. Let us consider the last solution. Although it is very light, it is uniformly co lo ured. Consequently, its every drop contains particles of the paint. But remember that we have dissolved a tiny grain of paint in the water and only a pa rt of it has got into the last solution. This means that the grain consists of many particles whose size is very small. These and many other observations and experiments, which will be considered later on, show that all bodies consist of vcr\ small particles. 1. Why should we know the structure of matter ? 2. What materials created by man do you know? 3. What phenomena show th a t substances consist of pa rticles with spaces between them ? 23
4. How does the volume of a body change when the distances between the particles decrease or increase? 5. How can we show that the size of the particles is very small? 8. Molecules The fact that substances consist of tiny particles was believed very long ago. This was stated by the Greek scientist Democritus about 2500 years ago. Whereas in antiquity scientists only assumed that substances consist of separate particles, the existence of the particles was proved by science at the beginning of the 20th century. The particles many substances consist of are called molecules. 1 A molecule of a substance is the tiniest particle of that substance. The smallest particle of water is a molecule of water, the smallest particle of sugar is a molecule of sugar and so on. What is the size of a molecule? We can crush a piece of sugar into very small grains and grind a grain of wheat into flour. Oil, spreading over water, forms a film which is 40 000 times as thin as a human hair. But both a grain of flour and an oil film contain not one but many molecules. This means that the size of the molecules of these substances is still smaller than that of a grain of flour or the thickness of the film. We can give the following comparison: a molecule is as many times smaller than a medium-sized apple as the apple is smaller than the earth. Molecules of various substances differ in size but all of them are very small. Modern instruments, electron microscopes, have made it possible to see and to photograph the largest molecules, and these photographs confirm the existence of molecules once again. Molecules being extremely small, there is an enormous multitude of them in every body. One cubic centimetre of air contains such a number of molecules that if we pile up the same number of sand grains, we shall obtain a hill that would cover a large mill. All bodies in nature differ somewhat from one another. There are no people with identical faces. You cannot find two quite similar leaves on the same tree. Even in a heap of sand you cannot find identical grains. Millions of balls of the same kind and size are produced for ball-bearings at the factories . But should we wish to measure them more accurately than it is done at the factory, we shall make sure that there are no two quite similar balls. Is there any difference between the molecules of the same substance? Numerous complicated experiments have shown that molecules of the same substance are alike. Every pure substance consists of identical molecules inherent only in that substance. This is a wonderful fact. We cannot, for instance, distinguish between the water obtained from some juice or milk and 1 A molecule is a Latin word for a tiny mass. 24
Fig. 14 Fig. 15 the water obtained by distilling sea water since the molecules of water are similar and no other substance has molecules of this kind. Although molecules are very small particles of a substance, they are, nevertheless, divisible. The particles constituting molecules are called atoms. For example, a molecule of oxygen consists of two identical atoms. A water molecule consists of three atoms, one atom of oxygen and two atoms of hydro- gen. Figure 14 illustrates two molecules of water. Such a schematic representation of molecules is accepted in science since it corresponds to the properties of molecules studied in physical experiments and is called a model of a molecule. When two water molecules are divided, four atoms of hydrogen and two atoms of oxygen are obtained. Every two atoms of hydrogen together form a molecule of hydrogen and the atoms of oxygen form a molecule of oxygen, as can be seen in the schematic representation in Fig. 15. Atoms are not indivisible particles either, they consist of still smaller particles called elementary particles. ? l. How do we call particles that make up substances? 2. What observations confirm that molecules are small in size? 3. What do you know of the size of molecules? 4. What do you know of the composition of a water molecule ? 5. What experiments and reasonings confirm that all molecules of water are identical ? Exercise l As is known, drops of oily liquid spread over the water surface forming a thin film . Why does oil stop spreading when the film attains a certain thickness? Assignment Use colour plasticine to make models of two water molecules. Then use those molecules to form models of the molecules of oxygen and hydrogen . 25
9*. Diffusion in Gases, Liquids and Solids 1 Numerous experiments show that molecules of a ll bodies are in perm anent motion . Let us consider one of them. A water solution of copper sulphate is poured into a glass vessel. The solution is dark blue and is heavier than water. Pure water is poured over the solution in the vesse l very carefully, lest the liquids are mixed up. At the beginning of the test, a sharp interface can be seen between the water and the solution of the copper sulphate. We leave the vessel for a time and begin to keep watch of the interface between two liquids. Several days later the interface begins to spread. In another two weeks, the interface separating one liquid from the other vanishes and now the vessel contains a homogeneous liquid light blue in colour. This signifies that the liquids have mixed up. The mixing of substances without external force is called diffusion .1 Here is the explanation of this phenomenon (Fig. 16). First, due to their motion, separate molecules of water and copper sulphate, which are close to the interface, change places. The interface becomes less distinct since the molecules of the copper sulphate get into the lower layer of the water and, conversely, the molecules of the water get into the upper layer of the solution of copper sul- phate. Then a part of these molecules change places with those lying in the adjacent layers. The interface between the liquids becomes still less distinct. Since the molecules move continuously and at random, finally the liquid in the vessel becomes homogeneous. Diffusion in gases is more rapid than in liquids. If we take some substances with a strong scent, say, naphthalene, into the room , very soon its scent will spread throughout the room. This means that the molecules of naphthalene penetrate everywhere, i.e., diffusion takes place. The molecules of naphthalene, moving at random, collide with the molecules of the air and scatter all over the room. 1 Asterisks are used to mark the sections which are supplied with a Material for Supplementary Reading at the end of the book. Fig. 16 26 2 Diffusion, from the Latin spreading, extending. ........................................................ .....................................................·····••·••··...... ......... ......................... ....... ................. ... .. .......... ........... .......... .. .......• • • • • ••• • • •• • ••• •• ••••••••••••••••..... ............. ............ ...................................... .·..·...... .......... .·.·.·.·.·.· .·.·.·.·.......... ......... .............................. ........... .............········............................................... ................................... ....................... ............ ........... ............ ............................................................ ... :. ~ : · ~ ·. ::: .........·.......................................... .::::: ~: ~:: · ............................................................: :: ::::::; :···....... .·.~ .......: ........·.··....................... .
Diffusion occurs in solid bodies too, but very slowly. In one of the experiments, smooth plates of lead and gold were put on one another and compressed by means of a weight. At ordinary room temperature (about 20 °C), five years were needed for the gold and lead to adhere and penetrate each other to the distance of 1 mm . The result was a thin layer of gold and lead alloy. Diffusion is of considerable importance in the life of man and animals. Thus, for instance, oxygen from the environment penetrates into a human body through the skin due to diffusion. It is also due to diffusion that nutrients get into the blood of the animals from their guts. Diffusion is also at work when metal parts are soldered. ' ) 1. What is diffusion? Describe the experiment which is made to observe diffusion in liquids. 2. How can diffusion be explained from the point of view of the structure of matter? 3. In what processes and how does diffusion occur in the body of a man or animal ? Exercise 2 1. What phenomenon do we bear in mind when we pickle cucumbers, cabbage, fish , and other products? 2. There are always molecules of gases, which are a constituent part of air, in the water of rivers, lakes, and other water reservoirs. Due to what phenomenon do the molecules get into the water? Why do they reach the bottom of the reservoir ? Describe how the water is mixed with the air in this case. Assignments 1. Take a glass of cold water and drop a small piece of potassium permanganate into it. Without stirring the water, determine the time in which the molecules of potassium permanganate will reach the upper layer of water. Explain the phenomenon observed. 2. Take two glasses containing equal quantities of water. Put one of them in a warm place and the other in a cold place (say, in a refrigerator). Some time later, put a piece of slate from an indelible pencil (or a drop of potassium permanganate) in each of them. Put the glasses in their places. In the morning and in the evening mark the interface between the pure and the coloured water in the glasses. Draw a conclusion on the basis of this experiment. 3. Read the section concerning the Brownian movement at the end of the book . 10. The Speed of Molecular Motion and the Body Temperature Such phenomena as, for instance, heating or cooling of air, melting of ice, melting of metals, boiling of water are known as thermal phenqmena. We know that when: we heat cold water it first becomes warm and then hot. A heated stove (or water radiator) gradually cools down and the air in the room becomes warmer. 27
The words "cold", "warm", "hot" designate the thermal state of a body. One of the quantities characterizing the thermal state of a body is tern pera ture. The temperature of hot water is higher than that of cold water. In winter, the temperature outdoors is lower than in summer. As is known, the body temperature is measured by a thermometer. The unit of temperature is a degree. If we decide to watch the diffusion of liquids in two vessels, one of which we put in a cold place and the other in a warm place, we shall see that at a higher temperature the diffusion is faster. This means that the speed of motion of molecules and the body temperature are interdependent. The higher the speed of the molecules of a body, the higher its temperature. Warm water consists of the same molecules as cold water. The only difference is that the molecules of warm water move faster than those of cold water. ? 1. What thermal phenomena do you know? 2. How does diffusion proceed at high and at low temperature? 3. What is the connection between the temperature of a body and the speed of motion of its molecules? 4. What is the difference between the motion of molecules of cold water and that of molecules of warm water? Exercise 3 1. Why do sugar and sa lt melt faster in hot water than in cold water? 2. In what pickle, hot or cold , do cucumbers become salted faster ? Why? 11. Mutual Attraction and Repulsion of Molecules We can see that solids and liquids do not disintegrate into separate molecules, although the molecules are spaced and are in constant random motion. Solids not only do not disintegrate into separate molecules, it is even difficult to stretch or break them. How·can we explain that molecules in bodies not only keep close to one another but it is even difficult in some cases to increase the spaces between them? The matter is that there is mutual attraction between molecules. Every molecule attracts the neighbouring molecules and is itself attracted by thern . However, if we break a piece of chalk into two parts and then again put the parts together, they will not keep close together. Why? The attraction between molecules becomes noticeable only when they are very close together. At the distances slightly larger than the molecules themselves, their attraction is considerably weaker. A negligibly small space between the particles of chalk (smaller than 0.000001· cm) is sufficient to weaken the attraction between the molecules appreciably. As to pieces of putty or 28
plasticine, the cohesion between them can be easily attained. This is because they can be put as close together as is necessary for the force of attraction to act. Two pieces of lead applied to each other by their fresh cuts stick together and cannot be torn off even when a considerably large force is applied (Fig. 17). Pieces of broken glass do not stick together. Now if we heat the edges of the pieces so that they begin melting, then we can attain a strong connection. This phenomenon underlies welding of metals as well as so ldering and gluing. Thus, there is mutual attraction between molecules, which is noticeable only at distances smaller than the molecules themselves. But then the question arises: why are there spaces between molecules? The molecules would seem to attract one another and stick together. It does not occur because coming too close together they repel each other. The existence of this repulsion is supported by many phenomena. For example, compressed bodies straight- en out because in a compressed state molecules are so close that they repel each other. Fig. 17 ? 1. Why do solids and liquids not disintegrate into separate molecules by themselves? 2. Under what conditions is the attraction between molecules noticeable ? 3. Why do two pieces of chalk not stick together under pressure whereas two pieces of putty or lead do ? What phenomena can you cite which indicate that molecules not only attract one another but also repel one another? 29
12. Three States of Matter In winter, water on the surface of lakes and rivers freezes and passes into a solid state, ice. Under the ice, water remains liquid (Fig. 18). Here two different states of water, solid (ice) and liquid (water), exist simultaneously. There is also a third, gaseous, state of water, i. e. , an invisible water vapour in the air around us. You can see liquid mercury in the glass tube of a thermometer. There is mercury vapour over its surface, which is a gaseous state of mercury. At the temperature of - 39 °C mercury solidifies and passes into a solid state. Using water and mercury as examples we can see that substances in nature can be in three states : solid, liquid, and gaseous. The properties of bodies differ in different states. A solid body is difficult to compress or stretch in ordinary conditions, it retains its volume. An effort must be made to change the shape of a solid body, say, to bend or to tear it. A solid body has a property of retaining its volume and shape. Liquid changes its shape easily and acquires the shape of its container. In ordinary conditions, only small drops of liquid have shape, that of a ball. Such ball-shaped drops of water can be seen while the dew is still on the ground (Fig. 19). The property of a liquid to change its shape easily is used in manufacturing glassware from melted glass (Fig. 20). · While it is easy to change the shape of a liquid, it is very difficult to change its volume. There is a description of an experiment that went down in history, consisting in an attempt to compress water: the water was poured into a lead ball which was soldered to keep the water from flowing out on compression. Then the lead ball was stricken by a heavy hammer to compress the ball and the water inside it. And now what? The water did not compress, but leaked through the walls of the ball. Consequently, liquids retain their volume but easily change their shape. Many gases are transparent and colourless and, therefore, we cannot see them. We cannot see air, for instance. But moving fast, in a car or in a train , or when there is a wind, we feel the presence of air around us. Let us take a glass, turn it upside down, and try to immerse i.t in water. The water will not fill the glass since it is full of air. If we immerse a funnel connected Fig. 18 30
Fig. 19 Fig. 20 Fig. 21 by means of a rubber hose with a glass tube in water (Fig. 21), the air will leave the funnel through the tube. These two experiments show that gas occupies some volume which can be very easily changed, and this is an essential difference between liquids and gases. We can compress gas to a considerable extent. It is even easy to compress the air in a ball by hand so that its volume will decrease noticeably. Gases are thousands of times more compressible than liquids. Gases possess one more peculiar property which is absent in solids and liquids, namely, they completely occupy the volume of their container. Consequently, gases have no shape of their own, they assume the shape of the premise or vessel they occupy: a room , a cylinder, a bottle. Thus, gases do not have a constant volume and any shape of their own, they completely occupy the volume presented to them ? 1. Name a substance which can often be seen in three states : solid, liquid or gaseous. 2. Name the common properties of solids. 3. What liquids do you know? Enumerate the common properties of liquids. 4. What are the common properties of gases? Ex.:rc1 e 4 1. A body retains its volume but easily changes its shape. In what state is the substance constituting the body? 2. A body retains its volume and shape. In what state is the substance constituting the body ? 3. Give examples of using the properties of solids and liquids in engineering. 31
13. The Difference in the Molecular Structure of Solids, Liquids and Gases Ice, water, and water vapour are three states of the same substance, water. This means that the molecules of ice, water, and water vapour are the same. Consequently, these three states differ not in molecules but in the way the molecules are arranged and move. How are the molecules of gas, liquid, and solid arranged and how do they move? Gas can be compressed so that its volume will decrease several times. This means that the distances between molecules in gases are large, much larger than the molecules themselves. On the average, the distances between molecules of gases are dozens of times as great as the molecules themselves. At such distances the attraction between molecules is very weak. That is why gases have no shape or constant volume. It is impossible to fill with gas half a bottle, say, or half a glass, since moving in all directions almost without attracting each other, the molecules will quickly fill the whole vessel. The properties of liquids can be explained by the fact that the spaces between their molecules are small: the molecules in liquids are packed so close that the distance between every two molecules is smaller than the molecule itself. At such distances the attraction between molecules is rather considerable. There- fore, molecules of Liquids do not spread to Large distances and in ordinary conditions Liquids retain their volum es. The attraction of molecules in liquids is, however, not great enough for the liquid to retain its shape. This is why liquids acquire the shape of the vessel and it is easy to spray them and pour them from one vessel to another. While compressing a liquid, we bring its molecules so close together that they begin repelling each other. That is why it is so difficult to compress a liquid. In ordinary conditions, solids retain their volume and shape. This can be explained by the fact that the attraction between their particles is still greater than in liquids. Some of the solid bodies, snowflakes, for instance, have a natural regular and fair shape. The particles (molecules and atoms) of the majority of solids, such as ice, salt, naphthalene, metals, are arranged in a certain order. Solids of this kind are called crystalline bodies. Although the particles of these bodies are in motion, each of them moves about a certain point just as the pendulum of aclock, i.e., it oscillates. The particle cannot move far away from that point and, therefore, a solid retains its shape. The great Russian scientist Lomonosov was one of the founders of the teaching on the molecular structure of matter. Here is how Lomonosov imagined the structure of gases: "The gas particles knock against other, neighbouring particles in a disordered interaction, jump away from each other and again run into other, closer particles, rebound again, so that they strive to spread in all directions, being constantly repelled from one another due to such frequent mutual impacts." Having acquired an idea of molecules, Lomonosov could explain numerous phenomena. 32
? 1. Is there any difference between the molecules of ice, water, and water vapour? 2. How are the molecules of gases arranged? 3. Why do gases occupy the whole volume of the vessel they are in? 4. How can the very small compressibility of liquids be explained? Why do they not retain their shape? 5. Why do crystalline solids retain their shape and volume? 6. Who of the Russian scientists is considered to be the founder of the teaching on the structure of matter?
Motion and Forces 14. Mechanical Motion To decide whether or not a body moves, it is necessary to see whether there is any change in its position with respect to the other bodies around it. If, for instance, the position of a car changes with respect to the houses and trees, then the car is said to be in relative motion with respect to those bodies. Water in a river moves relative to the banks, a train moves relative to the railway track. A contmuous change m the fXlSitiOn of a body relatin: to other bodies is called a mechanical motion . Let us get acquainted with some kinds and laws of this motion. A person in a train coach is moving relative to the railway track but is at rest relative to the coach. Speaking of a movement of a body, it is therefore necessary to indicate relative to what bodies the motion occurs. The movement of a man, a car, an airliner (Fig. 22), a rocket, a boat relative to the earth, flying of birds, the flow of water, the motion of air (wind), these are all examples of mechanical motion. A movement of a molecule is also a mechanical motion. When a body is displaced from one point to another, it describes a certain curve, which is called a trajectory of a fill\ ing bod; . A falling meteor, for instance, leaves a luminous trace in the night sky so that its trajectory is visible (Fig. 23). The trajectory of the movement of a body molecule is a polygonal line (Fig. 24). The length of the WLJector} along which a body moves for a certain time intenal1s sa1d to be the nath tr;l\cr~cd by the body during that t1me intcn.LI. A dash line in Fig. -25 shows the trajectory of a skier who has descended the Fig. 22 34
Fig. 23 l· ig. 24 Fig. 25 hill. The length of the trajectory 0 A is the path covered by the skier during his descent. \ path traversed is a physical quantity. It is measured by a special unit of length , a metre (m). Also in use in practical applications are units which are 10, 100, 1000, etc. times larger (multiples) or smaller (submultiples) of a metre, say, a ktlometre 1111 a centimetre (cm). \ ' I km= 1000 m, I cm = 0.01 m. 1. What is known as a mechanical motion? 2. Why must we indicate relative to what bodies a body moves ? 3. What is the trajectory of movement? 4. What is known as a path traversed during a certain time interval? rx.:rusc 5 1. Name the objects relative to which a passenger in a moving train is at rest and relative to which he is moving. 2. Why is it impossible to indicate the direction in which a boat moves in the fog, when the banks of the river are invisible? 3. What kind of a curve is the trajectory described by the tip of a clock hand? Assignment Measure the length of your step and, using that measure, calculate the distance you cover when returning home from school. Note the time of your movement. 35
15. Uniform and Nonuniform Motions If a body covers equal distances in any equal time intervals, say, a car travels 60 km every hour, 30 km every half-hour, 15 km every quarter-hour and so on, up to minutes, seconds, and fractions of a second, then 1ts motion is unifom1. Figure 26 shows a moving block with a dropper attached to it. Drops fall from the dropper in equal time intervals. The distances between the traces left by the drops on the paper during the movement of the block are equal. This signifies that the block covers equal distances in equal time intervals. We can repeat the experiment turning the tap of the dropper so that drops will fall more frequently. In that case as well the traces of the drops will be at equal distances, which means that the block covers equal distances in smaller but equal time intervals, i. e., it moves uniformly. The movement of the earth about its axis and the movement of watch hands are close to uniform motion . A gas molecule is in uniform motion between collisions. As to the majority of other motions, they are nonuniform. For example, a train pulling out of a station covers larger and larger distances in equal time intervals. Conversely, when it approaches a station, it covers smaller and smaller distances in equal time intervals. A skater taking part in a contest covers equal distances in different time intervals. These are examples of a non uniform motion. A non uniform motion of a block can be observed in the experiment shown in Fig. 27. The traces left by the drops falling in equal time intervals show that the block moves nonuniformly because the distances between the traces of the drops falling in equal time intervals are different. ? 1. What motion is known as uniform? 2. Give examples of movements, which are close to a uniform motion. 3. What experiment can be staged to observe a uniform motion? 4. Give an example of a nonuniform motion. 5. What motion is known as non uniform? Fig. 26 Fig. 27 36
16. The Speed of Uniform Motion. Units of Speed A car travelling uniformly along a highway leaves behind a man walking uniformly. What is the difference between these two uniform movements, the movement of a car and that of a pedestrian? The difference is that the car travels faster than the pedestrian. An aircraft moves faster than a car, and an earth satellite moves faster than an aircraft. This means that in the same time interval a car covers a larger distance than a pedestrian a nd an aircraft covers a larger distance than a car. The movements of a pedestrian, a car, and an aircraft differ in their speeds. The speed of a body moving uniformly shows what path the body covers per unit time. For example, if a combine harvester covers 9 km and an airplane flies 600 km every hour, then it is said that the speed of the combine is 9 km per hour and that of the airplane is 600 km per hour. The body which covers a larger distance in unit time moves with a higher speed. To find the speed of a body moving uniformly, the distance traversed by the hndy in some time interval must be divided by that interval : speed = distance time Let us use the following designations : s for the distance travelled, t for the time interval in which the path is traversed, and v for the speed; then we get s V= - . t \ un it of speed is the speed of the unifo rm motion of a body covcnn g a mc tn; path during I second . This unit of speed is written as 1 m s. In the experiment described in Sec. 15, the moving block covered a distance of 0.45 m during 3 seconds. Having determined the distance traversed in I s, we find the speed of the block, which ts 0.45 m m -- =0.15 - . 3 s s Other units . of speed are also used in practical applications, they are km 1 - h ' km 1-- , s cm 1 - . s EXA MPL,E. The TU-154 airliner covers the distance between Moscow and Tashkent, equal to 2736 km, in 3.8 h. Find the speed of the liner assuming its motion to be uniform. In physics, the problem and its solution are written as follows : 37
Fig. 28 Given : s = 2736 km, t = 3.8 h. V .. . ? Solution: s V= - . t V= 2736 km 3.8 b km =720-. h Now we shall express the speed obtained in metres per second. For that purpose, we convert kilometres into metres and hours into seconds : 720 km= = 720 000 m ; 1 h = ~600 s. Then km 720000 m m v=720 - = =200 - . h 3600 s Thus, the numerical value of speed just as of any other physical quantity (length, volume) depends on the unit of measurement chosen. If the speed of a body is denoted by an arrow in a figure (see Fig. 28), then in addition to the numerical value, the speed has a direction . In that case it is called a velocity, hence the designation, v. ') 38 1. What is the difference between the uniform motions of a pedestrian, a car, and an aircraft? 2. What does the speed of a uniform motion show? 3. How can the speed be determined if the path traversed and the time are known? 4. How can the speed given in km/h, m j s be expressed? 5. How, besides the numerical value, can the speed of a body be characterized? F\crcise li 1. A raft fl owing down the river covered 900 m in 20 min. Find the speed of the raft (in m/s ).
Table SPEEDS OF C ERTAIN BODIES, OF SOUN D, RADI O WAVES, AN D O F LIGHT, m/s Snail Pedestrian Carrier-pigeon Skater Train (on the average) Ostrich Car (on the average) Jet plane (on the average) Sound in the air (at 0 oq A bullet of a tommy-gun (on its escape from the barrel) The moon about the earth Hydrogen molecule (at 0 oq Hydrogen molecule (at 20 °C) Artificial earth satellite The earth about the sun Light and radiowaves 0.0014 1.2-1.8 17-19 up to 12.5 20 22 30 200 332 715 1000 1693 1755 8000 30000 300000000 2. A cyclist travelling at a uniform speed covered the distance of 9 km in 30 min. Find the speed of the cyclist (in m/s). 3. The speed of the electric locomotive is 90 km/h. Express this speed in mfs. 4. The figure on p. 18 shows a powerful modern electric locomotive. Compare its speed with that of the locomotive of the previous problem . 17. Average Speed of Nonuniform Motion In a nonuniform motion, a body covers different distances in equal time intervals. The speed of such a motion is not constant. We speak, however, of some defmite speed of a train or a car although we know that at stations the speed of the train is zero, then it increases, and then decreases again when it approaches the next station. What kind of a speed do we mean when we say that the speed of a train is 60 km per hour? Speaking of the speed of non uniform motion, we mean the a veragc speed \ r a given part of the distance travelled or during the given time interval. To calculate it, we divide the distance covered by the time of travel, i.e., do the same operation as in calculating the speed of a uniform motion. Let us consider an example. The distance between Moscow and Novosibirsk is 3200 km. Travelling non uniformly, the train covers this distance in 64 h. Let us assume that the train covered the same distance in the same 64 h but moved un iform ly. 39
Then the speed of that uniform motion would be equal to s 3200 km km V= -, V= =50 - . t 64 h h And this is the average speed of the non uniform motion of the train. way s Average speed = - .-, or v t1me av ? 1. What speed do we have in mind when we speak of the speed of a train or a car? How can the average speed of a nonuniform motion be determined? Exercise 7 1. In 1963 the Soviet skater Grishin set the world record for 500 m. He covered the distance in 39.5 s. Find his average speed. In 1983 the Soviet skater Pegov set a world record for the same distance having covered it in 36.57 s. Compare the average speeds achieved by Grishin and Pegov. 2. When descending a mountain, a skier covered 50 m in 6 s. Having descended the mountain he kept moving and covered 30 m more in 15 s until he stopped. Find the average speed at which the skier moved down to the bottom of the mountain and the overall speed from the top until he stopped . 18. Calculating the Path and the Time of Motion Knowing the speed of the uniform motion of a body, we can find the path it covered during a certain time interval. Suppose, for instance, a train travels uniformly with a speed of 20 m/s. This means that it covers 20 m every second. Then, during 5 s it covers the distance 5 times as large as in 1 s, i. e., 20 m/s · 5 s = 100 m, and in 10 s it covers a distance 10 times as large, i.e., 20 m/s ·10 s = 200 "m and so on. To find the distance covered in uniform motion, we must multiply the speed of the body by the time of its motion : s = vt. Knowing the path traversed and the speed of the uniform motion of a body, we can find the time spent by the body. Let us determine the time a pedestrian will need to cover a distance of 3 km, i.e., 3000 m, walking with a speed of 1.5 mj s. It follows from the formula s = vt that 40 s t= - · V
Substituting into this formula the numerical values of the distance and speed, . 3000m we find the tune : t = = 2000 s.1.5 m j s We can find the average speed ofnonuniform motion assuming the motion to be uniform . Therefore, if we have to find the path, proceeding from the average speed, we can use the rule established for uniform motion . Thus, the distance traversed by a body in nonuniform motion is equal to the average speed multiplied by the time of motion , i.e., S = Vavl· The time required to cover a certain path in nonuniform motion is equal to that path divided by the average speed. ? 1. How to find the path travelled by a body in uniform motion if the speed S,km 500 400 300 200 100 1/ 0 2 Fig. 29 and the time taken are known? How can we determine the time of uniform motion knowing the distance travelled and the speed of the body? 2. Answer the same questions for the case of nonuniform motion. Exercise 8 1. Find in Table 1 the speeds of a pedestrian, a skater, and a train and determine (orally) the distances covered by those bodies in I 0 s.2. An airplane travels with an average speed of 750 km/h. What distance does it cover in 6 hours of its flight? 3. What time do a train and an airplane need to cover the distance of4000 m? (The speeds of these bodies are given in Table 1.) 4. Figure 29 shows a graph of a distance covered in uniform motion. Os on the graph is the axis of the paths traversed ; Ot is the time axis. Use S,m 12 I / / ./ V 8 V V 11 / V v 10 6 / I' 1/ / 4 t,h /p.V I,S 2 4 6 10 12 0 2 4 6 Fig. 30 41
V,mjs 10 8 6 4 2 r,s Fig. 31 0 2 4 6 7 the graph to determine the path covered in 10 h and the speed of motion. 5. Figure 30 shows the graphs of two paths I and I/ traversed by a body in uniform motion. Using the graphs, determine the case in which the body moved with a greater speed. Substantiate your answer. 6. Figure 31 presents a graph of the speed of a body in uniform motion. What is the speed of the body? Find the path covered by the body in 5 s. 19. Inertia We know from experience that the speed of a body can only change when it is acted by another body. For instance, a ball lying on the ground begins moving only when another ball collides with it or when somebody hits it by the foot. But if no other body acts on the ball, it will not change its speed, it will not begin moving with respect to the earth. A moving body does not decrease its speed or comes to a complete stop by Fig. 32 42
(a I I b I I c I Fig. 33 itself, but only as a result of the action of other bodies. The speed of a bullet decreases when it passes through a board, i.e., the board acts upon it. A rolling ball stops due to friction between the ball and the ground. The direction of a body can also change under the action of some other body. A thrown ball changes its direction when it hits a wall or somebody's hand. A boy running fast (Fig. 32) catches hold of the pole in order to run round it. Let us consider the following experiment. A board is put on the table in an inclined position. A small mound of sand is made on the table a small distance from the end of the board. A block of wood on wheels is put on top of the board. Rolling down and hitting the mound of sand, the block stops abruptly, having come across an obstacle (Fig. 33a). If we leve l the sand on the table and let go of the block again, it will now roll a greater distance before it stops (Fig. 33b). If we now remove the sand from the path of the block, it will roll still farther before it stops (Fig. 33c). Consequently, the fewer obstacles on the path of the block, the farther it moves and the closer its movement is to the uniform motion. How a body moves if there are no obstacles in its way? The Great Italian scientist Galileo Galilei answered the question: ifno other bodies act on a body, then it is either at rest or moves rectilinearly and uniformly. In both cases, the speed of the body does not change. The tendency of a body to keep moving when no other bodies act upon it is ,t iled inertia. 1 A bullet escaping from barrel of a gun moves by inertia, since the action of the powder gases on it ceases after it leaves the barrel. A car keeps moving by 1 Inert ia in Latin means immob ility, inactivity. 43
Galileo Galilct (1564-1642), an Italian physicist a nd astronomer. He discovered the laws of falling bodies and the oscillation of a pendulum and was the first to indicate the existence of inertia. He invented a thermoscope, a device to meas ure temperature and was the first to apply the telescope for as tronomic investigations, he discovered the satellites of Jupiter, sun s pots and the phases of the Venus. inertia after its engine is switched off as well as a puck after it is hit by a stick. The movement of a gas molecule can be cited as an example of movement by inertia since each molecule moves by inertia rectilinearly and uniformly from one collision to another. ? 1. Give examples showing that the s peed of a body changes only when some other body acts upon it. 2. Describe the experiment showing how the movement of a body changes when the obstacles in its way become less active. 3. What causes a change in the direction of movement ? 4. How would a body move if there were no obstacles in its way? 5. What is inertia ? 20. Inertia in Everyday Life and in Engineering We often come across the phenomenon of inertia. A running man cannot stop suddenly, he keeps running by inertia for some time, gradually decreasing his speed. When a bus or a tram begins moving after a stop, the legs of passenger also begin moving because of friction between them and the floor. Whereas his body remains in the state of rest by inertia. That is Fig. 34 44
Fig. 35 Fig. 36 why he leans opposite to movement (Fig. 34a). Conversely, upon a sudden stop, he continues moving and leans forward (Fig. 34b). If you switch off the car engine without braking, the car will not stop at once. The distance passed until a complete stop is called a free rolling path. For instance, a car , travelling along an asphalt coated highway with a speed of50 km/h, will run another 355 metres until a complete stop after the driversw itches off the engine, and that is exactly the free rolling path. Even if we manage to stop the wheels of the car and thus cease their rotation, the car will st ill roll on for some time, its wheels sliding along the road. It is dangerous to cross the road close before a moving car since the car cannot stop instantaneously upon braking. 'I 1. Give examples of inertia occurring in everyday life and in engineering. 2. Why is it impossible for a moving train, car or motorcycle to stop instantaneously after its engine is switched ofT? E>.ercise 9 1. Figure 35 shows a technique of putting a hammer on a handle. Explainit. 2. Why does it sometimes happen that a person who has stumbled or slipped falls down? In what direction does he fall ? 3. Figure 36 shows how to impart a necessary position to a plane iron. Why the iron enters the plane when we strike the iron and falls out of it when we strike the plane stock? 4. In what direction do the passengers jerk relative to the bus when it makes a right turn? a left turn? Why? 21. Interaction of Bodies Let us consider the phenomena as a result of which a body ' changes its speed, say, begins moving. Figure 37a shows a wheeled block with an elastic plate attached to it. The plate is bent and tied with a thread. The block is at rest relative to the table. Will the block begin moving if the plate is straightened out? To answer the question , 45
(a) (b) Fig. 37 (b) Fig. 38 let us burn through the thread. The plate straightens out instantaneously but the block remains motionless (Fig. 37b). Let us now put one more block of the same kind on the other side of the bent plate (Fig. 38a). When we burn through the thread both blocks begin rolling in opposite directions (Fig. 38b). As could be expected (see Sec. 19) another body 1s needed, a second block in this case, to change the speed of the block. We saw that the second block also began rolling, they both started moving relative to the table, they acted upon each other. Consequently, an action of one body upon another cannot be one-sided. Both bodies act upon each other. they intenll:t. Thus, for instance, a bullet is at rest relative to the gun until a shot is fired . Upon interaction, the bullet and the gun begin moving in the opposite directions. This is known as phenomenon a recoil. If a man in a boat pushes off another boat, an interaction occurs and his own boat also moves (Fig. 39). When a boy jumps from the boat to the bank, the boat moves in the direction opposite to the jump (Fig. 40). Thus, the speed~ of bod1e~ change only upon their interaction . Fig. 39 46
Fig. 40 ? 1. Describe the experiments showing that bodies begin moving only as a result of their interaction. 2. Give examples showing that both bodies change speed as a result of interaction. 3. Describe the phenomenon of interaction using the example of a shot fired from a gun. 22. The Mass of a Body. Units of Mass The speeds at which stationary bodies will move after interaction may either differ considerably from each other (those of a bullet and a gun), or be almost the same (those of a man and a small boat). How can it be explained? Let us consider once again an interaction of wheeled blocks, but this time we shall use different blocks (Fig. 41). After the thread is burned through, the blocks will roll with different speeds. This happens because the blocks have different masses The block, which moves with a smaller speed after an interaction, has a greater mass. The speeds of the bodies after an interaction can '· Fig. 41 47
Fig. 42 be measured. Speeds can be used to compare the masses of the interacting bodies. For example, the blocks have zero speeds before an interaction, and after the interaction the speed of one block is 20 cm/s and that of the other is 40 cm j s. Since the speed of the second block is twice that of the first block, its mass is half that of the first block. Now if the blocks have the same speed after an interaction, then their masses are equal too. We observed this in the experiment with identical blocks (Fig. 38). When a man jumps from a boat to the bank, an interaction occurs between the boat and the man . The boat moves in the direction opposite to the jump of the man (see Fig. 40). If the mass of the boat is greater than that of the man, then its speed will be smaller than the speed of the jumping boy. If the masses of the boy and the boat are the same, then their speeds after the interaction will be equal. When considering the phenomenon of interaction of bodies, we got acquainted with a physical quantity known as the mass of a body. The notion of mass will be considered in more detail as we go into a deeper study of physics. For the time being, we have only to bear in mind that every body, a man , a table, the earth, a drop of water, possesses a mass and we can use speeds acquired by stationary bodies upon their interaction to compare their masses. A kilogram, l kg, is accepted as a unit of mass. A kilogram is the mass of the standard (a thoroughly manufactured specimen). It is made from an alloy of two metals, platinum and iridium. The international standard of a kilogram is kept in France in the town of Sevres near Paris (Fig. 42). Very accurate copies of this standard are manufactured for use in other countries. Units of mass greater or smaller than a kilogram, such as a ton (t), a gram (g), a milligram (mg), are also used in practical applications. I t = 1000 kg, l g = 0.001 kg, l mg = 0.(){)()()()1 kg. Modern physics has most perfect measuring techniques at its disposal, which make it possible to determine the size and the mass of the smallest particles of a substance, i.e., molecules, with great accuracy. At present, the masses of the molecules constituting all substances are known. A hydrogen molecule has the smallest mass, equal to 0.000 000000 000000 000 000 0033 g or 33/1025 g. If we put a dot on a sheet of paper by the tip of a thinly sharpened pencil, then the mass of the graphite left on the paper will be millions of times greater than the mass of a hydrogen molecule. 48
The mass of a mercury molecule is lOO times greater, that of an oxygen molecule is 16 times greater, and that of a water molecule is 9 times greater than the mass of a hydrogen molecule. ? l. Describe the experiment dealing with the interaction of two different blocks. 2. Which of these blocks has a greater mass? 3. Give an example showing how to compare masses of bodies by the speeds acquired by them. 4. What unit is accepted as the unit of mass? 5. What other units of mass do you know? Exercise 10 l. A man jumps from a small boat to the bank. Why does the boat move back with a lmost the same speed as that of a man jumping from the boat? 2. When you fire a gun, you should keep it close to your shoulder. Why does the speed of recoil decrease in that case? 3. When manufacturing cartridges for sporting guns, the mass of the gun is taken into account: the charge of the shot is made smaller for lighter guns than for heavy guns. Why? 4. A man jumped from a stationary boat with a speed of 5 m j s and the boat moved off with the speed of 0.5 m j s. How many times is the mass of the boat greater than that of the man? 23. Defining the Mass of a Body by Balances We have learned by now that by comparing the speeds acquired by stationary bodies as a result of their interaction, we can find how many times the mass of one body is greater than that of the other. That is how the mass of a body can be measured provided that the mass of the other interacting body is known. But there is another, much simpler method of finding the mass of a body, that of using balances· A school balance (Fig. 43) consists of a beam which can turn freely about Fig. 43 49 4 - 971
Fig. 44 "a point at the centre of the beam. The pans of the balance are suspended from the ends of the beam. We established in Sec. 21 that the masses of the wheeled blocks we used in the experiment are equal (see Fig. 38), since as a result of interaction they acquired the same speed. Let us put the blocks on the pans of the balance. The balance will be in equilibrium. This means that when the balance is in equilib- rium, the masses of the bodies on their pans are equal. This serves as the basis for determining the mass of a body by means of a balance. The body whose mass we are to find is put on one pan of the balance and the weights whose masses are known and written on them are put on the other pan. The weights are chosen so that an equilibrium is attained. Then the total mass of the weights balancing the body is calculated. The mass of the body is equal to the mass of the weights. A special collecti0n of weights of different masses is used for weighing. Figure 44 shows such a collection of weights going with a school balance. It contains 9 weights with masses of 100, 50, 20, 20, 10, 5, 2, 2, and 1 g. Using them, we can choose any mass from 1 g to 210 g. The weights whose masses are less than 1 gram are made as thin aluminium plates with masses of 500, 200, 200, 100, 50, 20, 20, and 10 m g. Using special scales, we can determine large masses as that, say, of the Volga car equal to 1885 kg (with the full service load) and small masses, such as, for instance, the mass of a mosquito equal to 1 mg. ? 1. Under what condition the balance is in equilibrium? 2. How can the mass of a body be determined with the aid of a balance and a collection of weights? 3. What weights go with a school balance? 50
Exercise ll How can we show, without using a balance, that the masses of two billiard balls are equal? How can it be checked by means of a ba lance ? 24. The Density of a Substance Objects made of different substances and having the same mass occupy different volumes. If we take two cylinders of the same mass, one of which is made of lead and the other of aluminium (Fig. 45a}, we shall see that the volume of the aluminium cylinder is almost four times that of the lead one. An iron bar with a mass of 1 ton occupies a volume of 0.13 cum, and 1 ton of ice occupies a volume of 1.1 cu m , i.e., almost 9 times as large (Fig. 45b). It can be seen from these examples that the mass of 1 cu m of different substances differs. Substances differ from one another by their densities. The density shows the mass of a substance per 1 cum. The mass of 1 cum of iron, for instance, is 7800 kg. Consequently, the density of iron is 7800 kg per I cu m. Let us consider an example. Two cubic metres of ice have a mass of 1800 kg. Find the density of ice. If two cubic metres of ice have a mass of 1800 kg, then the mass of one cubic metre of ice is half as large, i. e. 1800 kg: 2 = 900 kg. This means that the density of ice is 900 kg per 1 cu m. It follows from this example that knowing the mass and volume of a substance, we can calculate its density. To find the density of a substance. we must divide the mass of the body by its \olume : Fig. 45 (b) SI
water Fig. 46 mercury mass density = --- volume iron air Let us designate the quantities by letters: p will be the density of the substance, m, the mass of the body, and V, its volume. Then we can write the rule for calculating the density of the substance as a formula: m p= - · V The unit of density of a substance is I kg/m 3 • Consequently, t~e density of iron is 7800 kg/m 3 , and that of ice is 900 kg/m 3 . The density of a substance can also be expressed in grams per cubic centimetre (gjcm 3 , Fig. 46). Let us calculate, for instance, the density of iron, equal to 7800 kgjm 3 , in these units. For that purpose, we convert kilograms to grams, and cubic metres to cubic centimetres: 7800 kg= 7 800000 g; I cum= = 1 000 000 cu cm. Dividing the mass by the volume, we find the density of iron: 7 800000 g = 7.8 _ g_. p = I 000000 cm 3 cm 3 The density of the same substance in a solid, liquid, and gaseous state differs. For example, the density of ice is 900 kg/ m 3 , that of water is 1000 kg/ m 3 , and that of water vapour is 0.590 kgjm 3 . 52 ? I. What does the density of a substance show? 2. Write down what the density of iron is equal to. What does the number you have written mean ? 3. How can the density of a substance be calculated? 4. How can you express the density in gjcm 3 if it is given in kgjm 3 ? Exercise 12 I. The density of the rare metal osmium is 22 500 kg/m 3 What does this number mean? 2. Three bricks of marble, ice, and brass have the same vol ume. Which of them has the greatest mass and which has the least one? 3. Which of the two bodies, each with a mass of 2 kg, has the larger volume, a porcelain body or an iron one? Why ? 4. The lightest wood is balsa. The mass of 100 cu cm of that wood is equal to 12 g. Calculate the density of the balsa wood in gjcm 3 and in kg/m 3 .
Assignment Take a piece of soap in the shape of a rectangula r parallelepiped with its mass written on it. Find the density of the soap. 25. Calculating the Mass and Volume of a Body from Its Density It is very important to know the density of a substance in order to put it in practice. An engineer designing a machine-tool can calculate the mass it will have proceeding from the density and volume of the materials used for its manufacture. Before designing a house, it is possible to calculate its mass and thus determine the quantity of the construction materials that will be needed. Suppose we have to define the mass of petrol in a railway tank wagon having a volume of 50 cu m. We find the density of petrol from Table 3. It is equal to 710 kg/m 3 . Consequently, the mass of 1 cum of petrol is 710 kg. The mass of 50 cu m of petrol is 50 times as large as that of 1 cu m of it, i.e., it is 710 kg. 50= 35 500 kg= 35.5 t. Thus, to calculate the mass of a body from its density and volume, we must multiply the density by the volume: mass = density x volume, or m= p V. It the mass of the body is known, then, knowing the density of the substance from which the body is produced, it is possible to find its volume. Such a method of calculating the volume is especially convenient in the case when the body is of an irregular shape and it is impossible, therefore, to measure its volume by means of a rule. Let us consider an example. The mass of a block of granite is 6.5 t, the density of granite is 2600 kg/m 3 . What is the volume of the block? We know that m= p V . In this formula the unknown quantity is the volume, which can be easily found: •) m 6500 kg V= - V= = 2.5 cum . p ' 2600 kg/m 3 _ ___c.__ l. How can we calculate the mass of a body from its density and volume? 2. How can we find the volume of a body from its dens ity and mass? Exercise 13 , 1. Find the mass of 10 litres of water, petrol, and mercury. 2. What IS the mass of 100 cu cm of lead ? Do I 00 cu cm of lead small sho t have the same mass? Why ? . 3. Find the mass of kerosene contained in a five-litre bottle. 53
26. Expressing the Density of a Substance in Terms of the Mass of a Molecule and the Number of Molecules in Unit Volume Since all substances consist of molecules, the mass of any body is composed from the masses of its molecules, like, say, the mass of a bag with peas is corn posed from the masses of all the peas contained in the bag. It is easy enough to find the mass of peas, it is sufficient to weigh the bag with the peas. But should all the peas be identical, then the mass of all the peas could be found by multiplying the mass of one pea by the number of peas in the bag. The molecules of a pure substance are identical and, therefore, the mass of a drop of water, for instance, is equal to the product of the mass of one water molecule and the number of molecules in the drop. The density of a substance shows what the mass of 1 cu m of that substance is equal to. The density of oxygen, for instance, is 1.43 kg/m 3 . This number can be obtained by multiplying the mass of one oxygen molecule by the number of molecules contained in 1 cu m of its volume. The density of a substance is equal to the product of the mass of one molecule of that substance by the number of molecules per unit volume. In practical applications, it is not, of course, the way to calculate the density of a substance, there is a simpler method to find the density from the mass of the body and its volume. But then, knowing the density of the substance and the mass of one molecule, we can determine the number of molecules in 1 m 3 of the substance, which cannot be calculated in any other way. To fmd the number of molecules in 1 m 3 , the density of the substance must be divided by the mass of one of its molecules, and the mass of a mole- cule can be found experimentally. In that way, for instance, it has been calculated that 1 cu m of pure water contains 3.34 · 1028 molecules, and 1 cu m of oxygen contains 2.7 · 1025 molecules. These numbers are so enormous that it is, of course, impossible to carry out a direct calculation. Even if we released a million molecules from 1 cu m of oxygen every second, we would need 900 thousand million years! Tables 2-4 feature the densities of some solids, liquids, and gases. Consider the tables and pay attention to a great difference between the densities of gases and those of solids and liquids. The density of the oxygen gas is 1.43 kgfm 3 . By means of deep cooling and compression of gaseous oxygen, we can obtain liquid oxygen, which has the density of 1140 kg/m 3 . Both gaseous and liquid kinds of oxygen consist of identical molecules, those of oxygen. Why do then their densities differ so greatly, almost 1000 times? Let us recall (see Sec. 13) that in gases the molecules are at larger distances from one another than in liquids. Therefore, the number of molecules in 1 cu m of a gas is smaller than in 1 cu m of a liquid. ? 54 l. How can the density of a substance be expressed in terms of the mass of a molecule and the number of molecules in I cu m?
Table 2 DENSITIES OF SOME SOLIDS Solid p, kg/m 3 p, g/cm 3 Osmium 22500 22.5 Iridium 22400 22.4 Platinum 21 500 21.5 Gold 19 300 19.3 Lead 11 300 11.3 Silver 10 500 10.5 Copper 8900 8.9 Brass 8500 8.5 Steel, iron 7800 7.8 Tin 7300 7.3 Zinc 7100 7.1 Cast iron 7000 7.0 Aluminium 2700 2.7 Marble 2700 2.7 Granite 2600 2.6 Glass 2500 2.5 Porcelain 2300 2.3 Concrete 2200 2.2 Brick 1600-1400 1.6-1.4 Organic glass 1200 1.2 Kapron 1100 1.1 Polyethylene 940 0.9 Paraffin 900 0.9 Ice 900 0.9 Dry oak wood 800 0.8 Dry pine wood 440 0.4 Cork 240 0.2 Porolon 200-600 0.2-0.6 2. Why are the densities of gases smaller than those of liquids and solids? 3. What is it necessary to know to determine the number of molecules in 1 cum of a substance? Exercise 14 1. At 100 °C the density of water is 950 kg/m 3 , and the highest density of water vapour at that temperature is 0.590 kg/m 3 . How can you explain the difference between the densities of water and water vapour? 2. The density of gaseous hydrogen is 0.09 kg/m 3 , and that of solid hydrogen is 80 kg/m 3 . Give the reason for this difference. 3. Why does compressed gas have a higher density than a noncompressed one ? 4. Check whether 1 cum of wa ter contains 3.34 ·1028 molecules. The mass of one water molecule is 2.99/10 26 kg. 55
Table 3 DENSITIES OF SOME LIQUIDS Liquid p, kg/m 3 p, g/cm 3 Mercury 13 600 13.60 Sulphuric acid 1800 1.80 Sea water 1030 1.03 Pure water 1000 1.00 Honey 1350 1.35 Machine oil 900 0.90 Kerosene 800 0.80 Alcohol 800 0.80 Petroleum 800 0.80 Acetone 790 0.79 Ether 710 0.71 Petrol 710 0.71 Liquid tin, at l = 400 °C 6800 6.80 Liquid air, at t = - 194 ac 960 0.96 Table 4 DENSITIES OF SOME GASES Gas p, kg/m 3 p, g/cm 3 Chlorine 3.210 0.00321 Carbon(IV) oxide (carbon dioxide) 1.980 0.00198 Oxygen 1.430 0.00143 Air, at ooc 1.290 0.00129 Nitrogen 1.250 0.00125 Carbon(II) oxide (carbon monoxide) 1.250 0.00125 Water vapour, at 100 °C 0.590 0.00059 Hydrogen 0.090 0.00009 27. The Force The phenomena of inertia and interaction of bodies considered in Secs. 19 and 21 show that the speed of motion of a body can only be changed by another body acting on it. Let us substantiate this assertion by new examples. By pushing a truck we set it in motion (Fig. 47). In this case the speed of the truck is changed under the action of a hand of a man. If we put a piece of iron on a stopper made of cork, immerse it in water, 56
Fig. 47 Fig. 48 and then act upon it by a magnet, the magnet will attract the iron and set it in motion (Fig. 48). In this case, the magnet is the body changing the speed of the piece of iron and the stopper. If we push a ball by the hand (Fig. 49a), the spring becomes compressed, i.e., its end begins moving. When the spring straightens out, it sets the ball in motion (Fig. 49b). First, the hand was the acting body, it set in motion the ball and the end of the spring. Then the spring became the acting body, it set the ball in motion. We can stop a flying ball or change the direction of its movement by our hand or by a racket. In all the examples cited, a body, acted upon by another body, starts moving, stops or changes the direction of its movement. In other words, in all the examples, the velocity of a body changes under the action of other bodies. It is often inessential in physics to know what body acts on another body and how, it is simply said that a force acts on a body or a force is applied to the body. Force is the cause for a change in the speed of a body. A force can change not only the speed of a whole body, but also of its individual parts. This occurs, for instance, when we hit a tennis ball by a racket. Because of the nonidentical shift of separate parts of the ball, it becomes compressed, deformed (changes shape) (Fig. 50). A board on which a boy is sitting (Fig. 51) is deformed because the middle of the board shifts to a larger extent than its ends. Different forces are required to produce the same change in the speed of motion of various bodies. It is more difficult to displace a car than (a) ·Owww:i. ( h ) Fig. 49 Fig. 50 Fig. 51 57
a motorcycle. To put it otherwise, a greater force is required to set a car in motion than a motorcycle. Hence, the numerical value of a force can be greater or smaller. Force is a phystcal quantity. Like velocity, force has a direction. ') 1. What is the result of the action of one body on another? 2. Give examples showing that the speed of a body changes under the action of another body. 3. What is force? 4. Why does the shape of a body change under the action of a force? 28. The Gravitation. The Force of Gravity Let us see how a ball flies when it is thrown in a horizontal direction (Fig. 52). The ball does not fly rectilinearly and uniformly, its trajectory is a curve. A satellite launched from the earth does not fly in a straight line but rotates about the earth (Fig. 53). Consequently, a force acts on these bodies, the force of attraction of the earth. It is due to the attraction of the earth that bodies raised to some height and then dropped, fall down (Fig. 54), that water flows down the river. A man jumps and then comes down to the earth because the earth attracts him. The earth attracts all bodies which are on it or close to it : people, sea water, water in oceans and rivers, houses, the moon, the satellites, etc. But these bodies, in turn , attract the earth. For instance, the attraction of the earth by the moon causes ebbs and tides on the earth, huge tidal waves rise in seas and oceans twice a day several metres high. The earth and all other planets rotating about the sun are attracted by the sun and by each other. All bodies on the surface of the earth attract each other. Therefore, mutual attraction of all bodies of the universe is called universal gravitation . Of especial importance to us is the force of attraction of the earth, the planet we live on. Fig. 52 Fig. 53 Fig. 54 58
Isaac Newton ( 1643- 1727), a British physicist and mathematician. He discovered the main laws of motion and the law of gravitation. He also discovered and investigated many significant properties of light and elaborated the most essential branches of higher mathematics. The force with which the earth attracts a body is called the force of gravity. Experiments show that the force of gravity is directly proportional to the mass of the body. The force of gravity acting on one body is as many times greater than that acting on the other body as the mass of the first body is greater than that of the second body. Therefore, we say that a body having a large mass is heavy. If we consider bodies with different masses, we say that one body is heavier than the other. Thus, we express the relation between the force of gravity and the mass of the body. If the masses of the bodies are equal, then the forces of gravity acting on them are also equal. ') 1. Why does the stone thrown in a horizontal direction not keep a rectilinear direction? 2. What is the force that keeps bodies on the surface of the earth? 3. What force is known as the force of gravity? 4. What is the relationship between the force of gravity and the mass of the body? 29*. The Elastic Force. The Weight of a Body As we saw in Sec. 28, all bodies on the surface of the earth are subject to the force of gravity. Due to the force of gravity all bodies devoid of supports and suspensions fall on the earth. Drops of rain, snow flakes, leaves tom from the branches of trees drop on the earth under the action of the force of gravity. However, when the snow lies on the roof, and the force of gravity acts on it, it, nevertheless, does not fall down but is at rest. Let us look for the reason why bodies resting on a support or suspended by a thread are at rest. Figure 55a shows a board resting on two supports and keeping 59
(a) (b) Fig. 55 Fig. 56 a horizontal position. If we put a weight on its middle, the weight will move downwards for some time under gravity, bending the board, and then will stop (Fig. 55b). Why did its movement cease? The only explanation is that besides the force of gravity directed downwards, another force, directed upwards, acted on the weight. . Where did that other force come from? To answer this question, let us see what becomes with the board when it moves downwards. When moving downwards, the board (or any other support, Fig. 55b) sags, undergoing deformation. At the same time, a force arises with which the support (the board, in our case) acts on the body resting on it, the force being directed upwards, i. e., opposite to the force of gravity. It is called an elastic force. The more the support sags, the greater the elastic force. When the elastic force becomes equal to the force of gravity, acting on the body, the support and the body stop moving. Figure 56 shows spring which is compressed under the weight acting on it. If a body is suspended, then the suspension (a thread, a rope, a wire) stretches. An elastic force arises in the suspension as well as in the support. As the suspension stretches, the force increases. When the elastic force and the force of gravity become equal in value, the stretching of the thread ceases. When a body is put on a support, not only the support undergoes deformation, but also the body attracted by the earth. The deformed, compressed body presses upon the support. When a body is suspended, the same thing occurs: not only the suspension becomes deformed, but the body itself as well. The body being deformed (stretched) deforms (stretches) the suspension (Fig. 57). The force with which a body acts on the support or suspension, as a result of attraction by the earth. is called the weight of the body. Distinction should be made between the force of gravity acting on a body and the weight of the body. The force of gravity acts on the body and the weight of that body acts on the support or suspension (see Figs. 57 and 62). 60
Fig. 57 ? 1. What is the action of the force of gravity on a body ? 2. What force is known as an elastic force? 3. What is known as the weight of a body? 4. What is the difference between the weight of a body and the force of gravity acting on it? 30*. Units of Force. The Relation Between the Force of Gravity and the Mass of a Body Force is a physical quantity. It can be measured, 1. e., compared to the force accepted as a unit of force. We know that units of measurement of various quantities are conventional. We can, therefore, accept any force, say, the elastic force of a definite spring stretched to a definite length, as a unit of force. We can also choose a force of gravity acting on some body as a unit of force. One newton ts accepted as an international unit of force. It is defined as the force which, during one second, changes the speed of a body with a mass of I kg by I metre per second. This unit of force was named after the eminent British physicist Isaac Newton who discovered the law of gravitation. The unit of force, a newton, is abbreviated as J N . Also in use is a large unit of force, l kilonewton (I kN). lkN=IOOON. 61
One newton is approximately equal to the force of gravity acting on a body with a mass of 0.1 kg, or, to be more precise, 1/9.8 kg. It should be borne in mind that the force of gravity acting on a body depends on the latitude of the place the body is in. Therefore, the force of gravity acting on a body of the mass of 1/9.8 kg is equal to 1 N only at the defmite latitude, namely, at the latitude of the French town of Sevres, where the standard of the mass is kept. How can we calculate the force of gravity acting on a body of any mass, using the unit of force of 1 N? It is known that the force of gravity is the greater, the larger the mass of the body. Since 1 N is the force of gravity acting on a body with a mass of 1/9.8 kg, it follows that a mass of 1 kg is subject to a force of gravity equal to 9.8 N. It can be abbreviated as 9.8 Njkg. But whereas a mass of 1 kg is subject to the force of gravity of 9.8 N, a body with the mass of 2 kg is subject to a force twice as large and equal to 19.6 N, and a body of 3 kg is subject to a force thrice as large and equal to 29.4 N , etc. Consequently, to find the force of gravity acting on a body, we must multiply 9.8 Njkg by the mass of the body, i. e., N F = 9.8 - m, or F = gm, kg where F is the force of gravity in newtons, g = 9.8 Njkg, and m is the mass in kg. We have learned that the force with which a body, being attracted by the earth, acts on a support or suspension is called the weight of the body. If the support is horizontal and stationary with respect to the earth, then the weight of the body is equal to the force of gravity. In what follows, when speaking of the weight of a body, we shall always relate it to a stationary and horizontal support. Therefore, the weight of a body P in newtons will be calculated by the formula P = gm, where the mass m IS m kg, and g = 9.8 Njkg. In a number of cases, when a strict accuracy is not necessary, we can make an approximation and consider that g = 10 Njkg. '! 62 1. What does it mean "to measure some force?" 2. What is accepted as a unit of force? 3. What force is called a newton? 4. What force of gravity acts on a body with a mass of l kg ? 5. How can we calculate the force of gravity acting on a body of any mass ? 6. In what case can we apply the formula for the force of gravity to calculate the weight?
Exercise 15 1. What force of gravity acts on a body with a mass of 2.5 kg? 800 g? 1.2 t? 50 g? 2. How many newtons does the weight of a body equal if its mass is lO kg? 200 g? 3. The weight of a man is 800 N. What is his mass? 4 . Read the sections "Weightlessness" and "The Force of Gravity on Other Planets" at the end of the book and use them to make reports on these subjects. 31. A Spring Balance The device used to measure forces is called a spring balance or a dynamometer 1 . The design of a spring balance is based on the fact that the elastic force of a spring increases as many times as the deformation of the spring. Here is how the simplest spring balance is made. A spring with a rod and a hook at the end is attached to a plank covered with white paper (Fig. 58a). A pointer is fixed at the upper part of the rod. The indication of the pointer is marked on the paper when the spring is not stretched, this is a zero scale. Then a weight with a mass of 1/9.8 kg, i.e., 102 g, is suspended from the hook. A force of gravity of 1 N acts upon the weight. The force of 1 N stretches the spring and the pointer goes downwards. Its new position is marked on the paper with the digit 1 (Fig. 58b). Next a weight with a mass of 204 g is suspended and the new indication is marked with the figure 2, which means that in this case the elastic force ::>f the spring is equal to 2 N. Using the weight of 306 g, a mark of 3 N is made and so on. (a) Fig. 58 1 From the Greek dynamis meaning power, and metreo meaning I measure. (b) Fig. 59 63
Fig. 60 We can mark scale divisions corresponding to the tenths of a newton: 0.1; 0.2; 0.3 N, etc. For that purpose, we must divide the distances between the marks 0 and I; I and 2; 2 and 3, etc., into I 0 equal parts. The graduated spring is the simplest spring balance (to graduate a device means to calibrate it with a scale). Other forces, besides that of gravity, can be measured by a spring balance, e. g., the force of friction, the elastic force, etc. A hand-grip spring balance, shown in Fig. 59, is used to mea~mre the mus- cular strength of your hand. Its principal part is an oval spring connected to the mechanism of a pointer. When the spring is compressed, the mechanism actuates the pointer, which indicates the value of the force on the scale. To measure large forces, as, for instance, the traction force of a tractor, use is made of special traction dynamometers (Fig. 60), capable of measuring forces up to tens of thousands of newtons. ? 1. What device serves to meas ure forces? What is its design based on? 2. How can a simple spring balance be made? 3. How can divisions corresponding to 0.1 N be marked on the scale of a spring balance? 4. What purpose is served by a hand-grip spring balance? a traction dynamometer? 32. A Force Is a Vector Quantity The action of a force on a body depends on its numerical value. For example, the more we stretch the spring, the longer it becomes. But the action of a force also depends on its direction. Depending on the direction of force, the spring will be stretched or compressed, the door will be closed or opened. The quantities which have a direction as well as a numerical value (a modulus) are called vector quantities. A force is a vector quantity. Vector quantities are designated by corresponding letters with arrows, or are 64
100 N F Fig. 61 Fig. 62 given in blue print, say, F(f ), and the modulus (the absolute value) is designa- ted by the same letter but without an arrow, or is given in ordinary print, F, or, else, in blue print with vertical bars, If l- It is also very significant to what point of the body the force is applied. It is not by chance that the door-handle is attached as far from the hinges as possible. Try to open the door pushing it at the point which is close to a hinge, it is more difficult to do this than to open the door by the handle. The examples cited lead to the following conclusion: the action of a force on a body depends on its absolute value, its direction and the point of its application. On a drawing, a force is represented as a line segment with an arrow at the end (Fig. 61), which indicates the direction of force. The beginning of the segment A is the point of application of the force. The length of the segment denotes the absolute value of the force in the chosen scale units. For instance, if we agree to denote 1 N by a line segment 0.5 cm long, then the force of 5 N must be represented by a segment 2.5 cm long. EXAMPLE. A bag with flour with a mass of 50 kg is on the floor. Calculate the force of gravity and the weight of the bag and represent those forces on a drawing. Given: m= 50 kg, g = 9.8 N/kg. F .. . ? p ... ? Solution: F=gm, P=gm. N F = P= 9.8 - ·50 kg::::: 500 N. kg Let us choose scale units and represent the forces obtained graphically (Fig. 62), keeping in mind that the force of gravity acts on the body itself and the weight acts on the support (Sec. 29). ? 5-97 1 I. Give examples showing that the action of the force depends on its absolute value, direction, and the point of application. 2. Why is a force a vector quantity? 65
3. How are forces represented on a drawing? 4. What is the difference between the representation of a force of gravity and the weight of a body on a drawing? Exercise 16 1. Represent on a drawing the following forces in the scale units you will choose: (a) the weight of a body of 400 N; (b) the force of 50 N with which you push a ball, the force having a horizontal direction. 2. A tractor can develop a traction force up to 60 000 N. Represent the force graphically to the scale of 1 cm= 10 kN. 3. A box full of bricks with a mass of 3 t is on a stationary goods truck. Calculate the force of gravity and the weight of the box and represent it in the scale units you choose. 33. Addition of Two Forces Directed Along the Same Straight Line. The Resultant of Forces In the majority of cases we come across in everyday life, a body is acted upon not by one force but by several forces at once. Thus, for instance, when we saw a board, three forces act on the saw: the muscular force of a man, the force of resistance of the board, and the force of gravity. A sailing ship is acted upon by the traction force of the rotating propeller, the forces of resistance of the water and the air, the force of gravity, and the buoyancy of water. Two forces, the force of gravity and the elastic force of the spring, act on a body suspended by a spring. In every such case, we can replace several forces actually applied to the body by one force of the same value. A single force, whose effect is identical to the effect of several actual forces that act on a body, is called the resultant of those forces. The seeking of the resultant of several forces is the addition of the forces or finding their sum. The forces being added are called the component forces. Let us find the resultant of two forces acting on a body along the same line in the same direction and in opposite directions. Let us make an experiment. We suspend two loads of 1 N and 2 N by a spring, one under the other (Fig. 63a). We mark the length to which the spring has stretched. Then we remove the loads and replace them by one load, which can stretch the spring to the same length (Fig. 63b ). The weight of this load proves to be equal to 3 N. The experiment has shown that the resultant of the forces acting along the same line in the same direction has the same sense, and its absolute value is equal to the sum of the absolute values of the component forces. In Fig. 64, the resultant of the forces acting on a body is denoted by the letter R and the component forces, by the letters F 1 and F 2 • In this case, 66
(a ) Fig. 63 (b) Fig. 64 Let us now see how to find the resuilant of two forces acting along the same line but in opposite directions. For that purpose, we put a l9ad of 5 Non the pan of the household scales shown in Fig. 65a. We tie a thread to the pan and, hooking the thread by a spring balance, pull up with a force of 2 N (F ig. 65b). In that case, the balance whose pan bears the load will show the force of 3 N . This is the resultant of two forces, 5 Nand 2 N, its absolute value is equal to the difference between the absolute values of the component forces (3 N = 5 N - - 2 N), and acts in the direction of the larger force. Fig. 65 (a I (b) 67
Thus, the resultant of two forces acting along the same line but opposite in sense is in the direction of the force larger in absolute value, and its modulus is equal to the difference between the moduli of the component forces. (Fig. 66) If two equal forces opposite in directions are acting on a body, then the resultant of these forces is equal to zero. If in our experiment, for instance, we pull the thread up with a force of 5 N, the pointer of the spring bal- ance will show the zero division. In that case, the resultant of two forces is Fig. 66 equal to zero (5 N - 5 N = 0). Under the action of two equal and oppositely directed forces, the body is either at rest or moves uniformly and rectilinearly. ? 68 1. What force is known as the resultant of several forces? 2. What do we mean by addition of forces? 3. Give an example of an addition of two forces acting along the same straight line in the same direction. 4. Describe the experiment enabling us to find the resultant of two forces acting along the same line in the same direction. What is that resultant equal to? 5. What is the resultant of two forces equal to if the forces act along the same line but in opposite directions? 6. How will a body move under the action of two equal and oppositely directed forces? Exercise 17 1. A man, whose mass is 70 kg, holds on his shoulders a box weighing 20 kg. With what force does the man press upon the earth? 2. In the tug-of-war game, four people participate. Two of them pull the rope in one direction with the forces of 330 Nand 380 N, and the other two pull it in the opposite direction with the forces of300 Nand 400 N. In what direction will the rope move and what is the resultant of these forces equal to? Make a drawing. 3. Performing a parachute jump, the man moves uniformly. The force of gravity of the man with the parachute is 700 N. What is the air resistance? 4. There are two spring balances, each designed for the force of 10 N. How can they be used to calculate the weight of a body with the mass of 1.5 kg? What is it equal to?
34. The Friction Force Coming down a hill in a hand-sledge, you keep sliding in the horizontal way by inertia. You do not move uniformly, however, the speed of the sledge gradually decreases and in some time you come to a stop. Having worked up speed, the skater keeps moving for some time, but however smooth the ice is, he eventually stops. The bicycle also rolls to a stop when the cyclist stops pedalling. We know that a force is responsible for every change, decrease in the given case, in the speed of motion. This means that in the examples considered a force acts on a moving body. A force arising when one body moves over the surface of another body and d irected opposite to the motion is called a friction force (Fig. 67, F). A force of friction is one more kind of force that differs from the force of gravity and the elastic force we have considered. One of the causes offriction is the roughness of the faces of the bodies in contact. Even seemingly very smooth surfaces of bodies have lumps and scratches. In Fig. 68a they are shown magnified. When a body slides or rolls over the surface of another body, these tiny lumps catch on one another and a force arises that tends to prevent motion. Another cause of friction is mutual attraction of molecules of the surfaces in con tact. When the sunaces of bodies are rough-finished, friction originates due to the first cause, as a rule. But if the surfaces of bodies are highly polished, then, when they come in contact, some of their molecules are so close to one another that the attraction between them becomes essential. The force of friction can be decreased considerably by lubricating the contacting surfaces. A layer of lubricant (Fig. 68b) separates the surfaces of Fig. 67 F Fig. 68 69
(b) Fig. 69 contacting bodies and prevents them from touching each other. Now it is not the surfaces of bodies that slide over each oth'er, but the layers of lubricant. In the majority of cases, lubricants are liquid, and the friction between layers of liquids is usually less than between solid surfaces. The small friction in skating, for instance, is also due to lubrication: a thin layer of water is formed between the skates and the ice. Various oils are usually used as lubricants in engineering. When one body slides over the surface of another, we speak ofsliding friction We can cite the movement of a sledge or skis on the snow as an example of this kind of friction. Now if one body rolls, rather than slides, over the surface of another body, we speak of rolling friction which shows up in the rotation of the wheels of a coach or a car, in the rolling of round logs or barrels on the ground. The force of friction can be measured. For instance, to measure the sliding friction of a block of wood over a board or a table, a spring balance should be attached to the block (Fig. 69a) and the block should be moved uniformly over the board. What is the reading of the balance? Two forces act on the block : the elastic force of the spring acting in the direction of motion and the force of friction opposing it. The uniform motion of the block signifies that the resultant of these two forces is equal to zero, i.e., the forces are equal in absolute value and opposite in direction. The spring balance shows that the elastic force (traction force) is equal to the friction force in absolute value. Thus, measuring the force exerted by a spring balance on a body in uniform motion, we find the force of friction . If we put a weight on the block or press it with the hand, and then measure the force of friction by the method described above, it will prove to be greater. The larger the force pressing the body to the surface, the greater the friction force. If we put the block of wood on two round sticks (Fig. 69b) and measure the rolling friction , it proves to be smaller than the sliding friction . Thus, the loads 70
being equal, the rolling friction is always less than the sl iding friction . This is the reason why even in antiquity people used some kinds of rollers to shift loads, and some time later they began to use wheels. ? I. 2. 3. 4. 5. 6. 7. 8. 9. 10. What observa tions and experiments can you cite that show the existence of friction? What force is known as friction? What are the causes of friction? How does lubrication affect friction ? Explain this. What kinds of friction do you know? When do we spea k of sliding friction? What is rolling friction? How can friction be measured? How can we show that friction depends on the force pressing the body to the surface? How can we show by experiments that with the loads being equal the sliding friction is greater than the rolling friction? 35. Static Friction We have studied the friction that occurs when a body moves over the surface of another body. But can we speak of friction between two contacting bodies at rest? When a body is at rest on an inclined plane, it holds on due to friction force. Indeed, if there were no friction, the body would slide down the inclined plane by gravity. Let us consider the same problem in the case when a body is at rest on a horizontal plane. Suppose, for example, a table is on the floor and we try to move it. If we exert a small effort, the table will not move. Why? In this case, the acting force is balanced by the force of friction between the floor and the legs of the table. Since that force prevents bodies from moving, it is called static fr iction . The force of static friction always opposes the motion that would have been initiated. It arises when we try to disturb the state of rest of the body. The maxtmum force of static friction is that which disturbs the state of rest of a body. F ig. 70 71
Figure 70 shows a model of a conveyer for transporting bales of cotton. The bales are kept on the conveyer belt by friction . ? 1. Give examples showing the existence of static friction. 2. What conditions are needed for static friction? 3. Give examples of practical application of static friction. 36. Friction in Nature and Engineering Friction is of great significance in nature and engineering. Friction can be advantageous and disadvantageous. In the former case, we try to increase it, in the latter case, we try to reduce it. Let us consider some exam pies. It is due to static friction that people and animals can walk. Indeed, when walking, we push off from the ground. Now if the friction between the sole of the shoe and the ground (or ice) is small, say, when the roads are ice-covered, it is difficult to push off from the ground, and we begin slipping. To prevent slipping, the pavements are sprinkled with sand. This increases friction between the sole and the ice. If there was no friction, things \ would slip out of our hands. Friction is responsible for braking a car. If there were no static friction, the car could not start moving. The wheels would rotate, spin, and the car would not move. To increase friction, the tread of their tires is given a suitable pattern (Fig. 71). In winter, when the road becomes especially slippery, chains are put on the driving wheels. Many plants and animals are supplied with special organs for catching hold (tendrils of plants, the trunk of an elephant, tenacious tails of climbing animals). Fig. 71 72 3 Fig. 72. A plain bearing: 1 - bearing housing, 2- bear- ing shell, 3 - shaft, 4 - oil hole Fig. 73
Roller bearings All of them have a shape convenient for winding and a rough surface to increase friction. Let us indulge in some fantasies: what would happen to all of us if friction sudden ly ceased to exist in nature? But we have mentioned that in many cases friction is disadvantageous and must be reduced. In all machinery, for instance, friction is responsible for overheating and wearing out of moving parts. To reduce friction, the contact surfaces are made smooth by some lubricants. To reduce friction between the rotating shafts of machine-tools, they are carried in ball bearings . The part of the bearing directly touching the shaft is called an insert or she ll. The inserts are produced from hard materials, such as bronze, cast iron or steel. Their inner surface is covered with special materials, with the babbit 1 in most cases, and is lubricated. Figure 72 shows a bearing in which shaft 3, when rotating, slides over the surface of insert 2. Bearings of this kind are called slide or plain bearings . We know that with the same load the rolling friction is less than the sliding friction. The use of ball bearings and roller bearings is based on this phenomenon. In bearings of this kind, the rotating shaft does not sljde over the stationary insert but rolls along it on steel balls or rollers. Figure 73 shows the design of ball and roller bearings. The inner ring of the bearing, made of hard steel, is fitted on a shaft. The outer ring is fastened to the body of the machine. When the shaft rotates, the inner ring rolls on the balls or ro llers located between the rings. 1 Babbit is an alloy of lead or tin with some other metals. 73
A substitution of ball or roller bearings for slide bearings in a machine reduces friction 20 to 30 times. Ball and roller bearings are used in various machines : cars, turning lathes, electric engines, bicycles, etc. Present-day industry and transport cannot be imagined without bearings. ? l. What does friction mean in the life of men and animals? 2. What does friction mean for transport? 3. What ways do you know to reduce friction? 4. What purposes are served by bearings in machines? 5. How is a slide bearing constructed? How is a ball bearing constructed? 37. Intermolecular Forces. The Wetting Phenomenon Forces of attraction and repulsion act between molecules. We overcome the forces of attraction between molecules when we tear a thread, break a stick, chop ice, sprinkle water. For example, to tear a silk thread 1 sq mm in cross section, we must apply a force of about 250 N (to suspend a weight of 25 kg in mass, Fig. 74). Such is the force that is needed to overcome the attraction of the enormous number of molecules in the place where we tear the thread . When corn pressing bodies, we overcome the forces of repulsion of molecules. Repulsive forces are considerable at distances even sma !I er than those needed for attraction forces to come into action. Imagine two molecules at a distance several times la rger than the molecule itself (Fig. 75, top drawing). At such a distance the force of attraction of molecules is very small and the force of repulsion is smaller still. When the molecules come closer to each other, both forces increase, the repulsive forces increasing faster. With a further mutual approach of molecules, the force of repulsion becomes equal to that of attraction in absolute value (Fig. 75, in the middle). But when the molecules come still closer, both forces will keep Fig. 74 Fig. 75 74 I I I I I I ~ : --o-- 1
\we~~~? \0) (b) (c) F ig. 76 increasing. But since the force of repulsion increases faster, its absolute va lue becomes la rger than that of the force of attraction, and the molecules will repel each other (Fig. 75, bottom drawing). When we stretch, say, a steel cable, its molecules are separated, the attractive force becomes larger than the repulsive force, and the cable contracts again if we sto p stretching it. When we compress the cable, the molecules come close to each other, the force of repulsion becomes larger than that of attraction, and the cable will resume its previous length if we stop compressing it. This all means that the elastic force in the cable is caused by intermolecular forces . The phenomenon of wetting a solid by a liquid , often observed in practice, can also be explained by attraction of molecules. Let us make an experiment to get acquainted with this phenomenon. We suspend a glass plate in a horizonta l position by means of a thin spring. Then we take a vessel full of water and put it under the plate so that the latter lies on the surface of the water (Fig. 76a). If we now try to raise the plate very slowly, it will stick to the water for some time and the spring will gradually stretch (Fig. 76b). By the amount of the spring extension we can estimate the force of attraction between the molecules that keeps the plate on the surface of the water. Finally, the glass plate breaks away from the water (Fig. 76c) and it proves to be wetted. This means that the break occurs not in the places where the water molecules are in touch with those of the glass, but in the places of contact of the water molecules. Water wets glass, as well as wood , lea ther, and many other substances. If we immerse a plate of wax or paraffin in water and then take it out, the plate turns out to be dry. This means that water does not wet wax and paraffin. It does not wet all oily surfaces either. Mercury does not wet cast iron (it is usually stored in cast-iron vessels), but it wets go ld, zinc, and some other subs tances. In the cases when a liquid wets a solid, the mutual a ttraction of its molecules is weaker than the attraction between its molecules and those of the solid. Whereas when a liquid does not wet a solid, that means that the attraction between the molecules of the liquid is stronger than that between its molecules a nd the molecules of the solid. The phenomena of wetting and nonwetting are taken into account and used 75
in practice. We dry ourselves with a towel made of a fabric which can be wetted with water, write on the paper which can be wetted with ink, and use pens made of metal which can also be wetted with ink. It is of interest that water-fowls grease their feathers with fat, extracted by a special gland , by means of their beaks. There is a layer of down under the feathers, which contains air; since the feathers cannot be wetted with water, an air bubble results. The average density of a bird is small and this helps it to keep on the surface of the water. ? I. Give an example of overcoming the forces of attraction of molecules. 2. Why do the molecules of a body not come very close to each other? 3. How do the forces of attraction and repulsion of molecules change when the molecules gradually approach one another? 4. Why does a stretched steel cable contracts when the action of the force ceases? 5. Describe the experiment in which we observe the wetting of glass with water. 6. Give examples of wetting and nonwetting of solids with liquids. 7. How can you explain wetting and nonwetting proceeding from the molecular interaction? 8. How is wetting taken into co nsideration in practical applications? 38. Pressure. Units of Pressure You know how difficult it is to walk through soft snow, you sink into it at every step (Fig. 77a). But if you are on skis, you can run over the snow without sinking into it (Fig. 77b). Why is it so? On skis or without them , you act on the snow with a force equal to your weight. But the action of that force is different in the two cases because of the difference in the surface area on which you exert pressure. The surface area of a ski is almost twenty times as large as that of the soil of your shoe. Therefore, on skis, you Fig. 77 (ll) (b) 76
Fig. 78 (a) (b) exert pressure on each square centimetre of the surface area of the snow which is almost twenty times as small as that when you walk through the snow without skis. A school-boy pinning a wall newspaper to a board acts on each drawing-pin with the same force. But a pin with a sharper end enters the wood of the board much easier. Hence, the result of the action of a force depends not only on its absolute value, but also on the area of the surface on which it acts at right angles. This inference is substantiated by experiments. Drive a nail into each corner of a small board. Then put the board on sand with the nail-heads downwards and press it down with a weight (Fig. 78a). The nail-heads go down into the sand only very slightly. Then turn the board over and put it on the sand nail-heads upwards (Fig. 78b). In this case, the supporting area becomes smaller and the nails sink much deeper into the sand under the action of the same force. Thus, the result of the action of a force depends on the value of the force acting on. each unit of the surface area. In the examples considered, the forces acted at right angles to the surface of the body. The weight of the body was perpendicular to the surface of the snow; the force acting on a pin was perpendicular to it~ surface. Pressure is the quantity equal to the ratio of the force acting at right angles to a surface to the area of that surface. Consequently, to determine the pressure, we must divide the force, acting at right angles to the surface, by the area of the surface. force F pressure = - - , or P = -A , area where pis the pressure, F is the force acting on the surface, and A is the area of the surface. The unit 61 6ressure is the pressure exerted by a force of 1 N on 1 sq m. In the abbreviated form, this unit is written as 1 N /m 2 . In honour of the French scientist Pascal, the unit of pressure equal to l N /m 2 is called a pascal (abbreviated as Pa). Thus we have 77
I Pa =I N/m 2 . In practical applications, hectopascals( hP~ and kilopascals( kP~ are also used as units of pressure. 1 hPa = I 00 Pa; 1 kPa = 1000 Pa. EXAMPLE. Calculate the pressure exerted on the floor by a boy whose mass is 45 kg and the area of whose shoe sole is 300 sq cm. ? Given : m= 45 kg, A= 300 cm 2 = = 0.03 m2 . p ... ? Solution: p = F/ A, F=P, P= gm. P = 9.8 Njkg · 45 kg::::: 450 N, 450 N p = --- = 15 000 Pa = 0.03 m 2 = 15 kPa. 1. Give examples showing that the action of a force depends on the bearing area on which the force acts. 2. Why does a boy on skis not sink into soft snow ? 3. Why does a sharp drawing-pin enter a block of wood easier than a blunt one? 4. What experiment can you cite which would show that the action of a force depends on the bearing area? 5. What is pressure? 6. How can pressure be determined? 7. What pressure units do you know? Exercise 18 1. A caterpillar tractor with the mass of 6610 kg has the bearing area of both caterpillars equal to 1.4 sq m. Find the pressure exerted by the tractor on the ground. 2. A man presses the spade with the force of 600 N. What pressure does the spade exert on the ground if the width of the spade is 20 cm and the thickness of its cutting edge is 0.5 mm? 3. A boy with the mass of 45 kg stands on skis. Each ski is 1.5 m long and 10 cm wide. What pressure does the boy exert on the ·snow? 39. Pressure in Nature and Engineering A heavy caterpillar tractor, whose weight is hundreds of thou- sands of newtons, exerts a pressure on the ground which is only twice or thrice as large as that of a boy weighing 450 N. That pressure is approximately equal to 40-50 kPa. This is due to the fact that the weight of the tractor is distributed over the larger area. The larger tly! bearing area, the smaller the pressure exerted by the same force on that area. Depending on w)lether a high or a low pressure must be obtained, the bearing area is either increased or reduced. For example, for the ground to bear the pressure of a building constructed on it, the area of the lower part of its foundation must be increased (Fig. 79). 78
The tires of trucks and the undercarriages of aircraft are made considerably wider than those of passenger motorcars (see the picture on p. below). Cars intended for travelling in deserts over sand are made with especially wide tires. A heavy-duty tractor, a tank or a car intended for crossing marsh land (see the picture on p. 80), with a large bearing area of their tracks, negotiate marshland, which even a rider on horseback will not be able to cross. On the other hand, if the bearing area is small, high pressure can be produced by a small force. For instance, pressing a drawing-pin into wood, we act on it with a force of about 50 N. Since the area of the pin The TU-144 airplane undercarriage Fig. 79 79
point IS 0.1 sq mm, the pressure exerted on the wood is 50 N P = 0.0000001 m 2 500 000 000 Pa = 500 000 kPa. This pressure is 10000 times that exerted by a caterpillar tractor on the ground. That is why cutting and piercing tools, such as knives, scissors, cutters, saws, needles, are well sharpened. Cutting and piercing devices can also be met in nature. Here belong teeth and claws, beaks and thorns, all made of hard material, smooth and very sharp. ? 1. Give examples of using large bearing areas to reduce pressure. 2. Why are the wheels of agricultural machinery made with wide rims? 3. Why do cutting and piercing tools exert very high pressure on objects? Exercise 19 1. Consider the design of flat pliers and pincers (Fig. 80). Which of these tools can exert a higher pressure on the object gripped by them if the same force is applied? 2. Why must heavy objects be placed on a harrow when hard soil is being harrowed? 3. When does a man exert a higher pressure on the floor: when he is standing or running? Assignments 1. Knowing your mass and the area of your shoe, calculate the pressure you exert on the ground when you are walking and when you are standing. A heavy-duty car intended for soft snow and marshland 80
Fig. 80 Fig. 81 Find the bearing area of your shoe as follows. Put your foot on a sheet of graph paper and outline the contour of the part of the sole bearing the leg (Fig. 81). Count the number of full squares within the contour and add half the number of incomplete squares crossed by the outline of the contour. Multiply the number obtained by the area of a square and then find the area of the sole of your shoe. 2. Measure the length, width, and height of a brick. Find its volume. Use Table 2 to find the density of a brick and calculate its mass, and then its weight. Calculate the area of the faces and sides of the brick. Find ti1e pressure the brick exerts when it lies on its face. What is its pressure when it lies on the larger side? on the smaller side? Make drawings of various positions of the brick. 40. Gas Pressure We have learned that as distinct from solids and liquids, gases fill up the whole volume of the container, say, a steel cylinder for storing gases, automobile inner tube or a volley-ball. The gas exerts pressure on the walls of the cylinder, tube or any other body with which it is in contact. Let us consider the following experiment. A small rubber ball, with its neck tied up, is placed under the glass bell of an air pump. The ball contains a small amount of air (Fig. 82a) and is irregular in shape. Then the air is pumped out of the bell. The casing of the ball, around which the air becomes more and more rarefied, gradually distends and assumes the shape of a ball (Fig. 82b). How can you explain this experiment? Gas molecules are known to move in disorder with great speeds. In their motion, they collide with other molecules and with the walls of the vessel containing the gas (Fig. 83). Since there is an (a) Fig. 82 6-971 (b) Fig. 83 81
enormous quantity of molecules in a gas, the number of the collisions is very large. It has been calculated that in an ordinary, noncompressed gas, the number of collisions of molecules per 1 sq cm of the walls of the vessel per second is expressed by a 23-digit number. Although the force exerted by one molecule is very weak, the action produced by a large number of molecules when they hit the walls of the vessel is rather considerable, and that is precisely the pressure of the gas. Thus, the pressure of a gas on the walls of the vessel (and on a body in the gas) is caused by the gas molecules that hit the walls of the vessel. In our experiment, the moving molecules keep bombarding the ball from within and from without. When the air is pumped out, the number of molecules in the ball, around the ball casing, decreases. But inside the tied-up ball, their number does not change. Therefore, the molecules knock against the inner walls of the casing more often than against the outer walls, and the ball begins to distend until the elastic force of its rubber casing becomes equal to the force of gas pressure. A spherical shape the casing of the ball assumes shows that the pressure of the gas on the walls of the casing is the same in all directions, or, to put it otherwise, the number of hits of the molecules per every square centimetre of the surface area is the same in all directions. The same pressure in all directions is characteristic of a gas and is a consequence of a chaotic motion of a huge number of molecules. It is evident that the pressure of a gas on the walls of the container is the greater, the more often the molecules hit the walls. If we reduce the volume of the gas, but so that its mass remains unchanged, the number of molecules per cubic centimetre will increase and the density of the gas will become greater. Then, the molecules will hit the walls of the container more often, i.e., the pressure of the gas will increase. This assertion can be substantiated by an experiment. Figure 84a shows a glass tube, one end of which is closed with a thin rubber membrane. A piston is inserted into the tube. When the piston is pushed in, the volume of air in the tube decreases, i.e., the gas is corn pressed (Fig. 84b ). In that case, the rubber membrane stretches and bulges out indicating that the air pressure in the tube increased. Conversely, when the volume of a given mass of the gas increases, the number of molecules per cubic centimetre decreases. Consequently, the number of hits against the walls of the container will reduce and, hence, the pressure of the gas will decrease. Indeed, when we pull the piston out of the tube, the air volume in it increases and the membrane bulges in (Fig. 84c) indicating a decrease of air pressure in the tube. If we fill the tube with any other gas instead of air, we shall observe the same phenomena. Thus, the pressure of a gas increases when the volume of the given mass of the gas is reduced, and drops when the volume is increased. And how will the gas pressure change upon heating, the volume remaining constant? We have learned that the speed of gas molecules increases upon heating. Moving faster, the molecules will hit the walls of the container more often. In addition, their hits will become harder. Consequently, the walls of the container will be subjected to a higher pressure. 82
! (a) (b) (c) Fig. 84 Fig. 85 ·:~ ..................··~...·.::·.. Thus, the pressure of the same mass of a gas in a given volume is the greater, the higher is the temperature of the gas. When a gas is to be stored or transported, it is compressed to a large extent, which causes a rise in pressure. Therefore, gases are stored in special, very strong steel cylinders (Fig: 85). Such cylinders are used, for instance, to store compressed air in submarines, oxygen used in welding, and many other gases. ? 1. What experiment can we perform to show that gas exerts pressure on the walls of the container? 2. How can the gas pressure be explained from the point of view of molecular motion? 3. What facts indicate that gases exert the same pressure in all directions? 4. Why does the gas pressure increase upon compression and decrease upon expansion? 5. In what state does the gas exert a higher pressure, cold or heated? Explain why it is so. 6. Why are compressed gases stored in special cYlinders? 7. How will the pressure of a gas change if we connect the container with a similar empty cylinder?
Pressure of Fluids (Hydrostatics and Aerostatics 1 ) 41. Transmission of Pressure by Fluids. Pascal's Law As distinct from solids, separate layers and fine particles of fluids 2 can move freely relative to one another in all directions. It is sufficient, for instance, to begin slightly blowing at the surface of the water in a glass to cause its motion; a slight wind sends ripples over the surface of a river or a lake. Due to the free mobility of particles of fluids, the pressure exerted on them is transmitted not only in the direction of the force applied, as in solids, but in all directions. Let us consider this phenomenon in more detail. Figure 86 illustrates a vessel with a fluid in it. The vessel is covered with a movable piston. The dots represent the particles of the fluid distributed uniformly over the whole volume of the vessel (Fig. 86a). Applying some force, we make the piston move slightly into the vessel and compress the fluid immediately under the piston. Then, the particles in that place will be still closer to each other than they were before (Fig. 86b). Due to their mobility, the fluid particles will move in all directions and, consequently, their distribution will again become uniform though more dense than before (Fig. 86c) and, therefore, the pressure of the fluid will increase everywhere. Hence it follows that an additional pressure is transmitted to all particles of the fluid. For instance, if the pressure exerted on the gas immediately under the piston increases by 1 Pa, the pressure will increase by the same amount at all the points inside the gas. The pressure exerted on the walls of the vessel will also increase by 1 Pa. 84 1 From the Greek words hydro meaning water, aero, a ir, and sraros, standing. 2 A collective term embracing liquids and gases.- Tr. Fig. 86
Pasca l, Blaise (1623- 1662), a French scientist. He discovered and investigated a number of significant properties of fluids. His interesting and convincing expe riments confirmed the existence of a tmospheric pressure discovered by the Ital ian scientist Torricelli. Th e pressure exerted on a Ouid is transmitted undiminished to every point of the fluid . This statement is known as Pascal's law. Proceeding from Pascal's law, we can easily explain the following experiments. Figure 87 shows a hollow sphere with sma ll holes in its sides. A tube with a piston inserted into it is attached to the sphere. If we fill the sphere with water and push the piston, the water spurts out of all the holes. In this experiment, the piston exerts pressure on the surface of the water in the tube. The particles of water immediately under the piston become denser and transmit pressure to the other layers down the tube. Thus, the pressure of the piston is transmitted in all directions. As a result, part of the water is squeezed out of the sphere in the form of little jets flowing out of all the holes. If we now fill the sphere with smoke and then push the piston, jets of smoke will spurt out from all the holes (Fig. 88). This confirms that gases. too. transmit the pressure exerted on them identically in all directions. Fig. 87 F ig. 88 85
Fig. 89 Fig. 90. Bottle manufacture: I - tube, 2- glass, 3 - mould ? 86 I. How is pressure transmitted by fluids ? 2. How can you explain that fluids transmit pressure identically in all directions? 3. Quote Pascal's law . 4. What experiments show the peculiarities of pressure transmission by fluids? Exercise 20 I. Using Fig. 89, explain the transmission of press ure by so lids, loose materia ls, and liquids. Draw a diagram and show by arrows how pressure is transmitted . 2. When a ta rpaulin water hose is not filled with water, it has a shape of a flat ribbon. What shape will the hose assume after it is filled with water? Ex plain this phenomenon. 3. To manufacture a bottle, air is blown through a tube a nd the molten glass assumes the shape of a bottle (Fig. 90). What physical phenomenon is responsible here?
\s'>Ignments l. Make soapy liquid and blow soap-bubbles with the aid of a glass tube. What shape do they assume and why? 2. Analyse pressure transmission in a loose material. For that purpose, pour sand or peas into a paper bag and exert a strong pressure on the bag from above. Is there anything in common with pressure transmission in liquids and gases? 42. Free Surface of a Liquid A free surface of a liquid is the surface which ts not in contact w tth the walls of the vessel. A force of gravity acts on a liquid contained in a vessel. Under gravity the liquid is displaced from the higher to the lower places until all the molecules forming the free surface are distributed on the same height or the same level. \m horizontal surface is called a level. A device making it possible to set a surface in a horizontal position is also called a level (Fig. 91). As distinct from liquids, gases have no free surfaces. And it is clear why. In a gas, molecules are at considerably larger distances from one another than in a liquid (Sec. 13). Their mutual attraction is, therefore, very small and gas molecules scatter in all directions filling up the whole volume of the container. •) ~- .... .. - ..,, . - . ~ Fig. 91 Fig. 92 l. What surface of a liquid is known as a free surface? 2. How can you explain that in sufficiently wide containers the free surface of a liquid is horizontal? 3. How do you call the device used to verify whether the surface is really horizontal? 4. How can you explain the absence of a free surface in a gas? As.,ignments I. Verify with the aid of a plumb and a right triangle that the free surface of a liquid in the vessel is horizontal. Make a drawing of the experiment. 2. Figure 92 illustrates a water-lcn:l made from hard paper or cardboard. 87
Make such a device and verify with its aid whether the window-sill, the table, and the floor are horizontal. 3. With the aid of a level and wooden wedges set a sheet of a plywood or a small board in a horizontal position. Put a steel ball on the surface of the plywood. If the surface of the plywood is horizontal, the ball will not roll down. 43. Pressure in Flu ids A force of gravity acts on liquids just as on all the bodies on the earth. Therefore, a liquid poured into a vessel creates pressure, due to its weight, which is transmitted in all directions in accordance with Pascal's law. Consequently, there is pressure inside the liquid. We can make an experiment to confirm this fact. We pour water into a glass tube whose lower end is closed with a thin rubber membrane. Under the action of the weight of the liquid the rubber bottom of the tube bulges out (Fig. 93a). The experiment shows that the higher the water column above the rubber membrane, the more it bulges out (Fig. 93b). But every time the rubber bottom bulges out, the water in the tube attains equilibrium (stops in a horizontal position) since besides gravity it is acted upon by the elastic force of the rubber membrane. Let us immerse a tube, which has a rubber bottom and is filled with water, in another, wider vessel filled with water (Fig. 93c). We see that as we gradually push the tube down, the rubber membrane gradually straightens out. Finally the membrane becomes plane which indicates that the forces acting on it from (a) Fig. 93 ( c ) Fig. 94 88
Fig. 95 (a) (b) above and from below are equal. At that moment the level of the water in the tube coincides with that in the vessel. The same experiment can be performed with a tube in which a rubber membrane covers a side opening as shown in Fig. 94a. If we immerse the tube with water in another vessel filled with water as shown in Fig. 94b, we shall see again that the membrane will straighten out as soon as the water levels in the tube and in the vessel coincide. This means that the forces acting on the rubber membrane are equal on both sides. Especially illustrative is an experiment with a vessel whose bottom can drop off. Such a vessel is immersed in a jar with water (Fig. 95a). The bottom of the vessel is pressed tightly to its edge by the pressure of the water from below. Then water is accurately poured into the vessel. The bottom drops off when the water level in the vessel coincides with that in the jar (Fig. 95b). At the moment when the bottom separates from the vessel, a water column in the vessel presses it from above and the same column of water in the jar presses it from below. The pressure from above and that from below are equal, and the bottom drops off from the vessel because of gravity. In the experiments described we used water, but it is easy to infer that the result would be the same if we took some other liquid instead of water. Thus, experiments show that there is pressure inside a liquid, and at the same level it is the same in all directions. Pressure increases with depth . In this respect, gases do not differ from liquids since they also have weight. But it should be borne in mind that the density of gas is hundreds of times smaller than that of liquid. The weight of the gas contained in the vessel is very small and the pressure due to its weight can be disregarded in many cases. ? I. How can we prove experimentally that pressure inside a liquid is different at different levels and the same in all directions at the same level? 2. Why can we disregard in many cases the pressure in gas created by its weight? 89
44*. Calculating the Pressure of a Liquid on the Bottom and Walls of a Vessel Let us see how we can calculate the pressure exerted by a liquid on the bottom and walls of a container. We shall first solve a problem with numerical data. Assume that a rectangular tank is filled with water (Fig. 96). The area of the tank bottom is 16 sq m, its height is 5 m. Find the pressure exerted by the water on the bottom of the tank. The force with which the water acts on the bottom of a vessel is equal to the weight of a column of water 5 m high and with the bottom area of 16 sq m; in other words, that force is equal to the weight of all the water in the tank. To find the weight of the water, we must know its mass, which can be found from the volume and density of the water. Let us find the volume of the water in the tank, multiplying the area of the bottom of the tank by its height: V= = 16m 2 · 5 m= 80m 3 . Now we shall seek the mass of the water, for which purpose we shall multiply its density, p = 1000 kgjm 3 , by the volume: m= = 1000 kg/m 3 ·80m 3 = 80 000 kg. We know that to find the weight of a body, we must multiply its mass by 9.8 N/kg, since a body with a mass of 1 kg has a weight of 9.8 N. Consequently, the weight of water in the tank is P = = 9.8 Njkg · 80000 kg~ 800 000 N. This is the force with which the water presses on the bottom of the tank. Dividing the weight of the water by the area of the bottom of the tank, we find the value of p : 800000 N p = = 50 000 Pa = 50 kPa . 16m 2 We can also calculate the pressure exerted by a liquid on the bottom of a vessel by using a formula which is much simpler to do. To derive that formula, let us return to the problem, but this time we shall solve it in a general form. We designate the height of the liquid co lumn in a vessel ash and the area of its bottom as A. The volume of the liquid column V= Ah. The mass of the liquid m= p V, or m= pAh. Fig. 96 90
The weight of the liquid P =gm, or P = gpAh. Since the weight of a column of a liquid is equal to the force exerted by the liquid on the bottom of the vessel, we can divide the weight P by the area A to obtain the pressure p: that is, p = gph . gpAh or p= - A-, We have obtained a formula for calculating the pressure exerted by a liquid on the bottom of a vessel. We can see from this formula that the pressure exerted by a liquid on the bottom of a vessel is directly proportional to the density and height of the column of liquid . This formula can also be used to calculate the pressure exerted on the walls of the vessel as well as the pressure inside the liquid, the upwards pressure inclusive, since at the same depth the pressure is the same in all directions. To calculate the pressure by the formula p = gph, the density p must be in kilograms per cubic metre (kg/m 3 ), and the height of the liquid column h in metres (m), g = 9.8 Nfkg. Then the pressure will be in pascals (Pa). EXAMPLE. Find the pressure exerted by petroleum on the bottom of a tank if the height of the column of petroleum is 10 m and its density is 800 kg/m 3 . Given: h= 10 m, kg p =800 - 3. m p ... ? Solution: p = gph . N kg p= 9.8 - ·800 - ·10 m~ kg m 3 ~80000 Pa~80 kPa. 1. On what quantities does the pressure of a liquid on the bottom of a vessel depend? 2. What is the relation between the pressure exerted by a liquid on the bottom of a vessel and the height of the liquid column? 3. What is the relation between the pressure exerted by a liquid on the bottom of a vessel and the density of the liquid? 4. What quantities must we know in order to calculate the pressure exerted by a liquid on the walls of a vessel? 5. What formula do we use to calculate the pressure exerted by a liquid on the bottom and walls of a vessel? 91
Fig. 97 - I ~ Fig. 98 Exercise 21 I. Find the pressure in water, kerosene, mercury at a depth of 0.6 m. 2. Calculate the pressure exerted by water on the bottom of one of the deepest sea hollows, whose depth is 10 900 m. The density of sea water is 1030 kg/m 3_ 3. Figure 97 shows a football bladder connected with a vertical glass tube. There is water in the bladder and in the tube. The bladder is covered with a small plate and a weight of mass of 5 kg is on the plate. The height of the water column in the tube is 1 m. Find the contact area of the plate and the bladder. Assignments 1. Take a tall vessel. Make three small vertical holes in its lateral surface at different heights from the bottom. Close the holes with matches and fill the vessel with water to the brim. Then open the holes and watch the jets of water spurting from the vessel (Fig. 98). Answer the following questions. Why does the water flow out of the holes? What indicates that pressure increases with depth? 2. At the end of the book you will find the sections "A Hydrostatic Paradox. Pascal's Experiment" and "Pressure at the Bottom of Seas a nd Oceans. lnvestigation of Sea Depths". Read them. 45. Communicating Vessels Figure 99 illustrates two vessels connected by means of a rubber tube. Vessels of this kind are known as communicating vessels. A watering-can, a tea-pot, a coffee-pot are examples of communicating vessels (Fig. 100). We know from experience that water poured into a watering-can , for instance, is always at the same level in the reservoir and in the side tube. The following simple experiment can be performed with communicating vessels. We take two glass tubes and connect them by means of a rubber tube (Fig. 99a). At the beginning of the experiment, we clamp the rubber tube at its middle and pour water into one of the glass tubes. Then we remove the clamp and the water begins flowing into the other tube until the surfaces of water in both tubes become level (Fig. 99b). We can secure one of the tubes in a holder and raise or lower the other tube, or incline it as we please. In that case, the levels in both tubes will be equal as soon as the liquid becomes stationary (Fig. 99c). 92
I I I- a a b b ( I ( ~ -(a) (b) (C) Fig. 99 Fig. 100 n Fig. 101 Fig. 102 The free surfaces of a liquid at rest in communicating vessels of any shape (F ig. 101) are on the same level. In a liquid at rest in communicating vessels the pressure at any level, aa, bb, cc (Fig. 99b), is the same, and therefore, the heights of the columns of liquid above those levels are also the same. If we pour a liquid of one kind into one limb of the communicating vessels and of another kind into the other limb, then, upon reaching equilibrium, the liquids will not be at the same level. And this is quite understandable since we know that the pressure exerted by a liquid on the bottom of a vessel is in direct proportion to the height of the column and to the density of the liquid. The forces of pressure being equal, the column of the liquid having greater density is lower than that of the liquid having smaller density (Fig. 102). 'I 1. What examples of communicating vessels can you give? 2. What positions do the free surfaces of a homogeneous liquid take in communicating vessels? 3. What positions do the free surfaces of different liquids take in communicating vessels? 93
Fig. 103. Water-level gauge a steam boiler: 1 - steam, 3 - water-level gauge glass glass of 2 - valve, Fig. 104 Fig. 105 94 ~---- Exercise 22 l. Figure 103 shows a water-level gauge glass of a steam boiler. Explain the principle of operation of this device. 2. Figure 104 shows a model of a geodetic level used to establish a horizontal line on a site. Explain how the instrument works. 3. Figure 105 illustrates the design of an artesian well. Earth layer 2 consists of sand or some other porous material easily penetrated by water. Conversely, layers 1 and 3 are watertight. Explain the operating principle of such a well. 4. Prove that the heights of different liquids in communicating vessels are inversely proportional to the densities of the liquids. Hint. Use the formula for · calculating the pressure of a liquid. Fig. 106
Lock of the Moskva canal Fig. 107 Ass ignments I. Figure 106 shows a tall tin can which is closed from all sides and has a hole in the cover. The hole can be closed by means of a stopper with a funnel covered by a rubber membrane. Three holes are made in the side surface of the can into which narrow glass tubes are inserted. Make such an instrument, fill the can with water and answer the following questions : ( 1) Why the water columns in the tubes are different in height? (2) What do the heights of the water columns in the tubes indicate? Pressing slightly the rubber membrane in the funnel, watch the change in the heights of the water columns in the tubes. (3) Why is the change in heights of the water columns the same in all the tubes? 2. Think of the simplest techniques that can be used to construct a fountain somewhere in a park or in a garden. Draw a diagram of the design and explain its operating principle. 3. Figure I 07 shows the lock of a canal and Fig. 108 presents a schematic 95
96 Fig. 108 8 Fig. 109 Water tower Fig. 110 diagram of ship locking. Look carefully at the diagram and explain the operating principle of locks. What phenomenon that you know is used in the operation of locks? Look at the scheme of location of the locks in the Lenin Volgo-Don Canal (Fig. 109). To what height is a ship raised when it passes the canal, going from the Volga to the Don and back again from the Don to the Volga? 4. Figure 110 is a schematic diagram of a water-supply system of some kind. Explain the principle of the water supply using this diagram. What is the part played by a water-tower in this scheme?
46. The Weight of Air. Atmospheric Pressure The force of gravity acts on air as on any body on the earth and, consequently, air possesses weight. The weight of air can be measured by way of an experiment. For that purpose, we must take a strong glass bulb closed with a stopper with a clamped rubber tube inserted into it (Fig. 111). We pump the air out of the bulb and weigh it on a balance. If now we open the clamp and let air into the bulb, the balance will be disturbed. To attain the equilibrium again, we must put weights on the other pan of the balance equal to the weight of the air in the volume of the bulb. It has been found by means of very accurate experiments that in ordinary conditions the weight of 1 cubic metre of air is 13 N. The air envelope surrounding the earth is called the atmosphere' . As the observations of earth satellites have shown, the atmosphere extends as far as several thousands of kilometres. We live at the bottom of a huge air ocean. The surface of the earth is the bottom of that ocean. Due to gravity the upper layers of air, like the water of the ocean, compress the lower layers. The air layer adjacent to the earth is compressed more than the other layers and, in accordance with Pascal's law, transmits the pressure exerted on it in all directions. As a result, the earth surface and all the bodies on it experience the pressure of the whole column of air or, as is customary to say, experience the atmospheric pressure. Many phenomena can be explained by the existence of the atmospheric pressure. Let us consider some of them. 1 From two Greek words: atmos meaning vapour, and sphere, a ball. ' Fig. 111 Fig. 112 Fig. 113 97 7-971
Figure 112 shows a glass tube with a tightly fitting piston working inside it. The end of the tube is immersed in water. If we now pull up the piston, the water will follow it upwards. This occurs because when we pull up the piston, a vacuum is created between the piston and the water. Under the pressure of the outer air, the water rushes into that space, following the piston. Figure 113 shows a cylindrical vessel closed with a stopper into which a tube with a tap is inserted. The air is pumped out of the vessel. Then , the end of the tube is immersed in water. If we now open the tap, the water will spout like a fountain into the vessel. The water flows into the vessel because the atmospheric pressure exceeds the pressure of the rarefied air in the vessel. In what follows, we shall consider a number of other phenomena, which can be explained only by the atmospheric pressure. ? I. How can you detem1ine the weight of air experimentally? 2. What is the weight of 1 cu m of air? 3. What is the atmosphere of the earth? 4. What is the cause of the atmospheric pressure? 5. Describe the experiments proving the existence of the atmospheric pressure. 47. The Existence of an Air Envelope of the Earth As all other bodies, molecules of gases constituting the air envelope of the earth are attracted by the earth. But why then do they not fall on the earth surface? How is the air envelope of the earth, its atmosphere, preserved? To answer these questions, it should be taken into consideration that molecules of gases constituting the atmosphere are in constant chaotic motion. But then another question arises: why do those molecules not fly away into outer space? To escape from the earth, a molecule, as well as a spaceship or a rocket, must have a speed not less than 11.2 km/s. This is the so-called escape velocity, whereas the average velocity of a molecule of the air envelope of the earth is considerably less than the escape velocity. And, therefore, the majority of them are tied to the earth by gravity. A chaotic motion of molecules and the gravitational attraction result in the fact that gas molecules "soar" in the space near the earth forming a free air envelope or its atmosphere. Measurements show that air density quickly diminishes with altitude. Thus, at an altitude of 5.5 km above the earth the air density is half that near the surface, at an altitude of 11 km, it is a quarter of that near the surface and so on. The higher up, the more rarefied the air is. And, finally , in the highest layers (hundreds and thousands of kilometres above the earth}, the atmosphere grad- ually turns into vacuum. The atmosphere does not have a precise boundary. Figure 114 is a schematic pattern of the distribution of gas molecules in the atmosphere of the earth. Strictly speaking, because of the force of gravit-y, the density of gas in any 98
closed vessel is not uniform throughout the entire volume of the vessel. It is greater at the bottom of the vessel than in its upper part and, therefore, the pressure in the vessel is not uniform: it is higher at the bottom than in the upper part. However, this difference in density and pressure of a gas in the vessel is so small that in many cases it can be neglected. But for the atmosphere extending to thousands of kilometres this difference is essential. ? Fig. 114 7' 1. Why do the molecules of gases constituting the atmosphere not fall on the earth under gravity? 2. Why do the molecules of gases constituting the atmosphere and moving in all directions not escape from the earth? 3. How does the density of the atmosphere change with altitude? Exercise 23 1. Figure 115 shows a siphoning tube serving for taking sam pies of various liquids. You immerse the tube in a liquid, close the upper end Fig. 115 Fig. 116 Fig. 117 99
with your finger, and then remove it from the liquid. When you remove your finger, the liquid begins flowing out of the tube. Make the experiment and explain the principle of operation of the device. 2. A pipette is an instrument serving to get drops of liquids (Fig. 116). Make an experiment using a pipette and explain the principle of its operation. 3. What physical phenomenon do we use when filling a pen with ink? 4. An automatic bowl for poultry (Fig. 117) consists of a bottle filled with water and placed upside down into a pan so that its neck is a little lower than the water level in the pan. Why does the water not flow out of the bottle? If the water level in the pan drops and the bottle neck comes out of the water, some water will flow out. Why? When does the water stop flowing out? Make such a device and stage the indicated experiments. 5. It is assumed that some time past the moon was surrounded with an atmosphere but gradually lost it. How can you explain this fact? 48*. Measuring the Atmospheric Pressure. Torricelli's Experiment It is impossible to calculate the atmospheric pressure in the way we calculated the pressure of a column of liquid in Sec. 44. Why? To make such a calculation, we must know the height of the atmosphere and the air density. But the atmosphere does not have a strict boundary, and the a a Fig. 118 Fig. 119 100
Torricelli. Evangclista (1608- 1647), an Italian scientist, a disciple of Galileo. He invented a mercury barometer and explained its principle by the existence of atmospheric pressure, and also worked up a number of other problems in physics and mathematics. air density, being the greatest at the earth surface, diminishes with altitude. And still it is possible to measure the atmospheric pressure, making use of the experiment suggested by the 17th-century Italian scientist Torricelli . Torricelli's experiment consists in the following. You take a glass tube, about 1 m long, soldered at one end, and fill it with mercury. Then, closing tightly the other end of the tube with your finger, you turn it upside down, and immerse it in a cup with mercury (Fig. 118). When you remove your fmger, some mercury Oows out into the cup and a column of mercury 760 mm high remains in the tube. There is no air in the tube above the mercury. Having suggested the experiment described above, Torricelli explained it. The atmosphere exerts pressure on the surface of mercury in the cup. The mercury is in equilibrium. This means that the pressure in the tube at the level aa (Fig. 118) is equal to the atmospheric pressure. But there is no air at the top of the tube and, therefore, the pressure at the level aa is created only by the weight of the mercury column in the tube. Hence it follows that the atmospheric pressure is equal to the pressure of the mercury column in the tube. Measuring the height of the mercury column in Torricelli's experiment, we can calculate the pressure exerted by the mercury, which is precisely equal to the atmospheric pressure. The higher the atmospheric pressure, the higher the mercury column in Torricelli's experiment and, therefore, the atmospheric pressure can be measured in practice by the height of the mercury column (in millimetres or centimetres). If, for instance, the atmospheric pressure is equal to 780 mm of mercury, then this means that air exerts the same pressure as a vertical mercury column 780 mm high. Consequently, l mm of mercury column (I mm Hg) is taken as a unit of atmospheric pressure. Let us find the relation between this unit and the unit of pressure we, know, a pascal. The pressure of a mercury column 1 mm high is: N kg p = gph, p= 9.8- ·13 6~ · 0.001 m:::::133.3 Pa. kg m 101
Fig. 120 Thus we have: 1 mm Hg = 133.3 Pa = 1.33 hPa . At present it is customary to measure the atmospheric pressure in hectopascals. Observing day by day the mercury column in the tube, Torricelli found that its height changed, either increasing or decreasing. Hence he inferred that the atmospheric pressure was not constant, it varied. He also noted that changes in atmospheric pressure were connected with changes in weather. If we attach a vertical scale to Torricelli's tube, we obtain a simple mercury barometer 1 , an instrument used to measure atmospheric pressure. ? I. Why is it impossible to calculate the pressure of air in the same way as we calculate the pressure a liquid exerts on the bottom or walls of a vessel? 2. Explain how Torricelli's tube can be used to measure the atmospheric pressure. 3. Explain what the following notation means: "The atmospheric pressure is equal to 780 mm Hg." 4. How do we call the device designed for measuring the atmospheric pressure? Describe it. 5. To how many hectopascals is the pressure of a mercury column of I mm equal? Exercise 24 I. Figure 119 shows a water barometer constructed by Pascal in 1646. How high was the water column in that barometer at the atmospheric pressure of 760 mm Hg? 2. To prove the existence of the atmospheric pressure, Otto von Guericke from Magdeburg made the following experiment. He pumped the air out of the cavity between two metal hemispheres fit together. The atmospheric pressure pressed the hemispheres so close together that they could not be separated by eight pairs of horses (Fig. 120). Calculate the force pressing the hemispheres together if it is assumed to be acting on an area of 2800 sq cm and the atmospheric pressure is 760 mm Hg. 3. The air is pumped out of a tube I m long, one end of which is welded and the other is fitted with a tap. Immersing the end with the tap in 1 The word barometer originates from two Greek words: haros meaning weight, gravity, and metreo, I measure. 102
Fig. 121 mercury, we open the tap. Will the mercury fill up the whole tube? If we take water instead of mercury, will it fill up the whole tube? Assignments 1. Put a glass into water, turn it upside down under the water, and then slowly pull it up. Why does the water remain in the glass (does not flow out) as long as the edge of the glass is under water? 2. Pour water into a glass, cover it with a sheet of paper and, slightly pressing the sheet to the glass with your hand, turn the glass upside down. If you now remove your hand, the water will not flow out of the glass (Fig. 121). The paper remains as though glued to the edge of the glass. Why? Substantiate your answer. 49. The Aneroid Barometer A metal barometer, called aneroid 1 , is commonly used to measure atmospheric pressure. It is shown in Fig. 122.. Its main part is a metal box 1 with wavy (corrugated) surface (Fig. 123). Air is pumped out of the box and, to save it from being crushed by the atmospheric pressure, a spring 2 is attached to its cover to pull it upwards. When the atmospheric pressure increases, the cover sags and stretches 1 Translated from the Greek, the word aneroid means without liquid. This barometer is so called because it does not contain mercury. Fig. 122 Fig. 123 103
the spring. When the pressure decreases, the spring straightens out the cover. A pointer 4 is attached to the spring by means of a system of levers 3, and can move to the right or to the left when the pressure changes. A scale fixed under the pointer is graduated by comparing its readings with those of a mercury barometer. Thus, the number 750, against which the pointer of the aneroid rests (Fig. 122), shows that at the given moment the height of the mercury column in a mercury barometer is 750 mm. Consequently, the atmospheric pressure is 750 mm Hg or approximately 1000 hPa. It is very important to know the atmospheric pressure in order to forecast weather for the next few days since changes in the atmospheric pressure are connected with changes in weather. A barometer is an instrument necessary for meteorological observations. ? I. How is an aneroid barometer designed? 2. How is the scale of an aneroid barometer graduated? 3. Why is it important to measure the atmospheric pressure systematically in various parts of the world? Assignments I. There is a barometer on the wall of the physics laboratory in your school. Use it to read the air pressure. Observe the changes in the atmospheric pressure for some time. 2. Look attentively at Fig. 122 and answer the following questions: (a) In what units of pressure are the upper and lower scales of the barometer graduated? (b) What is the value of a division of each scale? 3. Read the section entitled "How the Atmospheric Pressure Was Discovered" and be ready to make a report. SO. Atmospheric Pressure at Various Altitudes As we know (see Sec. 43), the pressure in liquids differs at different levels and depends on the density of the liquid and the height of its column. Because of the small compressibility of a liquid, its density at various depths is almost the same and, therefore, when calculating the pressure of the liquid, we assume its density to be constant and take into account only the changes in its level. The situation is more difficult when we deal with gases. Gases can be corn pressed to a large extent, and the more the gas is compressed, the greater its density and the more pressure it exerts. Remember that the gas produces pressure when its molecules hit the surface of the body. The air layers close to the surface of the earth are compressed by all the air layers above them. But the higher the air layer from the earth surface, the less it is compressed and the smaller its density, and, consequently, the less pressure it exerts. If, for instance, a balloon rises above the earth surface, the air pressure on it becomes less with altitude, not only because the air column becomes less above it, but also because the air density diminishes, it is less above than below. The relationship between the air pressure and the altitude is, therefore, more 104
ll!!tJ. mm 1000 900 son !OIJ 700 5lJ() 666 5JX) iOO j/}() 2110 232 200 354 171 308 267 /JJ !OV 0 0 At sea 1 km 2km 3km 4km Skm 6km 7km 8km 9km !Okm 11 km le vet Fig. 124 complicated than the dependence of the pressure of a liquid on the height of its column. Observations show that the atmospheric pressure at sea level is 760 mm Hg, on the average. The higher the place is above sea level, the less is the pressure there. The atmospheric pressure balanced by a column of mercury 760 mm high at 0 oc is said to be normal. The normal atmospheric pressure is equal to 101300 Pa = 1013 hPa. Figure 124 shows how the atmospho::ric pressure changes with altitude. When the altitude we rise to is not very high, the pressure diminishes by 1 mm Hg (or 1.33 hPa) with every 12 m, on the average. Knowing the relationship between pressure and altitude, we can determine the altitude above sea level by the change in the reading of the barometer. Aneroid barometers with a scale, which can be used to make direct measurements of the altitude, are called altimeters . They are employed in aviation and in mountaineering. ? I. How can you explain that the atmospheric pressure drops with rise above the earth surface? 2. What atmospheric pressure is said to be normal? 3. What do we call the instrument used to measure altitude according to the atmospheric pressure? What is it like? Exercise 25 I. Explain why airplane passengers feel pain in the ears when the airplane rapidly loses height. 2. How can you explain why ink flows out of a fountain-pen when a plane gains height? 3. At the foot of the mountain the barometer reading is 760 mm Hg and at the top it is 722 mm Hg. What is the height of the mountain? 4. Express the normal atmospheric pressure in hectopascals (hPa). 105
Hint. The pressure can be measured by the formula p = pgh, where g = = 9.8 Nfkg, h = 760 mm= 0.76 m, p = 13600 kg/m 3 . 5. The mass of a boy is 60 kg, his height is 1.6 m, and the surface of his body is approximately 1.6 sq m. Calculate the force the atmosphere exerts on him. How can you explain that he withstands such a large force without feeling it? Assignment Using the aneroid barometer, measure the atmospheric pressure on the ground and at the height of the last storey of your school building. Proceeding from the data obtained, find the distance between the storeys. Verify the result by means of direct measurements. 51. Manometers Instruments called manometers 1 or pressure-gauges are used to measure pressures higher or lower than the atmospheric pressure. We distinguish between liquid-column manometers and metal ones. Let us first consider the design and operation of an open liquid-column manometer. It is a glass U-tube containing some liquid. To understand the principle of its operation, we can use a rubber tube to connect it to a round fiat box, whose one end is covered with a rubber membrane (Fig. 125). If you slightly press the membrane with your finger, the level of the liquid in the limb of the manometer connected to the box becomes lower, and in the other limb it rises. How can you explain this? When you press the membrane, the air pressure in the box increases. According to Pascal's law, the pressure of the liquid in the limb of the manometer connected to the box also increases. There- fore, the pressure exerted on the liquid in this limb exceeds that ih the other limb, where the liquid is exposed to the action of the atmospheric pressure. Under the action of the force of the excess pressure, the liquid is displaced: it drops in the limb with the compressed air and rises in the other limb. The liquid will attain equilibrium (stop moving) when the excess pressure of the compressed air is balanced by the pressure exerted by the excess column of the liquid in the other limb of the manometer. The stronger we press the membrane, the higher the co lumn of the liquid and the greater the pressure it exerts. Therefore, we can judge the changes in pressure by the height of that column. Figure 126 shows how such a manometer can be used to measure pressure inside a liquid. The deeper we immerse the box in the liquid, the greater the difference in the heights of the liquid columns in the limbs of the manometer becomes and, consequently, the higher the pressure exerted by the liquid. If we place the box at some depth of the liquid and begin turning it with the membrane upwards, sideways, downwards, the readings of the manometer will not change. And it must be the case, since the pressure inside the liquid at the same level is the same in all directions. 1 The word manometer originates from two Greek words: manos meaning rare, thin, and metreo, I measure. 106
Fig. 125 Fig. 126 Figure 127 shows a metal manometer. Its main part is a metal tube 1 bent to form an arc (Fig. 128). Its one end is closed and the other end is connected by means of a tap 4 to a vessel in which the pressure is measured. When the pressure increases, the tube straightens out and the motion of its closed end is transmitted, via a lever 5 and a ratchet 3, to the pointer 2 moving along the scale. When the pressure drops, the tube assumes its original position due to elasticity, and the pointer reads zero again. ? l. How do we ca ll the instruments used to measure pressures above or F ig. 127 below the atmospheric pressure? 2. What is the design and the principle of operation of an open liquid- column manometer? 3. What is the design and the principle of operation of a metal manometer? 4 Fig. 128 2 107
52. Piston Pumps In Sec. 46 we described an experiment showing how the water was sucked by the piston moved up inside a glass tube under the action of atmospheric pressure. This phenomenon is used in the design of piston pumps The pump shown schematically in Fig. 129 consists of a cylinder with a tightly fitted piston 1 moving up and down inside it. Valves 2, which can open only upwards, are in the lower part of the cylinder and in the piston itself. With an upstroke of the piston, the water enters the tube under the action of atmospheric pressure, raises the lower valve, and moves behind the piston. With a downstroke of the piston, the water under the piston exerts pressure on the lower valve and closes it. At the same time, under the pressure of water, the valve inside the piston opens and the water passes into the space above the piston. Upon a subsequent upstroke of the piston, the water, which is above it, rises together with it and flows into a side tubing. A new portion of water simultaneously rises behind the piston and turns out to be above it with the following downstroke of the piston, and so on. ? 1. What phenomenon is used in the design of a water piston pump? 2. What is the design and the principle of operation of such a pump ? Fig. 129 108 Fig. 130. A piston pump with an air chamber: I - piston, 2 - suction valve, 3 - discharge valve, 4 - air chamber, 5 - hand le
Exercise 26 1. What is the limit height to which water can be raised by means of a piston pump (see Fig. 129) at normal atmospheric pressure? 2. What is the greatest height to which alcohol, mercury can be raised by means of a piston pump (see Fig. 129) at normal atmospheric pressure? 3. Explain the principle of operation of a piston pump with an air chamber (Fig. 130). What is the role of the air chamber in that pump? Can that pump be used to raise water from the depth exceeding 10.3 m? 53*. Hydraulic Press The operation of a hydraulic machine 1 is based on Pascal's law. A hydraulic machine used for pressing (compressing) is called a hydraulic press (see photograph on p. 11 0). The main part of a hydraulic press consists of two cylinders of different diameters fitted with pistons and connected by a pipe (Fig. 131). The space under the pistons and the pipe are filled with a liquid (mineral oil in most cases). When no forces act on the pistons, the columns of liquid in both cylinders are of the same height. Let us ass time now that F 1 and F 2 are forces acting on the pistons, and A 1 and A 2 are the areas of the pistons. The pressure under the first (small) piston is F 1/A1 , and under the second (large) piston, F 2/A 2 . In accordance with Pascal's [ 1 A hydraulic machine (from the Greek hydraulikos meaning water pipe) is a machme whose operation is based on the laws of motion and equilibrium of liquids. Fig. 131 109
A gigantic press in a shop of a mill law, the pressure is the same at all points of a liquid at rest, i.e., FtfA 1 = F 2/A 2 , whence we have A2 F2=Ft - · At Consequently, th ~ force F 2 is as many times larger than F 1 as the area of the larger piston is larger than that of the smaller piston. For example, if the area of the larger piston is 500 sq cm apd that of the smaller one is 5 sq cm, and a force 110
Fig. 132 of 100 N acts on the smaller piston, then a force 100 times as great will act on the larger piston, i.e., 10 000 N. Thus, using a hydraulic press, we can balance a large force by a small force. Hydraulic presses are used where large forces are required, say, for squeezing oil out of seeds at oil mills, for pressing plywood, cardboard, hay. At iron-and-steel plants, powerful presses are used in manufacturing steel shafts, railway coach wheels, and many other articles. Modern hydraulic presses can develop pressure forces of tens and hundreds of millions of newtons. Figure 132 is a schematic diagram of the design of a hydraulic press. The object A to be compressed is placed on a platen connected with the larger piston B. When this piston moves upwards, the object is pressed against the stationary upper platen and is thus compressed. In Fig. 132, M is a manometer used to measure the pressure of the liquid, and P is a safety valve, which opens automatically when the pressure exceeds the permissible value. The liquid is pumped out of the small cylinder and into the large one by repeated movements of the small piston. This is how it is done. When the small piston moves upwards, the liquid is sucked into the space under it. At the same time, the check valve K opens and the check valve K' closes under the pressure exerted by the liquid. Conversely, when the small piston moves downwards, the valve K closes and the valve K' opens, and the liquid runs into the larger cylinder. ? 1. What law is used when a hydraulic machine is designed? 2. What gain in force is achieved due to a hydraulic press (when there is no friction)? Exercise 27 I. Figure 133 is a simplified schematic diagram of a hydraulic lift (hy- draulic jack). What mass can be lifted by means of such a machine if it is known that the area of the small piston is 1.2 sq cm, and that of the large piston is 1440 sq cm, and the force acting on the small piston can be as large as 1000 N? Friction can be neglected. Ill
Fig. 133. A schematic diagram of a hyd- raulic jack: J - body being lifted, 2 - small piston, 3- valves, 4 - valve for lowering a load, 5 - large piston 5 4 Fig. 134 3 112 2. The area of the small piston in a hydraulic press is 5 sq cm, that of the large one is 500 sq cm. The force acting on the small piston is 400 N, and that acting on the large piston is 36 kN. What gain in force can be achieved by using this press? Why does the press not give the maximum (greatest) gain in force? What gain in force would be achieved if there were no friction between the piston and the walls of the press? . 3. Can we design a machine which is similar to a hydraulic one but uses air instead of water? Substantiate your answer. Assignments 1. Figure 134 shows schematically an automobile hydraulic brake, where I is a brake pedal, 2 is a cylinder with a piston, 3 is a wheel cylinder, 4 are brake blocks, 5 are brake drums, 6 is a spring. The cylinders and pipes are filled with a special liquid. Using the scheme, describe the principle of operation of the brake. 2. Read "Pneumatic Machines and Instruments" at the end of the book.
54. How a Fluid Acts on a Body Immersed in lt Under water we can easily lift a stone which it is difficult to lift on the ground. If we place a cork in water and release our hold on it, it will rise to the surface. How can this phenomenon be explained? We know (see Sec. 44) that liquid exerts pressure on the bottom and walls of a vessel, and, if a solid body is inside it, the liquid exerts pressure on this solid as well. Let us consider the forces with which liquid exerts pressure on a body immersed in it. To make our discussion easier, we choose a body shaped as a parallelepiped with the bases parallel to the free surface of the liquid (Fig. 135). The forces acting on the lateral faces of the body are pairwise equal and balance each other. These forces compress the body. As to the forces acting on the upper and lower faces of the body, they are different. A column of liquid h 1 in height acts upon the upper face with a force F 1 . The lower face experiences the pressure of a column of liquid h2 in height. As we know (see Sec. 43), this pressure is transmitted in all directions inside the liquid. Consequently, a column of liquid h2 high acts on the lower face of the body from below with a force F 2 . But h2 is greater than h 1 and, therefore, F 2 is larger in absolute value than F 1 . Thus, the body is pushed out of the liquid with the force F equal to the difference between the forces, F 2 - F 1 . It is easy to discover experimentally the force pushing a .body from a liquid. Figure 136a shows a body suspended by a spring with a pointer attached to it. The pointer indicates the extension of the spring. When we immerse the body in water, the spring contracts (Fig. 136b). The spring will also contract if we act on the body from below with· some force, say, the force exerted by the hand. Consequently, the experiment confirms that a body immersed in a liquid ex periences the action of a force that pushes the body out of the liquid. As we know, gases resemble liquids in many respects. Pascal's law can also be applied to them. Therefore, bodies, which are in a gas medium , experience a force pushing them out of the gas. This force makes balloons rise upwards. We can make an experiment to observe the force pushing a body out of a gas. A glass sphere or a large corked flask is suspended from a shorter balance pan. The pans are balanced out. Then a wide vessel is placed under the flask (or the sphere) so that it envelops the flask. The vessel is filled with carbon dioxide whose density exceeds that of air. Now the equilibrium of the balance is dis- Fig. 135 Fig. 136 (a l (b) 113 8- 971
Fig. 137 turbed. The pan with the flask rises upwards (Fig. 137). The force pushing the flask immersed in carbon dioxide (the buoyant force or buoyancy) is larger than that acting on it in the air. The force pushing a body out of a fluid opposes the force of gravity applied to that body and, therefore, if some body is weighed in a fluid, its weight will prove to be less than in a vacuum. This explains why in water we easily lift bodies, which we can hardly hold in air. ? 1. What phenomena do you know from experience that indicate the existence of a buoyant force? 2. How can you prove, proceeding fr om l'."cal's law, the existence of a buoyant force acting on a body imm~rsed in a liquid? 3. What experiment can you make to show that a buoyant force acts on a body submerged in a liquid? 4. What experiment can show that a buoyant force acts on a body in a gas medium? 55*. Buoyancy. Archimedes' Principle The force that pushes the body out of a liquid can be calculated. But it is easier to find it by way of an experiment, using the apparatus shown in Fig. 138. A small bucket ·and a cylindrical body are suspended from a spring. The extension of the spring is indicated on the holder by a pointer attached to the spring (Fig. 138a). This extension shows the weight of the body in air. Then an overflow can with a spout, filled with a liquid, is placed under the bucket so that the body is totally immersed in liquid (Fig. 138b). A volume of liquid , equal to that of the body, will overj7ow into a beaker, the pointer will deflect upwards since the spring contracts, thus showing a reduction in the weight of the body in the liquid. In the given case, in addition to the force of gravity, the body experiences the action of an upthrust force pushing it out of the liquid. If we pour the liquid fro¥1 the beaker back into the bucket, the pointer will return to its original position (Fig. 138c). The experiment leads to the following conclusion: the force pushing out 114
Ar n· d (287-21 2 B. C.), a scientist, pn JSll!lS~ , es and mathematician from Ancient Greece. He established the principle of the lever, and the Jaw of hydrostatics named after him. a body totally immersed in a liquid is equal to the weight of the liquid dis- placed by the body If we make the same experiment with a body immersed in a gas, it will show that the force pushing the body out of the gas is equal to the weight of the gas displaced by the body The force pushing a body out of a fluid is known as a. buoyancy and was first discovered and calculated by Archimedes If the weight of a body in vacuum P = gm, where m is the mass of the body, then the weight of the same body in a fluid P 1 is less by the value of buoyanc~ Fb, i.e., where m 1 is the mass of the fluid in the vo lum e of the body immersed in the fluid. Therefore, we sometimes say that when a body is immersed in a fluid Fig. 138 (a) (b) (C) s• 115
there is a loss in the weight of the body which is equal to the weight of the fluid displaced . This is a customary formulation of the Archimedes principle. Let us calculate the buoyancy acting on a body of volume V immersed in a liquid whose density is p. The buoyancy is equal to the weight of the liquid in the volume of the body. Hence, Fb = P =gm. The mass m of the liquid displaced by the body can be expressed in terms of its density and volume: m= p1V. Then we have EXAMPLE. Determine the buoyant force acting on a stone, 1.6 cu m in volume, immersed in sea water. ? 116 Given: Solution: V= 1.6 m 3 , N kg F = 9.8 - ·1030 -·1.6 m 3 = b kg m3 p1 = 1030 kg/m 3 . = 16480 N::::: 16.5 kN. I. What experiment can you make to determine the buoyant force acting on a body totally immersed in a liquid? 2. What is that force equal to? 3. How do you call the force which pushes bodies out of a fluid they are immersed in? 4. How can buoyancy be calculated? 5. Cite the formulation of the Archimedes principle. Exercise 28 1. Two cylinders, one made of lead and the other of aluminium, both of the same mass, are suspended from the arms of a beam balance. The balance is in equilibrium. Will the equilibrium be disturbed if we simultaneously immerse both cylinders in water? alcohol? Substantiate your answer. Verify it by means of an experiment. How does the buoyancy depend «;>n the volume of the body? 2. Two aluminium cylinders, equal in volume, are suspended from the arms of a beam balance. Will the equilibrium be disturbed if we immerse one cylinder in water and the other in alcohol? Substantiate your answer. Make an experiment to verify it. Does the buoyancy depend on the density of the liquid? 3. Two cylinders of the same volume, one made of iron and the other of aluminium, are suspended from the arms of a beam balance. With the aid of an additional load equilibrium is attained. Will the equilibrium be disturbed if both cylinders are immersed in water? Substantiate your answer. 4. The volume of a piece of iron is 0.1 cu dm. What buoyant force will act on it when it is totally immersed in water? in kerosene?
56. Flotation Two forces act on a body completely immersed in a liquid, the force of gravity directed vertically downwards and buoyancy directed vertically upwards. Under the action of these forces, the body, initially motionless, will move in the direction of the greater force. Three cases are possible here: (1) if the force of gravity is larger than the buoyancy, the body will sink to the bottom: (2) if the force of gravity is equal to the buoyant force, the body can be in equilibrium at any place in the liquid; (3) if the force of gravity is smaller than the buoyancy, the body will rise to the surface, it will float. Let us consider the latter case in more detail. When the rising body reaches the surface of the liquid, the buoyant force decreases with its further upward movement. Why? Because the volume of the submerged part of the body diminishes, and the buoyancy is equal to the weight of the liquid in the volume of the submerged part of the body. When the buoyancy becomes equal to the force of gravity, the body stops and, being partly submerged, will float on the surface of the liquid. The result obtained can be easily verified by means of an experiment. We pour water into an overflow can to the level of the side tube. Then we immerse a floating body in the can (Fig. 139), first weighing it in the air. Once in the water, the body displaces the volume of the water equal to that of the submerged parr of the body. Weighing the displaced water, we find that its weight, the buoyant force, is equal to the force of gravity acting on the floating body, or to the weight of that body in the air. Making similar experiments with various other bodies floating in different liquids, in water, alcohol, salt solution, we can make sure that the weight of <~ floating body in the air is equal to the weight of the liquid displaced by the body. It is easy to prove that if the density of a solid body is larger than that of a liquid, then the body sinks in that liquid. A body with a smaller density rises to the surface of that liquid. The body whose density is equal to that of the liquid remains in equilibrium in the liquid. A piece of iron, for instance, sinks in water but rises to the surface in mercury. Ice floats on the surface of water since its density is smaller than that of water (see the photograph on p. 118). The smaller the density of a body as compared to that of a liquid, the smaller part of the body submerged (Fig. 140). Two-immiscible liquids, say, water and kerosene, take positions in a vessel in Fig. 139 -· Efrn Fig. 140 ll7
(a) (b) (C ) Fig. 141 accordance with their densities : water, which is denser (p = 1000 kg/m 3 ), in the lower part of the vessel , and kerosene (p = 800 kg/m 3 ) in the upper part. The density of animals and fish living in water differs little from the density of wa ter, and therefore their weight is almost completely balanced by buoyancy. That is why aquatic animals do not need massive skeletons like those of the terrestrial animals. This is also the reason why the trunks of water plants are elastic. Fish possess an interesting organ, a swimming-bladder, which is compressible. Due to this organ , the fish can easily change the volume of its body and hence its average density. It can , therefore, regulate the depth of its submersion within a definite range. ? An iceberg 118 I. What experiment can you make to show that the weight of the liquid displaced by a floating body is equal to the weight of the body in the air ? 2. What is the value of the upthrust force acting on a body floating on the surface of a liquid? 3. When does a body immersed in a liquid rise to the surface ? float? sink? 4. What is the relationship between the depth of submersion of a floating body and its density?
Fig. 142 Fig. 143 Fig. 144 5. How can you explain that aquatic animals do not need strong skeletons? 6. What role is played by the swimming-bladder of fish? Exercise 29 1. An overflow can filled with water is balanced on the scales (Fig. 141a). A wooden block is immersed in the water. First the equilibrium of the scales is disturbed (Fig. 14lb), but when all the water displaced by the block flows out, the equilibrium is restored (Fig. 141c). Explain this phenomenon. 2. Why does a heavy ship sail and a nail dropped into the water sink? 3. Figure 142 shows the same body floating in two different liquids. Which of the liquids has a greater density? Why? What can you say about the force of gravity acting on the body and the buoyant force in these two cases? 4. A wooden float with a lead load secured to it is immersed first in water and then in kerosene. The float does not sink in either liquid. In which of them does it sink deeper? 5. An egg sinks in fresh water but floats in salt water. Explain why it is so. Make an experiment and observe this fact. 6. Draw a diagram showing the forces acting on a body floating on the surface, rising to the surface of the water, and sinking in water. 7. Using Tables 2-4 for densities (see pp. 55-56) determine what metals float in mercury and which of them sink. ,8. Does a piece of ice float in petrol? in kerosene? in glycerine? 9. How will the following three immiscible liquids be positioned in a vessel: water, kerosene, and mercury? Make a requisite picture and explain it. 10. How will three solid balls, a cork one, a paraffin one, and a steel ball, be 119
positioned in a vessel containing water, kerosene, and mercury? Substantiate your answer. Draw a picture. Assignments I. The French scientist Descartes (1596-1650) invented a device to demonstrate certain hydrostatic phenomena. A tall glass can was filled with water, with a small open volume filled with air left at the top. A small hollow glass diver was immersed in the can. The diver was filled partly with water and partly with air so that its small part was out of the water. The top of the glass can was closed tightly with a piece of thin leather. Exerting pressure on the leather, the diver could be made to swim in water, on the surface of water, or to sink to the bottom. Make such a device and experiment with it. Replace the diver by a small float and cover the vessel with a rubber membrane (Fig. 143). The device shown in Fig. 144 is a variant of the device described above. You can blow air into the bottle with your mouth via a rubber tube. Explain the operating principle of the device. Use this device to illustrate Pascal's law, the buoyancy, and the laws for floating of bodies. 2. Read "A Legend about Archimedes" at the end of the book. 57. Why Ships Keep Afloat Ships sailing rivers, lakes, and seas are constructed from various materials with different densities. The hull of a ship is usually made of steel plates. All the internal strength rigging is also made of metals. Dozens of other materials, which have larger or smaller density as compared to water, are used in ship-building. Why do ships float then, and how can they take on board and carry such heavy cargo? The experiment with a floating body (Sec. 56) has shown that the submerged part of the body displaces an amount of water whose weight is equal to that of the body in the air. This is also true of any ship. The weight of the water displaced by the submerged part of a ship is equal to the weight of the ship with the cargo in the air or to the force of gravity acting on the ship with its cargo. The depth to which a ship is submerged is called a draught . The largest permissible draught is marked on the hull of a ship by a red line called a waterline . The weight of the water, displaced by a ship submerged to the waterline, equals the force of gravity acting on the ship with its cargo, and is called the displacement of the ship . The displacement of modem oil-tankers is up to 5 000 000 kN, i.e., their mass, together with their cargo, is 500 000 t. There are many navigable rivers, large lakes, and seas in the Soviet Union. Canals built during the Soviet years have joined five seas: the Black Sea, the Sea of Azov, the Caspian Sea, the Baltic Sea, and the White Sea. The Soviet Union maintains extensive trade relations with foreign countries. Water transport is the cheapest kind of transport, especially cargo transport. Our marine and river craft grows each year. 120
1000 Fig. 145 r a) A very significant problem that faces the Soviet people is to protect water in the seas, rivers, lakes, ponds, and canals from pollution. No waste products of factories and mills must get into water reservoirs without passing purification works. The vegetation on the banks of water reservoirs must also be carefully preserved. ? J. . Why do ships keep afloat? -2. What is the draught of ships? 3. What is the waterline? 4. What is the displacement of a ship? The Valerian Kuibyshev motor ship (develops a speed up to 26 km/h) 121
Exercise 30 I. How will the draught of a ship change when it leaves a river for a sea? Explain your answer. 2. The force of gravity acting on a ship is 100000 kN. What volume of water does the ship displace? Assignments l. Figure 145 shows two instruments immersed in water and known as hydrometers (aerometers). They are used to measure the density of liquids. Figure 145a illustrates a hydrometer for measuring the density of liquids that are lighter than water, and Fig. 145b shows a hydrometer for measuring liquids that are heavier than water. The figure 1000 denotes the density of water: p = 1000 kg/m 3 . (a) Describe the operating principle of these instruments. (b) Using a test-tube or a small wooden stick with pieces of lead, make hydrometers for measuring the densities of liquids both lighter and heavier than water. 2. Prepare a report on the theme "From a Canoe to a Modern Sea Liner". 58. Aeronautics For a long time people dreamed of flying above the clouds, of sailing in the skies just as they sailed the seas. At first balloons were used in aeronautics (Fig. 146), which were filled with warm air. Today they are filled either with hydrogen or with helium. At normal pressure, 1 cubic metre of hydrogen weighs only 0.9 N, that of helium, 1.8 N, whereas 1 cubic metre of air weighs 13 N. Hence it follows that a balloon 1 cum in volume, filled with hydrogen, is acted upon, in the air, by a buoyant force equal to the weight of 1 cum of air, i.e., 13 N, and such a balloon can lift a load that weighs 13 N- - 0.9 N = 12.1 N. The difference between the weight of 1 cum of air and that of a gas of the same volume is known as the lifting force of l cu m of that gas. Consequently, the lifting force of 1 cum of hydrogen is 12.1 N, and the lifting force of 1 cum of helium is 13 N- 1.8 N = 11.2 N. Although the lifting force of hydrogen is greater than that of helium, the latter is more convenient for filling balloons since helium is safer in use. As the balloon rises upwards, the buoyant force acting on it decreases since the density of air in the upper layers of the atmosphere is smaller than at the surface of the earth. To rise still higher, some of the sand, specially taken for the purpose, is poured out of the bags · to make the balloon lighter. At last the balloon attains its limit height (its ceiling). To bring the balloon down, some of the gas is let out of its envelope by means of a special valve. Small balloons, one to two metres in diameter, called sounding balloons or probes, are sent up daily in various parts of the country to investigate the upper layers of the atmosphere. They rise to the height of 35 to 40 km. These balloons carry very light instruments which send radio data about the height of the flight, pressure, temperatdre, and humidity of the air. The direction and velocity of the balloon indicate the direction and strength of the wind at different altitudes. The information given by such probes is very important for weather forecasting. 122
(b) Fig. 147 Fig. 146 Fig. 148 Not very long ago, huge balloons, 20000 to 30000 cum in volume, called stratospheric balloons, were used to investigate the uppermost layer of the atmosphere, the stratosphere. The record ascent of a stratospheric balloon was realized in the USSR in 1934. Fedoseenko, Vasenko, and Usyskin , courageous Soviet aeronauts, reached the height of 22 km flying in the stratospheric balloon called "Osoaviakhim-1". Their descent, however, ended in a crash and the heroic aeronauts perished. 123
At present, planes are the main means of air transportation. A plane is heavier than air, its rise and flight are based on the laws of nature, which you will study in senior forms. Exercise 31 1. A bottle filled with compressed air is balanced on the scales. A glass tube with a tap is inserted into the bottle through the cork and the envelope of a rubber balloon is attached to the outer end of the tube (Fig. 147a). If some of the air passes from the bottle to the envelope and inflates it (Fig. 147b), the equilibrium of the scales will be dis- turbed. Make such an experiment at the lesson and explain the phenomenon observed. 2. A light glass sphere is suspended from one arm of a beam balance and equilibrium is attained by means of a screw on the other arm. If we place the balance under the glass bell of an air pump and pump out the air, the equilibrium of the balance will be disturbed (Fig. 148). Why? Assignment Prepare reports on the following themes: (I) The history of the aeronautics. (2) The design of an airship (dirigible) and its use.
Work and Power. Energy 59. Mechanical Work. Units of Work In everyday life by work we mean any useful labour of a worker, engineer, scientist, student. In physics, the notion of work is somewhat different, being a definite physical quantity measured in special units. Physics studies primarily mechanical work. Let us consider some examples of mechanical activity. If you lift a stone with your hands, a mechanical work is performed by the muscular force of your hands. When a train travels under the action of the traction force of a locomotive, mechanical work is done. When you fire a shot, the force of pressure of the gun-powder gas does the work, it shifts the bullet along the barrel with an increasing speed. Mechanical work is also done in the case when the force acting on a body (say, a friction force) reduces the speed of its motion. These examples show that mechanical work is done when a body moves under the action of some force. A force of gravity acts on a stationary load suspended by a rope, but the load is not displaced and, therefore, in this case no mechanical work is done. If we want to move a wardrobe, we press on it applying some force, but no mechanical work is done unless we move it. If there is a force but no displacement, then no work is done. We can imagine a case when a body moves without any force being exerted (by inertia). Then there is no work done either. There is no work done without a force applied to a body. Thus,mechanical work is done when a force is exerted on a body and the body moves . In what follows, we shall refer to mechanical work as simply work. It is very important to know how to calculate the work done. It is easy to understand that the work done depends on the force applied and the length of the path traversed. Suppose we have lifted a load with the mass of 1 kg to a height of 1 m. For that purpose we had to apply a force of 9.8 N. We have done a definite amount of work. To lift a load of 5 kg to the same height, we must exert a force five times as great. The work done in that case will also be five times as great, since the work done to lift a load of 5 kg 1 metre high can be regarded as the work done to lift 1 kg 1 m high repeated 5 times. Let us now lift a load of 1 kg, not to a height of 1 m, but to a height of 3 m. 125
The work done over the first, second, and third metres will, evidently, be the same. Therefore, the work done in lifting a load to a height of 3 m is three times as great as that done in lifting the load 1 m high. The examples we have considered show that mechanical work is directly proportional to the force and to the displacement. Therefore, work is measured by the product of the force by the path traversed in the direction of the force: work = force x path , or W = Fs, where W is the work done, F is the force applied, and s is the path traversed. A unit of work is the work done by a force of one newton over a path of one metre. The unit of work is a joule (designated as J) named after the British scientist Joule who carried out experiments in measuring work significant for science. 1 joule= 1 newton x 1 metre, or 1 J = 1 N ·m.iooo 1 = 1 kJ. EXAMPLE 1. A tractor pulls a plough with a force of 10 000 N. What is the work done by the tractor on the path of 200 m? Given : F = 10000 N,s = 200 m. w ...? Solution: W=Fs. W = I 0 000 N · 200 m = = 2 000 000 J = 2 . 106 J. EXAMPLE 2. Calculate the work done to raise a granite plate 0.5 cu m in volume to the height of 20 m. The density of granite is 2500 kg/m 3 . Given : V= 0.5 m 3 , p = 2500 kg/m 3 , h = 20 m. w ... ? Thus we have Solution: W=Fs, where F is the force of gravity acting on the plate, which can be found from the mass of the plate, if we know its volume and the density of granite: · m=pV; s = h, i.e., to the height to which the plate is raised. m= 2500 kg/m 3 ·0.5 m 3 = 1250 kg. F = 9.8 N/kg ·1250 kg~ 12 250 N. W = 12 250 N · 20 m = 245 000 J = 245 kJ. ? 1. What two conditions are necessary to do mechanical work?2. On what two quantities does the work depend? 126
\ 3. What is accepted as the unit of work? 4. Give the definition of the unit of work of 1 J. Exercise 32 1. Determine in which of the following cases mechanical work is done : a boy climbs a tree, a girl plays the piano, a man is standing with a sack of grain on his back, a man props a door with his shoulder, water presses against the wall of a vessel. 2. A monkey is playing with a wooden block. Can we call it mechanical work? labour? Substantiate your answer. 3. A steel ball rolls along smooth horizontal ice. Assume that there is no resistance to the movement of the ball (friction and resistance are absent). Is any work done'! 4. A crane lifts a load of 2500 kg 12 m high. What work is done? 5. What work is done in lifting a hydraulic press with a mass of 20 t to the height of 120 cm? 6. A locomotive moves a 3000 t train uniformly along a horizontal way 5 km long. Find the work done on this path if the friction is 0.003 from the weight of the train. Assignments 1. Calculate the work you do when you go up the stairs in your school from the first to the second storey. Get all the necessary data yourself and put down the result in your copybook. 2. Find the work you do when you walk 1 km of a horizontal path. Put down the result in your copybook. Hint. A man walking uniformly along a horizontal path does 0.05 of the work that would be required to raise the man to the height equal to the length of the path. 60. Power. Units of Power Different engines take different times to do the same amount of work. For instance, it takes only several minutes for a crane to lift several hundred bricks to the top of the building on the construction site. But it would take a worker a whole day to do the same work. And here is another example. A horse can plough a hectare of land in 10 to 12 hours, while a tractor with a multiple-share plough will do the work in 40 to 50 minutes. It is clear that a crane does the same amount of work quicker than a worker, and a tractor quicker than a horse. In engineering, the rate of doing work is characterized by a quantity known as power Power is the ratio of work to the time during which it was done. To calculate power, we must divide the work by the time during which that work was done: work power =-- time ' w or P= - t- , where P is the power, W is the work, and t is the time during which the work was done. 127
The unit of power is the power at which 1 J of work is done in one second. This unit is called a watt (W) after the British scientist James Watt, the inventor of a steam engine. Thus we have 1 joule 1 watt= , or 1 W = 1 Jjs. 1 second Engineering makes wide use of larger units of power, such as kilowatt (kW) and megawatt (MW) 1 kW= 1000 W; 1 MW= 1000000 W. EXAMPLE. Find the power of water flowing over the dam if the height from which the water falls is 25 m and its expenditure is 120 cum a minute. Given: h = 25 m, V= 120m3, p = 1000 kgjm3 , t =60s, g = 9.8 Njkg. P ... ? Solution : The mass of the falling water : m = p V, m= 1000 kgjm 3 · 120m 3 = 120000 kg. The force of gravity acting on the water: F=ym, F = 9.8 Njkg-120000 kg;:::: 1200000 N. The work done by the falling water per minute: W=Fh, W = I 200000 N · 25 m= 30000000 J. The power of the flowing water: P = ~, t P = 30000000 J = 500000 W = 0.5 MW. 60s Different engines develop power varying from hundredths and tenths of a kilowatt (the motor of an electric shaver, that of a sewing machine) to hundreds of thousands of kilowatts (water and steam turbines). Each engine has a small plate attached to it containing some data on the engine, its power inclusive. POWER OF CERTAIN ENGINES, kW Volga car Diesel locomotive Nuclear icebreaker Sibir Carrier rocket of the spaceship Vostok 128 Table 5 70 2200 55200 15000
The average power of a person working under normal conditions is 70 to 80 W. Jumping or climbing a staircase, a person can develop power up to 730 W, or even higher in individual cases. Knowing the power of an engine, we can calculate the work done by it in some time interval. It follows from the formula P = W /t that W=Pt. EXAMPLE. The engine of a room ventilator has the power of 35 W. How much work can it do in 10 min? ? 9 - 971 Given: Solution: P = 35 W, W = Pt, t = 10 min = 600 s. w = 35 W. 600 s = 21000 W ·S = 21 OOOJ = = 21 kJ. w ...? 1. What does power show? 2. How can the power be calculated if the work and the time are known? 3. What is the unit of power? 4. What units of power are used in engineering? 5. How can we calculate work if we know power and time? Exercise 33 1. Five hundred tons of water fall from a dam 22 m high in 10 minutes. What power is developed in this case? 2. What power does a person develop when walking if he takes 10 000 steps in 2 hours and does 40 J of work each step? 3. How much work does a 100 kW engine do in 20 minutes? 4. A conveyer lifts 30 cum of sand 6 m high per hour. Determine the power that the engine must develop in order to do the job. The density of the sand is 1500 kgj m3 . Assignments 1. Calculate the power you develop when you walk up the stairs slowly and uniformly from the first storey of your school to the second or the third storey, and when you do it quickly. Obtain all the necessary data yourself. 2. Determine the power that can be developed by the engines of the cars and tractors which you know. 3. Prepare a report on the theme "Power Developed by Various Engines". 129
130 (a) Fig. 149 Fig. 150 Fig. 151 0 p (b)
61. Simple Mechanisms From time immemo- rial, people use var- ious devices to do mechanical work. Everybody knows that a heavy object (a stone, a cupboard, a machine- tool), which it is difficult or even impossible to move, can be easily shifted using a sufficiently long and strong pole, a lever (Fig. 149). Heavy stones and plates were dis- placed and raised to great heights with the aid of levers when pyramids were built in Ancient Egypt (Fig. 150). In many cases, instead of raising a heavy load to a certain height, it is rolled or shjfted to the same height along an inclined plane (Fig. 151) or is raised with the aid of a pulley (Fig. 152). Devices used to transform forces tre called mechanisms. Simple mech- anisms include a lever and its va- rieties, such as a pulley or a winch; an inclined plane and its varieties, such as a wedge and a screw. In most cases, simple mechanisms are used to get a gain in force, i.e., to increase the force acting on the body several times. Simple mechanisms can be found both in domestic appliances and in complicated factory machine-tools, which cut, twist, and stamp large sheets of steel, or draft the thinnest thread for manufacturing fabrics. The same mechanisms can be found in modem intricate automatic machines, printing and computing machines. Fig. 152 If you know how sim pie mechanisms operate, you will understand the design of complicated machines much more easily. ' ) 1. What is meant by a simple mechanism ? 2. When are simple mechanisms used? 3. What simple mechanism was used in Egypt for building pyramids? 131 9'
62. A Lever. Equilibrium of Forces on a Lever A lever is a solid body free to turn about a fixed turning-point. Figure 149 shows how a worker uses a crowbar as a lever for lifting a load. In (a), the worker uses the force F to press the end B of the crowbar downwards, in (b) he slightly raises the end B of the crowbar. The worker has to overcome the weight P of the load, i.e., the force directed vertically downwards. For that purpose, he turns the crowbar about an axis passing through the only fixed point of the bar, its pivot or fulcrum 0. In both cases, the force F with which the worker acts on the lever is smaller than the force P, i.e., as we say, the worker gains in force. Thus, with a lever we can lift a heavy load, which it would be impossible to lift without using a lever. Figure 153 shows a lever, whose axis of rotation 0 (the fulcrum) is between the points of application of forces A and B, and Fig. 154 is a schematic diagram of that lever. Both forces, F 1 and F 2 act on the lever in the same direction. The shortest distance between the turning-point and the straight line along which a force acts on the lever is called the arm of force. To find the arm offorce , we must drop a perpendicular from the fulcrum to the line of action ofthe.force. The length of the perpendicular is precisely the arm of the given force. It can be seen in Fig. 154 that 0 A is the arm of the force F 1 , and 0 B is the arm of the force F 2 . The forces acting on the lever can rotate it about the axis in two directions, clockwise and counterclockwise. Thus, the force F 1 (Fig. 153) rotates the lever clockwise, and F 2 rotates it counterclockwise. The condition in which the lever is in equilibrium under the action of the forces applied to it can be established experimentally. It should be borne in mind that the result of the action of a force depends not only on its numerical value (its modulus) but also on the point of its application and its direction. Various loads are suspended from the lever (Fig. 153) on boJh sides of the fulcrum so that every time the lever is in equilibrium. The forces acting on the 8 0 A 8 1,2 0 ~I A ~ .... Fl Fl -Fz F2 Fig. 153 Fig. 154 132
lever are equal to the weights of the loads. The absolute values of the forces and their arms are measured in each case. Figure 153 shows that the force of 2 N balances the force of 4 N. As can be seen from the figure, the arm of the smaiJer force is twice that of the greater force. These experiments helped to establish the condition of the equilibrium of a lever (lever law): a lever is in equilibrium when the forces acting on it are m in verse proportion to the arms of those forces This rule can be written in the form of a formula: where F 1 and F 2 are the forces acting on the lever, and /1 and /2 are the arms of these forces (Fig. 154). The rule of equilibrium of a lever was established by Archimedes. It can be seen from this rule that using a lever we can balance a larger force by a smaiJer one, the only condition being the proper choice of the length of the arms. In Fig. 149a, for instance, one arm of the lever is twice as large as the other. This means that a worker can lift a stone of, say,- 800 N, i.e., with the mass of 80 kg, applying a force of 400 N at the point B. To lift a heavier load, the arm of the lever on which the worker acts must be still longer. EXAMPLE. Friction being neglected, what force is required to lift a stone with a mass of 240 kg with the aid of a lever? The arm of force is 2.4 m, the arm of the force of gravity acting on the stone is 0.6 m. ') Given: m= 240 kg, g = 9.8 Nfkg, / 1 = 2.4 m, 12 = 0.6 m. F ... ? Solution: According to the lever law, F p whence I F = p _2_ /I The weight of the stone P =gm, P = = 9.8 Nfkg · 240 kg::::: 2400 N. l. What is a lever? Then 0.6 m F=2400 N·--=600 N. 2.4 m 2. What do we call an arm of force? ~. '5. How can we find the arm of force? 4. How do forces act on a lever? 5. What does the lever law consist in? 6. By whom was the lever law established? 133
63. Levers in Engineering, in Nature and in Everyday Life The operation of various instruments and devices used in engineering and everyday life when a gain in force or in distance is required is based on the lever law. We gain in force when we work with scissors. Scissors are also a lever (Fig. 155), whose axis of rotation passes through the screw that links the two halves of the scissors. The acting force F 1 is the muscular force of the hand of a person using the scissors; the counteracting force F 2 is the resistance of the material cut by the scissors. Depending on the purpose, the scissors can vary in design. The scissors used in the office to cut paper have long blades and the handles of almost the same length since no large force is required to cut paper and long blades are more convenient for cutting along a straight line. The handles of scissors intended for cutting metal sheets (Fig. 156) are considerably longer than the blades since the resistance of metal is large and the arm of the acting force must be increased considerably to balance the resistance force. In wire-cutters (Fig. 157), the difference between the length of the handles and the distance between the cutting part and the pivot is greater still. Many machines employ levers of various kinds. The handle of a sewing machine, pedals or the hand brake of a bicycle, pedals of a car or a tractor, keys F ig. 155 Fig. 156 Fig. 157 Fig. 158. Types of balance: 1 - medical balance, 2 - table balance, 3 - chemist's balance, 4 - decimal balance 134 4
(a) (d) (e) (j) (g) (i) Fig. 159 of a typewriter or a piano, these are all examples of levers used in those machines and instruments. You can find many examples of using levers in any workshop, e. g., the handles of a vice or a bench, the lever of a drilling machine, etc. The operation of a beam balance (Fig. 158) is also based on the lever law. Figure 43 (p. 49) shows an equal-arm beam balance. In the decimal balance shown in Fig. 158d, the arm from which the weights are suspended is ten times as long as the arm which carries the load. This essentially simplifies weighing of heavy loads. When weighing a load on the decimal balance, the mass of the weights must be multiplied by 10. The design of the balance intended for weighing goods, carriages, trucks, and carts is also based on the lever laws. Levers can also be found in various parts of the body of animals and a man, limbs or jaws, for instance. We can indicate many levers in the body of insects, birds, in the structure of plants. The trunk of a tree and its extension, the root, are a typical example of a lever. Figure 159c illustrates the bones of the forearm. The turning-point is in the elbow joint. The acting force F is the force of the muscles bending the forearm , the resistance force R is the force of gravity of the load supported by the arm. The force F is applied closer to the turning-point than the force R (see Fig. 159c). Consequently, F > R, i.e., due to the lever there is a loss in force and a gain in distance. 1. Give examples of levers used in everyday life, engineering, and in workshops. 2. Explain why wire-cutters give a gain in force. 135
Fig. 160 Fig. 161 Fig. 162 8 Exercise 34 1. Indicate the pivots and the arms of the levers shown in Fig. 159. For what position of the load (Fig. 159e, f) does the stick used to carry loads exert a smaller pressure on the shoulder? Substantiate your answer. 2. Explain the principle of an oar acting as a lever (Fig. 160). 3. Figure 161 shows a cross section of a safety valve 1• Calculate the load that must be suspended from the lever so that the steam should not pass through the valve. The pressure in the boiler is 12 times as large as the normal atmospheric pressure. The area of the valve is 3 sq cm, the weight of the valve and of the lever may be neglected. Measure the lever arms using the figure. In what direction must the load be shifted when the steam pressure in the boiler increases; decreases? Substantiate your answer. 4. Figure 162 is a schematic diagram of a lifting crane. Calculate the load 1 A safety valve is a special device, say, in a steam boiler, which opens a hole when the pressure of the steam in the boiler exceeds the safety level. 136
A movable crane which can be lifted by the crane if the mass of th~ counterweight is 1000 kg. Assignments 1. Consider the design of pliers (or wire-cutters, sugar tongs, scissors for cutting tin-plate). Find in them the pivot, the a rm of the resistance force, and the arm of the acting force. Calculate the gain in force due to the given instrument. 2. Regard the machines and devices you use at home : a mincing-machine, --~ 1 a sewing machine, a can opener, pincers, and others. Indicate in them the pivOt, the points of a pplication of the forces, the arms. 3. Prepare the report on the theme "Levers in the Organisms of a Man, of Animals, and Insects". 137
Fig. 163 -F Fig. 164 Fig. 165 64. Application of the Lever Law to a Pulley A pulley is a wheel with a groove for a rope, a cable or a chain to pass over, and is mounted in a lock (Fig. 163). A fixed pulley is a pulley whose axle does not rise or descend when a load is lifted (Fig. 164). A fixed pulley can be regarded as an equal-arm lever, in which the arms of force are equal to the radius of the wheel (Fig. 165): OA =OB= r. Such a pulley does not give advantage in force (P =F), but makes it possible to change the direction of the acting force. Figure 166 shows a movable pulley (the axle of the pulley rises and descends together with the load), and Fig. 167 shows the lever corresponding to it: 0 is the pivot of the lever, OA is the arm of the force P, and OB is the arm of the force F. Since the arm OB is twice the arm OA, the force F is half the force P Fig. 166 138 p F= -. 2 p Fig. 167 F B Fig. 168
A truck crane Fig. 169 Thus, a movable pulle) doubles the efTort force you exert. It is customary to use a combination of a fixed and a movable pulley in practical applications (Fig. 168). Figure 169 shows the application of a movable (1) and fixed (2, 3) pulleys in an automatic crane. ? 1. What pulley is known as fixed and what as movable? 2. What is the purpose served by a fixed pulley? ·-· ' 3. What gain in power is attained by means of a movable pulley? 4. Can we regard ftxed and movable pulleys as levers? Draw schematic diagrams of such levers. 5. Describe some practical applications of pulleys that you know. 139
Assignment Consider the machines shown in the photographs on pp. 137, 139 and name simple mechanisms employed in them. 65. Equality of the Amounts of Work Done with the Use of Simple Mechanisms. The "Golden Rule" of Mechanics The simple mechanisms we have considered are employed in doing work when the action of one force must be balanced by the action of another force. The natural question arises whether in addition to the gain in force or in distance we also gain in work when using simple mechanisms. We can make an experiment to answer this question. Having balanced on the lever two forces, F 1 and F 2 , different in absolute value (Fig. 170), we set the lever in motion. We find that during the same time the point of application of the smaller force F 2 covers a longer distance s2 , and the point of application of the greater force F 1 covers a smaller distance s 1 . Measuring these distances and the absolute values of the forces, we fmd that the paths traversed by the points of application of the forces on the lever are inversely proportional to the forces : Thus we see that acting on the larger arm of the lever, we gain in force , but lose as many times in the length of the distance covered. The product of force by distance is work. Our experiments show that the amounts of work done at the two ends of the lever are equal: i. e., W1 = W 2. Thus, no gain in work is attained when a lever is used. Using a lever, we can gain either in force or in distance. If we apply a force to the longer arm, we gain in force, but lose as much in distance. And when we act on the shorter arm, we gain in distance, but lose as much in force. There is a legend stating that Archimedes, delighted by the discovery of the lever law, exclaimed: "Give me a place to stand and I will move the earth." Archimedes would not cope with such a problem, of course, even if he were given a place to stand and a lever of the requisite length. To move the earth even by 1 cm, the larger arm of the lever should have described an enormous arc. 140
Fig. 170 Fig. 171 Millions of years would be required to displace the larger arm of the lever along that arc with the speed of 1 m/s. A fixed pulley, which is a variety of a lever, does not give a gain in work either, which can be easily verified experimentally (see Fig. 165). The paths traversed by the points of application of forces P and F are the same, the forces are also equal, and, hence, the amounts of work done are equal too. The amounts of work done with the aid of a movable pulley can be measured and compared. To lift a load to the height h with the aid of a movable pulley, it is necessary, as the experiment illustrated by 'Fig. 171 shows, to raise the end of the rope to which a spring balance is attached to the height of 2h. This means that getting a two-fold advantage in force, we lose as much in distance, and, consequently, a movable pulley does not give any gain in work either. Hundreds of years of experience show that no mechanisms give any advantage in work . Various mechanisms are employed only for the purpose of gaining in force or in distance, depending on the conditions under which the job is done. The ancient scientists knew the following rule, which can be applied to all mechanisms: the gain in force is directly proportional to the loss in distance . This rule has become to be known as the "golden rule" of mechanics . ? 1. What is the relation between the forces acting on a lever and the arms of these forces (see Fig. 154)? 2. What is the relation between the paths traversed by the points of application of forces on a lever and those forces? 3. Can we gain in force by using a lever? What is the loss then? 4. How many times do we lose in distance when we use a movable pulley to lift a load? 5. What is the "golden rule" of mechanics? Exercise 35 1. A load was lifted to a height of 1.5 m with the aid of a movable pulley. To what length was the free end of the rope pulled up? 2. A movable pulley was used to lift a load to the height of 7 m. What amount of work did the worker do if he applied a force of 160 N to the end of the rope? What amount of work will the worker do if he lifts the same load to the height of 7 m without using a pulley? (The weight of the pulley and the friction may be neglected.) 141
3. How to use end pulley to gain in distance? 4. How should fixed and movable pulleys be connected to get a four-fold gain in force? a six-fold gain? i\ ssignmcn 1 Prove that the rule of equality of works done, the "golden rule" of mechanics, is applicable to a hydraulic machine. Do not take into account the friction between the pistons and the walls of the vessels. Hint. To prove this proposition, use Fig. 132. When the small piston moves downwards to a distance h 1 under the action of force F 1 , it displaces a certain volume of liquid. The volume of the liq!Jid under the large piston increases by the same amount and the piston rises to a height h2 • 66. The Efficiency of a Mechanism When we considered the design and operation of a lever, we did not take into account the friction and the weight of the lever. In those ideal conditions the work done by the force applied (we shall call that work tota l) is equal to the useful work of lifting a load or overcoming some resistance. In practice, the total work done with the aid of a mechanism is always somewhat greater than the useful work. A part of the work is done to overcome the forces of friction in the mechanism and to displace its individual parts. Thus, when we apply a movable pulley, we perform an additional work of lifting the pulley block itself, the rope, and of overcoming the friction force in the axle of the block. Whatever mechanism we take, the useful work done with its aid always constitutes only a part of the total work. Consequently, designating the useful work as W u, and the total work as W, we can write Wu<W , wor --" < l. w The ratio of the useful work to the total work done is the effictency of the mechanism employed. wuEfficiency = --. w The efficiency is usually expressed in per cent: wuEfficiency = --· 100%. w EXAMPLE. A load with the mass of 100 kg is suspended from the shorter arm of the lever. To lift the load, a force of 250 N is applied to the longer arm. The load is raised to the height of h 1 = 0.08 m, and at the same time the point of application of the effort lowered by h2 = 0.4 m. Find the efficiency of the lever. 142
? Given: Solution : Effiwciency = P = 9.8 N /kg· 100 kg :::: 1000 N. m= 100 kg, 9 8 N/k = - " ·100°10 • w. = 1000 N ·0.08 m= 80 J.g = . g, W / o F = 250 N, W = 250 N ·0.4 m= 100 J. Total work W= Fh 2 • 80 J h, = 0·08 m, Useful work w. = Efficiency=- - . 100°% = 80°1 h 0 4 · • 1001 / o· _2 _=_ . _m_._ =Ph,. Efficiency ... ? p = gm. 1. What do we mean by useful work and what by total work? 2. Why is the useful work not equal to the total work when mechanisms are employed to lift loads and overcome resistances? 3. What is known as the efficiency of a mechanism? 4. Can the efficiency exceed unity? Substantiate . your answer. 67. Energy To actuate machine tools at mills and factories, use is made of electric engines which consume electric energy. Cars and aircraft, diesel locomotives and motor ships operate on the energy of the fuel burned, hydraulic turbines use the energy of falling water. And we, ourselves, must periodically replenish the stock of energy in order to live and work. The word "energy" is often used in everyday life too. For instance, if a man can easily cope with a very labourious job, we say that he is full of energy. What then is energy? To answer this question, let us consider some examples. A load raised above the table does not do any work, but if that load drops, it performs some work. A compressed spring (Fig. 172a) can do some work when it stretches out, say, lift a load (Fig. 172b) or displace a cart. Figure 173 shows a cart with a pulley fixed to it. A thread passes around the Fig. 172 (b) Fig. 173 143
Fig. 174 pulley whose one end is wound on the axle of the cart and the other end carries a small load. When the load drops, it actuates the cart and, hence, does work. Any moving body is capable of doing work. Thus, when a steel ball A rolls down an inclined plane (Fig. 174), it hits a wooden cylinder B and displaces it by some distance. It does work. If a body or several interacting bodies (a system of bodies) can do work, they are said to possess energy. In the examples we have considered, the load raised above the table, the compressed spring, the moving steel ball, all possess energy. Energy is a physical quantity showing what amount of work can be done by a body (or several bodies). Energy is measured in the same units as work, in joules. The greater the amount of work a body can do, the more energy it possesses. When work is being done, the energy of the body changes. The work done is equal to the change in energy. ? 1. What examples can you give to show that work and energy are interrelated physical quantities ? 2. In what case can we say that a body possesses energy? 3. What are the units of energy? 4.. How can we defme work using the concept of "energy"? 68. Potential and Kinetic Energies Potential 1 energy is the energy which is defined by the mutual positions of the interacting bodies or parts of a body. For example, a body raised above the earth possesses potential energy since its energy depends on its position relative to the earth and their mutual attraction. We shall consider the potential energy of a body lying on the ground to be equal to zero. Then the potential energy of a body above the ground is defined by the work done by the force of gravity when the body drops to the ground. And, as we know, work is equal to the product of a force by a distance, i.e., W=Fh, 1 From the Latin word potent meaning potency. 144
The Chumysh dam on the Chu river in the Kirghizian SSR and this means that in this case the potential energy E is E=Fh. Water in rivers raised by dams possesses enormous potential energy (see the photograph above). Falling down, the water does work in actuating powerful hydraulic turbines of power stations. The potential energy of a pile-driver is used to drive piles in the process of construction (Fig. 175). When opening a door held by a spring, we do work in stretching (or compressing) the spring. At the expense of the energy obtained, the spring does work in closing the door when it c:ontracts or extends. The energy of compressed and coiled springs is used in guns to actuate the striker, in watches, and in various mechanical toys. Every deformed elastic body possesses potential energy. The potential energy of compressed gas is used in thermal engines, in hammers widely employed in the mine industry, in road building, excavating hard soil, etc. The more the gas is compressed, the greater the potential energy it possesses, and, consequently, the greater the work it does when it expands. The energy a body possesses due to its motion is called kinetic 1 energy. The falling water that sets the turbines of electric power stations in motion spends its kin~tic energy and does work. The wind, which is moving air, also possesses ,J(metic energy. What does kinetic energy depend on? Let us make an experiment. Figure 174 1 From the Greek word kinema meaning movement. 145 10-97 1
shows an inclined groove connected with a horizontal groove. A small wooden cylinder B lies on the horizontal groove. If we make a ball A roll down from different heights, we see that the larger the height the ball rolls from, the greater its speed andthe farther it moves the cylinder, i.e., it does more work. A flying bullet possesses large kinetic energy due to its high speed. If we perform an experiment using balls with different masses, we shall see that the kinetic energy of a ball depends on its mass. The larger the mass of a body andits speed, the greater its kinetic energy. The kinetic energy of bodies is used in engineering. The kinetic energy offlowing water is especially widely used. Falling from dam, the water actuates a turbine which is connected to an electric current generator. Thus, electric energy is generated due to the kinetic energy of falling water. Lately, water power acquired especially great significance in national economy and was named "white coal". In the Soviet Union , the energy of "white coal" is used in powerful electric stations. Fig. 175. A pile-driver Construction of electric power stations is a very important task of the national economy of the USSR, which is successfully coped with due to oursocialist way of life. A number of hydroelectric stations have been constructed in the Soviet Union: V. I. Lenin Dnieper Power Station with the capacity of 648 000 kW; V. I. Lenin Volga Power Station with the capacity of 2 300 000 kW ; the Yolga Power Station named after the 22nd Congress of the CPSU with the capacity of 2 530000 kW; Bratsk Power Station on the Angara with the capacity of 4 500 000 kW. The Krasnoyarsk Power Station on the Enisei is the most powerful in the world , its capacity is 6 000 000 kW ; new hydroelectric units have been put into operation at the Sayano-Shushenskaya Power Station with the capacity of 640 000 kW. These hydroelectric generating sets are the most powerful in the world. With respect to the conventional zero value, all bodies in nature possess either potential or kinetic energy or both. A flying airplane, for instance, possesses both the potential and the kinetic energy with respect to the earth. 146
' ) I. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. I. 2. 3. 4. 5. What energy is called potential? Give examples of bodies possessing potential energy. In what case do we consider the potential energy to be equal to zero? What is a measure of the potential energy of a body at a certain height above the surface of the earth? How can we show that a deformed spring possesses potential energy? How can we measure that energy? In what state of the spring is it more convenient to assume its potential energy to be equal to zero? What is kinetic energy? In what case does the kinetic energy of a body is assumed to be equal to zero? Give examples of bodies possessing kinetic energy. What is the relationship between the kinetic energy of a body and its mass and speed? What energy does a flying airplane possess with respect to the earth? What kind of energy does the water in a dam possess? Where is the kinetic energy of flowing water used? Exercise 36 What potential energy does a body possess with respect to the earth, if its mass is I 00 kg and the height it is raised to is 10 m? The hammer of a pile-driver (Fig. 175) with a mass of 500 kg falls from a height of 10 m. What is the potential energy of the hammer at the height of 4 m? What amount of work does the hammer do? In what places of the river, at the estuary or at the source, does each cubic metre of water possess greater potential energy? Substantiate your answer. In what river. running in the mountains or in the plain, does each cubic metre of running water possess greater kinetic energy? The height of the falling water at the power station is 275 m. Every second, 155 cum of water pass through one of the turbines. What amount of energy is consumed by the turbine per second? What is the efficiency of the turbine if its electric power is 300 MW? 69*. Transformation of One Kind of Mechanical Energy into Another In nature, engineering, and everyday life we can often observe transformations of mechanical energy, e. g., the transformation of potential energy into kinetic energy and kinetic energy into potential energy. For example, when water falls from a dam, its potential energy is transformed into kinetic energy. In an oscillating pendulum, these kinds of energy are periodically transformed into one another. Figure 176 shows a device which is convenient for observing the phenomenon of transformation of one kind of mechanical energy into another. The disc of the device is raised by means of winding the thread on the axle. When the disc is raised, it possesses a certain potential energy. If we release it, it will fall down rotating. While falling, it gradually loses its potential energy and at the same time acquires kinetic energy. At the end of its fall, the disc possesses a store of 147 10*
(I \J ~ 'Fig. 176 I Fig. 177 kinetic energy sufficient to raise it almost to the same height 1 . The disc rises, then falls again, and then rises once more. In this experiment, when the disc moves downwards, its potential energy is transformed into kinetic energy, and when it moves upwards, its kinetic energy is transformed into potential energy. The transformation of one kind of energy into another can also be observed in a collision of two elastic bodies, for instance, when a rubber ball falls on the floor or a steel ball hits a steel plate. If we raise a steel ball above a steel plate (Fig. 177) and then release it, it falls down. As the ball moves downwards, its potential energy decreases and the kinetic energy increases since the speed of the ball increases. As the ball hits the plate, they both become compressed, and the kinetic energy of the ball is transformed into potential energy of the compressed plate and the compressed ball. Then, due to elastic forces, the plate and the ball acquire their original forms; the ball rebounds from the plate, and their potential energy is again transformed into kinetic energy of the ball: the ball bounces upwards with the speed equal to that it possessed when it hit the plate. When the ball rises upwards, its speed and, consequently, kinetic energy decrease, while the potential energy increases. Having bounced from the plate, the ball rises to almost the same height from which it began to fall. At the upper point of its rise, all its kinetic energy is again transformed into potential energy. 1 A rotating part of a turbine with discs fixed to it (from the Latin rotare meaning to rotate). 148
Natural phenomena usually involve transformations of one kind of energy into another. Energy can also be transmitted from one body to another. Thus, for instance, in bow shooting the potential energy of the drawn bowstring passes into the kinetic energy of the flying arrow. ' ) I. What experiment can we perform to show the transformation of one kind of mechanical energy into another? 2. What transformations of energy occur when a steel ball hits a steel plate? 3. What transformations of energy occur when water falls from a dam? Exercise 37 1. Describe the transformations of energy that occur in the following cases: (a) when water falls in waterfall ; (b) when a ball is tossed vertically upwards; (c) when winding the spring of watch ; (d) on the example of a door spring. 2. The masses of the falling bodies are the same. Find whether the values of the potential energy of the bodies are the same at the same height and whether the values of the kinetic energy are the same at that height. 3. Give examples of bodies possessing both potential and kinetic energy at the same time. Assignments 1. Make a thread and a spring pendulum. Observe their oscillations. Give a brief description of the transformation of energy occurring when the pendulums oscillate. Hint. A thread pendulum consists of a thread with a load at the end. A spring pendulum is a spring with a load suspended from its end. In the experiment, the upper end of the spring is either fixed or held by the hand , the load is slightly pulled downwards and then released. 2. Read "Energy of Moving Water and Wind. Hydraulic and Wind Engines" at the end of the book. Prepare reports on the themes: (1) From waterwheels to modern hydraulic turbines. (2) Wind engines and their application. 149
2 Heat Phenomena Heat Transfer and Work 70. Thermal Motion We know that bodies consist of molecules which are in constant motion. Since the motion of molecules is mechanical, we can find the path traversed by a single molecule and its average speed. We can imagine it colliding with other molecules of the body. Figure 178 illustrates segments of the trajectories of individual gas molecules magnified millions of times . But the motion of all molecules taken together is a very complex motion . It suffices to recall that 1 cu cm of gas contains about 25 000 000 000 000 000 000 (2.5·10 19 ) molecules. And each molecule has a very intricate trajectory. It is hard to imagine the pattern of this common motion of all molecules of a body. Billions of billions of tiny particles move with high speeds in various directions, collide with one another and with the walls of the vessel, which causes changes in their speed, and again move until the next collision. Fig. 178 150
Such a motion is disorderly, chaotic. Thermal phenomena (Sec. 10) are a manifestation of this incessant molecular motion. Therefore, a chaotic motion of molecules in a body is called thermal motion . Knowledge of the internal structure of matter and of thermal motion makes it possible to explain various thermal phenomena. ') I. What do we know about the movement of a single molecule of a body? 2. Why is the common motion of all molecules of a body very complex? 3. Why is the disorderly motion of molecules called thermal motion? 4. Give examples of thermal phenomena. 71. Internal Energy We have learned that there are two kinds of mechanical energy, potential and kinetic. Bodies that interact with one another, are attracted or repelled, possess potential energy. For example, a stone raised above the ground, compressed or extended spring, compressed gas, all possess potential energy. Moving bodies, such as flowing water, wind, a rolling ball, a flying bullet, possess kinetic energy. The value of the kinetic energy depends on the mass of the moving body and on its speed. Potential and kinetic energies can be transformed into one another. Examples of such a transformation of energy were given in Sec. 69. Let us now consider one more example of energy transformation. A lead ball lies on a lead plate. Let us raise it above the plate and then release (Fig. 179). When we raised the ball, we imparted potential energy to it. While the ball is moving downwards, its potential energy is diminishing. But then the kinetic energy of the ball increases gradually since its speed increases. The potential energy of the ball is transformed into kinetic energy. But now the ball hits the lead plate and stops (Fig. 180). At that moment, its potential and kinetic energies with respect to the plate are equal to zero. Does it mean that the energy the ball had possessed disappeared altogether? No, it does not. Looking at the ball and the plate after the collision, we see that the ball has slightly flattened and a small dent has formed in the plate, i.e., both the ball and the plate have deformed upon a collision. Fig. 179 Fig. 180 151
If we measure the temperature of the ball and the plate just after the collision (and it is possible to do that), we find that they have become warmer. Thus, as a result of a collision, the states of the ball and the plate have changed, they have become deformed and heated. But if the states of the bodies have changed, then the energy of the particles constituting the bodies has changed too. Indeed, we have learned that the average speed of molecules increases when a body is heated (Sec. 10) and, consequently, their average kinetic energy increases too. Molecules also possess potential energy: when they interact (Sec. 11), they are attracted to one another, and when they turn out to be very closely spaced, they repel one another. When a body is deformed, the mutual position of its molecules changes and, consequently, their potential energy also changes. Thus, upon a collision, both the potential and kinetic energies of molecules change. The energy of motion and interaction of the particles a body consists of is called the internal energy of the body. We have learned by now that besides the mechanical energy, there is one more kind of energy, the internal energy The internal energy of a body does not depend either on the motion of the body or on its position with respect to other bodies. A body always has a certain store of internal energy, and at the same time it can possess mechanical energy. For example, an airplane flying at a certain altitude above the earth possesses, besides the internal energy, also a mechanical energy, potential and kinetic. The kinetic and potential energies of a single molecule are very small since the mass of the molecule is small. But there are an enormous number of molecules in a body and , therefore, the internal energy of a body, equal to the sum of the energies of all the molecules, is sufficiently large. Thus, the kinetic energy of a single hydrogen molecule at room temperature is equal to 0.000000000 000000000005 J (5/1021 J = 5 ·10- 21 J). Calculations show that the sum of the kinetic energy of all the hydrogen molecules contained in 1 cum of hydrogen under these conditions is equal to 140 000 J, and this is a considerable amount of energy. If we manage to raise a huge forging hammer, with a mass of 5 t, 3 metres high , its potential energy will also be about 140 000 J. But it is easier to use the potential energy of a hammer than the internal energy of 1 cu m of hydrogen. It is sufficient to release the hammer for it to do work upon falling on the article to be forged. Its potential energy will find use. But it is not so easy and even not always possible to use the internal energy of a body. Scientists pay much attention to various methods of using it. Progress in engineering depends in many ways on the ability of man to "extract" the internal energy of a body. The atomic energy is a kind of internal energy. When thermal phenomena are studied, only the molecular energy is taken into account since only that energy noticeably changes in these phenomena. Therefore, in what follows, when speaking of the internal energy of a body, we shall mean the kinetic energy of thermal motion and the potential energy of molecular interaction. 152
? 1. How is the energy transformed when we raise a ball and release it? 2. How does the state of a lead ball and a lead plate change upon their collision? 3. Into what energy is the mechanical energy of the ball transformed when it hits the plate? 4. What energy is known as the internal energy of a body? 5. Does the internal energy of a body depend on whether the body possesses a kinetic or a potential energy? 6. What kind of energy, mechanical or internal, is easier to use? 72. Means of Changing the Internal Energy of a Body The internal energy of a body is not a constant quantity, it can change in one and the same body. When the temperature of a body rises, its internal energy increases since the average speed and, hence, the kinetic energy of the molecules of a body increase. Conversely, when the temperature of the body becomes lower, its internal energy decreases. Thus, the internal energy of a body changes with a change in the speed of motion of its molecules. What are the means of increasing or decreasing the speed? Let us conduct an experiment. Fasten a brass tube with thin walls to a stand (Fig. 181) and pour a little ether into it. Close the tube tightly with a stopper. Wind a piece of thread round the tube and keep pulling the thread quickly from one side to the other. Some time later, the ether will start boiling and the steam will push out the stopper. The experiment shows that the internal energy of the ether has increased ; it has become heated and even started boiling. The internal energy increased as a result of the work done in rubbing the thread against the tube. Fig. 181 Fig. 182 153
5. What two mechanisms can be used to change the internal energy of a body?Assignment Put a coin on a sheet of plywood or a wooden board. Press the coin to the board and move it fast from side to side. Note how many times shou ld the coin be moved to make it warm, hot. Make a conclusion on the relation between the work done and the increase in the internal energy of a body. 73. Heat Conduction As any other kind of energy, the internal energy can be transferred from one body to another. We have considered an example of such a transfer, e. g., the transfer of energy from hot water to a cold spoon. Heat transfer of this kind is called heat conduction . We can stage the following experiment to observe heat conduction. Fix one end of a thick copper wire in a holder and attach some nails to the wire by means of wax, as shown in Fig. 183. When the free end of the wire is heated in the name of a spirit-lamp, the wax melts and the nails fall down one by one, first the nails that are nearer to the flame and then the others in turn. How is the energy transferred along the wire? First the hot name causes an increase in the vibratory movement of the metal particles at one end of the wire and its temperature rises. Then that increased motion is transferred to the neighbouring particles and their speed of vibration also increases, i.e., a rise in temperature occurs in the next part of the wire. Then the speed of vibration of the following particles also increases and so on. It is very important to note that in heat conduction matter itself is not transferred from one end of a body to the other. Different substances differ in their heat conduction. This can be verified by means of an experiment, in which energy is conducted along rods made of different metals (Fig. 184). We also know from experience that some substances conduct heat better than others. You cannot, for instance, heat an iron nail for a long time holding it in your hand, whereas you can hold a burning match till the name touches your hand. Metals, especially silver and copper, are very good heat conductors. Liquids (except for molten metals such as mercury) are poor heat conductors . • T T T Fig. 183 155
T Fig. 184 Gases are still worse heat conductors, since their molecules are far spaced and the transfer of motion from one molecule to another is rather difficult. Wool, down, fur, and other porous bodies Contain air between their fibres and are, therefore, poor heat conductors. That is why wool, down, and fur protect animals from overcooling. A layer of fat that water fowl, whales, walruses, and seals possess also protects them from overcooling. The worst heat conductor is vacuum, a strongly rarefied gas. This can be explained by the fact that heat conduction is a transfer of energy from one part of the body to another realized by molecules or some other particles. Consequently, heat conduction cannot take place where there are no particles of any kind. Substances with poor heat conduction are employed where it is necessary to conserve energy. Brick walls, for instance, help to conserve the internal energy in the premise. Bodies can also be prevented from heating. For instance, ice can be kept in a cellar by covering it with straw, sawdust, earth or some other substances possessing poor heat conduction. ? 156 I. What experiment can show how internal energy is transferred by a solid body? 2. How is energy transferred along a metal wire? 3. What substances are the best heat conductors and what are the poorest? Where are they used? Exercise 38 I. Why does deep soft snow protect winter crops from frost? 2. Explain why straw, hay, and dry leaves are poor heat conductors. 3. It has been calculated that the heat conduction of pine boards is 3.7 times greater than that of pine sawdust, and the heat conduction of ice is 21.5 times greater than that of fresh snow {the snow consists of tiny crystals of ice). How can you explain such a difference? 4. Why is the expression "Your coat warms youn incorrect? 5. The temperature of the scissors and the pencils lying on the table is the same. Why then do the scissors seem cold er when you touch them? 6. Explain why the fur, down, and feathers of the animals and the clothes of man keep them warm.
74. Heat Convection Liquids and gases are usually heated from below. A pot with water is usually put on the flame, the central heating radiator, which makes the air in the room warmer, is placed under the window by the floor. Is it done by chance? If we place a hand over a hot stove or over a burning electric lamp, we feel warm air rising upwards from the stove and from the lamp. These air streams can even rotate a small sheet of paper made into a screw and placed over the lamp (Fig. 185). This is another kind of heat transfer called convection 1 • Convection is a transfer of energy by streams of a gas or a liquid . The air, which is in contact with a stove or a lamp, becomes heated by its surface and expands. The density of the expanded air is smaller than that of cold air and, therefore, a layer of warm air is displaced upwards by the cold air, since the buoyant force with which the cold air acts upwards on the warm air exceeds the force of gravity acting on the warm air downwards. Then the next layer of cold air gets warm and begins moving upwards and so on. The same is true of liquids. To observe the transfer of layers of a liquid upon heating, we can drop a crystal of a dyeing substance, potassium permanganate, for instance, onto the bottom of a glass flask, and put the flask on the flame. We can see that the water begins moving along closed loops, i.e., it circulates: the heated lower layers of water are pushed out by the cold water and are displaced upwards (Fig. 186). Owing to circulation, the water is heated uniformly. Here, as well as in a gas, energy is transferred from one place to another together with the streams of a substance, water in our case. It is due to convection that the air in our rooms becomes warm (Fig. 187). We have considered free or natural convection. But if we use a pump or a mixer to stir a nonuniformly heated fluid, then forced convection takes place. 1 From the Latin convectio meaning transference. Fig. 185 Fig. 186 !57
\ Fig.. 187 Now we can answer the question posed at the beginning of this section: why are fluids heated from below as a rule? Let us try to heat the air in the test-tube as shown in Fig. 188. The upper layer of the water will begin to boil while the lower layers will keep cold. If we put pieces of ice on the bottom of the test-tube, they will not melt. Why? This heating technique cannot cause convection since the heated layers of water cannot get under the cold, heavier, layers. Perhaps the water will be heated due to heat conduction? But the experiment shows that the heat conduction of water is very small and a long time would pass before the water gets warm. The same explanation holds for the air in the test-tube, which is heated from above (Fig. 189). There is no convection in solids where the freedom of motion of the molecules is restricted. Recall that every particle of a crystalline solid body is Fig. 188 158 f Fig. 189
only free to oscillate about a single point, being kept in place by strong attraction of other particles. Therefore, no streams of particles are produced in a solid when it is heated. This is confirmed by our everyday experience. In solid bodies energy is transferred by means of heat conduction. ? I. Describe the experiment showing that the air over the burning electric lamp is displaced. 2. Explain how and why the air is displaced over a burning lamp. 3. Explain how the water is heated in a flask placed over the flame. 4. What is convection? 5. What is the difference between the natural convection and the forced one? 6. Why are fluids heated from below? 7. Why is convection impossible in solid bodies? 75. Convection in Nature and Engineering l. Winds. All winds in the atmosphere are convectional huge air streams. It is due to convection, for instance, that breezes originate on sea shores. On summer days, the ground is heated by the sun sooner than water and, therefore, the air over the ground is warmer than over the water, its density decreases and its pressure becomes smaller than that of the cooler air over the sea. As a result, as in communicating vessels, cold air is displaced, in lower layers,from the sea to the shore, wind begins to blow. This is breeze. At night water cools down slower than the ground and the air above the ground becomes cooler than over the water. A night breeze originates, that is the movement of cool air from the shore to the sea. 2. Draught. We know that the fuel will not burn without an inflow of fresh air. If no air gets into a stove or a boiler, the fuel will not burn. Usually the natural flow of air, or draught, is used. Chimneys are installed to create a draught through the furnaces in boiler rooms in factories, mills, and electric power stations. When fuel is burning, the air in the chimney is heated and its density decreases. This means that the pressure of the air in the furnace and the chimney becomes smaller than that of the air outside. Because of the difference in pressures, cold air gets into the furnace and the hot air rises upwards, thus creating draught. Figure 190 shows the installation used to conduct the experiment explaining the origination of draught. The higher the chimney over the furnace, the greater the difference between the pressures of the air in the chimney and outside. Therefore, the draught increases with the length of the chimney. 3. Central water-heating. The majority of modern buildings are provided with central water-heating. A boiler 1 (fig. 191) is installed in the basement of the building to heat water. The main pipe 2 runs from the upper part of the boiler to the garret where it is connected to an expansion tank 3. It is called expansion tank because it takes the excess water formed when it expands upon heating. A network of distribution pipes 4 is laid in the garret with vertical pipes 5 connected to them 159
Fig. 190 Fig. 191 and running through all the rooms of the building. The water from these pipes flows into the radiators 6 made of cast-iron tubes and usually installed under the windows. Hot water heats the tubes of the radiators giving off part of its energy to them. From the tubes the energy is transmitted to the air in the room. The water itself becomes cooler and through the network of the lower branch pipes 7 laid in the basement gets into the boiler, where it is heated again, rises to the garret, again gets into the radiators, giving off its energy to them and so on. Such a movement of water in the central heating system and, consequently, the transfer of energy from the boiler to the radiators goes on all the while the boiler is heated, and takes place due to convection. In large premises, artificial (forced) circulation of water is sometimes created by means of a pump, which continuously forces the water in the right direction. In the heating systems used in towns and some settlements hot water is obtained not from the boiler installed in the house but from the central heating electric stations supplying with hot water several blocks of houses and even en tire town districts. 160
Even with very good thermal insulation, energy leaks outside from our buildings. Therefore in winter, hot water in the pipes must be in constant motion to ensure the required room temperature. Fxercise 39 1. Explain how the wind and the draught are produced. 2. How is the energy transferred from the boiler to the radiators in the central water-heating system? 3. Why is the cellar the coolest place in the house? 4. Why are the air vents, serving for airing the room, made in the upper part of the window? 5. Why are the factory chimneys made so tall? 6. Why is the draught in the stove chimneys greater in winter than in summer? Explain your answer. 7. Why is the draught in metal chimneys smaller than in the brick chimneys of the same height? 76. Heat Radiation Let us make an experiment to get acquainted with one more kind of heat transfer. Take a heat absorber, a flat round box, whose one side is polished like a mirror and the other is painted dull black. There is air inside the box, which can escape from the box through an aperture. We connect the heat absorber with a liquid column manometer (Fig. 192) and place beside the device an electric range or a piece of metal heated to a high temperature. We see that the column of the liquid in the manometer has shifted. The air in the heat absorber has, evidently, become hot and expanded. The heating of the air in the device can only be explained as the transfer of energy from another heated body. How was the energy transferred in this case? In no way by means of heat conduction since there is air between the heated body and the heat absorber, which is a poor heat conductor, There is no convection here either since the device is placed not over the heated body but beside it. Consequently, energy is Fig. 192 Fig. 193 161 I I - 97 1
transmitted here from the heated body to the heat absorber by a new kind of heat transfer called heat radiation , inherent in all heated bodies. This experiment can also be conducted with a hand-made device which is a flask, whose one side is blackened with smoke. A glass tube bent at right angles is inserted into the flask through a cork. The narrow channel of the tube contains a little amount of coloured liquid (Fig. 193). Heat radiation differs from other kinds of heat transfer in that it can be carried out in vacuum. It is also by means of radiation that the solar energy is transmitted to the earth. All bodies radiate energy, both hot and slightly warm : a human body, a furnace, a burning electric lamp. But the higher the body temperature, the larger the amount of energy it transfers by radiation. The radiation energy falling on bodies is partly absorbed by the bodies and is transformed into their internal energy. As a result, the bodies become heated, to a greater or lesser extent, depending on the state of their surfaces. If, in the experiment with the heat absorber, we first turn it to the heated body with its black side and then with the polished side, the liquid in the manometer will rise higher in the first case than in the second. This shows that bodies with dark surfaces absorb more energy and become hotter. At the same time bodies with dark surfaces cool faster by means of radiation than bodies with light surfaces. In a light pot, for instance, the water remains hot much longer than in a dark pot. People have learned to use the ability of bodies to absorb radiation energy in different amounts. For example, balloons and airplane wings are painted silver to prevent them from being heated by the sun. Conversely, to use the solar energy, say, to heat parts of certain instruments installed on earth satellites, those parts are painted dark. ? 162 1. How is a heat absorber designed? 2. What experiment can be made to show a transfer of energy by radiation? 3. What bodies absorb radiation energy better than other bodies ? 4. How do people employ different abilities of bodies to absorb radiation energy? Exercise 40 1. In summer, the air in the building gets warmer, receiving energy in different ways: through the walls, through an open window, through the glass in the window, which transmits solar energy. What kind of heat transfer do we deal with in each case? 2. Sitting beside a camp-fire or an open fire-place, we feel we are being warmed. How is the energy of the camp-fire transmitted to us? Substantiate your answer. 3. Give examples illustrating that bodies with dark surfaces are better heated by radiation than those with light surfaces. 4. Why can we state for sure that the solar energy cannot be transmitted to the earth either by convection or by heat conduction?
77. Examples of Heat Transfer 1. Heat transfer and the vegetable kingdom . The temperature of the lower layer of air and of the surface of the ground is very important for the growth of vegetation. There are very frequent changes in the temperature of the air layer adjacent to the earth and in the upper layer of the ground. In the daytime, the earth absorbs energy and gets heated, and at night it cools down. Its heating and cooling are due to the presence of vegetation. Thus, dark ploughed land absorbs more radiation and quickly gets warm, but it cools as quickly, much faster than the earth covered with vegetation. Weather is also an important factor in the heat exchange between the earth and the air. During clear cloudless nights the earth cools considerably; the heat the earth radiates goes into space without hindrance. On such nights in the early spring a light frost can form on the ground. Now if the weather is cloudy, the clouds cover the earth and play the role of a screen protecting the earth from loss of energy through radiation. One of the means of raising the temperature of a portion of the ground and the surface layer of air is to make hotbeds, which make it possible to make a fuller use of the solar radiation. A portion of the ground, usually made a little deeper than the surrounding ground, is covered with glass frames. The glass transmits the visible solar radiation, which gets onto the dark earth and heats it. But, at the same time, the glass prevents the surface layer of the air from cooling because it detains the invisible radiation emitted by the heated surface of the earth. Thus, the glass frames of the hot beds act as a "trap" for energy. Inside the hotbeds, the temperature exceeds that outside by approximately i0 °C. 2. A thermos flask . A heat transfer from a hotter body to a cooler one leads to the equalizing of their temperatures. Therefore, if we bring a hot pot in the room, for instance, it will cool. A part of its internal energy will pass to the sur- rounding bodies. To prevent bodies from cooling or heating, the heat transfer must be reduced. It must be ensured that energy is not transferred by any of the three kinds of heat transmission, i.e., by convection, conduction, or radiation. A thermos flask is used to prevent hot food or water from cooling or, conversely, to prevent ice or ice-cream from melting (Fig. 194). Figure 195 shows the design of a thermos for liquids 3. It consists of a glass flask 5 with double walls. The inner surface of the walls is covered with a bright metal layer and the air is pumped out of the space between the walls of the flask. The vacuum between the walls practically does not conduct heat, and the bright F ig. 194 Fig. 195 163 11*
layer reflecting the rays prevents the transfer of energy by radiation. To protect the glass from damage, the thermos is placed into a cardboard or metal case 4. The flask is tightly closed with a cork 2, and a cap 1 is screwed onto its neck (Fig. 194). Exercise 41 l. When a spaceship flies in outer space, its skin is heated because of the friction against the air and due to solar radiation. Which of these two causes acquires more importance when the altitude of the flight is increased? decreased? Substantiate your answer. 2. One of the means to keep a certain constant temperature in a spaceship or a satellite is to make it with a double skin and fill up the inner space with a gas (nitrogen, for instance). Using a fan, the gas is made to move about the heat emitting instruments and transfer the energy to the skin. Why is forced convection used here rather than natural one? 78. Quantity of Heat. Units of the Quantity of Heat In the previous sections, we considered various kinds of heat transfer. Let us now return to the problem of using internal energy. How can we calculate a change in the internal energy of a body in various cases? We shall begin with heat transfer, which means a transmission of internal energy of one body to some other body by means of heat conduction, radiation or convection. The part of the internal energy that a body obtains or loses in the course of heat transfer is called the quantity of heat. The term "quantity of heat" is customarily referred only to a change in the internal energy by means of heat transfer. It is not applied to a change in the internal energy as a result of some work done on a body. To learn how to calculate the quantity of heat, let us find what quantities it depends on. If we want to heat water in a pot so as to make it warm, we heat it for a short time imparting to it a small quantity of heat. To make it hot, we transmit to it a larger quantity of heat. Consequently, the more the degrees by which we heat the water, the greater the quantity of heat we must transmit to it. When it cools, the water is sure to transmit to the surrounding bodies the greater quantity of heat, the more degrees its temperature becomes lower. But it is not sufficient to know by how many degrees the temperature of a body has become higher or lower in order to calculate the quantity of heat received by the body in heating or lost in cooling. Indeed, a red-hot iron will not heat a cold room whereas a warm stove or a radiator of water heating, whose temperature is about 60 cc, can make the room very warm. We are all used to heat water in a pot and know very well that a greater quantity of heat is required to heat a pot full of water than to heat the same pot only half full. Let us verify it by an experiment. Let us put two vessels on the same stove, one containing 200 g of water and 164
-}-p~ .i ,rn;ll._, Fig. 196 I , ill 1:-bI ,q ® - -the other 400 g, In the first vessel the water will begin boiling earlier than in the second. Let us remove the first vessel from the stove and observe the second vesseL It will require some more quantity of heat before the water in it begins boiling. Consequently, the quantity of heat transferred to a body in heating depends on the mass of the body: the greater the mass of the water, the larger the quantity of heat required to heat it. When a body is cooling, the surrounding bodies acquire the greater quantity of heat, the larger the mass of the cooling body. Thus, the larger the number of sections in the radiator of water heating, the warmer it makes the room. Let us put two vessels, one containing 400 g of water and the other 400 g of vegetable oil, on two identical gas-burners. Thus, the two vessels contain 400 g of a substance each, i.e., the masses of the bodies being heated are the same (Fig. 196). The conditions of heating are also the same since the vessels receive energy from identical burners. The difference is only in the substances, the first vessel containing 400 g of water and the second 400 g of oiL Thermometers will show that the oil in the second vessel is heated quicker. For the temperature of the water in the first vessel to become the same as that of the oil, an additional quantity of heat must be transmitted to it. Evidently, different quantities of heat are required to heat the same masses of water and oil by the same number of degrees. More heat is required to heat water and less to heat oiL Consequently, the quantity of heat transferred to a body in heating also depends on the substance the body consists of Thus, the quantity of heat transferred to a body in heating depend!> on the k 1nd l)f the substance it consists of, on the mass of the body, and on the change m its temperature. As any other kind of energy, the internal energy is measured in joules. As we have learned, the quantity of heat is that part of the internal energy which a body receives or loses in heat transfer. This means that quantities of heat are also measured in joules (J), or kilojoules (kJ) 1 kJ = 1000 J. l. What do we mean by a quantity of heat? To what way of changing the internal energy does this term refer? 2. What is the relationship between the quantity of heat and a change in a body temperature? 165
3. Why can we not judge the quantity of heat obtained by a body by the change in its temperature alone? 4. How does the quantity of heat depend on the mass of the body? 5. Describe the experiment showing that the quantity of heat depends on the kind of substance the body consists of. 6. What does the quantity of heat transmitted to a body in heating depend on? 7. What units are used to measure the internal energy and the quantity of heat? A Little of History From time immemorial, a certain unit, a calorie (from the Latin word kalor meaning warmth, heat), has been used to measure quantities of heat. t\ calorie is the quantity of heat required to raise the temperature of one gram of water by one degree Centigrade. It is abbreviated as ea!. We can also say that a calorie is the quantity of heat lost by 1 g of water cooling by one degree Centigrade. Also of use is a larger unit for measuring the quan~it)' of heat, a kilocalorie. I kcal = 1000 cal. _;v- There are the following relations between these two units and the units of 1 J and 1 kJ: 1 cai=4 . 19J~4.2J. 1 kcal=4190J~4200J . 79. Specific Heat Capacity To increase the temperature of 1 kg of water by 1 °C, a quantity of heat equal to 4200 J is required. But if 1 kg of another substance must be heated by 1 oc, then some other quantity of heat may be required (Sec. 78). Consequently, every substance with the mass of 1 kg requires a definite quantity of heat for changing its temperature by 1 oc. The physical quantity showing how much heat is required to raise the temperature of a substance 1 kg in mass by 1 oc, or how much heat is released by a substance with the mass of 1 kg when its temperature is lowered by 1 °C, is known as the specific heat of the substance. The specific heat capacity of a substance is designated as c. The unit of the specific heat capacity of a substance is I J /kg· 'C. The specific heat capacity of lead is 140 J /kg· oc. This means that the quantity of heat needed to heat 1 kg of lead by 1 oc is 140 J (or, to put it otherwise, the quantity of heat lost in cooling 1 kg of lead by 1 oc is 140 J). The specific heat capacity shows oy how many Joules the internal energy of a substance 1 kg in mass changes upon a change in temperature by 1 C. The specific heat capacity of a substance changes when it passes (rom one state to another. For example, the specific heat capacity of water is 1200 J/kg· °C, and that of ice is 2100 Jfkg ·oC. _ Note that water has a very great specific heat capacity, and, therefore, water 166
Table 6 SPECIFIC HEAT CAPAC ITIES OF SOME SUBSTANCES, Jfkg- °C Gold 130 Laboratory glass 840 Mercury 140 Aluminium 920 Lead 140 Vegetable oil 2000 Tin 230 Ice 2100 Silver 250 Kerosene 2100 Copper 380 Ether 2350 Zinc 380 Wood (oak) 2400 Brass 380 Alcohol 2500 Iron 460 Water 4200 Steel 500 Cast iron 540 Brick 750 in seas and oceans, being heated in summer, absorbs a large quantity of heat. That is why in the places located close to large water reservoirs it is not so hot in summer than in those far from water reservoirs. In winter the water cools down and gives off large quantities of heat and, therefore, it is not so cold in winter in such places. Thanks to its great specific heat capacity, water is the most convenient liquid to use both in radiators and in hot water flasks. •) f. What is known as the specific heat capacity of a substance ? 2. What is the specific heat capacity of water ? 3. The specific heat capacity of lead is 140 1fkg · oc. What does it mean ? 4. What is the relationship between the specific heat capacity of a substance and a change in its internal energy? 5. Why does a close location of water reservoirs affect the air temperature? 80. Calculating the Heat Required to Raise the Temperature of a Body and That Given Off by a Cooling Body We have learned what quantities the specific heat capacity depends on and what units are used to measure it. To calculate the quantity of heat required, it is necessary to know the specific heat capacity of the substance the body is made of, the mass of that body and the difference between its initial and final temperatures. We have to calculate, for instance, the quantity of heat received by an iron article with a mass of 5 kg when it is heated to 600 oc. The specific heat capacity of iron is 460 Jfkg · oc, and this means that the quantity of 460 J is required to heat a mass of iron of 1 kg by 1 oc. Five times as much heat is required to heat a mass of iron of 5 kg by 1 °C, i. e., 460 J x 5 = 2300 J; to heat an iron article with the mass of 5 kg by 600 oc, 600 times more heat is required, i.e., 2300 J x 600 = 1 380 000 J. 167
Thus, to calculate the heat required to raise the temperature of a body, the specific heat capacity must be multiplied by the mass of the body and by the difference between its initial and final temperatures . This rule can be formalized by introducing the following designations: Q is the quantity of heat, c is the specific heat capacity of the substance, m is the mass of the body, t 1 is its initial and t 2 its final temperature. Then Q = crn(t2 - td . EXAMPLE 1. An iron boiler with a mass of 10 kg contains 20 kg of water. What quantity of heat must be transmitted to the boiler to heat it, together with the water in it, from 10 to 100 °C? Both bodies, the boiler and the water, will be heated together. Since heat exchange takes place between them, their temperatures can be assumed to be equal. Hence, the temperature of both the boiler and the water is raised by the same number of degrees: 100 °C- 10 °C = 90 °C. But the quantities of heat received by the boiler and the water are not the same since their masses and the specific heat capacities are different. The quantity of heat received by the boiler is Ql = clrnJ (t1- tl), Q1 = 460 Jjk:g · oc ·10 kg· 90 °C = 414000 J ~ 400 kJ. The quantity of heat received by the water is Q2 = 4200 Jjkg . oc. 20 kg. 90 oc = 7 560 000 J ~ 7600 kJ . The quantity of heat required to heat both the boiler and the water is Q=Qt+Q2 , Q = 400 kJ + 7600 kJ = 8000 kJ. EXAMPLE 2. The water with the mass of 0.8 kg at a temperature of 25 oc is mixed with 0.2 kg of boiling water. The temperature of the mixture obtained is measured and proves to be 40 oc. Calculate what quantity of heat the boiling water lost upon cooling and what quantity of heat the cooler water received. Compare these quantities of heat. The boiling water has cooled from 100 to 40 °C, and the quantity of heat it has lost is Ql = 4200 Jjk:g · °C · 0.2 kg · (100 °C- 40 °C) = 50 400 J. 168
The water into which the boiling water was poured has been heated from 25 to 40 aC and received the following quantity of heat: Q2=c2m2(t-t1), Q2 = 4200 Jfkg. oc. 0.8 kg. (40 °C- 25 oq = 50400 J . We see that the quantity of heat lost by the hot water and that gained by the cold water are equal. And this is not an accidental result. Experience shows that if a heat exchange takes place between bodies, the internal energy of all bodies being heated increases as much as the internal energy of all cooling bodies decreases. However, if we carry out more accurate measurements in the experiments with mixing hot and cold water, we shall see that the energies lost and gained are not the same. The lost energy will exceed the energy received. This is so because a part of the energy is transmitted to the air and the vessel during the experiment. The difference between the quantities of energy lost and gained is the smaller, the smaller the energy losses during the experiment. ? 1. What should you know to calculate the quantity of heat received by a body being heated? 2. Give an example showing how, to calculate the quantity of heat transmitted to a body being heated or lost by it upon cooling. 3. What is the formula for calculating the quantity of heat? 4. What conclusion can be made from the experiment with mixing cold and hot water? Exercise 42 1. The specific heat of aluminium is 920 Jfkg · oc. What does it mean? 2. Which of the liquids given in Table 6 is quicker to heat under the same heating conditions? Why? 3. Why is it more convenient to use water than any other liquid as a cooling agent (say, for cooling an internal combustion engine)? 4. Calculate the quantity of heat required to heat: (a) a flat iron with a mass of 1.5 kg by 200 °C, (b) an aluminium spoon with a mass of 50 g from 20 to 90 °C, (c) a brick stove with a mass of 2 t from 10 to 60 °C. 81*. Energy of Fuel. Heat of Fuel Combustion We know that molecules consist of atoms. A water molecule, for instance, consists of one atom of oxygen and two atoms of hy- drogen. A molecule can be divided into atoms. Such a division of a 'molecule is known as a chemical reaction of decomposition. To divide a molecule into atoms, it is necessary to overcome the forces of attraction of the atoms, do work, and, hence, spend energy. Experiments show that when atoms combine to form a molecule, energy is given off. We can give the following comparison: forces of attraction exist between the earth and all bodies and, therefore, when we lift a body, removing it farther from the earth, we expend energy and do work. But if a body, say, a forging hammer, falls on the earth, it does the work itself and its energy is consumed. 169
Fig. 197 · The use of fuel is based on the phenomenon of liberation of energy when atoms combine into a molecule. Conventional fuel (coal, petroleum, petrol, etc.) contains carbon. In the process of burning, the atoms of carbon are combined with those of oxygen contained in air. Each carbon atom is combined with two oxygen atoms (Fig. 197). The resulting molecule is a molecule of carbon (IV) oxide (carbon dioxide). Its formation is accompanied by a liberation of energy. There are various kinds of fuel , e. g., coal, peat, wood, petroleum, shale, and natural gas. When designing engines, an engineer must know precisely what quantity of heat will be liberated when this or that kind of fuel is burned. And for that purpose experiments must be carried out to find the quantity of. heat that will be liberated upon a combustion of the same amount of different kinds of fuel. The amount of heat liberated upon a complete combustion of fuel with a mass of 1 kg is called the heat of combustion of the fuel. The heat of combustion of fuel is designated as q and is measured in Jjkg. The heat of fuel combustion can be found experimentally. The experimental results are given in Table 7. Dry firewood Peat Brown coal Coal Alcohol Coke Anthracite H EAT OF F UEL COMBUSTION, J(kg 1.0 · 107 1.4 · 107 1.3 · 10 7 2.7 · 107 - -3.0·107 2.7 · 10 7 2.9 . 10 7 3.0·107 Charcoal Natural gas Petroleum Petrol Kerosene Hydrogen Table 7 3.4- J0 7 4.4 ·107 4.4 ·10 7 4.6 · 107 4.6·107 12· 10 7 It can be seen from the table that, say, the heat of combustion of peat is 1.4 · 107 Jjkg. This means that 1.4 · 107 J of heat will be liberated as a result of a complete combustion of peat with a mass of 1 kg. To estimate the quantity of heat Q liberated upon a complete combustion of fuel of any mass m, we must multiply the heat of its combustion q by the mass of the fuel burned : Q=qm . 170
') 1. What is the heat of fuel combustion ? 2. What units are used to measure the heat of fuel combustion ? 3. What do we mean by the expression "the heat of fuel combustion is 1.4- J01 Jfkg"? 4. How can we calculate the quantity of heat liberated by fuel burned? Exercise 43 1. In Table 7, the number 4.4 · 10 7 refers to petroleum. What does this number mean? 2. What fuel, dry firewood or brown coal, can release more heat in burning under the same conditions? Substantiate your answer. 3. What quantity of heat is liberated upon a complete combustion of 15 kg of charcoal ? of 200 g of alcohol? 4. What quantity of heat is liberated upon a complete combustion of kerosene whose volume is 2 litres? 5. A complete combustion of dry firewood resulted in a liberation of50 000 kJ of energy. What mass of wood has burned? 82. The Law of Conservation and Transforma- tion of Energy in Mechanical and Thermal Processes In Sec. 71 we considered the transformation of one kind ofenergy into another. We have learned that when a body falls, its potential energy is transformed into kinetic energy. When a lead ball falls on a lead plate, its mechanical energy is transformed into the internal energy of the ball and the plate. In the engine of a car or a tractor, the internal energy of the fuel is transformed into the mechanical energy of motion. Mechanical and internal energies can be transferred from one body to another. The kinetic energy of running water can, for instance, be transferred to the wheels of a turbine, and the energy of blowing wind, to the wings of a windmill. We have observed a transfer of internal energy from one body to another in heat transfer, when the internal energy of a body (say, a heated stove) was transferred to another body (the air in the room). Is the energy conserved when it is transferred from one body to another or transformed from one kind into another? Having considered an example given on p. 168 and conducted an experiment consisting in mixing hot and cold water (p. 295), we have made sure that the amount of heat given off by the hot water is equal to the amount of heat gained by the cold water. This means that a body receives as much internal energy as another body has given off, i.e., the value of the internal energy remains the same when it is transferred from one body to another. This inference refers not only to internal energy. All other, more complicated experiments, which we shall study later on, show that the value of the energy remains the same in any of its transforn1ations. Observations and experiments have led to the discovery of one of the principal laws of physics, the law of conservation and transtorrnation 01 energy. This law states that energy can neither be created nor destroyed, but may be wnverted from one form to another or transferred from one body to another.171
A body cannot have energy unless it obtains it from another body. As we know, the energy of flowing water and the wind is obtained at the expense of the energy of the sun; the potential energy of a rocket launched, at the expense of the fuel burned; the air in the room becomes warmer, i.e., its internal energy increases at the expense of the energy of a stove or the radiator of water heating. The law or wnscrvation of energy is one or the most significant laws of nature. It manifests itself in both organic and inorganic worlds, it is always taken into account in science and engineering. When studying various mechanisms, we have got acquainted with the "golden rule" of mechanics, according to which no mechanism can give gain in work. This rule is one of the manifestations of the law of conservation of energy. Indeed, if, when lifting a body by means of a lever, we obtained an amount of work exceeding the work we did, then the potential energy of the lifted body would be greater than the expended energy, and that is impossible according to the law of conservation of energy. The law of conservation of energy refutes the legends stating that the world was created by god. It follows from the law that the material world was not created by anybody, its existence is everlasting and its development is constant. ? 1. Give examples of transformation of mechanical energy into internal and that of internal energy into mechanical. 2. Give examples that show the transfer of mechanical energy from one body to another. 3. What experiment can you remember which shows that the value of the internal energy remains the same when it is transferred from one body to another? 4. Cite the law of conservation of energy. 5. How significant is the law of conservation of energy for science and engineering? Exercise 44 1. When the hammer of a pile driver falls down, it strikes a pile and drives it into the earth. What transformations and transmissions of energy occur in this case? (It should be borne in mind that the pile and the earth become heated upon a strike.) 2. What transformations of the kinetic energy of a car occur when a car brakes down? 3. Two identical steel balls fall from the same height. One of them falls on a steel plate and bounces upwards and the other gets into sand and stays put. What transformations of energy occur in each case? 4. Describe all transformations and transmissions of energy, which take place when a tube containing ether and closed with a stopper is rubbed (Fig. 181).
Changes in the States of Aggregation of Matter 83. States of Aggregation of Matter Depending on the conditions, one and the same substance may be in a solid, liquid or gaseous state. We can cite ice, water, and water vapour as an example. These states are known as states of aggregation . Transition of a substance from one state of aggregation to another is widely used in practice. In metallurgy, for instance, metals are smelted to obtain alloys, such as cast iron, steel, bronze, brass, and others. Steam resulting from heating water is used in electric power stations and steam turbines and for many other engineering purposes, liquefied gases are employed in cooling installations. Changes in the states of aggregation of matter can be frequently observed in nature. Water evaporates from the surfaces of oceans, seas, lakes and rivers, and the cooling water vapour is transformed into clouds, dew, fog or snow. In many places of the earth, rivers and lakes freeze in winter and snow and ice melt in spring. To understand the processes described above and to know how to control many of them, we must know when and under what conditions a substance is in this or that state of aggregation, what the properties of each state are and what is necessary for a certain substance to pass from one state of aggregation to another. We have learned that molecules of a substance are the same whether the substance is in a solid, liquid or gaseous state, they in no way differ from one another. An aggregate state is determined by the mutual positions and the interaction of molecules (Sec. 13). In gases at atmospheric pressure the distances between molecules are much larger than the size of the molecules themselves and, therefore, the attraction between gas molecules is small. The average kinetic energy of gas molecules is quite sufficient to do work in overcoming the forces of molecular attraction. That is why gas molecules fly away unless the walls of a vessel are in their way. In liquids and solids, whose density is many times as great as that of a gas, molecules are more closely spaced. Their kinetic energy is not sufficient to overcome the forces of molecular attraction and, therefore, in liquids and, especially, in solids the molecules cannot fly very far from one another. Bodies which have a crystalline structure are known as solid bodies in physics. As distinct from liquids and gases, particles in them are in a perfect order. To disturb their order, work must be done to overcome molecular attraction. If that is done, the internal energy of a substance changes. When a substance passes from a solid into a liquid state and then into a gaseous state, the internal energy of the body increases even if the temperature of the body 173
remains constant. When a reverse transformation takes place , i. e., a body passes from a gaseous into a liquid state and then into a solid state, a certain quantity of energy is liberated, and, consequently, the internal energy of the body decreases . l. In what three states of aggregation can a body be? 2. What practical application can be found for the phenomenon of transition of a substance from one state of aggregation into another? 3. How can a certain state of aggregation be defined? 4. What are the peculiarities of the molecular structure of gases, liquids, and solids? 5. How does the internal energy of a body change when a substance passes from a solid to a liquid state and from a liquid to a gaseous state? 84*. Melting and Solidification of Crystalline Bodies Transferring energy to a body, we can transform it from a solid to a liquid state (say, melt the ice) and from a liquid to a gaseous state (transform water into steam). Depriving a gas of its energy, we can obtain a liquid, and then get a solid from the liquid. The transformation of a substance from a solid to a liquid state is called melting. To melt a body, it must be first heated to a defmite temperature. The temperature at which a solid melts is called the melting temperature (or melting point) of the substance. Some crystalline bodies melt at low temperature, others at high temperature. Ice, for instance, melts at 0 oc, and naphthalene at 80 oc. Placing a test-tube containing naphthalene into boiling water, we can obtain liquid naphthalene. We can melt a piece of tin or lead in a steel spoon by heating it over the flame of a spirit-lamp. As to cast iron and steel, they melt at very high temperature, about 1500°C. The change of a fluid into the solid state is called snlidtfication or crystallization. For a melted body to crystallize, it must cool to a definite temperature. The temperature at which a fluid solidifies (crystallizes) is called the . solidification temperature. . Experience shows that substances solidify at the same temperature at which they melt. Water, for instance, crystall~es (and ice melts) at ooc, and pure iron melts and crystallizes at the temperature of 1539 °C. If we heat a crystalline body, we can note that its temperature increases until the body begins melting, and during the whole process of melting the body temperat1Jre remaiJ;IS constant . At that temperature, a part of the body is in a liquid state and the other part in a solid state. It can be seen from Table 8 that the range of the melting points of various substances is very wide. 174
') Table 8 MELTING POINTS OF SOME SUBSTANCES. ' C (AT NORMAL ATMOSPHERIC PRESSURE) Hydrogen -259 Zinc 420 Oxygen -219 Aluminium 660 Nitrogen -210 Silver 962 Alcohol -114 Gold 1064 Mercury -39 Copper 1085 Ice 0 Cast iron 1100-1300 Cesium 29 Steel 1300-1500 Potassium 63 Iron 1539 Sodium 98 Platinum 1772 Tin 232 Osmium 3045 Lead 327 Tungsten 3387 Amber 350-380 1. What process do we call melting? 2. What process do we know as solidification? 3. What do we call the temperature at which a substance melts and solidifies? Exercise 45 1. Compare the melting points of solid mercury and solid alcohol. Whose melting temperature is higher? 2. Which of the metals presented in Table 8 is the most low-melting? the most high-melting? 3. Will the lead melt if we put it into a molten tin? Substantiate your answer. 4. Can we melt zinc in an al.uminium vessel? Substantiate your answer. 5. Why do we use alcohol thermometers rather than mercury ones to measure temperature outside the premises in cold regions? 6. Read "Amorphous Bodies. Melting of Amorphous Bodies" at the end of the book. Prepare a report on that theme. 85. The Graph of Melting and Solidification of Crystalline Bodies Figure 198 shows the graph of melting and crystallization of naphthalene. The observation began at the moment when the temperature of solid naphthalene was 55 oc. With further heating the temperature of the naphthalene rose until it reached 80 oc (portion AB of the graph). At 80 oc it began melting . During the whole period of melting the temperature of naphthalene did not change though the heating continued. This period is associated with the horizontal portion BC of the graph. As soon as the naphthalene melted, i.e., became liquid, its temperature began to rise and reached 90 °C (point Don the graph). Then the burner was 175
c F K Fig. 198 /0 Ttrne, min. 20 turned ofT and the liquid naphthalene was allowed to cool ofT. When its temperature fell to 80 °C, the process of crystallization began, and until all naph- thalene solidified, its temperature did not change. (The portion EF of the graph.) Only after that, did the temperature of the now solid naphthalene begin falling (the portion FK of the graph). ? l. How does the graph show changes in the temperature of a substance on heating and cooling? 2. What portions of the graph refer to melting and what to solidification of naphthalene? Why are these line segments parallel to the time axis? 86. Melting and Solidification from the Point of View of Teaching on the Molecular Structure of Matter Let us examine the melting and solidification of crystalline bodies from the point of view of the atomic-molecular theory of the structure of matter. We have learned that molecules (or atoms) in crystals are arranged in strict pattern. This explains why the crystals of the same substance have a definite shape. However, molecules and atoms in crystals are also in constant motion. But as distinct from gases, for instance, where the particles move independently of one another, each particle in a solid body affects the motion of other particles. As we know, the temperature of a body depends on the speed of molecular motion. When a body is heated, the average speed of molecules increases and, consequently, their average kinetic energy increases as well. Because of that, the amplitude of oscillations of molecules (or atoms) increases and the forces connecting them weaken. When the body reaches its melting point, the amplitude of oscillations becomes so large that the orderly pattern in the arrangement of the particles in crystals is violated. Crystals become shapeless: the substance melts and passes from a solid to a liquid state. When a substance solidifies, the process is reversed: the average kinetic energy and the speed of molecules in the cooled melted substance decrease. The forces of attraction can again keep these slowly moving molecules close to each other. As a result, the arrangement of particles again becomes regular. Crystallization is much easier if from the beginning some foreign particles, say, dust particles, are present in the liquid. They become centres of 176
crystallization. In ordinary conditions, there are usually many centres of crystallization in a liquid, around which crystals are forming. ? 1. How can we explain the process of melting and solidification of substances from the point of view of molecular structure of matter? 2. What is necessary for the crystallization of a substance to begin? 87. Specific Heat of Melting It is clear from the graph in Fig. 198 that in the process of melting naphthalene its temperature does not change, and only when it melts down will the temperature of the resulting liquid begin rising. But in the process of melting, as well, naphthalene gets energy from the burning fuel. And the law of conservation of energy states that the energy cannot be destroyed. How is then the energy of the fuel expended in the process of melting? We can answer this question if we remember that in the process of melting the crystal is destroyed. And that is what the energy is spent on. Consequently, the energy received by a crystalline body, after it has been heated to its melting point, is expended on changing its internal energy when the body passes into a liquid state. The quantity of heat necessary to transform 1 kg of a solid crystalline substance into a liquid at the melting temperature is called the specific heat of melting. The specific heat of melting is measured in Jjk:g and is designated as A. (lambda). The specific heat of melting can be determined experimentally. Thus it was found, by means of an experiment, that the specific heat of melting of ice is 3.4 · 105 J jk:g. This means that the transformation of a lump of ice with the mass of 1 kg, taken at 0 oc, into water of the same temperature requires 3.4 · 105 J. Consequently, at the melting point, the internal energy of a substance with me mass of 1 Kg in a liquid state is greater than the internal energy of the same mass of the substance in a solid state by the specific heat of melting. For example, the internal energy of water with the mass of 1 kg at ooc exceeds by 3.4 · 105 J the internal energy of ice with the mass of 1 kg at the same temperature. 12-971 Table 9 SPECIFIC HEAT OF MELTING OF SOME SUBSTANCES, J/kg (AT NORMAL ATMOSPHER IC PRESSURE) Aluminium 3.9. 10 5 Steel 0.84 ·10 5 Ice 3.4 ·105 Gold 0.67 · 105 Iron 2.7 ·105 Tin 0.59·10 5 Copper 2.1 ·105 Lead 0.25. 10 5 Silver 0.87 ·10 5 Mercury 0.12. 105 177
To calculate the quantity of heat Q required to melt a body of mass m taken at the melting temperature, the specific heat of melting A. must be multiplied by the mass of the body: Q = A.m. EXAMPLE. To make tea, a tourist put into a kettle 2 kg of ice at a temperature of 0 oc. What quantity of heat is required to transform the ice into boiling water at the temperature of 100 °C? How much heat would be needed if the tourist had taken 2 kg of water from an ice hole, instead of ice, at 0 °C? Given: m= 2 kg, t, = 0°C, t 2 = 100°C, A.= 3.4 · 10 5 1/kg, c = 4.2 ·103 1/kg 0 oc. Q .. .? Solution: First of all the ice must melt, for which purpose the following quantity of heat is required: Q, =3.4·10 5 Jfkg · 2 kg=6.8·10 5 1. To heat the water obtained from the ice from 0 to 100 °C, the following quantity of heat is required: Q2 = cm(t 2 - t 1 ), Q2 = 4.2 · W 1/ kg · oc ·2 kg (100 °C- ooq = = 8.4·10 5 1. The total quantity of heat required is Q= Q, +Ql, Q = 6.8 ° 105 1 + 8.4 ° 10 5 1 = 1.52 ° 10 5 J. If instead of ice he had taken 2 kg of water at 0 °C, then the quantity of heat required to heat it from 0 to 100 oc would be Q2 = 8.4. 105 J. Temperature Fig. 199 Time 178
' ) 1. How can you explain why the temperature of a crystalline body remains constant during the whole process of melting ? 2. What is the energy of the burning fuel expended for when a crystalline body is being melted? 3. What is the specific heat of melting ? 4. What units are used to measure the specific heat of melting ? Exercise 46 Figure 199 shows temperature vs time for two bodies of the same mass. Which of the bodies has a higher melting point? What body has a high- er melting heat? Are the specific heat capacities of the bodies the same ? 88. Energy Release in Solidification of a Substance Let us return to the graph of melting and crystallization of naphthalene (Fig. 198) and consider the part referring to its cooling. When the molten naphthalene is cooling, its temperature lowers. But as soon as the naphthalene begins to solidify, the lowering of its temperature ceases, although the naphthalene keeps giving off its internal energy to the surrounding bodies . That is so because its temperature is still higher than that of the sur- rounding bodies. And until the whole amount of naphthalene becomes solid, its temperature remains constant. But as soon as it becomes entirely solid, the temperature again begins to drop. This is true of all crystalline bodies. Why does not the temperature of a crystalline body drop during its solidification? We have learned that at the solidification temperature the internal energy of a body in a liquid state exceeds its internal energy in a solid state. During the whole process of solidification, the excess internal energy is liberated and makes up for the loss of energy in cooling. Therefore, the average energy of the molecules and, consequently, the body temperature as well, remain constant as long as the process of solidification lasts. And then the temperature of the solid body begins lowering since the loss of its internal energy is no longer made up for. Experiments conducted very carefully show that the same amount of heat is ltberated during the solidification of a crystalline body as is absorbed during its melting. Thus, when a mass of water of 1 kg solidifies at 0°C, 3.4 · 105 J of heat is liberated. But the same amount of heat is required to melt 1 kg of ice at 0 oc. ' ) 1. How can you explain that in the process of solidification of a substance its temperature does not change ? 2. What quantity of energy is released in solidification of 1 kg of water ? 179
Exercise 47 1. Melting ice is brought into a premise where the temperature is o oc. Will the ice continue melting in the premise? 2. Lumps of ice are floating in a pail of water. The temperature of both the water and the ice is o oc. Will the ice melt or the water freeze? What does it depend on? 3. How much energy is required to melt 4 kg of ice at 0 °C? 4. How much energy is required to melt 20 kg of lead at the melting temperature? How much energy is required in the case when the initial temperature of lead is 27 oc? Assignments I. Place two identical tin cans on the ranges of a gas stove. Pour 0.5 kg of water into one of them and _place 0.5 kg of snow in the other. Note what time is needed for the water in the two cans to begin boiling. Write a brief report about the experiment and explain its results. 2. Prepare a report on the theme "Metal Casting" having read the section on this theme at the end of the book. 89. Evaporation and Condensation We have learned that the temperature of a liquid, as well as of a solid and a gas, is associated with the motion of molecules. The higher the average speed of molecules, the higher the temperature of the liquid. But individual molecules move with speeds either smaller or larger than the average speed. If some sufficiently fast molecule comes to the surface of the liquid, it may overcome the attraction of the neighbouring molecules and escape from the liquid. The molecules, which escape from the liquid, form vapour over its surface. The phenomenon of conversion of a liquid to the vapour state is known as evaporation or vaporization. The speed of evaporation is due to several causes. If we wet a sheet of paper by ether in one place and by water in another, we shall see that the ether evaporates faster than water. Hence, the speed of evaporation depends on the kind of a liquid. The process of evaporation is faster in a liquid whose intermolecular forces are weaker, because in that case a larger number of molecules can overcome attraction and escape from the liquid. Since there are always a number of fast molecules in a liquid, evaporation must occur at any temperature. This fact is confirmed by observations. Pools of water, for instance, which remain after rain, dry out both in summer when it is hot and in autumn in cold weather. But in summer they dry out quicker than in autumn. The matter is that the higher the temperature of the liquid, the larger the part of fast molecules in it that can overcome the forces of attraction of the neighbouring molecules and escape from the surface of the liquid. Hence, the evaporation is the quicker, the higher the temperature of the liquid. The conversion from a liquid to the vapour state goes on simultaneously with the reverse process. Moving in disorder over the surface of the liquid, a part of 180
0 0 00 0 0 0 Q 0 i-Fig. 200 the molecules, which have escaped from it, return to it. Transformation from a vapour to the liquid state is called condensation 1 • If evaporation occurs in a closed vessel, then very soon the number of molecules escaping from the liquid becomes equal to the number of the molecules of the vapour returning to the liquid. Therefore, the quantity of the liquid in a closed vessel does not change, although the liquid keeps evaporating (Fig. 200). In an open vessel, as a result of evaporation, the quantity of the liquid gradually diminishes since the majority of the molecules of the vapour scatter in the air and do not return into the liquid. Only a small part of them return, thus decelerating the evaporation of the liquid. Therefore, when there is a wind, which carries away molecules of the vapour, the evaporation of the liquid is faster. If we pour the same quantity of water in a narrow vessel and in a wide vessel, we shall see that evaporation goes on quicker in the wide vessel. For example, water evaporates quicker from a saucer than from a cup. Wet clothes dry faster when they hang on a rope than when they lie in a heap. This can be explained by the fact that liquid evaporates from the surface, and the larger the free surface of the liquid, the larger is the number of molecules escaping from it. Hence, the speed of evaporation of a liquid depends on the area of its surface. Observations and experiments show that solids evaporate too. Since ice evaporates, clothes can dry in a frosty weather. Smells emitted by solids can also be explained by their evaporation. ? 1. What is the relationship between the temperature of a liquid and the speed of motion of its molecules? 2. What phenomenon is known as evaporation? 3. How can you explain that evaporation occurs at any temperature? 4. How do you call the process of conversion of a vapour into a liquid? 5. Enumerate and explain all the causes for a change in the s~ed of evaporation of liquids. 1 From the Latin word condensare meaning to thicken. 181
90*. Absorption of Energy in Evaporation of Liquids and Its Release in Vapour Condensation When molecules escape from a liquid, they overcome the attraction of the remaining molecules, i.e., do work against the forces of attraction. Not all the molecules of the liquid can do the necessary work but only those which have sufficient kinetic energy, sufficient speed. But when the fastest molecules escape from the liquid in the process of evaporation, the average speed of the remaining molecules becomes lower and, consequently, the average kinetic energy of the molecules remaining in the liquid diminishes. This means that the internal energy of the evaporating liquid decreases. Therefore, unless there is an inflow of energy to the liquid from outside sources, the evaporating liquid cools down. We can make an experiment to observe cooling of a liquid in evaporation. For that purpose, we must cover the ball of the thermometer with cotton wool or a piece of cloth and pour ether on it. Quickly evaporating ether takes away a part of the internal energy of the ball of the thermometer and the temperature of the latter becomes lower. If you wet your hand with ether, you will feel how your hand becomes cooler. Coming out of the water, even in a hot day, we feel cold. Evaporating from the surface of our body, the water takes away a quantity of heat. However, we do not notice the drop of temperature of the water in a cup when it is evaporating. How can it be explained? The matter is that in this case the evaporation proceeds very slowly and the temperature of the water keeps constant at the expense of the quantity of heat given off by the surrounding air. This means that for the temperature of the evaporating liquid to remain constant, some energy must be delivered to the liquid. Thus, 2.4 · 106 J of energy is required to evaporate water with the mass of 1 kg at 35°C, and 0.4 · 106 J of energy is enough to evaporate 1 kg of ether taken at the same temperature. Evaporation plays an important part in the life of animals. Some disturbance in evaporation may violate heat exchange and cause overheating of a body. We have said that conversion from a vapour to a liquid state is called condensation. Condensation of vapour is followed by energy release. In a summer evening, when the air becomes cooler, dew falls on the ground. That is the water vapour which was in the air and now falls on the grass and leaves as small drops of water when the air becomes cooler. The formation of clouds is also due to condensation. The water vapours, rising above the earth, form clouds in the upper, colder layers of air which consist of tiny drops of water. ? 182 1. What kind of work is done by the molecules escaping from a liquid in the process of evaporation? 2. How can you explain the drop of the temperature of the liquid in evaporation.
3. How can you explain that liquids evaporate at any temperature? 4. How can you explain that under the same conditions some liquids evaporate quicker than others? 5. What conditions are needed for condensation of vapour ? 6. What natural phenomena can you explain by condensation of vapour? Exercise 48 I. In what weather do the water pools left after rain dry out quicker: in windless or in wintry weather? in warm or cold weather? How can it be explained? 2. Why does hot tea cool quicker when we blow on it? 3. Sweat oozing from the pores in hot weather cools the body. Why? 4. Why is it easier to bear heat in dry air than in humid air? 5. To obtain cold water on a hot summer day, it is poured into jars made of weakly burned clay through which the water seeps slowly. In such vessels the water is cooler than the surrounding air. Why? 6. A small quantity of water is in a cup and the same quantity of water is in a saucer. Where will the water evaporate sooner? Why? 7. Take a brush, dip it in various liquids, e. g., ether, alcohol, water and oil, and put strokes on a glass or a plank. Observing the strokes, we note that the speeds of evaporation of the liquids are different. Make such an experiment and explain it. 8. Why do they put layers of humus, manure or peat around fruit tree trunks in summer after rains or watering? 9. Read "Refrigerators" at the end of the book. 91. Boiling It is interesting to observe the phenomena occurring in a liquid being heated. Let us make an experiment for which purpose we shall heat water in an open glass flask (Fig. 201a). Note first of all that water evaporates from the surface. Sometimes, we can even notice steam forming over the flask, the water vapour mixes with cold air and condenses in the form of tiny drops. The steam itself is invisible for the eye, of course. When we keep rising the temperature, we notice the appearance of numerous small bubbles in the water. They gradually grow in size. These are the bubbles of the air which is always dissolved in water. The cold er the water, the larger the quantity of air dissolved in it. Therefore, upon heating, the excess of air is released from the water in the form of bubbles. These bubbles contain not only Fig. 201 (a) (b) 183
air but also water vapour since the water evaporates into the interior of these air bubbles. As the water heats up, the bubbles become larger and more numerous. With the growth of the bubbles, the buoyant force increases and pushes them out of the water, and the bubbles rise to the surface. At that moment we can hear "noise", usually preceding boiling. At a certain temperature, the bubbles approaching the surface grow sharply. At the surface they burst and the water vapour they contain is released into the atmosphere, the water boils (Fig. 201b). The temperature at which a liquid boils is known as the boiling point. During boiling the temperature of the liquid does not change. Table 10 THE BOILING POINT OF SOME SUBSTANCES, "C (AT NORMAL ATMOSPHERIC PRESSURE) Hydrogen -253 Water 100 Oxygen - 183 Mercury 357 Ammonia -33 Lead 1740 Ether 35 Copper 2567 Alcohol 78 Iron 2750 It can be seen from the table that substances, which are gases in ordinary conditions turn into liquids upon sufficient cooling and begin boiling at very low temperature. Liquid oxygen, for instance, boils at atmospheric pressure at -183 oc. And conversely, the substances which are in a solid state in ordinary conditions, turn into liquids upon melting and boil at very high temperatures. Copper, for instance, boils at 2567 oC and iron at 2750 oC. ? 1. What phenomena can we observe in a liquid being heated before it reaches its boiling point? 2. What forces act on air bubble filled with vapour, when the bubble is inside the liquid? 3. What is the boiling point of liquid? 92. Specific Latent Heat of Vaporization and Condensation We have learned (Sec. 90) that to keep the temperature of the evaporating liquid constant, it is necessary to deliver to the liquid a definite quantity of heat. As we have seen, boiling is a kind of evaporation, followed by a quick formation and growth of vapour bubbles. It is evident that a definite quantity of heat must be delivered to the liquid when it boils. This quantity of heat is spent on vapour formation. The quantity of heat necessary to evaporate 1 kg of a liquid without changing its temperature is known as the specific latent heat of vaporization. 184
It has been established experimentally that the specific latent heat of vaporization of water at 100°C is equal to 2.3 ·106 Jjkg, or, in other words, to convert water with the mass of 1 kg into vapour at the temperature of 100 °C, we must deliver to it 2.3 ·106 J of energy. Table 11 SPECIFIC HEAT OF VAPORIZATION OF SOME SUBSTANC ES. J /kg (AT BOILING POINT AND NORMAL ATMOSPHERIC PRESSURE) Water Ammonia (liquid) Alcohol 2.3·106 1.4. 106 0.9 · 106 Ether Mercury The specific latent heat of vaporization shows how many times the internal energy of 1 kg of a substance becomes greater when it is converted from a liquid into the vapour state without a change in temperature. Thus, the energy of 1 kg of water vapour at 100°C is 2.3 ·106 J greater than the energy of water with the mass of 1 kg at the same temperature of 100 oc; the energy of alcohol vapour with the mass of 1 kg at the temperature of 78 oc is by 0.9 · 106 J greater than that of liquid alcohol of the same mass at the same temperature of 78 °C, etc. Touching a cold object (Fig. 202), water vapour condenses and in the process of condensing the energy is released which was absorbed when the vapour was forming. Accurate experiments show that in the process of condensation the vapour releases the same amount of energy that was spent on its formation . Consequently, when 1 kg of water vapour at 100 oc turns into water of the same temperature of 100°C, the energy released equals 2.3 ·106 J. As can be seen from the comparison with other substances (see Table 11), this quantity of energy is rather great. The energy released during the condensation of vapour can be utilized. At Fig. 202 185
large thermal power stations, the used-up steam from the turbines heats water, which is then used in heating systems of buildings and in public services. ? 1. How is the energy delivered to the boiling liquid expended? 2. What do we mean by the specific latent heat of vaporization? 3. How do you understand that the specific latent heat of vaporization of water is equal to 2.3 ·106 J(kg? 4. How many times is the internal energy of 1 kg of water vapour at 100 °C greater than that of 1 kg of water at the same temperature? 5. How can we show experimentally that energy is released during condensation of vapour? 6. What quantity of energy is released during the condensation of I kg of water vapour? 7. Where is the energy released in condensation of water vapour used in engineering? 93. How the Quantities of Heat Can Be Calculated EXAMPLE 1. What quantity of energy is needed to convert 5 kg of liquid ammonia into gas at the boiling temperature of ammonia? We fmd in Table 11 that the specific latent heat of vaporization of ammonia at normal pressure is L = 1.4 ·106 1/kg. Hence it follows that to convert 5 kg of liquid ammonia into gas at the boiling temperature, five times as much energy is required, i.e., Q = 1.4 ·106 1/kg. 5 kg= 7 ·106 1. Thus, to calculate the quantity of heat required to convert into vapour any mass m of liquid taken at the boiling point, the specific latent heat of vaporization must be multiplied by the mass: Q=Lm. EXAMPLE 2. What quantity of energy is required to convert 2 kg of water taken at 20 oc into vapour at 100 °C? 186 Given: m= 2 kg, t 1 = 20 °C, Solution: The total quantity of the energy spent: t 2 = too oc, Q = Q1 + Q2 , c = 4.2 ·103 J(kg · °C, where Q1 is the energy spent on heating water L= 2.3 ·106 J/ kg. from 20 to 100 °C: -------- Q 1 =cm(t 2 -t 1), Q... ? and Q2 is the energy spent on conversion of water into vapour without changing the temperature: Q2 = Lm.
N !)>' § ~ ~ "'~ 120 B c!00 80 50 'tO w Fig. 203 0 TiiTie, min . Substituting the numerical values of the quantities, we get Q=4200 Jjkg· °C·2 kg (100 °C-20 °C}+ + 2.3. 106 Jfkg· 2 kg~ 5.3. 106 J. This problem can be solved by first representing the process of water heating graphically (Fig. 203), by laying off, to a definite scale, the time of heating along the horizontal axis and the temperature along the vertical axis. The portion AB of the graph shows that the water is heated from 20 oc to the boiling point, and the quantity of energy required is Q1 =cm (t 2 - t 1) . The portion BC of the graph shows that the water turns into vapour without a change in temperature but absorbing energy: Q2 = Lm. And the total quantity of the energy spent is Q = Q1 + Q2 • Exercise 49 I. How do you understand the fact that the sJ'ecific latent heat of condensation of ammonia is equal to 1.4-10 Jjkg? 2. Indicate a substance presented in Table 11 whose energy increases more than that of the other substances when it is converted from a liquid into the vapour state. Substantiate your answer. 3. What quantity of energy is required to convert 150 g of water at 100 oc into the vapour state? 4. What quantity of energy must be spent to bring 5 kg of water at 0 oc to the boiling point and to evaporate it? 5. What quantity of energy will be released by 2 kg of water when it is cooled from 100 to 0 °C? What quantity of energy will be released if we take the same amount of vapour at 100 °C instead of water? Assignment Prepare reports on the following themes: (1) How dew, hoar-frost, rain, and snow are formed. (2) How clouds originate. (3) Circulation of water in nature. 187
Heat Engines 94. Work Done by the Expanding Gas or Steam We have learned by now that the development of engineering depends on the fullest possible utilization of the huge stores of the internal energy contained in fuel. To use internal energy means to do work at its expense, say, to lift a load, to transmit carriages, etc. And this means, in its turn, that the internal energy must be converted into mechanical energy. How to do it? Let us pour some water into a test-tube, close it tightly by a stopper and bring the water to the boil. Under the steam pressure, the stopper will be pushed out. In this case, the energy of the fuel was converted into the internal ene·rgy of the steam, and the steam, having expanded, did work, pushed out the stopper. The internal energy of the steam was converted into the kinetic energy of the stopper. Let us now replace the test-tube by a metallic cylinder and the stopper by a tightly fitting piston, which can move inside the cylinder. We have obtained the simplest heat engine, in which the internal energy of the fuel is transformed into the mechanical energy of the piston. Such an engine was invented at the end of the 17th century and was developed and perfected afterwards. Heat engines are the machines in which the internal energy of the fuel is transformed into mechanical energy. There are several varieties of heat engines: a steam engine, an internal combustion engine, steam and gas turbines, a jet engine. In all these engines, the energy of the fuel is first transformed into the energy of the gas (or steam). While expanding, the gas does work and cools down in the process, its internal energy being transformed into mechanical energy. We shall consider here two kinds of heat engines, the internal combustion engine and a steam turbine. ? 188 1. Give examples of transformation of the internal energy of gases into the mechanical energy of bodies. · 2. What engines are known as heat engines? 3. What types of heat engines do you know? 4. What transitions and transformations of energy occur in all heat engines?
95. The Internal Combustion Engine The internal combustion engine is the most common and widespread type of heat engine, in which the fuel burns inside the cylinder, in the interior of the engine. This accounts for the name of the engine. Internal combustion engines work on liquid fuel (petrol, kerosene, oil) or on combustible gas. Most of the motor-cars use this type of heat engine. Figure 204 shows a cross section of the simplest internal combustion engine. The engine consists of a cylinder in which piston 3 moves, connected by means of connecting rod 4 with crankshaft 5. Heavy flywheel6 is attached to the shaft and is intended to make the shaft rotate more smoothly. In the upper part ofthe cylinder there are two valves 1 and 2 which open and close automatically when it is needed. Fuel mixture enters the cylinder through valve 1 and is ignited by the plug 7, while the exhaust gases escape through the valve 2. Combustion of the fuel mixture, consisting of petrol vapour and air, occurs periodically in the cylinder of the engine. The temperature of the gaseous combustible fuel reaches 1600-1800 °C. Correspondingly, the pressure exerted on the piston increases sharply. The expanding gases push the piston and the crankshaft together with it, thus doing mechanical work. They cool down in the process, since a part of their internal energy is converted into mechanical energy. Let us consider in more detail how such an engine works. The end positions of the piston are called dead centres. The distance traversed by the piston from one dead centre to the other is called the stroke of the piston. One working cycle of the engine consists of four strokes of the piston or, as they say, of four steps. Engines of this type are, therefore, called four-stroke engmes. One stroke of the piston corresponds to a half-turn of the crankshaft. When the shaft turns at the beginning of the first stroke, the piston moves Fig. 204 189
22 2 Fig. 205 down (Fig. 205a). The space over the piston increases, and a vacuum is formed in the cylinder. Valve 1 opens and the combustible mixture is sucked into the cylinder. By the end of the first stroke, the cylinder is filled with the fuel mixture and valve I is closed. As the shaft turns again, the piston moves upwards (the second stroke) and compresses the fuel mixture (Fig. 205b). At the end of the second stroke, when the piston reaches the upper dead centre, an electric spark ignites the compressed combustible mixture which burns up quickly. The gases formed during combustion push the piston down (Fig. 205c). Under the action of the expanding gases (third stroke) the engine does work and this step is correspondingly called the working stroke . The movement of the piston is transmitted through the connecting rod to the crankshaft and the fly- wheel. Having received a powerful push, the flywheel keeps rotating by inertia and moves the piston in the next strokes. At the end of the third stroke, valve 2 opens and the products of combustion escape from the cylinder to the atmosphere. The expulsion of the combustion products continues during the fourth stroke when the piston moves upwards (Fig. 205d). At the end of the fourth stroke valve 2 closes. Then the working cycles of the engine are repeated. Thus, a cycle of an engine consists of the following four processes (steps) : inlet, compression, working stroke, outlet . In motor-cars, engines are usually started by means of an auxiliary electric engine called starter . Motor-cars are most often equipped with four-cylinder internal combustion engines. Figure 206 shows a cross section of such an engine. The work of the cylinders is in agreement so that a working stroke occurs in each cylinder in turn and the crankshaft is continuously supplied with energy from the four pistons. There are also eight-cylinder car engines. Multi-cylinder engines are more convenient since they provide more smooth rotation of the shaft and are more powerful. A cooling system is an inalienable part of any internal combustion engine since the fuel mixture can ignite prematurely and an explosion can occur. The cylinders are cooled by running water or air and, therefore, internal combustion 190
Fig. 206. The cross section of a four- 6 cy linder internal combustion engine: ] - piston, 2- connecting rod, 3 - flywheel, 4 - crankshaft, 5 - wheels of a gear transmission, 6 - inlet and outlet valves 5 engines can be equipped with either a liquid or an air cooling system. Internal combustion engines fmd various applications. They start aircraft, steamships, cars, tractors, diesel locomotives. River and sea ships are provided with powerful internal combustion engines. A Diesel-electric ship 191
A tractor used for steep slopes ? 1. What engine is called an internal combustion engine? 2. What are the principal parts of the simplest internal combustion engine? 3. What physical phenomena occur when the combustible mixture burns in an internal combustion engine? 4. How many strokes or steps constitute one working cycle of an engine? How many turns does the shaft make during one cycle? 5. What processes take place in an engine during one of the four steps? How are these steps called? 6. What is the role of the flywheel in an internal combustion engine? 7. What internal combustion engines are most often used in motor-cars? 8. Where else, besides cars, are internal combustion engines used? 96. The Steam Turbine Modern engineering makes wide use of a special type of steam engine in which steam or gas heated to a high temperature rotates the shaft of an engine without the aid of a piston, a connecting rod, and a crank- shaft. Such engines are called turbines (Fig. 207). The operation of a simple steam turbine is shown in Fig. 208. A disc 4 with blades 2 around its rim is fixed to a shaft 5. There are pipes or nozzles 1 near the blades through which steam 3 enters from the boiler. The jets of steam escaping from the nozzles exert a considerable pressure on the blades and set the disc of the turbine in fast rotatory motion. 192
Fig. 207. A steam turbine Modern turbines have not one but several discs fitted to a common shaft. The steam passes consecutively the blades of all the discs transferring a part of its energy to each of them. Figure 209 shows a rotor 1 of a powerful steam turbine. You can see discs with 1 A rotating part of a turbine with discs fixed to it (from the Lain rotare meaning to rotate). Fig. 208 193 13-971
Fig. 209. The rotor of a steam turbine rows of blades. In electric power stations, a generator of electric current is connected to the turbine. The speed of rotation of the turbine shaft reaches 3000 rpm which is very convenient for actuating electric current generators. Soviet factories now produce turbines with a capacity of up to 1 200 000 kW. Turbines are employed at thermal power stations and in steamships. The field of application of gas turbines, in which gas combustion products are used instead of steam, becomes ever wider. ? 1. What heat engines do we call steam turbines? 2. What is the difference in the designs of turbines and piston engines? 97. The Efficiency of a Heat Engine Any heat engine can convert into mechanical energy only a part of the energy released by the fuel, since the gas or the steam, having done the work, escapes from the engine still having energy. To evaluate the efficiency of a heat engine, it is very important to know what part of the energy lreleased by the fuel is spent on useful work. The greater that part is, the more efficient is the engine. The ratio of the part of the energy spent on the useful work done by the 194
engine to the total energy released upon a complete combustion of the fuel is called the efficiency of a heat engine. For example, if, out of the total energy released upon the complete combustion of the fuel, the engine spends only a quarter on doing useful work, then we say that the efficiency of the engine is 1/4 or 25% since the efficiency is usually expressed in per cent. The efficiency of an engine is always less than unity, i.e., less than 100%. This follows from the law of conservation of energy. The efficiency of an internal combustion engine, for instance, is 20-40%, and that of steam turbines is about 30%. An increase in the number of cars, especially in cities, pollutes the atmosphere by exhaust gases of internal combustion engines. These gases are harmful for living organisms and, in addition, they cause damage to valuable architectural structures. The struggle with atmospheric pollution is now one of the serious state tasks. One of the most efficient means of avoiding this pollution is to replace the internal combustion engine by electric engines. The sources of current required by such machines must have large stores of energy, and the creation of such sources is one of the main problems our scientists now deal with. To obviate air pollution, the engines of the existing cars must be always in order and use fuel which they are designed for. These rules must be carefully observed. ? 13* 1. Why is only a part of the fuel energy in heat engines converted into mechanical energy? 2. What is the efficiency of a heat engine? 3. Can an engine have an efficiency equal to 100"/o? Why? What are the efficiencies of modern heat engines? Assignment Prepare reports on the following themes : (1) The invention of heat engines. (2) The invention of turbines. (3) The first locomotives of Stephenson and Cherepanovs. (4) The use of the solar energy on the earth (read the corresponding section at the end of the book).