Newtonian Mechanics PDF
Preview Newtonian Mechanics
Newtonian mechanics A.R French Introductory ll'KHHS o o o o o senes OOOOOOO OOOOOOOOOOO OOOOOOOOOOO OOOOOOOOOOO OOOOOOOOOOO OOOOOOOOOOO 531.01 OOOOOOOOO FRE OOOOOOO I his tcxl prescnts the import m bot h cUlMlol and modern physics as relevani today, atartlng fiom ibout niotion and ending with an problcms in murinml dynamics. i lu- prime empha i the lopment and usc of New. i ii a cornpletc llret-yaar tnechanka couim and contains manj iiiggesdona i<>r further rcadh Aboul tbC Aulhor \ i eived bot h his B. A. Ph. D. degrees from ( amhridge i nivenlty, where he cootinued asa member of the Physics i tepartment from 1948 undi 1955. b ic joincd the staff of the l m. : South PhyalGS and became l»*)2 hc wenl to mi i Profc I was appointed t wo years later. has devoted ai half his timc during the past ala lopment of the \t i i . Introdw but his eapertaaca h bj do dm purel . He hai had extc carch assignments with the Cavendlah i aboratoriea, the Manhattan Project, and the U.K. Vtomk Eoergj Reseercb iblishmcnt THE LIBRARY THE HARRIS COLLEGE CORPORATION STREET, PRESTON AH liooks must be Returned to «he College Library or Renewed not later iban the last date sbown below. Re. NGV !974 Re -6. OCT. 19J W n< 975 ! FEB. 197L. -? M 197 . 19. m. [991 -3. MAY 1976 2 -07. I 21. FED. 1997 j _ The M.I.T. Introductory Physics Series Special RelatiVity A.P.FRENCH Vibrations and Waves A.P.FRENCH Newtonian Mechanics A.P.FRENCH TheM.I.T. Introductory Physics Series Newtonian Mechanics A. E French _ PROFESSOR OF MATHEMATICS, THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY Nelson » TIIOMAS NELSON AND SONS LTD 36 Park Street London wIy 4de po Box 18123 Nairobi Kenya THOMAS NELSON (AUSTRALIA) LTD 597 Little Collins Street Melbourne 3000 THOMAS NELSON AND SONS (CANADA) LTD 8 1 Curlew Drive Don Mills Ontario THOMAS NELSON (NIGERIA) LTD po Box 336 Apapa Lagos THOMAS NELSON AND SONS (SOUTH AFR1CA) (PROPRIETARY) LTD 51 Commissioner Street Johanncsburg Copyright © 1971, 1965 by the Massachusetts Institute of Technology First published in Great Britain 1971 PROTON L^bsbnn 17 77610745 81 (pbaopaerrd)s) per ic' 47809 —— 551 we Made and printed by William Clowes & Sons Ltd, Beccles, Colchester and London Contents Preface xi Prologue 3 PART I THE APPROACH TO NEWTONIAN DYNAMICS 1 A universe of particles 21 The particulate view 21 Eleclrons and nucleons 24 Atomic nuclei 25 Atoms 26 Molecules; licing cells 28 Sand and dust 31 Other lerrestrial objecls 32 Planels and satellifes 33 Stars 35 Galaxies 36 PROBLEMS 38 2 Space, time, and motion 43 What is motion? 43 Frames ofreference 46 Coordinale systems 48 Combination ofvector displacements 53 The resolution ofvectors 56 Vector addilion and the properties ofspace 59 Time 61 Uniis and standards oflength and time 63 Space-time graphs 66 Velocily 67 lnslantaneous velocily 68 Relatlve velocily and relative motion 72 Planetary motions: Ptolemy versus Copernicus 74 PROBLEMS 78 3 Accelerated motions 85 Acceleralion 85 The analysis of straight-line motion 87 A comment on exlraneous roots 93 Trujectory problems in two dimensions 95 Free fail of individual aloms 98 Other features of motion in free fail 102 Uniform circular motion 105 Velocily and acceleralion in polar coordinales 106 PROBLEMS 108 4 Forces and equilibrium 115 Forces in static equilibrium 116 Units offorce 118 Ekuilibrium conditions; forces as vectors 119 Action and reaction in the contact ofobjects 123 Rotational ekuilibrium; loraue 124 Forces without contact; weight 128 Pulleys and slrings 130 problems 132 5 The various forces of nature 139 The hasic lypes offorces 139 Gravitatkmal forces 140 Electric and magnetic forces 145 Nuclear forces 147 Forces between neutral atoms 148 Conlaci forces 150 Frictional contact forces 152 Concluding remarks 154 problems 154 VI 6 Force, inertia, and motion 161 The principle of inertia 161 Force and inertial mass: Newlon's law 164 Some comments on Newlon's law 167 Scales ofmass andforce 170 The effect ofa continuing force 173 The incariance ofNewton's law; relatioily 173 Incariance with specific force laws 176 Newlon's law and time reuersal 178 Concluding remarks 180 problems 181 PART II CLASSICAL MECHANICS AT WORK 7 Using Newton's law 187 Some inlroduclory examples 188 Motion in two dimensions 194 MoIion in a circle 198 Curoilinear motion with changing speed 200 Circular pailis of charged particles in uniform magnelic fields 202 Charged particle in a magnelic fielcl 205 Mass spectrographs 206 The fracture ofrapidly rotating objects 208 Motion against resistive forces 210 Deiailed analysis ofresisted motion 213 Motion gocerned by viscosily 218 Growlh and decay ofresisted motion 221 Air resistance and "independence ofmolions" 225 Simple harmonic motion 226 More about simple harmonic motion 231 problems 234 8 Universal gravitation 245 The discovery of universal gravitation 245 The orbits of the planets 246 Planetary periods 249 Kepler's third law 252 The moon and the apple 256 Finding the dislance to the moon 259 The gracitational attraciion of a large sphere 261 Other satellites of the eartli 265 The ualue of G, and the mass of the earth 268 Local uariations of g 270 The mass of the sun 274 Vll Finding the dislance to the sun 275 Mass and weight 279 Weightlessness 285 Learning about other planets 286 The moons ofJupiter 288 The discovery ofNeptune 291 Gravilation outside the solar system 295 Einstein's theory ofgravilation 299 PROBLEMS 301 \ 9 Collisions and conservation laws 307 The laws of impact 308 The conservation of linear momentum 309 Momentum as a vector guantity 310 Action, reaction, and impulse 313 Extending the principie ofmomentum conservation 318 The force exerted hy a stream ofparticles 321 Reaction from a fluidjet 324 Rocket propulsion 327 Collisions andframes ofreference 331 Kinetic energy in collisions 333 The zero-momentum frame 335 Collision processes in two dimensions 339 Elastic nuclear collisions 342 Inelastic and explosive processes 346 What is a collisionl 351 lnteracting particles subject to external forces 352 The pressure of a gas 354 The neutrino 356 PROBLtMS 357 10 Energy conservation in dynamics; vibrational motions 367 Introduction 367 lntegrals of motion 368 Work, energy, and power 373 Gravitational potential energy 376 More about one-dimensional situations 379 The energy methodfor one-dimensional motions 381 Some examples of the energy method 384 The harmonic oscillator by the energy method 393 Small oscillations in general 395 The linear oscillator as a two-body problem 397 Collision processes inuolving energy storage 400 The diatomic molecule 405 PROBLEMS 411 Vlll
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