Bukhovtsev-et-al-Problems-in-Elementary-Physics

B. B. 6yX08I4e8. B. JI. KpU8IleHIC08. r. fl. MRKuwe8, B. n. llJaAbH08 CBOPHHK 3A)lA q no 3JIEMEHTAPHOA H3AATEJlbCTBO cHAYKh MOCKBA PROBLEMS IN ELEMENTARY PHYSICS B.BUKHOVTSEV. v. KRIVCHENKOV, G. MY AKISHEV, V. SHALNOV Translated from the Russian bll A~ T roitsky Translatton edited by G. Leib MIR PUBLISHERS • MOSCOW First published 1971 Second printing 1978 This collection of 816 problems is based on the textbook "Elementary Physics" edited by Academician G. S. Landsberg. For this reason the content and nature of the problems and their arrangement mainly conform with this textbook. There is no section devoted to "Atomic Physics", however, since the exercises in Landsberg's book illustrate the relevant material in sufficient detail. Some problems on this subject have been included in other chapters. The problems, most of which are unique, require a funda- mental knowledge of the basic laws of physics, and the ability to apply them in the most diverse conditions. A number of prob- lems In the book have been revised from those used at the annual contests organized by the Physics faculty of the Moscow Uni- versity. The solutions of all the difficult problems are given in great detail. Solutions are also given for some of the simpler ones. The book is recommended for self-education of senior pupils of general and special secondary and technical schools. Many problems will be useful for first and second year students of higher schools. CONTENTS Chapter 1. Mechanics. • • • • • . • . . • • . • • • . • • 1-1. Kinematics of Uniform Rectilinear Motion ..•. 1-2. Kinematics of Non .. Uniform and Uniformly Variable Rectilinear Motion ••.•..•...••.•• 1-3. Dynamics of Rectilinear Motion . 1-4. The Law of Conservation of Momentum 1-5. Statics . . . . • . . . . . . . . • 1-6. Work and Energy •.•...••• 1-7. Kinematics of Curvilinear Motion .• 1-8. Dynamics of Curvilinear Motion 1-9. The Law of Gravitation . • • • • • • . 1-10. Hydro- and Aerostatics .• 1-11. Hydro- and Aerodynamics Prob- Answers lems and solutions 7 160 7 160 11 169 15 174 23 185 25 188 31 200 38 214 44 230 53 248 55 253 62 261 Chapter 2. Heat. Molecular Physics . 68 268 2-1. Thermal Expansion of Solids and Liquids . . . .. 68 268 2-2. The Law of Conservation of Energy. Thermal Con .. ductivity. . . . . . . . • • • • . • . 69 270 2-3. Properties of Gases . • • • • • • • • . 71 273 2-4. Properties of Liquids . • . • . • . . . • . 76 283 2-5. Mutual Conversion of Liquids. and Solids 80 287 2-6. Elasticity and Strength . • • 81 289 2-7. Properties of Vapours . . • • • 84 291 Chapter 3. Electricity and Magnetism 87 294 3-1. Electrostatics. • • • • • • • 87 294 3-2. Direct Current • • • •• ..•... 97 317 3-3. Electric Current in Gases and a Vacuum • . • • •• 107 336 3-4. Magnetic Field of a Current. Action of a Magnetic Field on a Current and Moving Charges . . . . •• 112 341 3-5. Electromagnetic Induction. Alternating Current . •. 116 347 3-6. Electrical Machines . • • • . • • • • • • . • . •. 123 359 Chapter 4. Oscillatlons and Waves 4-1. Mechanical Oscillations 4-2. Electrical Oscillations • 4-3. Waves •••••••• 127 127 131 133 365 365 373 376 6 Chapter 5. Geometrical Optics •••• 5-1. Photometry ....•••. 5-2. Fundamental Laws of Optics ••••• 5.-3. Lenses and Spherical Mirrors 5-4. Optical Systems and Devices Chapter 6. Physical Optics • • ~l. Interference of Light . • •.••• ~2. Diffraction of Light. . . . • . . . . . . . . • • • 6-3. Dispersion of Light and Colours of Bodies . CONTENTS Prob- Answen lems and solutions 135 380 135 380 136 382 142 395 146 402 151 421 151 421 156 429 158 434 PROBLEMS CHAPTER 1 MECHANICS 1·1. Kinematics of Uniform; Rectilinear Motion 1. A motor-boat travelling upstream met rafts tioating down- stream. One hour after this the engine of the. boat stalled. It took 30 minutes to repair it, and during this time the boat freely ftoated downstream. When the engine was repaired, the boat travelled downstream with the same speed relative to the current as before and overtook the rafts at a distance of s = 7.5 km from the point where they had met the first time. Determine the velocity of the river current, considering it constant. 2. A man walking with a speed v constant in magnitude arid direction passes under a lantern hanging at a height H above the ground. Find the velocity which the edge of the shadow of the man's head moves over the ground with if his height is h. 3. The distance between a town and a mill is 30 km. A man started to walk from the mill to the town at 6:30 8. m., while a cyclist left the town for the mill at 6:40 a.m., riding at a speed of 18 krn/h. The man met the cyclist after walking 6 km, Determine at what time they met and the man's speed. Also find the place where the man was when he met the twelfth bus coming from the town and the number of -buses which overtook the cyclist if bus traffic begins at 6 8. m. The buses leave their terminals every 15 minutes and their speed is 45 km/h, . • 4. Two trains left MosCow for Pushkino at an interval of t= 10 minutes and with 8 speed of V= 30 krn/h, What was the speed u of a train bound for Moscow if it met these two trains at an interval of 't = 4 minutes? 5. An engineer works at a plant out-of-town. A car is sent for him from the plant every day that arrives at the railway station at the same time as the train he takes. One day the 8 PROBLEMS engineer arrived at the station one hour before his usual time and, without waiting for the car, started walking to work" On his way. he met the car and reached his plant 10 minutes before the usual time. How long did the engineer walk before he met the car? Give a graphical solution. 6. Two landing-stages M and K are served by launches that all travel at the same speed relative to the water. The distance between the landing-stages is 20 km. It is covered by each launch from M to K in one hour and from K to M in two hours. The .launches leave the two landing-stages at the same time at an interval of 20 minutes and stop at each of them also for 20 minutes. Determine: (1) the number of launches in service, (2) the num- ber of launches met by a launch travelling from M to K, (3) the number of launches met by a launch travelling from K to M. 7. Two tourists who are at a distance of 40 km from their camp must reach it together in the shortest possible time. They have one bicycle which they decide to use iJ1. turn. One of them started walking at a speed of VI = 5 km/h and the other rode off on the bicycle a t a speed of v. = 15 krn/h. The tourists agreed to leave the bicycle at intermediate points between which one walks and the other rides. What will the mean speed of the tourists be? How long will the bicycle remain unused? 8. Two candles of equal height h at the initial moment are at a distance of a from each other. The distance between each candle and the nearest wall is also a (Fig. 1). With what speed will the shadows of the candles move along the walls if one candle burns down during the time t, and the other during the time tl? 9. A bus is running along a highway at a speed of VI = 16 m/s. A man is at a distance of a = 60 metres from the highway and b = 400 metres from the bus. In what direction should the man run to reach any point of the highway at the same time as the bus or before it? The man can run at a speed of VI = 4 int». to. At what minimum speed should the man run (see Problem 9) to be able to meet the bus, and in what direction? It. A man is on the shore of a lake at point A, and has to get to point B on the lake in the shortest possible time (Fig. 2). The distance from point B to the shore Be = d and the dis tance AC = s. The man can swim in the wa ter wi th a speed of VI and run along the shore with a speed of VI' greater than VI- Which way should he use-swim from point A straight

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