fizika 9 moswavlis wigni

qeTevan tatiSvilifizika9moswavlis wignisaxelmZRvanelo grifirebulia ganaTlebis xarisxisganviTarebis erovnuli centris mier(brZ. N375, 18.05.2012 weli)

SinaarsiTema I. meqanikuri moZraoba ....................................................................................... 71.1. meqanikuri moZraoba .................................................................................... 81.2. gadaadgileba .............................................................................................. 121.3. moqmedebebi veqtorul sidideebze .......................................................... 141.4. sxeulis koordinatebis povna .................................................................. 171.5. wrfivi Tanabari moZraoba ......................................................................... 201.6. wrfivi Tanabari moZraobis warmodgena grafikulad ........................... 231.7. moZraobis fardobiToba. siCqareTa Sekreba ........................................... 271.8. araTanabari moZraoba. saSualo siCqare .................................................. 321.9. fizika amocanebSi: araTanabari moZraoba. saSualo siCqare ................. 361.10. wrfivi TanabaraCqarebuli moZraoba ..................................................... 381.11. siCqarisa da aCqarebis grafikebi .......................................................... 401.12. gadaadgileba wrfivi TanabaraCqarebuli moZraobis dros ................. 42proeqti: TanabaraCqarebuli moZraobis Seswavla ......................................................... 461.13. Tavisufali vardna ................................................................................... 471.14. moZraoba wrewirze ................................................................................... 501.15. centriskenuli aCqareba .......................................................................... 541.16. wrewirze moZraobis periodi da sixSire ............................................... 57Seamowme Seni codna ................................................................................. 59Tema II. niutonis kanonebi. impulsi .......................................................................... 612.1. niutonis I kanoni ........................................................................................ 622.2. masa _ inertulobis zoma .......................................................................... 652.3. niutonis II kanoni ....................................................................................... 682.4. niutonis II kanonis Sedegebi ..................................................................... 702.5. niutonis III kanoni ...................................................................................... 732.6. impulsi ...................................................................................................... 762.7. impulsis mudmivobis kanoni ...................................................................... 792.8. reaqtiuli moZraoba .................................................................................. 822.9. aTvlis inerciuli da arainerciuli sistemebi ...................................... 85Seamowme Seni codna ................................................................................... 89Tema III. Zalebi ............................................................................................................... 913.1. msoflio mizidulobis kanoni .................................................................. 923.2. fizika amocanebSi: msoflio mizidulobis kanoni ................................. 963.3. simZimis Zala ..............................................................................................1023.4. drekadobis Zala .......................................................................................1043.5. myari sxeulis deformaciis saxeebi ........................................................1073.6. myari sxeulis meqanikuri Tvisebebi ........................................................1093.7. xaxunis Zala ...............................................................................................1123.8. wona .............................................................................................................1163.9. uwonoba. gadatvirTva ..............................................................................113Seamowme Seni codna ..................................................................................1224

Tema IV. sxeulTa moZraobis aRwera dinamikis kanonebis gamoyenebiT .............1234.1. fizika amocanebSi: moZraoba simZimis Zalis gavleniT...........................1254.2. fizika amocanebSi: moZraoba daxril sibrtyeze ..................................1304.3. fizika amocanebSi: gadabmuli sxeulebis moZraoba ..............................1354.4. fizika amocanebSi: mosaxvevSi moZraoba..................................................139Seamowme Seni codna ..................................................................................142Tema V. muSaoba. energia................................................................................................1435.1. meqanikuri muSaoba ....................................................................................1465.2. Teorema kinetikuri energiis Sesaxeb .....................................................1495.3. simZimis Zalis muSaoba ..............................................................................1515.4. drekadobis Zalis muSaoba .......................................................................1545.5. energiis mudmivobis kanoni ......................................................................156Seamowme Seni codna ..................................................................................159Tema VI. sinaTlis movlenebi .........................................................................................1616.1. sinaTlis wrfivi gavrceleba ..................................................................162proeqti: ratom xdeba mzisa da mTvaris dabneleba ......................................................1666.2. sinaTlis siCqare .......................................................................................1686.3. sinaTlis arekvla ....................................................................................172proeqti: kamera _ obskura ...............................................................................................1766.4. sinaTlis gardatexa ..................................................................................1776.5. sruli arekvla ..........................................................................................182proeqti: miraJi .................................................................................................................1846.6. linzebi .......................................................................................................185proeqti: linzebi _ xidi Seucnobelisken ......................................................................1896.7. gamosaxulebis ageba linzaSi ...................................................................1916.8. Txeli linzis formula ...........................................................................194proeqti: hukis mikroskopi ..............................................................................................1966.9. Tvali - cocxali optikuri sistema .......................................................197Seamowme Seni codna ..................................................................................202maTematika, romelic fizikis Seswavlisas dagexmareba ........................204damatebiTi kiTxvebi, amocanebi ...............................................................205testebis pasuxebi ......................................................................................2195

1.7 moZraobis fardobiToba.siCqareTa SekrebaZv. w. II saukuneSi aleqsandrielma swavlulmaklavdios ptolemeosma samyaros geocentrulimodeli (sur.1) Seqmna: man samyaros centraddedamiwa miiCnia da planetebis moZraoba mismimarT aRwera. aRmoCnda, rom calkeuli planetaormocamde erTmaneTisagan damoukidebelwriul moZraobas asrulebda. planetebis moZraobaimdenad rTuli da qaosuri iyo, rom kastiliismefe alfons X-s (me-13 saukune) gaocebulsaRmoxda: `me rom RmerTi vyofiliyavi,samyaros ufro mowesrigebuls Sevqmnidio.~me-16 saukuneSi kopernikma samyaros centradmze miiCnia da planetebis moZraoba mzis mimarTganixila (samyaros aseT models heliocentrulimodeli (sur.2) hqvia): planetebi mzis irgvlivmartiv, wriul orbitebze ganlagdnen!ra mizeziT Seicvala planetebis moZraobisxasiaTi kopernikis mier aRweril sistemaSi?sinamdvileSi xom planetebi isev winandeburadmoZraobdnen? am kiTxvaze pasuxis gasacemad CavataroTcdasur. 1sur. 2cda Imagidaze dade qaRaldis furceli da centrSi WikartiT daamagre.sTxove megobars, furceli damagrebuli centris garSemo atrialos.amave dros Seecade, furclis centridan magidis kidisken fanqriTswori xazi gaavlo (anu magidasTan dakavSirebul aTvlissistemaSi fanqris wveris traeqtoria wrfivia). es Zalian nela daauCqareblad unda gaakeTo.aRwere, rogoria fanqris wveris traeqtoria furcelTan dakavSirebulaTvlis sistemaSi? erTnairia Tu ara fanqris wveristraeqtoria magidis zedapirTan da furcelTan dakavSirebul aTvlissitemebSi? fanqris wveris mier gavlili manZili?gaakeTe daskvna: aris Tu ara damokidebuli moZraobis traeqtoriaaTvlis sistemis arCevaze? gavlili manZili?diax, Sen ici, rom moZraoba da uZraoba fardobiTia: sxeulis moZraobis ganxilvisasaucilebelia aTvlis sxeulis (aTvlis sistemis) miTiTeba, radgan ararsebobs absoluturad uZravi sxeuli: mocemuli sxeuli erTsa da imave drosSeiZleba erTi aTvlis sxeulis (sistemis) mimarT moZraobdes, xolo meorismimarT uZravi iyos.aseve, fardobiTia moZraobis traeqtoriac: traeqtoria damokidebulia aTvlissistemis arCevaze. cxadia, swored am mizeziTaa planetebis moZraobis traeqtoriagansxvavebuli dedamiwasTan da mzesTan dakavSirebul aTvlis sistemaSi.27

1.7 moZraobis fardobiToba. siCqareTa Sekrebacda IIsaWiro xelsawyoebi: saxazavi, fanqari,rveulis furceli.samuSaos msvleloba:dade magidaze rveulis furceli.furclis zeda mxares dade saxazavida Seecade, fanqari saxazavs horizontalurimimarTulebiT gaayoloda imavdroulad saxazavi furcelzeqveviT Caasrialo (sur. 3).sur. 3miuTiTe fanqris wveris gadaadgileba:a) furclis mimarT; b) saxazavis mimarT.imsjele cdis Sedegze.gaakeTe daskvna: aris Tu ara damokidebuli gadaadgileba aTvlissistemis arCevaze?dafiqrdi:daakvirdi sur.4-s: moZravi matareblis vagonSi mgzavri imyofeba.erTnairia Tu ara aTvlissxvadasxva sistemis mimarTY(romelTagan erTi dakavSirebuliamoZrav vagonTan (X’O’Y’), xoloY’meore dedamiwis zedapirTanO’X’(XOY)) mgzavris koordinatebi?gaakeTe daskvna: aris Tu arada mokidebuli aTvlis sistemisarCevaze, sxeulis mdebareoba, anukoordinatebi?OXsur. 4TviTmfrinavebi ise moZraoben, rom maTSo ris manZili ar icvleba (sur. 5). Seadare:erTnairia Tu ara dedamiwasTan da 1-l TviTmfrinavTandakavSirebul aTvlis sistemaSiTviTmfrinavebisa) traeqtoria;b) gavlili manZili;g) koordinatebi;d) gadaadgileba;maS ase, aTvlis sistemis arCevazeadamokidebuli, anu fardobiTia meqanikurimoZraobis maxasiaTeblebi: moZraobissur. 5.traeqtoria, gavlili manZili, gadaadgileba.(swored gavlili manZilisfardobiTobaSia is saidumlo, romelic zenonis paradoqsis amoxsnaSidagexmareba. scade!)1YOX28

siCqareTa SekrebamoZraobis fardobiToba. siCqareTa Sekreba 1.7aris Tu ara siCqare fardobiTi? pasuxi am kiTxvaze yvela zemoT ganxilulimagaliTidanac Cans, Tumca siCqaris fardobiTobis ukeT gasagebad ganvixiloTmartivi amocanebi, davakvirdeT erTi da imave sxeulis moZraobas aTvlis orisxvadasxva sistemis mimarT, romlebic erTmaneTis mimarTac moZraoben.amocana 1Yori avtomobili, romelTa siCqareebi dedamiwis mimarT 80 da 50 m/wm-ia, SemxvedrimimarTulebiT wrfivad da Tanabrad moZraobs gzatkecilze (sur. 6).vTqvaT, avtomobilebis moZraobas ori damkvirvebeli akvirdeba:erTi _ dedamiwaze O wertilSi uZravad mdgomi, xolo meore A avtomobilSimjdomi. ganvixiloT B avtomobilis siCqare A-sTan dakavSirebulaTvlis sistemaSi(X’O’Y’).gansazRvreT dakvirvebis dawyebis momentSi dedamiwasTan dakavSirebulaTvlis sistemaSi (sur 6. ):a) avtomobilebis koordinatebi; b) avtomobilebs Soris manZili.Y’B80 m/wm50 m/wmO’O10 x, msur. 6. avtomobilebis mdebareoba dakvirvebis dawyebis momentSi.AX’YgaaanalizeT, ras gviCvenebs siCqaris ricxviTi mniSvneloba, anu ristolia TiToeuli avtomobilis gadaadgileba 1 wm-Si. gansazRvreT 1 wm-isSemdeg dedamiwasTan dakavSirebul aTvlis sistemaSi (sur 7):a) avtomobilebis koordinatebi;b) avtomobilebs Soris manZili.Y’B80 m/wm50 m/wmO’X’O10 x, msur. 7. avtomobilebis mdebareoba 1 wm-is Semdeg.daakvirdiT sur. 6-7-s da dafiqrdiT:ra manZiliT uaxlovdebian avtomobilebi erTmaneTs 1wm-Si?ris tolia siCqaris moduli, romliTac avtomobilebi erTmaneTsuaxlovdebian, anu B avtomobilis siCqaris moduli A-sTan dakavSirebulaTvlis sistemaSi (an piriqiT)? SeadareT im siCqares, romelic B avtomobilsdedamiwis mimarT aqvs.gaakeTeT daskvna: damokidebulia Tu ara siCqare aTvlis sistemisarCevaze?dafiqrdiT, rogor gamoiTvleba B avtomobilis siCqaris moduliA -sTan dakavSirebul aTvlis sistemaSi anu avtomobilebis fardobiTisiCqare (siCqare, ra siCqariTac eCveneba moZravi B avtomobili A avtomo-A29

1.7 moZraobis fardobiToba. siCqareTa SekrebabilSi mjdom damkvirvebels, anu siCqare, ra siCqariTac avtomobilebiuaxlovdebian erTmaneTs)?maS ase, siCqare fardobiTia: is damokidebulia aTvlis sistemis arCevaze.erTi sxeulis fardobiTi siCqaris moduli meoris mimarT, roca isini erTiwrfis gaswvriv erTmaneTis Sesaxvedrad moZraoben, tolia dedamiwis mimarTmaTi siCqareTa modulebis jamisa.amocana 2+ori avtomobili, romelTa siCqareebi dedamiwis mimarT 40 da 30 m/wm-ia,erTi mimarTulebiT wrfivad da Tanabrad moZraobs gzatkecilze.(sur. 8).vTqvaT, maT moZraobas ori damkvirvebeli akvirdeba:erTi _ dedamiwaze O wertilSi uZravad mdgomi, xolo meore A avtomobilSimjdomi.gansazRvreT avtomobilebs Soris manZilis sawyisi mniSvneloba (sur. 8).YO 10x, msur. 8. avtomobilebis mdebareoba dakvirvebisdawyebis momentSi.3040 m/wmBmaS ase,AY’O’30 m/wmX’YO 1040 m/wmBAY’O’sur. 9. avtomobilebis mdebareoba1 wm-is Semdeg.30 m/wmgansazRvreT:ra manZiliT Sordeba dedamiwaze myof damkvirvebels B avtomobili1wm-Si?ra manZiliT Sordeba imave damkvirvebels A avtomobili 1wm-Si?avtomobilebis koordinatebi 1 wm-is Semdeg (sur. 9);avtomobilebs Soris manZili 1 wm-is Semdeg.dafiqrdiT, ra sididiT mcirdeba 1wm-Si avtomobilebs Soris manZili?ras SeamCnevs A avtomobilSi myofi damkvirvebeli: ra siCqariT uaxlovdebamas B avtomobili, anu ris tolia avtomobilebis fardobiTisiCqare? daakvirdiT, rogor gamoiTvleba is?erTi sxeulis fardobiTi siCqaris moduli meoris mimarT, roca isini erTiwrfis gaswvriv erTi mimarTulebiT moZraoben, tolia dedamiwis mimarT maTisiCqareTa modulebis sxvaobis modulisa.-x, mX’

axla ufro zogadi SemTxveva ganvixiloT.baOsur. 10amocana 3bamoZraobis fardobiToba. siCqareTa Sekreba 1.7daakvirdi sur.10-s: tivzemyofi adamiani A wertilidanB wertilisken miemarTeba.vTqvaT, adamianis moZraobasakvirdeba ori damkvirvebeli:erTi, romelic napirze imyofebaO wertilSi da meore,romelic tivzea A wertilSi.dafiqrdi romeli veqtorigamosaxavs:adamianis gadaadgilebas tivze myofi damkvirveblisadmi (anu moZraviaTvlis sistemis mimarT)?adamianis gadaadgilebas napirze myofi damkvirveblisadmi (anu uZraviaTvlis sistemis mimarT)?tivis gadaadgilebas napirze myofi damkvirveblisadmi (anu moZraviaTvlis sistemis gadaadgilebas uZravis mimarT)?maS ase,sxeulis (adamianis) gadaadgileba uZravi aTvlis sistemis (dedamiwis)mimarT tolia S 1da S 2gadaadgilebebis jamisa, sadac S 1sxeulis (adamianis)gadaadgilebaa moZravi aTvlis sistemis (tivis) mimarT, xolo S 2moZravi aTvlissistemis (tivis) gadaadgilebaa uZravis (dedamiwis) mimarT.S = S 1+ S 2(1)klasikur meqanikaSi, romelic galileisa da niutonis Sromebs efuZneba daromlis safuZvlebsac Cvens axla vswavlobT, dro ar aris damokidebuli aTvlissistemis arCevaze (ainStainis fardobiTobis Teoriis Tanaxmad ki dro fardobiTia).amitom Tu (1)-li tolobis orive mxares t -ze gavyofT, miviRebT, romsxeulis v siCqare uZravi aTvlis sistemis mimarT ase gamoiTvlebav = v 1+ v 2(2)sadac v 1sxeulis siCqarea moZravi aTvlis sistemis mimarT, xolo v 2moZraviaTvlis sistemis siCqarea uZravi aTvlis sistemis mimarT.me-(2)-s siCqareTa Sekrebis formula ewodeba.maS ase, meqanikuri moZraobis damaxasiaTebeli kidev erTi sidide _ sxeulissiCqare fardobiTi sididea. igi damokidebulia aTvlis sistemis arCevaze.31