jemal kiknaZejemal kiknaZejemal kiknaZejemal kiknaZejemal kiknaZe

martivimartivimartivimartivimartivi da usafrTxo da usafrTxo da usafrTxo da usafrTxo da usafrTxo

eqsperimentebieqsperimentebieqsperimentebieqsperimentebieqsperimentebi

fizikafizikafizikafizikafizika

moswavlisa da maswavleblisaTvismoswavlisa da maswavleblisaTvismoswavlisa da maswavleblisaTvismoswavlisa da maswavleblisaTvismoswavlisa da maswavleblisaTvis

pirveli nawilipirveli nawilipirveli nawilipirveli nawilipirveli nawili

meore Sesworebuli gamocema

gamomcemlobagamomcemlobagamomcemlobagamomcemlobagamomcemloba inteleqtiinteleqtiinteleqtiinteleqtiinteleqti

TbilisiTbilisiTbilisiTbilisiTbilisi20082008200820082008

2

wignSi ZiriTadad gamoyenebulia perelmanis, pa-krovskis, galperSteinis, uokeris, pinskis, razumovskis,langes da sxvaTa Sromebi. ganxilulia gazomvissaSualebebi, umartivesi gazomvebi, laboratoriulisamuSaoebi (VII klasi) da cneba cdomilebis Sesaxeb;eqsperimentebis Gatareba da Sedegebis analizi, yura-dReba gamaxvilebulia mecnieruli Semecnebis me-Todze, kanonzomierebaTa aRmoGenaze, Semowmebaze,praqtikaSi gamoyenebaze, martivi modelebisa da saTa-maSoebis damzadebaze.

wigni gankuTvnilia moswavlisa da fizikis mas-wavleblisaTvis.

redaqtori adelaida nikolaiSvili, adelaida nikolaiSvili, adelaida nikolaiSvili, adelaida nikolaiSvili, adelaida nikolaiSvili, Tbili-sis 37-e skolis fizikis meTodisti

recenzenti rusudan qanTaria, rusudan qanTaria, rusudan qanTaria, rusudan qanTaria, rusudan qanTaria, Tbilisis 55-eskolis fizikis maswavlebeli

ISBN 99940-10-87-5 © jemal kiknaZe, 2004© gamomcemloba ̀ inteleqti~, 2004

Zvirfaso moswavleebo!

aRwerili eqsperimentebi SeiZleba GaataroT rogorcSin, aseve skolaSi. maTi simartive nu SegacbunebT. isinidagexmarebian, rom gaerkveT rTul movlenebSi, dafiqrdeTda SeamowmoT mravali ram, romlebsac saxelmZRvaneloSigaecnobiT.

3

redaqtorisaganredaqtorisaganredaqtorisaganredaqtorisaganredaqtorisagan

moswavleTa ganmaviTarebeli es miniaturuli kursi, faqtobrivad,moicavs martiv da usafrTxo cdebs, uCveulo davalebebs, saxalisoda eqsperimentul amocanebs, zogierT laboratoriul samuSaos,romlebic xels Seuwyoben yuradRebis, dakvirvebisa da praqtikuliunar-Cvevebis ganviTarebas, logikuri da kritikuli azrovnebisformirebas.

davalebebSi miTiTebulia, Tu rogor SeiZleba xelmisawvdomisagnebiT, instrumentebiT, gamzomi xelsawyoebiT martivi da usaf-rTxo eqsperimentebis Catareba. isini Seesabamebian asakobrivTaviseburebebsa da interesebs, 11-14 wlis mozardebisas, romlebicjer kidev ar arian mzad unaklo logikuri msjelobebisaTvis,magram uyvarT moqmedeba, fantazia, gamomgonebloba, davalebebi for-mulirebulia asakobrivi Taviseburebebis gaTvaliswinebiT, coc-xali, saintereso formiT, zogjer gamoyenebulia istoriuli faq-tebi da mxatvruli ilustraciebi.

saxaliso amocanebisa da eqsperimentebis gaformebisas gamo-yenebulia mxedvelobiTi informaciis gadmocemis sxvadasxva saSua-lebebi, suraTebis, grafikebisa da cxrilebis saxiT. krebulismizania fizikiT dainteresebuli moswavleebis ganmaviTarebeliswavleba. igi maTTan muSaobis saukeTeso saSualebas warmoadgens.avtori did yuradRebas uTmobs eqsperimentul muSaobas. moswav-leebi eCvevian sakuTari xeliT cdisaTvis saWiro xelsawyoebisdamzadebas, danadgaris awyobas, daSlasa da maTs movlas; cdebisCatarebisas gamzomi xelsawyoebis skalidan Cvenebebis sworadaTvlas, pirdapiri gazomvis cdomilebis gaTvaliswinebiT; fizikurimovlenebis msgavsebasa da gansxvavebaze dakvirvebas, Sedegebis ana-lizs; kanonzomierebaTa Semowmebas da maTs safuZvelze martivisaTamaSoebis damzadebas.

yovelive amis safuZvelze moswavleebs ganuviTardebaT sag-nisadmi interesi da saganmanaTleblo standartis mixedviT dad-genili sxvadasxva codnis praqtikaSi gamoyenebis unar-Cvevebi,SemecnebiTi damoukidebloba da inteleqti.

adelaida nikolaiSviliadelaida nikolaiSviliadelaida nikolaiSviliadelaida nikolaiSviliadelaida nikolaiSvili

Tbilisis 37-e skolis fizikis meTodisti

4

SesavaliSesavaliSesavaliSesavaliSesavali

fizika eqsperimentuli mecnierebaa. masSi yvela Teoriulimtkiceba emyareba realur movlenebze dakvirvebas. winaswar saWiroa,viswavloT dakvirveba da movlenis aRwera. am dros gansakuTre-biT mniSvnelovania, vipovoT movlenis iseTi maxasiaTeblebi, rom-lebic SeiZleba SevafasoT raodenobrivad da SevadaroT erTma-neTs, Tu SevZeliT sidideebs Soris raodenobrivi damokidebule-bis dadgena, maSin mas maTematikuri formuliT gamovsaxavT.

fizika Seiswavlis ara marto movlenis kanonzomierebas, aramediswrafvis, daadginos am movlenis kanonzomierebis mizezebi daCaswvdes movlenis meqanizms. am mizniT fizikosebi wamoayenebenhipoTezebs, ageben abstraqtul modelebs. aseT hipoTetur mod-els aqvs evristikuli (SemecnebiTi) mniSvneloba, romlis logikuriganviTarebiT SeiZleba miviRoT Sedegebi _ axali codna movlenisSesaxeb. magram imisaTvis, rom darwmunebuli viyoT movlenis Teoriu-li modelis WeSmaritebasa da misgan gamomdinare Sedegebis sis-woreSi, aucilebelia maTi Semowmeba eqsperimentulad, es ki yovel-Tvis advili Sesasrulebeli ar aris. saWiroa, movifiqroT iseTicdebi, romelTa Catareba SesaZlebeli iqneba, raTa davrwmundeTimaSi, rom Teoriuli varaudi marTebulia. zogjer eqsperimentiiZleva moulodnel Sedegs, romelic miRebul models ar eTanxmeba.am SemTxvevaSi (Tu eqsperimentSi Secdoma araa daSvebuli!) saWirogaxdeba modelis Secvla da TeoriaSi Sesworebebis Setana.

wignSi, ZiriTadad, mocemulia davalebebi da cdebi sxvadasxvaTemaze, sabunebismetyvelo mecnierebis _ fizikis dawyebiTi kur-sidan, erovnuli saswavlo gegmis (proeqti ̀ ilia WavWavaZe~) mierdasaxuli standartis Sesabamisad. ganxiluli cdebi imdenad mar-tivi da usafrTxoa, rom maTi Catareba SeiZleba rogorc skolaSi,aseve _ saxlSic, umartivesi mowyobilobebis gamoyenebiT. yovelicdis Catarebisas ifiqreT, xom ar SeiZleba maTi kidev ufrogamartiveba, rom minimaluri daxarjuli saSualebebiT miiRoTmaqsimaluri efeqti.

jemal kiknaZejemal kiknaZejemal kiknaZejemal kiknaZejemal kiknaZe

Tsu Tengiz gegelias saxelobis fizika-maTematikisrespublikuri saSualo skola-internatis

fizikis maswavlebeli

380079, Tbilisi, g. rCeuliSvilis q. k. 3, b. 21. 29-21-23

5

umartivesi gazomvebiumartivesi gazomvebiumartivesi gazomvebiumartivesi gazomvebiumartivesi gazomvebi

sigrZis gazomvasigrZis gazomvasigrZis gazomvasigrZis gazomvasigrZis gazomva

1iswavle samasStabo saxazavisa da sazomi lentis

gamoyeneba.am instrumentebis gamoyenebiT gazome Semdegi sagnebis

sigrZe: fanqris, asanTis, saCvenebeli TiTis, Tavis garSemow-erilobis, saSeni aguris zomebi (sigrZe, sigane da simaR-le).

miRebuli Sedegebi Cawere rveulSi.samasStabo saxazaviT sigrZis gazomvisas miaqcie yura-

dReba Tvalis swor mdebareobas. sur. 1-ze gamosaxuliaTvalis sami mdebareoba. aqedan sworia 1-eli, xolo me-2da me-3 arasworia. (Tvalis araswori mdebareobiT si-grZis gazomvisas miRebul Secdomas ewodeba Secdomaparalaqsze).

2manZilis miaxloebiT gazomva.iswavle xelebisa da TiTebis daxmarebiT 1 dm, 1 m da

1 sm-is toli manZilebis TvaldaTval SemCneva da am wesiTsxvadasxva sagnis zomebisa da manZilTa gazomva.

Zalian sasargebloa, xolo zogjer _ aucilebelic,iqonio `sakuTari” metri, decimetri da santimetri.

sur. 1

6

1. aiRe danayofebiani (samasStabo) saxazavi, qaRaldzefanqriT aRniSne 1 dm sigrZe da gaSale saCvenebeli da SuaTiTebi, daimaxsovre, rogor unda gaSalo isini, rom Semdegsaxazavis gareSe gadazomo 1 dm (sur. 2).

2. qaRaldze TiTebiT ramdenjerme gadazome 1 dm-istoli sigrZe; aRniSne fanqriT, xolo Semdeg igi saxazaviTSeamowme.

3. SearCie agreTve `sakuTari” metri: horizontuladgaSlili xelis Sua TiTidan meore xelis mxris kidemdean maRla aweuli moxrili meore xelis idayvamde; verti-kalurad _ iatakidan TeZos Zvlis SemaRlebamde, welamde.

moxerxebulia, 1 sm sigrZe Seadaro romelime TiTisfrCxilis siganes.

3gazome TvaliT.1 dm, 1 m, 1 sm da 1 mm aRniSne SexedviT; am wesiT gazome

sxvadasxva sagnis sigrZe da manZilebi.....ase Sesrulebuli samuSao aucileblad Seamowme

saxazaviT.

4gazome Seni simaRle.1. saRamos, Zilis win, dasvenebamde, gaixade fexsacmelebi

da dadeqi zurgiT karebis amyolTan.2. mWidrod Seaxe quslebi, menji, zurgi da kefa karebis

amyols da daiWire Tavi pirdapir.3. sTxove vinmes, dagados Tavze kuTxedi da aRniSnos

karebis amyolze patara xazi.

sur. 2

7

4. gazome manZili iatakidan aRniSnul xazamde santi-metrebsa da milimetrebSi. Caiwere Sedegi da TariRi (weli,Tve, ricxvi, saaTi).

5. igive diliT Seasrule. monacemi kvlav aRniSne,erTmaneTs Seadare saRamosa da dilis Sedegi. SeamCnev, romadamianis simaRle diliT metia, vidre _ saRamos.

5Seamowme leonardo da vinGis

wesis siswore.1. gazome Seni simaRle, rogorc

naCvenebia wina davalebaSi.2. gazome manZili horizontulad

gaSlili xelebis Sua TiTebs Soris(isargeble kedliT). Seadare esmanZili Sens simaRles. adamianTaumravlesobas es manZilebi toliaqvT. pirvelad es leonardo davinCim SeniSna (ix. naxati).

6Seadare Seni terfis sigrZe da

idayvidan majamde manZili.gaizome:1. samasStabo saxazaviT terfis

sigrZe quslis bolodan didi TiTisbolomde.

2. agreTve manZili idayvidan xelismtevanTan axlos amoburculi Zvlis Suamde (sur. 3). essigrZeebi erTsa da imave adamians toli aqvs.

7gansazRvre Seni nabijis saSualo sigrZe.1. 10 nabiji gaiare wynarad, Tanabari moZraobiT.

sur. 3

8

2. gazome gavlili manZili santimetrebSi, miRebuliricxvi gayavi 10-ze.

3. Seni nabijis saSualo sigrZis dadgenis Semdeg, CaatarenabijebiT manZilis gazomvis ramdenime savarjiSo. manZilisnabijebiT gazomvis Semdeg aucileblad Seamowme isruletiT.

8sakeravi Zafis diametris gazomva.1. gazome romelime sakeravi Zafis diametri (mag. # 10,

30, 40 da 50), mavTulis diametris gazomvis wesis mixedviT,e.i. cilindrul joxze mWidrod daaxvie Zafi.

2. saxazaviT gazome yvela xveulas sigrZe milimetrebSi.miRebuli Sedegi gayavi xveulebis ricxvze; gamosaxe Zafisdiametri milimetrebsa da mikronebSi. monacemebi CawererveulSi da Seadare erTmaneTs.

9gazome qaRaldis furclis sisqe.1. aiRe romelime wigni. samasStabo saxazaviT gazome

misi sisqe ydis gareSe (orive yda gadakece). davuSvaTgazomvis Sedegi aRmoCnda 2 sm.

2. gaixsene, rom 1 sm = 10 000 mk (mikroni). maSin20 000 mikroni gayavi furclebis (da ara gverdebis)raodenobaze. erTi furclis sisqe gamosaxe mikronebSi.Sedegi Cawere rveulSi.

10 gazome Cais Wiqis yelis wrewir-gazome Cais Wiqis yelis wrewir-gazome Cais Wiqis yelis wrewir-gazome Cais Wiqis yelis wrewir-gazome Cais Wiqis yelis wrewir-isa da diametris sigrZe. gansazRvreisa da diametris sigrZe. gansazRvreisa da diametris sigrZe. gansazRvreisa da diametris sigrZe. gansazRvreisa da diametris sigrZe. gansazRvreπ (pi) ricxvis mniSvneloba.(pi) ricxvis mniSvneloba.(pi) ricxvis mniSvneloba.(pi) ricxvis mniSvneloba.(pi) ricxvis mniSvneloba.

1. gamoWeri qaRaldis viwro, 1_2 smsiganis zoli. mWidrod Semoaxvie Wiqiszeda nawils ise, rom lentis erTi naw-ili meores daedos.sur. 4

9

2. lenti mWidrod moWime da Zalian wvrili nemsiTgaxvrite misi orive bolo (sur. 4).

3. gaSale lenti da milimetruli saxazaviT gazomemanZili orive naxvrets Soris. es manZili Wiqis zedanawilis wrewiris sigrZis toli iqneba (sur. 5). vTqvaT,wrewiris l sigrZe aRmoCnda 223 mm.

4. TeTri qaRaldis furcelze dade Wiqa fuZiT zeviTda kargad wamaxvilebuli fanqriT Wiqis garSemo Semoxazewrewiri. qaRaldze miRebuli wrewiri gamoWeri makratliT.

5. qaRaldis wre gakece Suaze, saxazaviT gazome CaisWiqis zeda nawilis diametri (sur. 6). vTqvaT, diametri aRmoCnda 71 mm, maSin

π=l/ =223/71 ≈ 3,141.

11daamzade saxazavi-noniusi da iswavle misi xmareba.noniusi gamoiyeneba mcire zomis sxeulebis sigrZis

ufro zustad gazomvisaTvis. is warmoadgens damatebiTskalas, romelsac SeuZlia gadaadgileba ZiriTadi skalisgaswvriv. noniusis yoveli danayofi ZiriTadi skalis da-nayofis sidideze 0,1-iT naklebia. magaliTad, Tu ZiriTadiskalis erTi danayofi 1 sm udris (an 1 mm), maSin noniusiserTi danayofi 0,9 sm (an 0,9 mm) iqneba.

noniusiT ase sargebloben: sxeulis (romlis sigrZecunda gaizomos) erT bolos miadeben ZiriTadi skalisnulovan danayofs, xolo meore bolos miaWeren noniuss,

sur. 5

sur. 6

1 0

akvirdebian imas, rom saxazavi-noniusis gverdiTi mxaremWidrod iyos miWerili ZiriTad skalaze. sur. 7-zenaCvenebia, rom sxeulis sigrZe (ZiriTadi skalis mixed-viT) metia 3 sm-ze da naklebia 4 sm-ze. rom gavigoT,santimetris ramden meaTed nawils Seadgens sigrZis name-ti, vakvirdebiT, noniusis romeli Strixi emTxveva ZiriTa-di skalis romeliRac Strixs. Cvens magaliTSi noniusismeSvide Strixi emTxveva ZiriTadi skalis meaTe Strixs.amitom sagnis sigrZea 3,7 sm.

1. aiRe 9sm sigrZis, 1,5 sm siganis muyaos, aluminis anTeTri Tunuqis firfita da maxvili saWrisiT mis gaswvrivgaakeTe 9 Strixi ise, rom misi sigrZe daiyos 10 tolnawilad.

2. isargeble samaStabo saxazaviTa da damzadebulinoniusiT gazome ramdenime mcire zomis sxeulis (asanTiskolofis, saSlelis da sxv.) sigrZe.

SeniSvna: : : : : ganxiluli noniusi aris wrfivi. arsebobs wriuli

noniusic, kuTxeebis gasazomad.

sur. 7

sayrdeni

gasazomi sxeulisaxazavi-noniusi

1 1

farTobis gazomvafarTobis gazomvafarTobis gazomvafarTobis gazomvafarTobis gazomva

12kvadratuli firfita.diqtis an mkvrivi muyaosagan daamzade kvadratuli

formis fifita 1 dm2 (10x10 sm). dayavi is kvadratulsantimetrebad da misi TiToeuli ujra daStrixe Wadra-

kuli TanmimdevrobiT.

13wriuli firfita.1. gamoTvlebiT gansazRvre wris diametri, romlis

farTobia 1 dm2 (wris farTobi: s=πR2).

2. diqtisagan an mkvrivi muyaosgan daamzade aseTi di-

ametris wre da misi farTobi Seadare 1 dm2 farTobis

kvadratul firfitas.

14gansazRvre praqtikulad da Teoriulad Gais Wi-

qis fskeris farTobi.1. milimetrul qaRaldze dade gluvi Wiqa da mis

fskers Semoavle kargad wamaxvilebuli fanqari. daiTvale

wrewiris SigniT sruli kvadratuli milimetrebis ricx-

vi, gamosaxe isini kvadratul santimetrebSi. daTvale mi-

axloebiT, ramdeni kvadratuli milimetri miiReba wrewiris

gaswvriv arsebuli Seuvsebeli kvdratuli milimetrebi-

sagan (amisaTvis daTvale maTi ricxvi da gayaviT orze);

gamosaxe isini kvadratul santimetrebSi.

Sekribe kvadratuli santimetrebis orive ricxvi.

2. gansazRvre imave wris farTobi formuliT (fske-

ris farTobi moZebne me-10 davalebaSi naCvenebi wesiT).

3. Seadare orive Sedegi.

1 2

15gansazRvre fexebis sayrdenis farTobi.1. aiRe milimetrula an rveulis ujredebiani furce-

li da dade masze winaswar gaw-mendili Seni fexsacmeli (sur. 8).Semoavle fanqari lanCisa da qus-lis napirebs.

2. aiRe fexsacmeli da daTvale fexis sayrdenis far-Tobis kvadratuli santimetrebis ricxvi.SeniSvna: fexebis sayrdenis farTobis codna dagWirdeba Sem-

deg, wnevis Seswavlisas.

16TvaliT Sefaseba.1. iatakze an miwaze dax-

aze kvdrati farTobiT 1 m2.2. TvaliT Seafase, ramdeni

Seni amxanagi daeteva am far-Tobze, rac SeiZleba mWidrodganTavsebisas.

3. Seamowme Seni varaudiamxanagebTan (sur.9).SeniSvna: 1 m2 farTobze Sei-Zleba daetios 13_14 wlis

12_15 bavSvi.sur. 9

sur. 8

1 3

moculobis gazomvamoculobis gazomvamoculobis gazomvamoculobis gazomvamoculobis gazomva

17iswavle sazomi cilindris (menzuris) gamoyeneba.sazomi cilindri (menzura) gamoiyeneba siTxisa da

myari sxeulebis moculobis gasazomad.sanam gazomvebs Seudgebode, saWiroa, gansazRvro:gazomvis zRvari—sididis maqsimaluri mniSvneloba

(am SemTxvevaSi _ moculobis), romelic mocemuli xelsaw-yos gamoyenebiT gaizomeba;

danayofis fasi—skalis umciresi danayofis Sesabami-si moculobis mniSvneloba.

magaliTad, sur. 10-ze gamosaxulia menzura, romlisgamoyenebiT SeiZleba gaizomos 50 sm3 moculoba, xolodanayofis fasia 5 sm3.

nebismieri xelsawyos danayofis fasi rom ipovo, saWiroa,xelsawyoze naCvenebi sididis ori mezobeli mniSvnelobissxvaoba gayo maT Soris monakveTebis ricxvze. (gazomvebsgaecnobi laboratoriul samuSaoebSi).

18gansazRvre bardis (an safantis) marcvlis saSua-

lo moculoba.1. aiRe daaxloebiT erTnairi diametris 100 an 50

bardis (an safantis) marcvali.2. Caasxi menzuraSi wyali gansazRvrul danayofamde

da Cayare masSi barda (safanti).3. aRniSne menzuraSi wylis aweuli done da gansazRvre,

ramdeni kuburi santimetriT moimata menzuraSi moculo-bam.

4. miRebuli kuburi santimetrebi gayavi 100-ze(50-ze), miiReb erTi bardis marcvlis moculobas. miRebu-li Sedegi Cawere rveulSi.

1 4

19markuTxa paralelepipedis moculobis gansazRvra.1. aiRe aguri da gazome misi zomebi (sigrZe, sigane da

simaRle). am monacemebiT gamoiangariSe moculoba da gamo-saxe igi kubur santimetrebsa da kubur decimetrebSi.

2. iangariSe, ramdeni aguri Caeteva erT kubur metrmoculobaSi. miRebuli monacemebi Cawere rveulSi.

20daamzade kuburi metris

dasaSleli maketi.1. moamzade 12 erTnairi

Tamasa (an wneli), TiToeulisigrZiT erT metrze cota meti,da Tavebi waumaxve.

2 aiRe 8 erTnairi mrgvalikartofili da aawyve kuburi me-tris maketi ise, rogorc gamosa-xulia sur. 10-ze.

21iswavle wveTebis daTvla.1. asanTis Reros moatexe Tavi, gatexe Reros bolo da

dadevi daxrili Wiqis kideze, romelSic cota wyalia Casxmuli.asanTis Rerodan wyali wveTebis saxiT gadmova, romleb-sac wesieri burTulebis forma eqnebaT.

2. ufro srulyofili mwveTara Sei-Zleba moawyo izolatori milisagan, rom-liTac dafarulia feradi radiogamtari.20_25 sm sigrZis aseTi mili moacilegamtarisagan. moaTavse igi wylian WiqaSiise, rogorc naCvenebia sur. 11-ze. adamian-isagan dauxmareblad wyali Tanabari

sur. 10

sur. 11

1 5

porciebiT gadmoedineba milidan, patara burTulebis sax-

iT drois toli Sualedebis Semdeg. es mwveTara warmoad-

gens moxerxebul xelsawyos wveTebis dasaTvlelad.

22wveTebi kovzSi.1. daiTvale, ramdeni wylis wveTi moTavsdeba Cais kovzze

napirebamde avsebisas; Cawere es ricxvi.

2. axla Seecade, am wyalze daawveTo imdeni wveTi,

ramdenic daetia kovzze napirebamde.

SeniSvna::::: samuSao Zalian frTxilad unda Caataro, rom da-

vardnilma wveTebma ar gadmoRvaros kovzidan wyali.

samuSaos Sesrulebis dros miaqcie yuradReba wyl-

is zedapiris formas savse da gapipinebul kovzze

(sur. 12). am cdaSi SeiZleba imis miRweva, rom kovzze

wylis moculoba orjer gaizardos.

23gazome wylis wveTis saSualo moculoba.1. aiRe menzura, romlis danayofis fasia 1 sm3. CaawveTe

masSi 200 wveTi wyali da gazome maTi saerTo moculoba.

2. miRebuli moculoba gayavi 200-ze. miiReb erTi

wveTis moculobas. Cawere es ricxvi.

sur. 12

1 6

vertikaluri da horizontulivertikaluri da horizontulivertikaluri da horizontulivertikaluri da horizontulivertikaluri da horizontulimimarTulebamimarTulebamimarTulebamimarTulebamimarTuleba

24vertikaluri mimarTuleba.1. aiReT patara burTula da gauSvi xelidan silian

jamze (sur. 13). gaimeore es savarjiSo ram-denjerme, yuradRebiT daakvirdi burTulasmoZraobas. burTula yvela SemTxvevaSi erTida imave mimarTulebiT vardeba _ simZimis Za-lis mimarTulebiT. am mimarTulebas ver-tikaluri ewodeba.

horizontuli mimarTuleba2. daakvirdi naxazs, romelic gamosaxavs

vertikalur mimarTulebas dedamiwis sferossxvadasxva wertilSi (sur. 14). xedav, romyvela vertikaluri mimarTuleba midis dedami-wis centrisaken.

vertikaluri mimarTulebis perpendiku-larul mimarTulebas horizontuli ewodeba (sur. 15).

25daamzade Sveuli.1. aiRe Zafi da dakide masze raime tvirTi _ miiReb

Sveuls.2. Seamowme karebisa da fanjris amyolis, agreTve

karadisa da aguris kedlis vertikaluroba.

sur. 13

sur. 14 sur. 15dedamiwa dedamiwa

horizontuli mimarTuleba

horizontuli mimarTuleba

horizont

uli mimarTuleba

horizont

uli mimarTuleba

1 7

26iswavle brtyeli minis firfitis dayeneba hori-

zontulad.1. daikave xelSi minis gluvi firfita (magaliTad,

patara sarke), moaTavse masze foladis burTula da miaR-wie mis uZraobas (sur. 16).

burTulas uZraoba uCvenebs, rom firfita dgas hor-izontulad.

27Seamowme wylis zedapiris horizontuloba.1. Sveulis tvirTi da cota Zafi CauSvi WurWelSi

moTavsebul wyalSi. kuTxediT an transportiriT gazomekuTxe Zafsa da wylis zedapirs Soris.

2. daxaze cdis sqema.

28daamzade sadurglo Tarazo (vaterpasi1).1. kuTxedis gamoyenebiT gamoxaze da gamoWeri diqtis-

agan (an Tamasebisagan) sur. 17-ze naCvenebi formis Tarazo.2. masze qvemodan miamagre xis Tamasebi da dakide

Sveuli ise, rogorc sur. 17a-zea naCvenebi. es xelsawyoaris vaterpasi.

sur. 16

sur. 17 sur. 17a

2 jemal kiknaZe

1. vaterpasi (holand. waterpas) _ Tarazo.

1 8

Zalis gazomva. dinamometriZalis gazomva. dinamometriZalis gazomva. dinamometriZalis gazomva. dinamometriZalis gazomva. dinamometri

29daamzade dinamometri rezinis Zafis, an rgolisa

da ori muyaos milisagan.1. sqeli qaRaldisagan Seawebe, an aiRe ori mza muyaos

mili, iseTi diametris mqone, rom erTi Sediodes meoreSi(sur. 18). wvrili milis erT mxares daamagre sacobi,miamagre masze garedan kakvi, xolo SigniT _ rezinis Zafi(ukeTesia rezinis an kauCukis rgoli, sur. 19).

2. viwro mili moaTavse ganierSi, daWimuli rezinisZafis Tavisufali bolo miamagre mavTulis maryuJze. garedanmaryuJze wamoacvi rgoli (sur. 20).

3. patara tvirTebiT daagraduire dinamometri.

30daamzade dinamometri foladis zambarisagan.1. ipove foladis mavTuli (mag. gitaris simi #1,

sigrZiT 1,6 m), gazquris an navTquris alze wiTlad gavar-varebamde gaaxure is da daelode gacivebas. mavTuli dar-bildeba.

2. mavTuli gamoabi karebis saxelurs da kargad gaas-wore.

aiRe 1 sm diametrisliTonis mili, masze ZalianmWidrod daaxvie mavTuli,sanam xveulis sigrZe 4 smar gaxdeba (sur. 21).

sur. 18

sur. 19 sur. 20

sur. 21

1 9

SeniSvna: mavTulis daxveva yvelaze kargia ase: mavTulis erTibolo miamagre uZrav saganze, xolo meore _ cilin-drul milze (kargi iqneba, Tu mils erT-erT boloSiwvrili naxvreti eqneba, romelSic mavTuli gaeyreba_ maSin is masze damagrdeba).

3. moWime mavTuli milze, rac SeiZleba mWidrod dadaamagre ise, rom ar moeSvas. Seitane mavTuli milTanerTad alSi, daacade gawiTlebamde gaxureba da im wamsveCaZire civ wyalSi. spirali iwrToba. spi-ralis boloebi isev gaaxure gawiTlebamdeda daacade gaciveba (darbilebisaTvis).

4. xisagan daamzade patara ficari zome-biT: 16,5x4x0,5 sm; masze weboTi da lursm-nebiT miamagre xis ori Tamasa zomebiT:4x2x0,5 sm da 4x1x0,5 sm.

5. spirali erTi boloTi daamagre fi-carze, xolo meore mxareze miamagre 11 smsigrZis mavTuli rgoliT. am bolos gaukeTeficarze damagrebuli mavTulis maryuJi (sur.22), spiralis moZrav bolos _ mavTuli_ maCvenebeli, sigrZiT 1,5 sm.

6. skalisaTvis ficarze miamagre mili-metruli qaRaldis viwro zoli. daagradui-re dinamometris skala patara tvirTebiT(50g_0,5n; 100g_1n; 150g_1,5n; 200g_2n da a.S.).

saswori da wvrilsawonebisaswori da wvrilsawonebisaswori da wvrilsawonebisaswori da wvrilsawonebisaswori da wvrilsawonebi

31daamzade berketiani saswori.1. moamzade ficari 20x9x2 sm da sadgari 14x2x2 sm

zomebiT.2. sadgaris erT mxares gaukeTe 22 mm siRrmis Wrili

SuaSi, xolo 27 mm napirebTan. sadgaris bolos marTkuTx-ovani napirebi moamrgvale (sur. 23)

sur. 22

2 0

3. gaakeTe ficarSi kvadrat-uli xvreli zomebiT 2x2 sm damasSi weboTi daamagre sadgari.

4. moamzade berketi sigrZ-iT 17 sm, SuaSi gaukeTe naxvre-ti da mieci sur. 24-ze naCvene-bi forma.

5. daamagre berketi sadgarisWrilSi liTonis ReZze ise, romhorizontulad dadges; maszeZafebiT miabi pinebi, magaliTad,minis an yavis qilis saxuraveb-isagan. berkets gaukeTe isarida sadgarze miamagre skala(sur. 25).

cxadia, SeiZleba gaakeTosxva saxis saswori.

32daamzade wvrilsawonebi aluminisa da spilenZis

mavTulisagan.1. isargeble sasworiTa da mkvnetaraTi, SearCie mavTu-

lis naWrebi masiT: 1 g, 2 g (ori), 5 g, 10 g (ori), 20 gda 50 g.

2. mavTulis TiToeuli naWeri daaxvie arqimedes spi-ralis saxiT, gamoSverili boloTi (sur. 26).

SeniSvna: : : : : ukeTesia, winaswar Teoriulad davadginoT cnobilinivTierebisa da masis mavTulis sigrZe. amisaTvis

visargebloT formulebiT:

4lDρρSlρVm

2π=== ⇒

2Dρml

π=

4

sur. 23

sur. 24

sur. 25

sur. 26

2 1

sadac m masaa, ρ nivTierebis simkvrive (spilenZis analuminis, moiZebneba simkvrivis cxrilidan), -diametri(gaizomeba mikrometriT, mas Semdeg ganvixilavT), π ≈3,14,l-sigrZe. magaliTad, Tu spilenZis mavTulisagan, romlisdiametria 1,5 mm = 1,5.10-3 m, xolo simkvrive 8,96.103 kg/m3,gvinda davamzadoT sawoni masiT 1g, maSin

2Dρml

π=

4= 0630

10511431096800104

233 ,).,.(,..,

,.≈

− m 36,≈ sm.

drois gazomvadrois gazomvadrois gazomvadrois gazomvadrois gazomva

33pulsiT sargebloba.1. mieCvie, swrafad ipovo Seni pulsi, Semdeg aiRe

saaTi wamebiani isriT da daadgine, ramdeni dartyma daiTv-leba 1 wuTSi.

2. Seasrule Sebrunebuli samuSao: pulsis cemis daTv-liT daadgine erTi wuTis xangrZlivoba.SeniSvna::::: didma italielma mecnierma, galileo galileim, akvird-

eboda ra florenciis kaTedraluri monastris qor-

kandelis (WaRis) rxevebs da saaTis nacvlad sarge-

blobda Tavisi pulsis cemiT, daadgina qanqaras rx-

evis pirveli kanoni, romelic safuZvlad daedo

moZRvrebas rxeviT moZraobaze.

34wyliani saaTis modeli.1. aiRe sufTa naxevarlitriani boTli, aavse is wyliT,

TiTiT daaweqi mis yels da daikave vertikalurad.2. TiTis aSvebis momentSi wamebiani isriT zustad

daniSne dro da daadgine, ramden xanSi daicleba wylisaganboTli (sur. 27).

2 2

SeniSvna::::: naxevarlitriani wyliani boTliicleba 10 wm-is ganmavlobaSi.analogiuri dakvirvebebi Caataresxvadasxva moculobis polieTi-lenis boTlebiT.

35qviSis saaTis damzadeba.1. iSove qviSis saaTi (samwuTiani, xuTwuTiani, aTwuTiani).

kargad Seiswavle misi mowyobiloba da moqmedeba. moifiqre,rogor SeiZleba daamzado TviTnakeTi qviSis (ori xraxnianisaxuravis mqone boTlisa da plastmasis wvensasmelisaganwylis saaTi _ klefsidra berZ. Klepsydra) saaTi.SeniSvna: xom ar SeiZleba, gamoiyeno grZeli minis sinjara,

romlis Sua adgils gazquraze an spirtquraze gax-urebis Semdeg gaWimav?

StangenfargaliStangenfargaliStangenfargaliStangenfargaliStangenfargali

wrfivi noniusi gamoyenebulia StangenfargalSi.Stangenfargali (sur. 28) aris mm-iani saxazavi 1 sabjeniT,romlis gaswvriv Tavisuflad moZraobs noniusi 2 sabjen-iT. gasazom obieqts (sxeuls) amagreben 1 da 2 sabjenebsSoris. anaTvals noniusze iReben zemoaRwerili wesiT. 3da 4 sabjeniT izomeba milebis Siga diametrebi. CarCosTandakavSirebulia 6 Sverili, romlTa daxmarebiT izomebasiRrme. 5 xraxni saSualebas iZleva, davamagroT moZraviCarCo mocemul mdebareobaSi.

sur. 27

sur. 281 2

3 4

6

5

2 3

mikrometrimikrometrimikrometrimikrometrimikrometri

sigrZis gasazomad milimetris measedi nawilis si-zustiT iyeneben mikrometruli xraxnis meTods. mik-rometruli xraxni warmoadgens mikrometris ZiriTad naw-ils. mikrometrs aqvs giragis saxe (sur. 29), romelSicgasazom obieqts amagreben mikrometruli xraxnis saSu-alebiT. xraxnis 1 Reros gare mxridan aqvs 2 skala. amskalis danayofis fasi 0,5 an 1 mm-ia: skalaze danayofebismarTobulad gatarebulia wrfis monakveTi. xraxnis 1 Rerozedamagrebulia 3 doli, romlis skalac Seicavs 50 an 100danayofs. xraxnis erTi sruli Semobrunebisas Reros gada-dgilebas RerZis gaswvriv biji ewodeba. Tu xraxnis biji0,5 mm-ia, 2 skalis danayofis fasic 0,5 mm-ia da 3 dolisskala 50 danayofs Seicavs. Tu xraxnis biji 1 mm-ia, maSin2 skalis danayofis fasi 1 mm-ia da 3 dolis skala 100danayofs Seicavs. orive SemTxvevaSi xraxnis mobrunebas 3dolis skalis erT danayofze Seesabameba 1 Reros gada-adgileba 0,01 mm-iT. esaa mikrometris sizuste. rocamikrometruli xraxnis bolo mis mopirdapire sayrdensexeba (xraxni moWerilia bolomde), 3 dolis napiri 2skalis nulovan danayofs unda uswordebodes, xolo 2skalaze gavlebuli wrfis monakveTi _ 3 dolis skalisnulovan danayofs. 4 xraxnis sabrunebeli Wrialaa.

mikrometriT sxeulis sigrZis gasazomad mas aTavsebenxraxnsa da mis mopirdapire sayrdens Soris. mikromer-trul xraxns abruneben, sanam misi bolo sxeuls ar Seexe-ba. 2 skalaze aiT-vlian milimetrebs,3 dolis skalazeki milimetris mea-sed nawilebs.

sur. 29

5

12

34

2 4

gazomvis Sedegebis damuSavebagazomvis Sedegebis damuSavebagazomvis Sedegebis damuSavebagazomvis Sedegebis damuSavebagazomvis Sedegebis damuSaveba

(samaxsovro VII_VIII klasis moswavleTaTvis)

gazomva aris fizikuri sididis mniSvnelobis moZebnaeqsperimentis gziT gazomvis saSualebebis (gamzomixelsawyoebis) daxmarebiT;

pirdapiri gazomva _ _ _ _ _ fizikuri sididis mniSvnelobisgansazRvra uSualod gazomvis saSualebebis (gamzomixelsawyoebis) daxmarebiT;

arapirdapiri gazomva _ fizikuri sididis mniSvne-lobis gansazRvra formuliT, romelic am sidides akavSirebsuSualod gazomvad fizikur sidideebTan.

pirdapiri gazomvis cdomilebispirdapiri gazomvis cdomilebispirdapiri gazomvis cdomilebispirdapiri gazomvis cdomilebispirdapiri gazomvis cdomilebisgansazRvragansazRvragansazRvragansazRvragansazRvra

1. m fizikuri sididis miaxloebi-

Ti mniSvnelobaa. is gazomvis gziT mi-iReba. gazomvis saSualebidan (gamzomixelsawyodan) Cveneba aiTvleba da Caiw-ereba ise, rogorc naCvenebia sur. 30-ze,

m=18,5 mm.

2. Δ fizikuri sididis gazomvis absoluturi cdomi-lebaa (gamoisaxeba imave erTeulebSi, rogorc TviT fizi-kuri sidide). is ikribeba instrumentis absoluturi cdom-ilebisa Δ

i (gamowveulia gazomvis saSualebis uzusto-

biT, misi mniSvnelobebi mocemulia cxrilSi) da aTvlisabsoluturi cdomilebisagan Δ

a (gamowveulia gazomvis

saSualebis Cvenebis arazusti aTvliT da Cveulebrivad,umravles SemTxvevaSi, udris xelsawyos danayofis fasisnaxevars):

Δ = Δi

+ Δa

.Δ-s mniSvneloba unda damrgvaldes erT niSnad cifram-

de; m-is mniSvneloba unda damrgvaldes ise, rom bolo

ricxvi aRmoCndes imave TanrigSi, rogorc absoluturicdomilebis ricxvi.

saxazavi

Zelaki

sur. 30

00000 11111 22222sm

2 5

magaliTad, Tu m=10,332 da Δ=0,17, maSin unda dai-

weros: Δ=0,2 da m=10,3.

3. ε _ fizikuri sididis fardobiTi cdomileba gan-isazRvreba formuliT:

ε = ( Δ /m) .1 0 0 % .

4. fizikuri sididis gazomvis Sedegi ase Caiwereba:=

m ± Δ , ε= ...%.cxrili

#

gazomvissaSualeba

gazomviszRvari

danayofisfasi

instrumentis

cdomileba

moswavlis1

2

3

4

5

6

7

8

9

10

saxazavi

xazvis

dinamometri(laboratoriuli)

sademonstracio

sazomi lenti

Stangenfargali

menzura

saswori saswavlo

barometr-aneroidi

Termometri(laboratoriuli)

ampermetrisaskolo

voltmetrisaskolo

moswavlis 50 sm-mde 1 mm ± 1 mm

30 sm 1 mm ± 0,2 mm

20 sm 1 mm ± 0,1 mm

100 sm 1 sm ± 0,5 sm

150 sm 0,5 sm ± 0,5 sm

150 mm 0,1 mm ± 0,05 mm

250 ml-mde 2 mm ± 1 ml

200 g _ ± 0,1 g

4 n 0,1 n ± 0,05 n

720_780

mm. vwy. sv.1 mm. vwy. sv. ± 3 mm. vwy. sv.

0_ o100 C o1C ± o1 C

2 a 0,1 a ± 0,05 a

6 v 0,2 v ± 0,15 v

instrumentuli

(foladis)

2 6

meqanikameqanikameqanikameqanikameqanika

siCqaresiCqaresiCqaresiCqaresiCqare

36saaTis isris bolo wertilis siGqaris gansazRvra.1. aiRe majis saaTi da gazome saaTis maCvenebeli isris

sigrZe milimetrebSi.2. gamoTvale wrewiris sigrZe, e.i. gza, romelsac gaivlis

saaTis maCvenebeli isris bolo wertili 12 saaTis ganmav-lobaSi (wrewiris sigrZe l=2πR).

3. gansazRvre am isris bolo wertilis siCqare mik-roni wamSi. ipove manZili, romelsac gaivlis saaTismaCvenebeli isris bolo wertili 1 saaTSi.SeniSvna: saaTis maCvenebeli isris (sigrZiT 1,5 sm) moZraobi-

sas bolo wertilis siCqare cota metia 2 mikronzewamSi (2 mk/wm). am siCqariT 1m manZilis gasavlelad

daaxloebiT saWiroa 6 dRe-Rame.

37Tanabari moZraoba.....1. aiRe erTi bolodan darCiluli, daaxloebiT 1 m

sigrZis mqone minis mili da aavse gliceriniT, an romelimegamWvirvale blanti siTxiT.

2. Cadevi milSi msxvili safanti da milis bolokargad daxure.

3. aiRe rezinis mili, moWeri misgan 9 viwro rgoli,wamoacvi isini milze da ganalage eTmaneTisagan 10 smmanZilis daSorebiT.

4. aiRe saaTi da aRniSne dro wamebSi, daakvirdi safan-tis moZraobas milis vertikalur mdgomareobaSi (sur. 31).

rodesac safanti miaRwevs milis bolos, gadaabrunemili da gaimeore igive.

2 7

SeniSvna: blanti siTxe Tu ar gaqvT, mili aavse wyliT

da safantis magivrad milSi Cadevi fisis an

kupris patara burTulebi. SesaZlebelia cdis

gacilebiT martivad Catareba, Tu orive mxri-

dan daxurul wylian milSi davtovebT ha-

eris patara buSts. sakmarisia milis odnav

daxra, rom buStma imoZraos Tanabrad. daxris

kuTxis cvlilebiT icvleba buStis moZrao-

bis siCqare. (am xelsawyos Cven viyenebT wr-

fivi Tanabari moZraobis Seswavlis dros).

38adamianis moZraobis saSualo siGaris gansazRvra.1. gadazome 60 m an 100 m manZili.2. gazome drois Sualedi, romelic saWiroa Sen mier

gazomili manZilis wynari nabijebiT gasavlelad.3. isargeble formuliT: v

saS = s/t, gansazRvre Seni

moZraobis saSualo siCqare.

39mdinaris dinebis siGqaris gansazRvra.1. ori moswavle dadgeba mdinaris napirze, erTmaneTi-

sagan 10 nabijze. erTi mdinareSi agdebs tivtivas (xis anpenoplastis naWers), meore yuradRebiT iWers im mo-ments, rodesac tivtiva mis gaswvriv Cacurdeba da mkveTradaqnevs patara alams.

2. mesame da meoTxe moswavle dinebis mimarTulebiT,qveviT, ikaveben adgils, agreTve 10 nabijze. mesame ise, rogorcmeore, iWers im moments, rodesac tivtiva mis gawvrivCacurdeba da agreTve aqnevs alams, meoTxe wammzomiT (ansaaTis wamebiani isriT) afiqsirebs tivtivas moZraobaze

dakvirvebisa da damTavrebis dros.

sur. 31

2 8

3. manZili, romelic dakvirvebis drois ganmavlobaSigacura tivtivam (xis an penoplastis naWerma) didi si-zustiT unda gaizomos.

4. gavlili manZiliTa da Sesabamisi droiT moiZebnebagzismieri siCqare.

40yvelaze didi siGqare.cnobilia, rom sinaTle vakuumSi c=300 000 km/wm

siCqariT vrceldeba. bunebaSi es yvelaze didi siCqarea.dedamiwasTan yvelaze axlo varskvlavia (mzis Semdeg)

centavris Tanavarskvlavedis varskvlavi proqsima (berZnulisityvaa da uaxloess niSnavs). am varskvlavidan dedamiwam-de sinaTlis sxivi mosvlas t=4,3 weliwads andomebs.maSin proqsimadan dedamiwamde manZili:

l=ct=(300 000.4,3.365.24.3600) km ≈ 4,07.1013 km.e.i. daaxloebiT 40,7 trilioni kilometri!cis yvelaze kaSkaSa da dedamiwasTan erT-erTi uax-

loesi varskvlavia didi qofakis Tanavarskvlavedis αvarskvlavi siriusi. dedamiwidan siriusamde manZili daax-loebiT 8,3.1013 km-ia (83 trilioni km! e.i. 2,04-jerufro Sorsaa proqsimaze). es daaxloebiT 500 000-jermetia dedamiwidan mzemde manZilze. sinaTlis sxivi siri-usidan dedamiwamde mosvlas TiTqmis 9 weliwads andomebs.100 km/sT siCqariT moZravi matarebeli am manZils 9.107

welSi (90 milion welSi) gaivlis.astronomiaSi xSirad sargebloben manZilis erTeuliT

_ sinaTlis weliwadiT. es aris manZili, romelsac sinaTle1 wlis ganmavlobaSi gaivlis. 1sin.w = 9,4.1012 km.

dedamiwidan mzemde manZili daaxloebiT 1,5.108 km-ia.igi mzis garSemo TiTqmis wrewirze moZraobs, amitom or-bitaze misi saSualo siCqare v

wr ≈30 km/wm (Seamowme for-muliT v=l/t, sadac t=365dR).

2 9

cnobilia, rom wriul orbitaze moZraobis siCqare vwr

da amave orbitidan ̀ gaqcevis” siCqare vgaqc

dakavSirebulia

martivi formuliT:

vgaqc

= 2 vwr ≈ 1,4 v

wr.

amitom, dedamiwis orbitidan mzis mizidulobas rom

`gaveqceT”, kosmosur xomalds unda mivaniWoT siCqare:

vgaqc ≈ 1,4 . 30 km/sT ≈ 42 km/sT.

inerciainerciainerciainerciainercia

41Wadraki da inercia.inerciis kanoni _ Tu sxeuli ar urTierTqmedebs sxva

sxeulebTan, maSin is inarCunebs wrfivi Tanabari moZrao-bis an uZraobis mdgomareobas.

1. gluvi magidis zedapirze

(napirTan axlos) gaSale gluvi

naWris gadasafarebeli da moaT-

avse masze figurebdalagebuli ma-

siuri Wadrakis dafa. gadasafa-

reblis erTi napiri xeliT dai-

kave (sur. 32).

2. moaxdine, rac SeiZleba, gadasafareblis swrafi gamowe-

va.

Wadraki gaunZrevlad darCeba magidaze, gadasafarebeli

gamosrialdeba misgan da xelSi SegrCeba.

SeniSvna: am cdis Catareba sakmaod Znelia. saWiroa sakmaod

mZime dafa gaprialebuli sadgamiT. agreTv gadasa-

farebelic gluvi, sriala unda iyos.

sur. 32

3 0

42SaSic ar vardeba.pirveli cda:1. gluv Wadrakis dafaze an mag-

idaze daawyve 10_12 SaSis saTamaSo erTsvetad (sur. 33).2. cota varjiSis Semdeg advilad Se-Zleb saxazaviT gamoagdo qveda SaSiise, rom masze dalagebuli danarCeniadgilze darCes.meore cda:

1. es cda ufro martivia. dafiskidesTan moaTavse saweri qaRaldis viwro zoli da maszedadevi ramdenime SaSi svetad. Tu qaRaldis zols nelagamowev, sveti wamohyveba, xolo Tu swrafad gamohkrav,sveti adgilze darCeba (sur. 34).SeniSvna: analogiuri cda SeiZleba Caataro asanTis kolofi-

Ta da wyliani WiqiT. asanTis kolofi saxazaviT

gamoagde wyliani Wiqis qveSidan.

43kvercxi WiqaSi.1. Cais WiqaSi naxevramde Caasxi wyali. Wiqaze dadevi

plastmasis patara saxazavi an misaloci baraTi. zemodanmoaTavse patara rgoli (an beWedi)

da masze kvercxi (sur. 35).2. Seasrule sakmaod

Zlieri wkipurti saxaza-vze (baraTze). saxazavi gas-rialdeba da kvercxi Wiqa-Si Cavardeba.SeniSvna. ukeTesia, aiRo mox-arSuli kvercxi.

sur. 33

sur. 34

sur. 35

3 1

44qaRaldi joxze ma-

garia.Zalian lamazi cda

SeiZleba Caataro xmelijoxiT, magram es garkveulvarjiSs moiTxovs.

1. SearCie wvrili, gamxmari joxi, sigrZiT _ daaxloe-biT 1 m. qaRaldisagan Seawebe ori rgoli. orma amxanagmadaikavos es rgolebi danis pirebze, rogorc naCvenebiasur. 36-ze. rgolebSi moaTavse joxis boloebi.

2. axla aiRe meore joxi da daartyi dakidebulijoxis SuaSi. ar SegeSindes qaRaldis rgolebis dazianeb-isa _ isini miT ufro darCebian dauzianebelni, rac ufromagrad daartyam. danebi ar gaWrian qaRaldis rgolebs,dakidebuli joxi ki gatydeba!

yvela cdis SemTxvevaSi mizezi aris inercia. dakidebu-li joxi miiswrafvis, SeinarCunos uZraobis mdgomareoba,xolo biZgi sakmaod mkveTri dartymis dros ver aswrebsgavrcelebas. joxi ufro adre gatydeba, vidre SeSfoTebamis boloebamde miaRwevs.

45inercia moZraobisas.1. aiRe 30_40 sm sigrZis ficari da gaakeTe misgan

daxrili sibrtye (sur. 37). wina mxares miaWede pataraficari, rom miiRo borti.

2. daamzade patara urika (an aiRe saTamaSo manqanismodeli). dadevi masze Zelaki da daagore daxril si-brtyeze.

sur. 36

sur. 37

3 2

3. urika bortTan dajaxebis Semdeg gaCerdeba, xoloZelaki SeinarCunebs moZraobis mdgomareobas da urikidangadavardeba (ise, rogorc waborZikebuli cxenidan mxe-dari).

rodis uxveven gverdzerodis uxveven gverdzerodis uxveven gverdzerodis uxveven gverdzerodis uxveven gverdze

46cota ram fexburTze.1. dartyma! zustad gaSvebuli burTi mifrinavs zeda

Zelis qveda mxrisaken. magram mekare xteba, burTi xvdebamis aweul xels, gadaixreba zeviT da gadis kuTxurze.

2. burTi mifrinavda inerciiT. ar aris gasaocari, rommekaris xelTan Sexebis Semdeg burTma Seicvala moZraobismimarTuleba. aq arsebobs mizezi. mekarem gaakeTa garkveu-li daZabva, rom gadaexara burTi. man ubiZga burTs dagadaxara is wrfivi gavrcelebis mimarTulebidan.

47wyali ar gadmoiRvreba qilidan.am cdis CatarebisaTvis saWiroa didi adgili. amitom

Caatare ezoSi.

3 3

1. aiRe badis xelCanTa (romel-sac sayidlebisaTvis iyeneben). wylianida TavRia minis qila Cadevi badeSi(sur. 38).

2. moiyvane rxeviT moZraobaSi daTandaTan gadaiyvane brunviT moZraoba-Si. qilidan wylis arc erTi wveTiar gadmoiRvreba.SeniSvna: analogiuri cda SeiZleba Caa-

taro wyliani vedroTi.

48wyali iRvreba zeviT.1. axla minis nacvlad aiRe Tunuqis qila (konservis

an yavis). lursmniT fskerSi gaukeTe naxvreti. Tu bade argaqvs, maSin qilas zeda kidesTan erTmaneTis mopirdapiredgaukeTe ori xvreli da gamoabi Toki an mavTuli.

2. Caasxi qilaSi wyali da moiyvane brunviT moZraoba-Si. wyali qilidan asxams yvela mdebareobaSi _ zeviTac ki(sur. 38 a).

ratom aris, rom ganieri yelidan wylis arc erTiwveTi ar gadmodis, xolo viwro xvrelidan ki zeviT asx-ams?

cxadia, aq mizezi brunviT moZraobaSia. rodesac qilamoZraobs, wyalic masTan erTad moZraobs. moZraobs in-erciiT. inerciiT moZravi sxeuli kiTavisiT gverdze ver mouxvevs. Toki,romelic iWers qilas, agreTve ewe-va Sen xels.

qila cdilobs, ifrinos sworad,inerciiT, xolo Toki ar uSvebs,abrunebs wrewirze. qila ewinaaRm-degeba, Wimavs Toks.

sur. 38

sur. 38 a

3 jemal kiknaZe

3 4

qilaSi wyali agreTve iswrafvis imoZraos pirdapirinerciiT. magram qila ar uSvebs, amoZravebs wreze. wyaliewinaaRmdegeba, awveba fskerze da, Tu fskerSi xvrelia,iqedan Sadrevani gamoasxams.

wona. uwonobawona. uwonobawona. uwonobawona. uwonobawona. uwonoba

Sen, albaT, ginaxavs telegadacemebi orbituli kosmo-suri sadguridan. iq kosmonavtebic dacuraven haerSi, ro-gorc Tevzebi _ wyalSi (sur.39). albaT, ici, rom am droskosmonavtebi uwonobis mdgomareobaSi imyofebian. sad wavidamaTi wona? SeiZleba wona daikargos?

Zalas, romliTac simZimisa da reaqciis ZalebiT de-formirebuli sxeuli awveba sayrdens (an Wimavs sakidels),sxeulis wona ewodeba.

cxadia, Tu sxeulze aRar imoqmedebs reaqciis Zala daimoqmedebs mxolod simZimis Zala (is ki yovelTvis mo-qmedebs), is deformirebuli aRar iqneba da sayrdens aRardaawveba (arc sakidels gaWimavs), swored maSin ikargebawona. e.i. sxeuli imyofeba uwonobis mdgomareobaSi.

sur. 39

3 5

49uwono wyali.SeiZleba iseTi cdis Catareba, rom fskergaxvretili

WurWlidan wyalma qveviT ar gamoasxas.

1. fskergaxvretil qilaSi Caasxi wyali da zeviT aswie.

xvrelidan wyali gamova, radgan wyals wona aqvs da cdi-

lobs Camovardes qveviT.

2. axla qila aswie rac SeiZleba, zeviT da yuradRebiT

daakvirdi wylis Wavls, gauSvi xeli WurWels. qila da-

vardeba miwaze, magram Sen, albaT, SeamCnev: sanam is vardeba,

wylis Wavli ar gamoedineba. wyali vardnil qilaSi imyo-

feba uwonobaSi! e.i. wyali sayrdens (fskers) aRar awveba.

50uwonoba TviTmfrinavSi.Zirgaxvretili qiliT Catarebulma cdam uCvena, rom

vardnili sxeuli kargavs wonas. sanam sxeulebi vardebian,

isini uwonoa!

Sen, albaT, wagikiTxavs, an, SeiZleba, televiziiT ginaxavs,

rogor aswavlian uwonobis mdgomareobis Seguebas mo-

maval kosmonavtebs. maT Casvamen did TviTmfrinavSi da

aiyvanen, rac SeiZleba, maRla. Semdeg mfrinavi axdens pikirebas,

e.i. miemarTeba cxviriT qveviT. cxadia, Zalian didxans pikire-

ba ar SeiZleba: SeiZleba miwaSi CaerWos. magram 10 km-is

simaRlidan vardna grZeldeba daaxloebiT 40 wm-s; am drois

ganmavlobaSi TviTmfrinavi da yvelaferi masSi uwonoa.

mfrinavi da ekipaJis sxva wevrebi RvedebiT arian dabmuli,

rom ar `gafrindnen~ TavianTi samuSao adgilidan. xolo

momavali kosmonavtebi Tavisuflad `curaven” salonSi.SeniSvna: astronavtebi (kosmonavtebi) varjiSoben wylis

uzarmazar avzSi. aq `uwonobis~ zustad iseTi efeq-

ti iqmneba, rasac isini kosmosSi ganicdian.

3 6

ratom mifrinavs raketaratom mifrinavs raketaratom mifrinavs raketaratom mifrinavs raketaratom mifrinavs raketa

51raketa sahaero buStiT.ratom curavs navi? imitom, rom menave usvams niCbebs

da wyals ukan `xvetavs~, wyali ki niCbebs da navs win

ubiZgebs.

ratom frinavs Citi? imitom, rom is arxevs frTebs.

frTebi, rogorc niCbebi, haers ̀ xvetavs~ da ubiZgebs frin-

vels.

ratom frens TviTmfrinavi sahaero xraxniT? imitom,

rom misi Zrava muSaobs da abrunebs xraxns. xraxni erWoba

haerSi, rogorc sWvali (Surupi) ficarSi da TviTmfri-

navs win eweva.

Tu ar aris ficari, ramdenic ginda ibrunos sWvalma,

is win ver wava. Tu ar aris haeri, agreTve sahaero xraxnma

ramdenic unda ibrunos, verc is wava win. maSasadame, xrax-

npropelerian TviTmfrinavs SeuZlia frena mxolod iq,

sadac haeria. ai, magaliTad, mTvareze xraxnpropeleriani

TviTmfrinavi ver ifrens.

Tu dedamiwidan did simaRleze avalT, iq haeri Zalian

cotaa. Semdeg ki uhaero sivrce iwyeba. iq rogorRaa Sesa-

Zlebeli frena?

sur. 40

3 7

SeiZleba mTvareze Wurvi inerciiT mifrindes. kidevufro ukeTesia _ raketa. mas haeri ar sWirdeba _ TavisTavs TviTon ubiZgebs. raketas gansakuTrebuli Zrava aqvs.masSi iwvis sawvavi da warmoiSveba bevri gaxurebuli airi(gazi). ZirSi raketas aqvs xvreli, e.w. saqSeni, saidanac airiZlieri WavliT gamoedineba. is raketis ukan cecxlovankuds tovebs (sur. 40). Wavli cems ukan _ raketa mifri-navs win. gaugebaria?

Caatare Semdegi cda.1. aiRe sabavSvo rezinis buSti. miidevi misi yeli

tuCebze da gabere. Semdeg moaSore tuCebi da yeli datoveRia. Sen igrZnob haeris Wavls saxeze. magram, radgan gaber-ili buStidan gamodis haeris Wavli, amitom mas SeuZliaraketasaviT frena.

2. gabere is xelaxla, aswie saxe zeviT.rogorc ki rezinis yels xels gauSveb,buSti afrindeba (sur. 41). am dros mTe-li haeri misgan gamova da `raketa” imwamsve ukan Camovardeba.

3. buSts wamoacvi saqSeni (Seviwro-vebuli bolo) da daamagre patara saTa-maSo avtomobilze, miiReb reaqtiul avtomobils.

52wylis karuseli.1. aiRe carieli konservis an yavis (Tunuqis) qila. mis

gverdiT kedelze, ZirSi, erTmaneTis mopirdapired, lursm-niT gaukeTe ori xvreli (ukeTesia 4). SemdegGdatove lurs-mani xvrelSi da gadaRune is gverdze. saWiroa, rom xvreligamovides daxrili da Wav-li misgan gverdze scemdes.

2. qilis zeda nawilSigaukeTe kidev ori xvreli dadakide grZel Zafze. xelsaw-yo ukve mzadaa da gacilebiTdidxans imuSavebs. (sur. 42).

sur. 41

sur. 42

3 8

3. cda SeiZleba Caataro ezoSi an abazanaSi. gaavse

qila wyliT da aswie is ZafiT. wyali qveda ori xvrel-

idan gamoedineba daxrili susti WavlebiT, magram isini

moaxdenen TavianT moqmedebas. Wavlebi scemen erT mxares _

qila dabrundeba meore mxares.SeniSvna: cdisTvis ufro mosaxerxebelia polieTilenis boT-

lis gamoyeneba, Tu fskerTan xvrelebs daxrilad

gaukeTeb.

53qaRaldis Tevzi.

1. gamoWeri mkvrivi qaRaldisagan

Tevzi. (sur. 43). Tevzs SuaSi aqvs

wriuli A xvreli, romelic kudTan

SeerTebulia viwro AB xvreliT.

2. Caasxi taStSi wyali da dadevi

Tevzi wyalze ise, rom misi qveda naw-

ili mTlianad dasveldes, xolo zeda

darCes mTlianad mSrali.

es moxerxebulad SeiZleba CangliT

gaakeTo. dadevi Tevzi Cangalze, frTx-

ilad CauSvi is wyalSi. Tevzi gacurdeba, xolo Cangali

ufro Rrmad CaZire da amoiRe.

3. sazeTaviT, an wveliT _ wvensasmeliT A xvrelSi

CaawveTe zeTis didi wveTi. wveli CauSvi zeTSi 2_3 mm-ze.

Semdeg zeda bolo daxure TiTiT da wveli gadaitane

TevzTan. daikave qveda bolo zustad A xvrelis zeviT da

xeli auSvi wvelis zeda xvrels. zeTi CaewveTeba zustad

xvrelSi.

zeTi gamoedineba AB arxidan, radgan igi cdilobs wy-

lis zedapirze gadinebas. sxva mxares gadinebis saSuale-

bas ar aZlevs Tevzi. rogor fiqrob, ras gaakeTebs Tevzi

zeTis ukan gamodinebisas? naTelia, is gacuravs win.

sur. 43

3 9

simZimis centri.simZimis centri.simZimis centri.simZimis centri.simZimis centri.sxeulTa wonasworobasxeulTa wonasworobasxeulTa wonasworobasxeulTa wonasworobasxeulTa wonasworoba

54Seiswavle zogierTi geometriuli figurisa da

sxeulis simZimis centris mdebareoba.1. daakvirdi sur. 44-ze geometriul figurebs da

daimaxsovre, rom monakveTis simZimis centri mis SuaSimdebareobs; samkuTxedisa_misi medianebis gadakveTiswertilSi; paralelogramis, marTkuTxedis, kvdratisa darombisa_maTi diagonalebis gadakveTis wertilSi; wrewiris,wrisa_maTs geometriul centrSi; xolo segmenti-sa_simetriis RerZze, fuZidan 2/5 nawilze.

2. sur. 44-ze naCvenebi figurebidan mkvrivqaRaldze daxaze, magaliTad, samkuTxedi dasegmenti; maxvili fanqriT gaatare samkuTxedSimedianebi da segmentSi simetriis RerZi. esRerZi dayavi 5 tol nawilad. gamoWeri orivefigura.

3. aiRe nemsi ZafiT, gamonaskve Zafis boloda erT-erTi gaxvrite simZimis centrze, dak-ide is Zafze. aseve gaxvrite meore figurada dakide Zafze (sur. 45).

sur. 44

sur. 45

4 0

55gansazRvre rgolis (gvergvis, saltes) simZimis cen-

tri.1. aiRe patara gvergvi (mag. qarga) an gaakeTe rgoli

mavTulisagan, fanerisagan an muyaosagan.2. rgoli da Sveuli

dakide lursmanze (sur. 46).3. rodesac Sveulis Zafi

gaCerdeba, rgolze aRniSne Sveu-lis Zafis Sexebis wertilebi.gaWime wvrili mavTuli da amwertilebze daamagre.

4. axla rgoli sxvawertiliT dakide da Seas-

rule igive. mavTulebis gadakveTis wertili iqneba rgol-is simZimis centri.

5. daakvirdi: rgolis simZimis centri mdebareobs sx-eulis nivTierebis gareT.

6. mavTulebis gadakveTis wertilze miabi Zafi damasze dakide rgoli. igi ganurCevel wonasworobaSi aR-moCndeba, radgan rgolis simZimis centri da sayrdeniwertili erTmaneTs emTxveva.SeniSvna: ganxiluli wesiT SeiZleba ipovo nebismieri formis

brtyeli nakvTis simZimis centri.

56TviTmawonasworebeli joxi.1. gaSlili xelebis saCvenebel TiTebze horizontu-

lad dade xis saxazavi da auCqareblad (nela) miuaxloveTiTebi erTmaneTs (sur. 47).

2. SeamCnev, rom saxazavi TiTebze Tanabrad ar imoZravebs,aramed rigrigobiT xan erT TiTze gasrialdeba, xan meo-reze, sanam TiTebi ar SeerTdeba. am dros saxazavi inar-Cunebs wonasworobis mdgomareobas!

sur. 46

4 1

3. Secvale saxazavi gluvi joxiT, biliardis kiiT,xistariani iatakis jagrisiT da sxv. Sedegi erTnairiaRmoCndeba, Tundac Tvalaxveulma Caataro eqsperimenti.

ra aris moulodneli finalis mizezi?pirvel rigSi, cxadia: radgan saxazavi SeerTebul TiTe-

bze wonasworobaSi imyofeba, e.i. TiTebi SeerTdnen saxaza-vis simZimis centris qveS (sxeuli wonasworobaSia, Tumis simZimis centrze gamavali Sveuli sayrdenis sazRvre-bis SigniT gadis).

rodesac TiTebi gaSlilia, didi datvirTva (wnevisZala) modis im TiTze, romelic saxazavis simZimis centr-Tanaa axlos. Sesabamisad am TiTze xaxunis Zala metia,amitom saxazavi simZimis centridan metad daSorebul TiTzesrialebs. rogorc ki moZravi TiTi simZimis centrTanaxlos aRmoCndeba, saxazavi srials daiwyebs meore TiTze.ase moxdeba ramdenjerme, sanam TiTebi ar SeerTdebian.

57zogjer intuicia gvRalatobs.1. Caatare wina cda xistariani iatakis jagrisiT an kiis

msgavsi joxiT. dasvi Sen winaSe kiTx-va: Tu joxs gavWriT im adgilas,sadac is TiTebs eyrdnoba da orivenawils davdebT berketiani sasworispinebze (sur. 48), romeli mxare gada-wonis?

2. Caatare cda da darwmunde-bi, rom mokle mxare (jagrisis)gadawonis.

sur. 47

sur. 48

4 2

intuicia ki sawinaaRmdegos gvikarnaxebs: radgan ja-grisis orive mxarem TiTebze erTmaneTi gaawonaswora, ami-tom sasworzec erTmaneTi unda gaawonasworos.

mizezis mixvedra advilia, Tu gaviTvaliswinebT, romTiTebze gawonasworebisas berketis orive nawilis simZi-mis Zalebis mxrebi sxvadasxvaa. kerZod, jagrisis (joxismsxvili bolos) mxares naklebia.

58erTi sayrdeni wertilis mqone sxeulis wonasworo-

ba.1. muyaosagan gamo-

Weri marTkuTxedizomebiT 25x5 sm. gaa-tare masze didi sim-etriis RerZi da miserT boloze daxateisari.

2. marTkuTxedididi simetriis RerZze gaxvrite oradgilas: erTi _ boloSi, meore _ mar-TkuTxedis simetriis centrSi.

3. dakide marTkuTxedi nemsze ga-napira xvreliT. rodesac marTkuTxe-di ̀ dawynardeba~, mis qveS vertikalursibrtyeze miaxate meore isari (sur.49). gaarxie marTkuTxedi. rodesacis ̀ dawynardeba~, dainaxav, rom isrebierTmaneTs gauswordeba. isev gaarxie,Sedegi igive iqneba. wonasworobas,romelSic sxeuli rxeviTi moZraobisSemdeg yovelTvis brundeba sawyismdebareobaSi, mdgradi ewodeba. mdgra-

sur. 50

sur. 49

4 3

di wonasworobis mdgomareobaSi imyofeba: Sveuli, kedlissaaTis qanqara, dakidebuli WaRi, amwes gvarlaze dakidebu-li tvirTi da mravali sxva sxeuli. miaqcie yuradReba,rom yvela am sxeuls simZimis centri dakidebis wertil-is qveviT aqvT.

4. Tu simZimis centri dakidebis wertilis zeviTmoeqceva, maSin wonasworoba aramdgradi iqneba (sur. 50).

59monorelsi (relsi caSi).msoflios bevr did qalaqSi ukve muSaobs aseTi ̀ ciuri”

gzebi. dedamiwaze, quCebSi xom simWidrovea, yovel gzaj-varedinze SuqniSania. gansakuTrebiT ver gaiqcevi. marTa-lia, miwis qveS, metroSi gza yovelTvis Tavisufalia daSeiZleba didi siCqariT moZraoba, magram miwisqveSa gvi-rabis aSeneba Zalian Zneli, rTuli da Zviria.

ai moifiqres relsebis gadeba caSi. iq, qalaqis quCeb-is Tavze, adgili ramdenic gindaT aris. cxadia, ageben fola-dis mdgrad anZebs da masze kideben ara or relss, aramederTs. swored aseT gzas monorelsurs (berZnuli sityvisagan`monos” _ ̀ erTi”) uwodeben. romelzec magnitur baliSe-bze srialebs specialuri urika. am urikaze ki _ relsisqveviT, dakidebulia vagoni mgzavrebisaTvis (sur. 51). e.i.vagoni imyofeba mdgrad wonasworobaSi.

sur. 51

4 4

60ratom mxolod erTi relsi?SemowmebisaTvis Caatare ramden-

ime cda. pirvel rigSi _ cda dom-inoTi.

1. scade, magidaze daayeno domi-nos yvela (28) saTvalavi (firfi-ta) ise, rogorc naCvenebia sur. 52-ze. magram amis gakeTeba advili araris.

pirvel rigSi saWiroa kargi,swori da myarad mdgomi magida. ma-gram am drosac ki saeWvoa, romSeZlo aseTi myife nagebobis aSene-ba erT saTvalavze (firfitaze)dayrdnobiT.

2. ukeTesia, Tavidan fexze daayeno ara erTi dominosfirfita, aramed, sami. Semdeg, rodesac yvela firfitasdaalageb, ori sayrdeni ganapira firfita frTxilad moa-Sore da isini miRebuli nagebobis Tavze dade.

sifrTxilis yvela RonisZiebis dacvis drosac ki bev-ri wvaleba mogiwevs, sanam nagebobas daamTavreb. Tu Zlie-rad Seuberav, nageboba daiSleba.

61fanqari ar vardeba.meore cda iqneba aseTi: 1. scade, fanqari daayeno wveroze.

Tu Sen didi nebisyofa gaqvs, cda dominoze gamogiva, magramfanqarze, albaT, ara, Tundac mTeli dRe iwvalo!

magram aris erTi martivi wesi, rom `vaiZuloT fan-qari~, dadges wverze.

2. fanqarSi CaarWve patara, naxevrad gaxsnili jibisdana ise, rogorc sur. 53-zea naCvenebi. danas didad gaxsni

sur. 52

4 5

Tu mcired, fanqari ara marto ver-tikalurad SeiZleba daayeno, arameddaxrilad. da mainc ar Camovardeba,Tundac mas ubiZgo. mcire rxevebisSemdeg isev darCeba wverze dayrd-nobili!

fanqari udanod vardeba, danas-Tan erTad ara, ratom? orive SemTx-vevaSi is xom wveriT eyrdnoba. esaris misi sayrdeni wertili. magrampirvel SemTxvevaSi simZimis centri sayrdeni wertilismaRlaa, xolo meore SemTxvevaSi _ dabla (dana fanqarzemZimea). Tu fanqari daixreba da daiwyebs vardnas, maSindana maRla aiwevs da simZimis gamo dabla eweva.

amrigad, wonasworoba mdgradi iqneba. analogiuriamonorelsis vagonis wonasworoba.vagonis simZimis centri, sayrdeniwertilis _ monorelsis qveviTaa!

patara monorelsiani gza Sen Se-giZlia naxo qarxanaSi, avtofarexSi,avto da vagonSemkeTebel saam-qroebSi_yvelgan, sadac sWiroa mZi-me tvirTis aweva, gadaadgileba dadaSveba, roca miwaze siviwrovea(sur. 54).

62dana SeiZleba zeviT iyos.fanqriT Catarebul cdaSi jibis dana imyofeba qveviT.

magram SeiZleba is zeviTac iyos. mxolod saWiroa ufromZime sagani, rom saerTo simZimis centri sayrdeni werti-lis qveviT aRmoCndes.

1. am cdisaTvis Zalian moxerxebulia danaze mZime CamCa.aiRe iseTi CamCa, romelsac boloSi aqvs kakvi.

sur. 53

sur. 54

4 6

2. magidis kideze dadevi nax-evrad gaRebuli jibis dana damasze CamCa dakide (sur. 55, a).mcire rxevebis Semdeg es mowy-obiloba gawonaswordeba. cxa-dia, CamCis gareSe dana wamiTacar gaCerdeba aseT mdebareoba-Si!

3. rac ufro mZimea CamCa, miTufro sworad dgeba dana. amaSi

rom darwmunde, Cayare CamCaSi marili (an Saqari). dana sulufro maRla aiwevs.

jibis daniTa da CamCiT SeiZleba ufro lamazi cdaCaataro:

1. sur. 55, b-ze Sen xedav rogor unda wamoacva CamCadanis pirze. dana ise unda moRuno, rom CamCa ar Camosri-aldes da ekidos daaxloebiT 450 kuTxiT.

2. daiyrdeni danis tari TiTze, mTeli sistema(dana_CamCa) aRmoCndeba wonasworobaSi. SeiZleba, wylianiWiqis napirzec ki dado, mxolod Wiqa wyliT unda aavso,rom ar gadayiravdes.

63cdebi GanglebiT.Tu gaqvs sakmaod mZime Canglebi, SeiZleba kidev Caata-

ro ori saintereso cda.1. pirveli cdisaTvis dag-

Wirdeba boTli, kvercxi dakorpis sacobi. cdas Caatarebise, rogorc naCvenebia sur.56, a-ze.

2. meore cdisaTvis saWir-oa sakmaod sqeli moneta. ismWidrod unda Sediodes Can-glebis kbilebSi (sur. 56, b).

sur. 55

ba

asur. 56

b

4 7

64mZime Sroma.adre, rodesac eleqtroenergia da manqanebi ar iyo,

morisagan ficrebs xeliT xerxavdnen. mors maRal sad-gamze debdnen, erTi mxerxavi dgeboda maRla, xolo meore _dabla. isini grZeli xerxis boloebs iWerdnen xelSi damanam amoZravebdnen zeviT-qveeviT, sanam morisagan ficarsar moaxerxavdnen. ase muSaobdnen isini mTel dRes! (sur.57, ̀ mxerxavebi”, moqandake kimi tabataZe).

amJamad ase TiTqmis arsad aRar xerxaven. amisaTvis te-qnikosebma da inJinrebma Seqmnes specialuri manqana _ xissaxerxi dgani. am manqanaSi zeviT-qveviT irxeva foladisCarCo maxvilkbilebiani xerxebiT. manqana CaiWers mors daubiZgebs mas pirdapir xe-rxisaken. vJii-vJii! vJii-vJii! naxerxi Sadrevaniv-iT cviva. manqanis meoremxares gamoZvreba aramori, aramed grZeli fi-crebis Sekvra.

SegiZlia gaakeTo sa-TamaSo `mxerxavi”. ro-gor?

1. `mxerxavis” tani-saTvis SearCie korpis sa-cobi (rac ufro didiiqneba, miT ukeTesia. mag.aseTia Sampanuris saco-bi). wamaxvilebuli asan-Tis ori Rero sacobsSearWve qvevidan. esenifexebia. asanTis Tavebiiqneba `mxerxavis” `fex-sacmlebi~.

sur. 57

`mxerxavebi~. moqandake kimi tabataZe.

4 8

2. ̀ mxerxavis” ̀ Tavi~ da ̀ xele-bi~ gamoWeri qaRaldisagan da mi-awebe tans, an gamoZerwe plastilin-isagan. xerxi moxare msxvili mavTu-lisagan. is orjer-samjer grZeliunda iyos figuraze. zeda bolosacobSi Rrmad SearWve iq, sadacmkerdi unda iyos. mavTulis qvedaboloze wamoacvi kartofili.

3. mavTuli rom metad daemgvanosxerxs, gamoWeri qaRaldis kbilebi-ani zoli. moxare misi napiri, waus-vi webo, moade mavTuls da mouWire.roca webo gaSreba, ̀ mxerxavi” mzadiqneba da SeuZlia, Tavis mZime Sro-mas Seudges.

4. dadgi is magidis kideze (sur.58) da moxare mavTuli ise, rom sworad dadges. axla gaarxiekartofili. ̀ mxerxavi” daiwyebs rxevas, Seudgeba muSaobas.

65horizontul sibrtyeze dayrdnobili sxeulis

wonasworoba.1. aiRe carieli asanTis kolofi da ori yuriani

qinZisTavi. erTi qinZisTavi gaatare meoris yurSi da daay-ene is kolofis SuaSi, gaxvrite kolofi gamWolad missimZimis centrze (sur. 59). qveviT dakidebuli qinZisTaviTavisuflad unda irxeodes pirvelze.

sur. 58

sur. 59

4 9

SeniSvna. Tu dakidebuli qinZisTavi gadis kolofis qveda

mxareze, maSin misi bolo motexe mkvnetaraTi.

2. daayene kolofi magidaze da nel-nela daxare, Seamowme

wonasworobis piroba: sxeulis wonasworobisaTvis simZi-mis centrze dakidebuli Sveuli mis sayrden farTobSiunda gadiodes.

miaqcie yuradReba im moments, rodesac kolofi Sei-

Zleba gadayiravdes marcxniv an marjvniv.

66horizontul sibrtyeze dayrdnobili sxeulis

wonasworobis pirobis Semowmeba.1. midi kedelTan da gverdiT ise dadeqi, rom mWidrod

miayrdno mas marjvena mxari da marjvena fexi. scade, aswio

marcxena fexi da moxaro igi muxlSi (sur. 60).

am dros wonasworobas ver SeinarCuneb. ratom?

2. aiRe saxazavi da azrobrivad gaatare su-

raTze wrfe safexuris Sua wertilsa da mis sim-

Zimis centrs (qamris abzindis Sua wertils) So-

ris.

rogor gadis wrfe iatakis mimarT ver-

tikalurad Tu daxrilad?

cxadia, am dros simZimis Zala qmnis mabru-

nebel moments, suraTze isris mimarTulebiT.

reaqciis Zalis momenti nulis tolia.

3. moSordi kedels, aswie marcxena fexi, moxare

is muxlSi. dadeqi sworad (sur. 61). ratom inar-

Cuneb wonasworobas? axla rogor gadis sayrdenis

Sua wertilze da simZimis centrze gamavali wrfe:

daxrilad, Tu vertikalurad? am dros simZimisa

da reaqciis Zalebis momentebi nulis tolia.

sur. 60

sur. 61

4 jemal kiknaZe

5 0

4. skamze ise dajeqi, rom Seni da skamis zurgi mWidrodebjinebodes erTmaneTs, weli da Tavi vertikalurad idges,xelebi qveviT iyos daSvebuli, wvivebi vertikalurad gaas-wore, fexsacmlis lanCebi iataks exebodes.

5. scade adgoma ise, rom tani ar daxaro, fexebi armoxaro da xelebi ar daixmaro. ratom ver dgebi?

6. upasuxe kiTxvebs: ratom ixreba adamiani win, rocais zurgiT eweva tvirTs? roca marcxena xeliT ewevatvirTs, ratom ixreba marjvniv? Tu tvirTs eweva winidan,ratom ixreba ukan? rogor moZraobs orsuli qali?

67beRura totze.gaukeTe saTamaSo Sen patara das an

Zmas (mdgradi wonasworoba).1. beRuras tani da Tavi gamoZerwe

plastilinisagan (SeiZleba moifiqro sx-vadasxva formis girCebisaganac). Sesani-Snavi niskarti gamova mzesumziras marcv-lisagan. CaarWve is blagvi boloTi.gaakeTe beRuras Tvalebi asanTis Taveb-

isagan, kudi _ ramdenime bumbulisagan, fexebi _ asanTisagan.beRuras tanSi SerWobili mavTulis meore boloze

daamagre plastilinis burTula. sakmaod mZime tvirTisSemTxvevaSi beRura SesaniSnavad dajdeba TiTze an xistotze (sur.62). ra moxdeba, TutvirTi beRuraze msubuqi iqneba_ Camovardeba, Tu dajdeba?

Seni varaudi cdiT Seamowme.gadaadgile plastilinis burTu-la mavTulze zeviT da qveviT.dainaxav, rom, msubuqi tvirTisSemTxvevaSi, Citi mdgradad zis,rodesac tvirTi gadaadgilebulia

sur. 62

sur. 63

5 1

Sors, qveviT. xolo, roca tvirTi zeviTaa, Citi vardebaTiTebTan axlos (sur. 63).

ase rom, wonasworobis mdgradoba damokidebulia aramarto masaze, aramed _ tvirTis mdebareobazec. araa auci-lebeli, rom mTavari masa iyos qveviT. mniSvnelovania, romsayrdeni wertilis qveviT iyos sistemis masaTa centri(simZimis centri).

68kolofi siurpriziT.gveCveneba, TiTqos masaTa centris

(simZimis centris) Sesaxeb yvelaferinaTelia. magram Sen gelis kidev erTisiurprizi.

1. Cadevi asanTis cariel kolof-Si mZime qanCi, romelic, rac SeiZlebaaxlos iyos erT mxaresTan. axla esmxare dakavebuli iqneba magidaze, Tun-dac mTeli kolofi ekidos haerSi(sur. 64).

am cdaSi aris erTi SesaniSnavi Tavisebureba. aq mTelimasa sayrdeni wertilis zeviT devs, xolo kolofi arvardeba. ratom?

2. Sen, albaT, SegiZlia mixvde, rom, Tu kolofi daiw-yebs gadmovardnas magidis kididan, qanCi aiwevs. sxva si-tyvebiT, wonasworobis darRvevisas masaTa centri aiwevs.amitom wonasworoba aRdgeba.SeniSvna: sainteresoa, rom am mizezis gamo mdgrad wonas-

worobaSi imyofeba magidebi, skamebi, karadebi, sa-wolebi, avtobusebi, qandakebebi, amweebi, sabaRe ska-mebi, wignebi magidaze da kidev uamravi sxvadasxvasagani, romelTa CamoTvla am wignSi ar daeteva. maTaqvT erTi saerTo Tviseba: wonasworobis dar-Rvevisas masaTa centri aiwevs!

sur. 64

5 2

69`damjeri~ da `jiuti~ kvercxi.1. kvercxis boloebSi gaakeTe asanTis Reros siganis

toli ori xvreli da CaberviT gamoacale SigTavsi. naWu-Wis Siga mxare wyliT kargad gamorecxe. kargad gamosaS-robad gaaCere 1_2 dRes. amis Semdeg erT-erTi xvreliamolese TabaSiriT, carciani weboTi an TeTraTi ise, romis ar Candes. (amdeni rom ar iwvalo, gamoiyene ̀ qinderis”kolofi).

2. naWuWSi Cayare sufTa da mSrali sila, daaxloebiTmeoTxedze. meore xvrelic pirvelis analogiurad amolese.`damjeri~ kvercxi mzadaa! SegiZlia, daayeno is nebismiermdebareobaSi. amisaTvis sakmarisia mxolod msubuqad Searx-io kvercxi, daiWiro is im mdebareobaSi, romelic man undadaikavos. sila gadaadgildeba da SerCeul mdebareobaSidadgmuli kvercxi SeinarCunebs mdgrad wonasworobas.

3. `jiuti~ kvercxis (an `qinderis” kolofis) gasa-keTeblad silis magivrad Cayare masSi wvrili safanti(`bekasiniki”, bekasi_Waobis frinveli; aqvs grZeli da sworiniskarti) da stearinis naWrebi sanTlisagan. Semdeg dadgikvercxi erTi boloTi da gaaTbe. stearini gadneba da,rodesac gacivdeba, safanti erTmaneTsa da naWuWis kedelsmiewepeba. xvreli amoavse.

4. SeuZlebelia, ̀ jiuti~ kver-cxi `daawvino~. is dadgeba aramarto magidaze, aramed Wiqis ki-deze, danis tarze, boTlis yelze(sur. 65).

5. aseTi saTamaSo _ `adgabi-Wi!~ SenTvis, albaT, cnobilia. SenSegiZlia, is yvela wesis Tanaxmadgaalamazo: amisaTvis tvirTi moaT-avse kvercxis blagv boloSi, xolo

sur. 65

5 3

naWuWi moxate da SeRebe. SegiZlia gaukeTo Tmebi, xelebi,Seukero patara xifTani.

70zeviT, aRmarTze.realur cxovrebaSi Cven ukve didi xania miveCvieT

TiToeuli sagnis masaTa centris gamocnobas. Cven ucebvxvdebiT, rogor unda davdoT an davayenoT mocemuli sa-gani, rom is ar waiqces. `adgabiWis~ fokusi mdgomareobsimaSi, rom is atyuebs Cvens Tvals: misi masaTa centri armdebareobs iq, sadac Cven vvaraudobT, amitom `adgabiWi~ase jiutad ikavebs im mdebareobas, romelic arabunebrivigveCveneba.

modi, kidev Caatare cda, romelic, erTi SexedviT, ewi-naaRmdegeba wonasworobis kanonebs.

1. sqeli qaRaldis an muyaosagan Seawebe rgoli. misSiga mxareze erT adgilze daawebe tvirTi: xis joxi, luqian raime patara tvirTi, romelic mets iwonis, vidre TviTrgoli.

2. tvirTi rom ar Candes,orive mxridan daawebe qaRal-di. masze SeiZleba raime dax-ato, magaliTad, saxe. Tu am sax-is nikapi iqneba iq, sadac tvir-Tia, maSin am suraTis dayenebaTavdayira SeuZlebeli iqneba.`saxe~ gagordeba manam, sanam ni-kapi ar moeqceva qveviT.

3. viciT, rom daxril si-brtyeze yoveli Ceulebrivi bor-bali qveviT dagordeba. dadewignze saxazavi da mis ZirSimoaTavse Sen mier damzadebuli

sur. 70

sur. 66

5 4

saTamaSo ise, rom nikapi TiTqmis zeviT iyos, marcxniv(sur. 66). gauSvi ̀ saxe” _ is daxril sibrtyeze gagorde-ba zeviT.

ra Tqma unda, is gaCerdeba, rogorc ki nikapi Seexebasaxazavs; am dros xom masaTa centri ikavebs SesaZloyvelaze qveda mdebareobas.

71kasrze gadamjdari.Tu gaqvs liTonis wriuli qila,

magaliTad, Saqaryinulisa, SegiZlialamazi saTamaSo gaakeTo, kvlav wonas-worobaze damyarebuli. misi mowyo-biloba naTelia sur. 67-dan.

1. kolofis fuZe da saxuravi dadeficarze, romlis gafuWeba ar genane-ba. maTs centrSi lursmniT gaakeTenaxvreti. sqeli mavTulisagan moRuneRerZi, muxliT SuaSi; am muxlzedaamagre tyviis naWeri an mZime qanCi.

2. mavTulis boloebi gauyarexvrelebSi da qila daxure. qaRaldze daxate klouni(takimasxara), daawebe muyaoze da gamoWeri. fexebi miamagreqilidan gamoSveril mavTulis boloebze.

3. ubiZge qilas, rom gagordes. klouni `kasrze gada-mjdari” iqneba da mxiarulad dagikravs Tavs.

72behemoTi da Giti.warmoidgine, rom ginda, aswio karada, magram Zala ar

gyofnis. karadas gverdidan Seude magari joxi da Sen masaswev gansakuTrebuli daZabvis gareSe.

sur. 67

5 5

ginda, gatexo kakali(Txili) da es ar Segi-Zlia xelebiT. amisaTvisarsebobs kaklis spe-cialuri satexi, roml-iTac advilad daamtvrev naWuWs.

ginda, gaWra Tunuqi. amisaTvis arsebobs liTonis saWre-li makrateli. kargi makrateli qaRaldiviT Wris TxelTunuqs.

erTi SexedviT, yvela es SemTxveva Zalian sxvadasxvaa,magram isini waagavs erTimeores.

raRac samuSaos Sesasruleblad Sen ar gyofnis Zala.maSin xelSi iReb raRac mowyobilobas da Sen ukve samuS-aos Tavisuflad asruleb.

yvelaze saocari isaa, rom mowyobilobebs_joxs, satexs,makratels_ar aqvT Zravebi, ar aqvT araviTari sakuTariZalebi. isini mxolod adideben im Zalebs, romelsac SenmaT mosdeb.

rom gaigo, rogor miiReba es, Caatare cda:1. aiRe ori sxvadasx-

va masis sagani. magali-Tad, faifuris behemoTida gacilebiT msubuqixis Citi. dasvi isinimrgval fanqarze dade-bul saxazavis boloeb-ze (sur. 68). romeligadawonis? ra Tqma unda,behemoTi _ is xom ufromZimea.

2. gawie fanqari be-hemoTTan axlos. dain-axav, rom isini gawonas-wordnen!

sur. 68

sur. 69

5 6

kidev ufro gawie fanqari behemoTisaken _ da Citigadawonis!

am cdaSi Cven gamoviyeneT saxazavi, imitom, rom maszefigurebis moTavseba advilia. SeiZleboda, gamogveyenebinawriuli joxi, grZeli Zelaki, mori, ficari da mravalisxva sxeuli. yvela es sxeuli berketebia. zemoT CamoTv-lil magaliTebSi saqme gvaqvs berketis sxvadasxva gamoy-enebasTan (sur. 69). grZel joxs sayrdeni wertiliT ber-kets uwodeben. es Zalian Zveli mowyobilobaa. Zveli droissirakuzelma udidesma meqanikosma da maTematikosma, ar-qimedem, berketis Sesaxeb Tqva: ̀ momeciT sayrdeni wertilida dedamiwas avwev!”

sayrdeni wertilidan (brunvis RerZidan) Zalis Tanx-vdenil wrfemde manZils Zalis mxari ewodeba. ramdenjer-ac metia erTi Zalis mxari meoreze, imdenjer SesabamisiZala naklebia meoreze.

maSasadame, berketiT vigebT ZalaSi, magram imden-jerve vagebT manZilSi. muSaobaSi arc vigebT da arcvagebT (roca xaxuni ugulebelyofilia).

esaa `meqanikis oqros wesi”.

73SeZlebda arqimede dedamiwis awevas?

graviura varinonas wignidan meqanikis Sesaxeb (1787)

sur. 70

5 7

cnobilia, rom berketi wonasworobaSia, Tu masze mode-boli Zalebis momentebi tolia (Zalis momenti aris Zalis modulisa da misi d mxris namravli: =d).

samyaroSi Cvengan yvelaze metad daSorebul obieqtam-de, kvazaramde, manZili 5_13 miliardi sinaTlis weliwa-dia. sayrdeni wertili rom hqonoda arqimedes, SeZlebdadedamiwis awevas berketiT?

dedamiwis masaa_6.1024kg, radiusi_6400km, s.w._s.w._s.w._s.w._s.w._arismanZili, romelsac sinaTle gaivlis weliwadSi. sinaTlissiCqare_300 000 km/wm. g ≈10m/wm2.

berketis (sur. 71) wonasworobis pirobis Tanaxmad:gR=x ⇒ x= gR/.

sadac g_dedamiwis simZimis Zalaa, _berketze ad-amianis moqmedebis Zala, x da R_berketze modebuli Zalebismxrebi. davuSvaT, adamians SeuZlia 1 000 n Zalis ganvi-Tareba, maSin:x ≈ (6.1024.10.6,4.106):1 000 ≈ 38,4.1028 (m) ≈ 38,4.1025 (km).

1 s.w.=300 000km/wm.(365.24.3 600wm) ≈ 12,5.1012 km.x ≈ 38,4.1025/12,5.1012 ≈ 3.1013 s.w.

amrigad, x manZili kva-zarebamde manZilze meti aR-moCnda (104-jer). cxadia, ar-qimede berketiT dedamiwis`awevas” ver SeZlebda.

74koWis Zafi.sxeulze moqmed Zalas, Tu misi Tanxvdenili wrfe sayrden

wertilze (brunvis RerZze) an masaTa centrze ar gadis,axasiaTebs mabrunebeli moqmedeba. igi xasiaTdeba fizikurisididiT _ momentiT: =d.

Caatare Semdegi cdebi da Seecade, axsna Sedegebi.1. aiRe Zafiani koWa da Zafi ise gawie, rogorc naCvenebia

sur. 72-ze. koWa gagordeba Sengan, iqiT. ratom?

sur. 71

5 8

2. axla Zafi ise gaswie, rogorc sur. 73-zea naCvenebi.am dros koWa Senken gamogordeba. ratom?

75berketiT yuTebis gaweva.magidis zedapirze devs ori erTnairi Zelaki da maT

Soris berketi (sur. 74), romelsac ewevian suraTze naCvenebimimarTulebiT. romeli Zelaki amoZravdeba, Tu maTi masaerTnairia?

Seni varaudi Seamowme cdiT da miRe-buli Sedegi daasabuTe msjelobiT:

1. magidis zedapirze dade daaxloe-biT ori erTnairi Zelaki (patara yuTian wignebi). berketad gamoiyene grZelisaxazavi an joxi. cda Caatare suraTismixedviT.

76xaxunis koeficientis gansazRvra asanTis kolofiT.ergvarovani Zelaki, romlis gverdi mniSvnelovnad

naklebia C-ze, moTavsebulia magidaze dadebul saxazavze(sur. 75). Zelakze fanqris wveriT moqmedeben monakve-Tis ( da wertilebi Sesabamisi wiboebis Suawertilebia) gaswvriv, magidis zedapiris paraleluri ZaliTda TandaTanobiT gadaadgileben Zalis modebis wertils-dan -isaken. wertilis axlos moqmedebisas ZelakigadataniT moZraobas asrulebs, xolo wertilTan mo-

sur. 73sur. 72

sur. 74

5 9

qmedebisas yiravdeba (waiqceva). moiZebneba Zalis moqmede-bis iseTi wertili, rodesac gadataniTi moZraoba Sew-ydeba da iwyeba waqceva. zomaven d= da a= man-Zilebs. daamtkiceT, rom xaxunis koeficienti μ gamoiTv-leba μ=a/2d formuliT.

1. Caatare cda magidis zedapirze asanTis kolofis,fanqris da saxazavis gamoyenebiT, zemoT aRwerili meTo-diT gansazRvre xaxunis koeficienti saxazavsa da asanTiskolofs Soris.

miRebuli Sedegi SeiZlebaSeamowmo sxva meTodiT (xerxiT),magaliTad daxrili sibrtyis gamoye-nebiT.

2. imave saxazavze igive gverdiTdadevi asanTis kolofi (sur. 76).TandaTan saxazavi ise daxare, romkolofma mudmivi siCqariT srialidaiwyos (mtkicdeba, rom aseT SemTx-vevaSi, xaxunis koeficientiμ=tgα=h/b. α _ daxrilobis kuTx-ea. Tu SeZleb, daamtkice). gazomedaxrili sibrtyis h simaRle,b_fuZis sigrZe da am formuliTgansazRvre xaxunis koeficienti.

Seadare orive meTodiT miRebu-li Sedegebi da Cawere rveulSi.

77nakadulze gadasvla.ori moswavle unda gadavides nakadulze: erTi marcxena

napiridan _ marjvenaze, meore _ sawinaaRmdego mimarTulebiT.orive napirze aris ficrebi, magram TiToeuli odnav mokleanapirebs Soris manZilze. moifiqre, rogor SeZleben isininakadulze gadasvlas?

sur. 75

C

C

α b

h

sur. 76

6 0

1. aiRe ori erTnairi si-grZis saxazavi. magidaze daa-lage wignebi or svetad ise, rommaT Soris manZili odnav metiiyos saxazavis sigrZeze (sur.77-is msgavsad), gamoiyene raimepatara tvirTi (magaliTad saTa-maSo kacuna an msgavsi ram). amsagnebis gamoyenebiT SeamowmeSeni varaudi.

78sxva martivi meqanizmebi.`meqanikis oqros wesi”: ramdenjerac vigebT ZalaSi, im-

denjer vagebT gadaadgilebaSi, anu muSaobaSi arc vigebT, arcvagebT. es aris zogadi kanonzomiereba ara marto berketi-saTvis, aramed nebismieri martivi meqanizmisaTvis (uZravi damoZravi WoWonaqi, owinari, daxrili sibrtye, xraxni, solida sxv.).

tvirTebis asawevad xSirad gamoiyeneba uZravi da moZraviWoWonaqebis erToblioba (tali_aseewodeba moZravi WoWonaqebis er-Tobliobas, romlebic SeerTebulia ram-denime uZrav WoWonaqTan). sur. 78-zetvirTi 6 Tokze kidia. cxadia, maTzedatvirTva Tanabrad nawildeba da TokisdaWimulobis Zala 6-jer naklebi iqnebatvirTis simZimis Zalaze. 1 t masis tvir-Tis asawevad saWiro iqneba10 000 n/6 ≈ 1666,6 n ≈ 1670 n Zala.

1. moifiqre, rogor SeaerTebdi moZravda uZrav WoWonaqebs, rom ZalaSi moigo3-jer; 5-jer? sqema rveulSi daxaze.

sur. 77

sur. 78

6 1

myari, Txevadi da gazurimyari, Txevadi da gazurimyari, Txevadi da gazurimyari, Txevadi da gazurimyari, Txevadi da gazurisxeulebis Tvisebebisxeulebis Tvisebebisxeulebis Tvisebebisxeulebis Tvisebebisxeulebis Tvisebebi

nivTierebis drekadobanivTierebis drekadobanivTierebis drekadobanivTierebis drekadobanivTierebis drekadoba

79gaecani foladis burTulas drekadobis Tvisebas.1. aiRe sqeli minis an foladis fila da minis mili

2_3 sm-is diametris, 60_80 sm-is sigrZis (rac ufro

grZeli iqneba, miT ukeTesia).

2. dade fila magar sayrdenze, xolo masze _ minis

mili vertikalurad. milis SigniT gauSvi burTulasakisa-

ris patara foladis burTula.

burTula, filaze davardnis Semdeg, maRla axteba.

3. gansazRvre, ra simaRleze axteba burTula filaze

pirveli davardnis Semdeg.

4. daTvale, ramdenjer axteba burTula. cda gaimeore

ramdenjerme.

mili dade sxvadasxva sxeulze (wignze, magidaze, bal-

iSze da sxv.) da gaimeore cda.

5. gaarkvie, romel SemTxvevaSi axteba burTula yve-

laze ufro maRla da romelSi sul ar axteba.

6. cdis Sedegebi Cawere rveulSi.

SeniSvna: cda SeiZleba Caataro Tanamedrove patara rezinis

an kauCukis burTiTac.

80gaarkvie wina cdis Sedegis mizezebi.1. dafiqrdi kiTxvaze, ratom xtis filaze

foladis burTula?

2. zusti kvlevebi uCvenebs, rom filaze dar-

tymis momentSi burTula CaiWyliteba, xolosur. 79

6 2

foladis drekadobis gamo Semdeg kvlav

miiRebs Tavis pirvandel formas (sur. 79)

3. analogiurad xdeba CogburTis Cogan-

Tan urTierTqmedebisas (sur. 80).

wnevawnevawnevawnevawnevacdebi wnevis gadacemazecdebi wnevis gadacemazecdebi wnevis gadacemazecdebi wnevis gadacemazecdebi wnevis gadacemaze

81Zalis moqmedebis damokidebuleba farTobze.1. wnevis SeswavlisaTvis xisgan (penoplastisgan) daamza-

de ori patara magida (sur. 81). TiToeuli magidis saxur-avis zomaa 10x10 sm (100 sm2).

pirveli magidis fexebi daamzade xisagan, TiToeulisigrZiT 6_7 sm da ganivWriliT 1 sm2; meore magidasgaukeTe lursmnis fexebi (lursmans fexebi kidev ufrowaumaxve qlibiT).

2. moamzade patara yuTi wvrili siliT. zedapirigaaswore horizontulad da cota daasvele.

3. moaTavse silaze pirveli magida fexebiT zeviT, dademasze rigrigobiT 20g, 500g, 1kg masis sawonebi da daakvir-di silaSi magidis CaZirvas.

4. silis zedapiri gaaswore. moaTavse igive magidasilaze fexebiT, daalage masze sxvadasxva masis sawonebida daakvirdi fexebis silaSi Caflobas.

5. moaTavse silaze meore magida fexebiT qveviT dagaimeore wina cda. Sedegi Seadare wina cdis Sedegs.

6. isargeble wnevis formuliT: p=/S, gansazRvremiRebuli wnevebi.

sur. 80

6 3

82gansazRvre Sen mier warmoebuli wneva sayrdenze.cxadia, am davalebis SesrulebisaTvis unda icode Seni

sxeulis m masa da fexebis sayrdeni S farTobi (ix.davaleba 15).

1. sayrdeni farTobi gansazRvre ise, rogorc me-15 davale-baSi;

2. sasworiT gaige Seni masa; gansazRvre sakuTari sim-Zimis Zala =mg;

3. gamoiyene wnevis formula da gansazRvre Sen mierwarmorbuli wneva dgomisas;4. Tu gaqvs Txilamurebi, Caatare Sesabamisi gazomvebi.gansazRvre wneva Txilamurebze dgomisas.

831. aiRe sabavSvo sahaero buSti, wamoacvi masze raime

mili da frTxilad Caasxi wyali. dainaxav, rom rezinisbuSti gamoibereba, ufro metad qveviT (sur. 82). buStirom ar gaskdes, dade magidaze. daakvirdi misi formisa damoculobis cvlilebas.

2. gadmoRvare wyali da gabere haeriT. daakvirdi buS-tis formisa da moculobis cvlilebas.

sur. 81

6 4

3. axla cariel buStSi Cayare wvrili sila ise, rombuSti magidaze idos. imoqmede masze raime ZaliT da daakvir-di, rom Zalva (dawola) gadaecema yvela mimarTulebiT.

rogor axsni am cdebis Sedegebs? raSia siTxisa dasilis msgavseba?SeniSvna: es cdebi SeiZleba Caataro celofanis (an polieTile-

nis) parkiTac.

841. axseni, sur. 83-ze naCvenebi sxeulebiT rogor gada-

ecema wneva.2. ganixile sur. 84.

pirvel suraTze ga-mosaxul cilindrulWurWelSi CadgmuliadguSi, cilindrSi, dgu-Sis qveS, fxvieri sx-eulia. dguSze dadebu-lia sawoni.

wnevis Zala (zeda-pirisadmi marTobuladmoqmedi), udris sa-wonisa da dguSis wo-nas. amrigad, wneva mo-

sur. 82

sur. 83

6 5

qmedebs vertikaluradqveviT, gadaecema fxvier sx-euls, e.i. agreTve qveviT.magram fxvieri sxeuli wne-vas gadascems ara martoqveviT, aramed _ sxva mxa-reebisakenac.

meore suraTze gamo-saxulia igive cilindri,magram axla cilindrSisiTxe asxia. siTxe, iRebsra wnevas dguSisagan, amwnevas gadascems yvela mimarTulebiT Tanabrad da ucvle-lad.

mesame suraTze Sen xedav e.w. paskalis sferos. aq wne-vas awarmoebs adamianis kunTebi, romelic awveba dguSissaxelurs. dguSi gadascems wnevas siTxes, xolo siTxe amwnevas gadascems yvela mimarTulebiT (yvela wertilSi)ucvlelad, amitom paskalis sferos xvrelebidan siTxisWavlebi yvela mimarTulebiT erTnairad gamoedineba.

3. Zalian martivad da swrafad SegiZlia, daamzado xel-sawyos _ paskalis sferos modeli: amisaTvis gamoiyene samed-icino Sprici 10_20 mg-iani (rac ufro didi iqneba, miTukeTesia) da magidis CogburTis burTi (`pingponkis” plas-tmasis burTi, an `qinderis” plastmasis kolofi).

sur. 84

sur. 85

5 jemal kiknaZe

6 6

4. plastmasis burTi mxvili nemsiT (maxaTiT an lursm-niT) ise gaxvrite, rom nemsis magivrad mWidrod wamoecvasSpricze. burTs wvrili nemsiT 7 naxvreti gaukeTe erTsibrtyeSi (burTis nawiburis gaswvriv).

5. Spricis bolos wamoacvi plastmasis burTi da daawebe.Spricidan amoaZvre dguSi, cilindrSi Caasxi wyali da burT-Tan erTad bolomdis aavse. Semdeg dguSi Tavis adgilzeCasvi. daaweqi dguSs da dainaxav, rom burTis yvela xvrel-idan erTnairi WavliT gamoasxams wyali (sur. 85).

85daamzade paskalis kanonis sademonstracio xel-

sawyo.am xelsawyosaTvis dagWirdeba polieTile-

nis 1,5 litriani boTli (koka-kolas, fantasan borjomis), minis an polieTilenis (po-lipropilenis) gamWvirvale milebi.

1. daamzade xelsawyo ise, rogorc sur. 86-zea naCvenebi.

2. boTli mTlianad _ aavse wyliT. cxadiamilebSi wyali erT doneze dadgeba, ziarWur-Welis kanonis Tanaxmad. boTls Tavi mWidroddaaxure.

3. daaweqi boTls amiT Sen awarmoeb wnevaswyalze. es wneva yvela mimarTulebiT Tanabradrom gadaecema, amas uCvenebs milebSi wylis iseverT doneze dadgoma.

86hidrostatikuri wnevis demonstracia.1. polieTilenis boTls sxvadasxva simaRleze max-

aTiT gaukeTe ramdenime xvreli (ori an sami). Caasxi boTlSiwyali da daakvirdi xvrelebidan gamosuli wylis Wavlis

sur. 86

paskaliskanonis

sademonstra-cio xelsawyo

6 7

formasa da mimarTulebas (sur. 87). axseni ratom aqvswyals ufro meti siCqare qveda xvrelidan gamodinebisas?wylis gamodenis procesSi didi TiTiT daaweqi boTlisyels. ra moxda? ratom Sewyda xvrelebidan wylis gamod-ineba?

2. boTlis yels mouWire tuCebi da Zlierad CaberemasSi haeri (sur. 88). rogor gamoedinebian wylis Wavle-bi? rogor gadascems wyali im wnevas, romelsac Sen awar-moeb masze SekumSuli haeriT?

87simon stevinis cda da hidrostatikuri paradoqsi.1. aiRe ganieri minis mili, magaliTad, SeiZleba navTis

lampis SuSis gamoyeneba. mis qveda xvrels miadevi mkvrivimuyaos (an minis) wre da TiTiT daWerili CauSvi wylianWurWelSi (sur. 89).

sur. 87 sur. 88

sur. 89

6 8

2. wylis SigniT muyaos moacile TiTi. muyao mils armoSordeba, radgan mas qvevidan (paskalis kanonis Tanax-mad) awveba siTxis wneva.

3. Caasxi milSi wyali (ukeTesia SeRebili) da daakvirdiwris moSorebis moments. milisagan wre im momentSi iw-yebs moSorebas, roca milSi wylis done WurWelSi wyl-is dones gauTanabrdeba.

4. maSasadame, eqsperimenti uCvenebs, rom fskerze moqme-di siTxis wnevis Zalebi qvevidan da milSi zevidan (e.i.siTxis vertikaluri svetis wona =ρghS, sadac S fsk-eris farTobia) tolia. (atmosferuli wneva milis Sig-niT da gareT tolia, amitom maTi moqmedeba erTmaneTsakompensirebs). es asec unda iyos, radgan fskeris donezehidrostatikuri wneva (p=ρgh) WurWelsa da milSi to-lia.

5. Tu am cdas CavatarebT fuZeSi erTnairi diametrismqone xvreliani, magram sxvadasxva formis minis milebiT(lampis SuSiT, cilindruli miliT, Zabriseburi miliT),Sedegi igive iqneba. xolo, Tu samive cdis dros muyaosfskeri erTsa da imave h siRrmeze iqneba, e.i. qvevidanmoqmedi wnevis Zalebi toli iqneba. gamova, rom milisSigniT sxvadasxva wonis siTxe eTnairi ZaliT awveba fskers,es ki hidrostatikuri paradoqsia (ar Seesabameba Cveulebrivwarmodgenas).

sur. 90

6 9

6. sinamdvileSi, aq araviTari paradoqsi ar aris. axsnaSeiZleba paskalis kanoniT_siTxeze warmoebuli wneva yve-la mimarTulebiT Tanabrad gadaecema; amitom awveba sxva-dasxa formis WurWlis daxril kedlebs, romlebic Tavismxriv, awvebian WurWelSi siTxes da akompensireben zedmetan nakleb dawolas fskerze (sur. 90).SeniSvna: 1586 wels holandielma mecnierma (maTematikosma,

fizikosma, inJinerma) simon stevinma (1548-1620) aR-moaCina siTxeebis wnevis kanoni, ziarWurWelis kanoni

da hidrostatikuri paradoqsi.

88ziarWurWeli.kedelze suraTi sworad rom dakido, dagWirdeba

vaterpasi (ix. 28, horizontulobis Sesamowmebeli xel-sawyo). magram amisaTvis SegiZlia daamzado Zalian mar-tivi mowyobiloba:

1. aiRe plastmasis naxevarlitriani borjomis (fan-tis, koka-kolas da sxv.) ori boTli. orives moaWerifskeri, maTi saxuravebi gaxvrite da miRebul xvrelebSimWidrod gauyare minis (an plastmasis_pastis saweriscilindruli tarisagan gamoWrili) 4_5 sm sigrZisa da8_10 mm diametris milebi. am milebze wamoacvi polipro-pilenis (gamWvirvale) 40_50 sm sigrZis mili (maTi SeZenaSeiZleba saafTiaqo maRaziebSi an bazrobebze). xelsawyo`ziarWurWelis moqmedi modeli” ukve mzadaa (sur. 91).

sur. 91

7 0

2. aseTi xelsawyos damzadeba ufro martivad SeiZle-ba: aiRe minis 40_50 sm sigrZis milebi da SeaerTe rezinismiliT (sur. 92). SeiZleba gamoiyeno mxolod polipro-pilenis gamWvirvale mili.

3. Caasxi ziarWurWelSi siTxe (wyali). amoZrave boT-lebi (milebi) da Seamowme ziarWurWelis kanoni: erTg-varovani siTxe ziarWurWelSi erT doneze dgeba. es doneyovelTvis horizontulia.

4. axla Sen advilad Seamowmeb, sworad kidia Tu arasuraTi kedelze.

89daamzade wyalmzomi milis modeli.1. gamoiyene maRali liTonis qila da minis mili. minis

milis moxra sasurveli kuTxiT SeiZleba gazquris anspirtquris alze misi nel-nela gaxurebiTa da Tanda-TanobiT moxriT. daamzade modeli sur. 93-is mixedviT.

sur. 92

sur. 93a

b

7 1

90daamzade Sadrevnis modeli.1. aiRe plastmasis boTli da moaW-

eri mas fskeri. misi plastmasis sax-uravi ise gaxvrite, rom masSi mWidrodgaeyaros sxvadasxva siTxis sasmeladgamosayenebeli wveli, romelic mo-Runulia ̀ Ï” asos msgavsad (sur. 94).

2. milis xvreli daxure TiTiT,aavse boTli wyliT. xvrelis gan-Tavisuflebis Semdeg SadrevaniamuSavdeba da manam imuSavebs, sanam wy-lis done boTlSi ar gauTanabrdeba milis Ria bolos.axseni, ratom xdeba ase?

3. Sen, albaT, mixvdi, rom Cveni pirveli Sadrevani muSaobsziarWurWlis kanonis Tanaxmad: ufro maRali donis Wur-Wlidan wyali gadadis milSi. is cdilobs, avides milSiimave doneze. magram mili Tavdeba _ Cndeba wylis Sadre-vani. SegiZlia Seamowmo, rom Sadrevani adis did WurWel-Si wylis donemde.

4. ziarWurWelis kanonzea damyarebuli wyalsadenismowyobiloba da muSaoba. es Zalian Zveli gamogonebaa.pirveli umartivesi wyalsadeni agebuli iyo ramdenimeaTasi wlis ukan. Zvel egvipteSiMmiwisqveSa wyali RrmaWebidan amohqondaT wyalsawevebiT da keramikuli an xismilebiT miewodeboda momxmarebels. Zvel romSi gamoiyene-boda ufro rTuli sistema, akvedukebi (Rarxidebi)_saxidenagebobebi, milsadenebis gadasayvanad xevebze, mdinareebze,gzebze da a.S.

parizSi wyalsadenebi xis milebiT agebuli iyo XVIIsaukunis bolos. XVIII saukuneSi_inglisSi, moskovSi_1804w., peterburgSi_1861 w., xolo litvaSi (vilniusSi) wyal-sadenis ageba daiwyes 1501 w.

sur. 94

7 2

saqarTvelos istoriidan SenTvis cnobilia, rom varZi-is gamoqvabulTa kompleqsis mSenebloba daiwyo mefe gior-gi III-is sicocxleSi. aSenda TiTqmis ori mesamedi. 1184wels, mamis gardacvalebis Semdeg mSenebloba gaagrZelamisma erTaderTma memkvidrem, mefe Tamarma. amave kompleqsSimanve daaarsa RvTismSoblis saxelobis samefo taZari (1184-1186 ww.). varZiis arqiteqturuli ansamblis (samefo cixe-simagre da taZari) mSenebloba mimdinareobda 48 wlisganmavlobaSi (1156-1204 ww.). omis dros am cixe-simagre-Si eteoda daaxloebiT 45_50 aTasi meomari. varZiis samo-nastro meurneoba maragdeboda sxvadasxva saSualebiT dasasmeli wyliT. jer kidev mefe giorgi III-is dros kldiscentralur nawilSi aRmoaCines wyaro. gaWres 16 metrisigrZis gvirabi da moawyves wylis Semgrovebeli avzi.dRevandlamde es wyaro dReRameSi iZleva 52_55 l wyals.magram mas ar SeeZlo qalaqis dakmayofileba. amitom Tam-aris dros gayvanili iqna samkilometriani wyalsadeni,romliTac dReRameSi moedineboda 155_160 aTasi litriwyali.

5. milsadenebsa da, Semdeg, SenobebSi wyali miedineba

wyalsacavebidan an wyalsawnevi koSkebidan, romlebsac maRal

adgilebze ageben. wyali milsadenebiT adis Senobis maRal

sarTulebze; mTavaria, es sarTuli ar iyos wyalsawnev

koSkze maRali. onkanis gaRebis Semdeg is daiwyebs muSaobas,

rogorc Cveni Sadrevani boTlidan.

marTalia, Sadrevanisagan gansxvavebiT, onkanis xvreli

qveviTaa daxrili, magram moxmarebisaTvis ase ufro ukeTe-

sia.

7 3

curva da CaZirvacurva da CaZirvacurva da CaZirvacurva da CaZirvacurva da CaZirva

91daamzade xelsawyo `̀̀̀̀arqimedes vedro””””” da Seamowme

arqimedes kanoni.1. iSove didi kartofili, sigrZiT 8-10 sm. kargad

galesili daniT moaWeri kartofils napirebi ise, rommagidaze daidgas (sur. 95).

2. aiRe erTjeradi 20 ml-iani (SeiZleba 10 ml-ianic)samedicino Sprici. Spricis cilindri, rac SeiZleba, fsker-Tan axlos imave daniT gadaWeri, cilindrs napirebi usa-frTxo samarTebliT waumaxve.

3. Spricidan dguSi amoaZvre, cilindriT daaweqi karto-filis erT-erT waWril kides, abrune is xan marjvniv, xan_ marcxniv da gaukeTe kartofils gamWoli cilindrulixvreli.

4. amoaZvre cilindri kartofilidan. mas gamohyvebakartofilidan amoWrili cilindruli Rero. gaxvretilikartofilis napirebi gaaswore, SeiZleba, mas Zelakis for-ma misce.

5. frTxilad daaweqi dguSs da Spricis cilindridangamoaZvre kartofilidan amoWrili cilindruli formisRero.

6. am Reros moaW-eri 2 sm sigrZis pat-ara cilindri. daaxviemasze qaRaldi (an ce-lofani) da, rogorcsacobi, gaukeTe karto-filis xvrels, romxvrelma wyali ar gaa-taros. Casvi karto-filSi mavTulisagan

sur. 95

7 4

damzadebuli rka-liseburi maryuJi.miiReb kartofil-is patara vedros.

7. kartofil-is Rero vedrosfskerTan daakav-Sire 1 mm diame-trisa da 7_8 sm

sigrZis mavTuliT (ubralod wamocmiT). vedros mavTu-lis maryuJze moabi 15_20 sm sigrZis rezinis Zafi.

8. SpricSi dguSi daayene kartofilis Reros sigrZistol manZilze (am dros Reros moculoba dguSis qveviTcilindris moculobis toli iqneba). arqimedes vedrorezinis ZafiT dakide skamis fexebis samagrze da iqvedaamagre saxazavi (sur. 96, a).

9. frTxilad Seudgi qvevidan kartofilis Reroswyliani Wiqa ise, rom Rero mTlianad CaiZiros wyalSi.rezinis Zafi damokldeba, radgan wyali Reroze amomgdebiZaliT imoqmedebs (sur. 96, b).

10. moaSore wyliani Wiqa. Zafi kvlav dagrZeldeba.cilindruli Rero isev CaZire wyalSi.

11. datove Rero wyalSi. SpricSi DdguSis gaunZrev-lad Caasxi wyali. cxadia, (Tu Spricis kedlebis moculo-bas mxedvelobaSi ar miviRebT) am wylis moculoba karto-filis cilindruli Reros moculobis toli iqneba (eski _ gamoZevebuli wylis moculobis toli). axla wyaliSpricidan Caasxi vedroSi (xvrelSi). dainaxav, rom cdiscdomilebis farglebSi rezinis Zafi Tavdapirvel sigrZemdegaiWimeba (sur. 96, g).

e.i. siTxeSi GaZirul sxeulze moqmedebs zeviT mi-marTuli amomgdebi Zala, romelic sxeulis miergamoZevebuli siTxis wonis tolia.

sur. 96

a b g

7 5

92cdiT daamtkice, rom siTxis zedapirze mcuravi

sxeuli imdens iwonis, ramdensac _ mis mier gamoZeve-buli siTxe.

1. gluvi saxazavi furclisagangamoWeri 20X20 sm zomis kvadrati.gadaRune is im xazebze, rogorcnaCvenebia sur. 97 da gaakeTe misgankvdratuli yuTi, romlis gverdebseqneba 5 sm simaRle, xolo fuZis far-Tobi iqneba 1 dm2 (10X10 sm). yuTisdawepeba araa saWiro (sakmarisia sa-magriT damagreba).

2. yuTi dade did qvabSi moTavse-buli wylis zedapirze. frTxiladdaade yuTis fskers SuaSi 100 g-ianisawoni (an tvirTi). yuTi mciredCaiZireba wyalSi (sur. 98). dainiSneyuTis wyalSi CaZirvis siRrme da ga-zome CaZiruli nawilis moculoba.

TiToeuli gverdi CaiZireba 1 smsiRrmeze. ase rom, yuTis CaZirulinawilis moculoba V=s.h==100 sm2 . 1 sm=100 sm3, xolo gamoZeve-buli wylis masa 100 g udris. maSasa-dame sawonisa da gamoZevebuli wyl-is simZimis Zalebi (maTi wonebic)1 n-is toli iqneba.

93daamzade areometris modeli.1. aiRe Txelkedliani sinjara da masSi imdeni safanti

Cade (an tyviis naWrebi, foladis burTulebi, patara lursm-

sur. 98

sur. 97

7 6

nebi da sxv), rom sinjara wyalSi vertikalu-rad idges. simZimis gasamagreblad Cayare masSisanTlis naWrebi da gaaTbe mis gadnobamde,Semdeg gaacive.

2. qlibiT aRniSne sazRvari (wylis done)wyalqveSa da wyalzeda nawilebs Soris(1 g/sm3).

3. imave tvirTiani sinjara CauSvi zeTSi;isev qlibiT aRniSne misi CaZirvis siRrme(0,9 g/sm3).

4. bolos, igive sinjara imave tvirTiTCauSvi navTSi (0,8 g/sm3) da Seasrule igivedavaleba (sur. 99).SeniSvna: ukeTesia, aiRo mokle sinjara (6 sm

sigrZis) da mis Ria boloSi Caamagro

(an Caawebo) sxvadasxva siTxis sasmeli plastmasis

msubuqi wveli; agreTve, SeiZleba gamoiyeno mcire

moculobis grZeli samedicino Sprici (mag. diabetiT

daavadebuli avadmyofebisaTvis), winaswar saWiroa

sanemse xvreli daixuros. SeiZleba, gamoiyeno peno-

plasti, romlisganac daamzadeb 1 X 1 sm kvadratuli

kveTis Reros, romlis erT-erT boloze sWvaliT

daamagreb tvirTs (mag. qanCs).

94daamzade hidrostatikuri saswori.1. aiRe penoplastis firfita da gamoWeri

misgan 1 X 1 sm kvadratuli kveTis Rero. miserT boloze sWvaliT daamagre qanCi, xolo meo-reze _ platforma, muyaos patara firfita.

2. CauSvi Rero wylian boTlSi (sur. 100).saswori ukve mzadaa, magram winaswar saWiroamisi dagraduireba. cxadia, aseTi ganivWrilisReros yovel santimetrze CaZirvas Seesabamebasasworis 1 g masiT datvirTva.

sur. 99

sur. 100

7 7

95sami burTula.1. aiRe erTnairi zomis sami burTula: erTi foladis,

burTulasakisarisagan, meore gamoZerwe parafinisagan (iyidebaafTiaqebSi) an sanTlis stearinisagan, mesame gamoWerikorpisagan, penoplastis an romelime msubuqi masalisagan.

2. garecxe maionezis qila an gadaWeri romelime plas-tmasis boTli, rom miiRo plastmasis Wiqa. Caasxi wyalidaaxloebiT naxevramde da masSi CauSvi samive burTula.ra mouva maT?

3. cxadia, foladis burTula CaiZireba, radgan foladimZimea wyalze (foladis simkvrive metia). xolo parafinida korpi itivtivebs.

4. daasxi wyals zevidan navTi an romelime zeTi. navTida zeTi wyalze msubuqia (simkvrive aqvs naklebi), arixsneba wyalSi; amitom moeqceva wylis zeviT da kargadgamoCndeba maTi sazRvari. am zedapirze aR-moCndeba parafinis burTula. misi qvedanawili iqneba wyalSi, zeda_navTSi. parafi-nis burTula navTis zedapirze ar amotiv-tivdeba, radgan parafini wyalze msubuqia,xolo navTze_mZime. magram korpis burTu-la ki navTSic curavs (sur. 101).

96kvercxi marilian wyalSi.1. aiRe ori naxevarlitriani qila, erTi aavse sufTa

wyliT. CauSvi masSi mouxarSavi kvercxi. is CaiZireba, daeSvebafskerze.

2. meoreSi Caasxi Zlier mariliani xsnari. naxevarlitrze sakmarisia 2 sufris kovzi marili, rom kvercxicuravdes. ase imitom xdeba, rom mariliani wyali mZimea.amitomaa zRvaSi curva advili, vidre _ mdinareSi.

sur. 101

7 8

3. axla aiRe erT litri-ani qila, gadaitane masSi kver-cxi da daasxi rigrigobiTorive qilidan siTxe. SegiZlia,miiRo iseTi siTxe, romelSickvercxi arc icuravebs da arcdaeSveba fskerze _ siTxis Sua-Si gaCerdeba (Sewonil mdgo-mareobaSi iqneba), rogorc dak-idebuli (sur. 102).

4. Tu am mdgomareobaSi daumateb sufTa wyals, kver-cxi CaiZireba, xolo Tu marilian wyals Caasxam, kvercxiamotivtivdeba! ratom xdeba ase?SeniSvna: analogiuri cda SeiZleba Caataro kartofilis gamoy-

enebiT, magram meti marili iqneba saWiro, vinaidan

kartofilis simkvrive metia kvercxis simkvriveze.

97rogor manevrirebs wyalqveSa navi.Sen ici, rom gaziani, xiliani da mineraluri wyali,

romlebic boTlebiT iyideba, wnevis qveS gajerebulia gaziT.boTlis gaxsnisas siTxidan gazi gamoiyofa.

1. Caasxi axalgaxsnili borjomis wyali WiqaSi daCaagde masSi yurZnis marcvali. is wyalze mZimea da CaiZireba,daeSveba fskerze. magram masze maSinve dasxdebian gazisbuStebi, rogorc haeris patara burTulebi, imdeni, romyurZnis marcvali amotivtivdeba.

2. magram zedapirze buStulebi gaskde-ba, gazi gamoiyofa. damZimebuli marcvalikvlav CaiZireba. isev garSemoekvreba maszebuStebi, marcvali amotivtivdeba da ase gagr-Zeldeba ramdenjerme, sanam siTxe gazisaganar daicleba (sur. 103).

sur. 102

sur. 103

7 9

aqvs Tu ara raime saerTo ganxilul cdas wyalqveSanavTan?

3. aseT navs SigniT aqvs specialuri cisternebi, rom-lebsac avseben wyliT (balastiT_tvirTiT). navi damZim-deba da daeSveba qveviT. rodesac navis zeviT amosvlaasaWiro, SekumSuli haeriT cisternebidan gamodevnian wy-als, mis adgils haeri daikavebs. navi msubuqi gaxdeba dazeviT amodis.

98Tevzis GaZirva da amotivtiveba.1. icvlian Tu ara Tevzebi CaZirvis siRrmes ise, rogorc

es xdeba wyalqveSa navSi? icvlian Tu ara isini amisaTvissacuravi buStis moculobas? xSirad swored amiT xsnianTevzebis curvas wyalqveS. magram es araa swori, radganTevzs ar SeuZlia kunTebiT marTos Tavisi sacuravi buS-ti. maSin rogor curavs Tevzi wyalqveS?

Tevzebi ver itanen siRrmis swraf cvlilebas. magali-Tad, napirze swrafad amoyvanisas kvdebian (zogjer buStiuskdebaT). magram did siRrmeebze maT cxovreba SeuZliaTda itanen Zalian did wnevas: magaliTad, 5 000 m siRrmezewneva aRwevs 500 atm. (e.i. normalur atmosferul wnevaze500-jer mets). rogor uZleben Tevzebi aseT did wnevas?

2. sacuravi buSti uzrunvelyofs Tevzis nulovan curvas,romlis gamo is ar amotivtivdeba zedapirze da ar iZire-ba fskerze. davuSvaT Tevzi micuravs qveviT. zrdadi wnevakumSavs gazs buStSi. Tevzis moculoba, da masTan erTadcurva mcirdeba da, rom ar CaiZiros, Tevzs uxdeba farflebismoZraoba. magram, amis garda Tevzi gamoyofs gazs sacuraobuStSi ise, rom misi moculoba TiTqmis mudmivi rCeba.amitom, miuxedavad gareSe wnevis gazrdisa, Tevzis mocu-loba mudmivi rCeba da amomgdebi Zala ar icvleba. Tevzisamotivtivebisas buStidan gazis nawili gamoiyofa, amiTamomgdebi Zala ucvleli SenarCundeba.

8 0

99karteziuli myvinTavi.1. aiRe plastmasis boTli (mag. koka-kolas, fantas,

borjomis da sxv.). Caasxi masSi wyali ise, rom sul ar

gaavso.

2. tivtivad gamoiyene Cveulebrivi samedicino pipeti

(TvalSi wamlis CasawveTebeli). Seiwove masSi cota wya-

li da CauSvi wylian boTlSi ise, rom gaCerdes raRac

siRrmeze (sur. 104, a). boTls xraxniani Tavsaxuri mWidrod

daaxure.

3. mouWire boTls xeli (SekumSe), dainaxav, rom tivtiva

CaiZireba. xelis gaSvebisas amotivtivdeba (sur. 104, b). ra-

tom?

4. cxadia, boTlze xelis moWer-

isas izrdeba boTlSi haeris wneva,

paskalis kanonis Tanaxmad, wneva gada-

ecema yvelgan. amitom pipetSi meti

wyali Seva da damZimdeba, ris gamoc

CaiZireba. boTlze xelis gaSvebisas

wneva Semcirdeba, pi petSi wylis

Tavdapirveli done aRdgeba da tiv-

tiva Tavdapirvel mdebareobas daika-

vebs.

pirvelad aseTi xelsawyo daamza-

da frangma mecnierma da filoso-

fosma rene dekartim, amitom aseT xe-

lsawyos `karteziul myvinTavs”

uwodeben (`rene dekarti” laTinurad

JRers rogorc ̀ renatus kartezius”).

SeniSvna. SeniSvna. SeniSvna. SeniSvna. SeniSvna. tivtivad SeiZleba gamoiy-eno patara sinjara, wamlis SuSa, saw-eri pastis saxuravi da sxv.

sur. 104

a

b

8 1

100rkina curavs.jek londonis erT-erT moTxrobaSi saubaria imis Sesax-

eb, rom eskimosebma ar daujeres Tavis Tanatomels, romel-mac maT uambo, rom TeTrkanian adamianebs aqvT rkinisagandamzadebuli xomaldi, romelic curavs. eskimosebma mTxro-bels crupentela daarqves, amtkicebdnen, rom es ar Sei-Zleba, radgan rkina wyalSi iZireba. ra Secdomaa mocemulmsjelobaSi?

1. Caagde wyalSi lursmani, sWvali, foladis burTu-la_yvela imwuTas CaiZireba. gamoWeri konservis qilisa-gan kvadratuli firfita da Caagde wyalSi_isic CaiZireba,rogorc liTonis yvela sagni: mag. najaxi, sawoni.

2. moxare es firfita, gaa-keTe kolofi da Cade wyalSi(sur. 105). xedav, curavs! axlaam kolofSi SeiZleba Caalagolursmani, sWvali, burTula, isufro metad Cajdeba wyalSi, ma-gram fskerze ar daeSveba.

ase curaven zRvebsa daokeaneebSi foladis gemebi, rom-lebic datvirTulia: manqanebiT,qvemexebiT, jaWvebiT, RuzebiT dasxvadasxva tvirTiT!

3. albaT, xvdebi, ratom xdeba ase? foladis gemebSiaris haeri. is ikavebs did adgils (moculobas), rogorcuzarmazari mcuravi buSti. Tu haeris magivrad iq Sevawyali, maSin gemi CaiZireba.

4. marTlac, amaSi rom darwmunde, gaukeTe kolofsxvreli qvevidan da gaimeore cda. naxav, TandaTan rogorCaiZireba kolofi. zogjer ase `iRupebian~ gemebi, Tu maTgauCndebaT naxvreti.

sur. 105

6 jemal kiknaZe

8 2

101wyals kani aqvs?albaT, ifiqreb: ra ucnauri kiTxvaa?_ra Tqma unda, ara.Caatare ramdenime martivi cda da Seni Tavdajerebu-

loba Seiryeva.1. Caasxi WiqaSi wyali zeda kidem-

de ise, rom galiclicdes. SearCie ram-denime patara moneta (TeTrebi) dafrTxilad CauSvi isini wyalSi erT-maneTis miyolebiT. wyliT savse Wiqa-Si Caeteva arcTu cota moneta, sanamwyali Wiqidan gadmoiRvreba (sur. 106).

2. sad midis zedmeti wyali? Wiqa-Si ramdenime monetis Cagdebis Semdegdajeqi ise, rom Tvali gauswordes

Wiqis napiris dones. dainaxav, rom wylis zedapiri gaxde-ba amoburculi, e.i. gaCnda wylis burcobi. rac ufro metmonetebs Cayri, miT ufro maRali iqneba burcobi. is ibereba,rogorc sahaero buSti, romelsac aqvs `kani”, esaa misi`rezinis~ garsi.

3. wyals? mas xom kani ar aqvs? magram, wyali iseiqceva, TiTqos mas garsi hqondes. romeliRac monetaze esuxilavi garsi gaskdeba da wyali Wiqis napirebidan gadmo-iRvreba. wylis burcobi maSinve vardeba, TiTqos buStigaskda.

102foladi, romelic wyalSi ar

iZireba.1. nemss wausvi cximi (mag. saWme-

li zeTi) da Zalian frTxilad dadewylis zedapirze. moxerxebelia Can-glis gamoyeneba. nemsi moaTavse Can-

sur. 106

sur. 107

8 3

galze da Cangali wyalSi CaZire; is nel-nela moabrunegverdze. rodesac moaSoreb Cangals, nemsi aRmoCndeba wyl-is zedapirze (sur. 107).

2. foladi wyalze mZimea, maSin rogor SeuZlia maswyalSi curva? kvlav dajeqi da sinaTlis sawinaaRmdegodSexede `mcurav” nemss. dainaxav, rom wylis zedapiriCaRunulia nemsis simZimis gamo. maSasadame, nemsi ar curavs.is devs wylis zedapirze, rogorc drekad afskze. sakmari-sia erTi arafrTxili moZraoba, biZgi da afski gaixeva.nemsi CaiZireba fskerze. wyals aqvs Zalian susti afski,magram faqtia, rom is arsebobs_uxilavi drekadi afski.

3. Sen, albaT, daginaxavs tboris wylis zedapirze rogordasrialeben mwerebi_wyalmzomela. SeiZleba dainaxo, rogoriRuneba wylis zedapiri.SeniSvna. wylis zedapirze SeiZleba dado foladis usa-

frTxo samarTeblis piri, xolo am SemTxvevaSi saWiro

iqneba ufro ganieri wyliani WurWeli, mag. TefSi.

103korpi, romelic ar tivtivebs.wylis zedapirze uxilavi afski ewinaaRmdegeba wnevas

ara marto zevidan, aramed qvevidanac. es Sen dainaxe mon-etebiT Catarebuli cdis dros. Caatare kidev erTi cda:

1. wvrili, SiSveli an emalirebuli mavTulisagan mo-Rune 8 sm diametris rgoli. kidev sami mavTulisagandaamagre es rgoli korpis sacobze an penoplastis naW-erze. rgols TiTebi wausvi, rom cota gacximiandes. Sem-deg dadevi rgoli magidis zedapirze da kargad gaaswore.

2. korps qvevidan miamagre raime tvirTi ise, rom Senitivtivas rgoli wylis zedapiridan daSordes 8_10 mm-ismanZiliT.

3. Semdeg tivtiva CaZire wyalSi mTlianad. is cdi-lobs amotivtivebas, magram amas veRar axerxebs! mas akavebs

8 4

wylis zedapiruli afski. Tu

gverdidan gaxedav, dainaxav, rom

wylis zedapiri rgolTan amobur-

culia zeviT, rogorc rezinis af-

ski (sur. 108).

haeri da misi Tvisebebihaeri da misi Tvisebebihaeri da misi Tvisebebihaeri da misi Tvisebebihaeri da misi Tvisebebi

1041. aiRe Wiqa da Tavdayira (fskeriT zeviT) nel-nela

CauSvi maRal wylian qilaSi.2. daakvirdi, ramdeniT Sedis WiqaSi wyali. ra mosdis

am dros haers?

1051. aiRe Zabri, wamoacvi masze rezinis mili, xolo mi-

lis meore boloze_ pipetis SeviwrovebulTaviani mina.2. Zabri wylian WurWelSi nel-nela CauSvi, xolo min-

is mili daikave wyliani Wiqis zeviT ise, rom milisSeviwrovebuli bolo iyos wyalSi 1-2 mm-is siRrmeze(sur. 109).

3. yuradRebiT daakvirdi, rogor gamodis milisbolodan haeris patara buStulebi.

sur. 108

sur. 109

8 5

106mamaci myvinTavi.1. qaRaldisagan gamoWeri kaci

sur. 109, a-s mixedviT. plastili-nis saSualebiT daamagre korpzean penoplastis naWerze.

2. Caasxi TasSi wyali da CademasSi korpze damagrebuli kaci.xedav, is curavs.

3. daaxure mas zemodan Wiqada nel-nela CaZire Wiqa Tasisfskeramde. myvinTavi masTan erTad CaiZireba fskeramde.

4. nel-nela amowie Wiqa da amoiRe wylidan. myvinTaviamotivtivdeba. ase SeiZleba, fskerze CaiZiron cocxaliadamianebi, rodesac isini muSaoben wylis fskerze, mag.,rodesac isini ageben xidebis sayrdenebs. am dros muSebiimyofebian rkina-betonisagan an liTonisagan damzadebulTavdayira dayenebul yuTSi (mas kesonikesonikesonikesonikesoni ewodeba).

masSi didxans muSaoba mZime daavadebas iwvevs _ keso-nis daavadeba.

1071. gaakeTe Zabri sqeli da gluvi qaRaldisa-

gan an celofanisgan, mWidrod moaTavse is boT-lis yelSi da Caasxi masSi wyali (sur. 110).

2. ratom ar Cadis wyali boTlSi?3. rogor gamoiyenebdi wvels am dros, rom

wyali Tavisuflad Cavides boTlSi?

1081. aiRe patara cilindruli

Wiqa, moaTavse masSi korpis saco-bi napirTan da Wiqa miitane pir-Tan (sur. 111).

sur. 109 a

sur. 110

sur. 111

8 6

2. Cabere WiqaSi da axseni, ratom gamovardeba sacobiWiqidan?

109daamzade heronis (Zveli berZeni mecnieri) Sa-

drevani.1. sqelkedliani boTlis sacobSi gaatare minis mili

da boTlSi Caasxi imdeni wyali, rom milis bolo wyalSiCaiZiros (sur. 112,a).

2. Semdeg piriT orjer-samjer CabereboTlSi haeri; yoveli Cabervis win daaweqimilis bolos. auSvi xeli da daakvirdi Sa-drevans (sur. 112,b).

3. ufro Zlieri Sadrevnis misaRebad milSihaeris Casatumbad gamoiyene saWirxni tumbo(mag. velosipedis an manqanis). magram am drossacobis xeliT dakaveba iqneba saWiro. agreTve,frTxilad unda viyoT, rom boTli ar gaskdes.

4. axseni movlena. sad iyeneben analogiurmovlenas?

110axseni Semdegi sami cdiT miRebuli Sedegebi (sur. 113 ):

Tu aertumbos zarxufidan gamotumbaven haers, maSin saco-bi amovardeba; rezinis sahaero buSti ibereba; wyali sa-cobiT daxuruli WurWlidan miliT gadaisxmeba WiqaSi.

sur. 112

a b

sur. 113

8 7

111daamtkice, rom haers aqvs masa.1. erTi metri sigrZis joxze dakide fexburTis gaub-

eravi burTi da raime tvirTis gamoyenebiT gaawonasworeskamis zurgze (sur. 114). zustad aRniSne joxze sayrdeniwertili.

2. aiRe saWirxni tumbo da kargad gabere burTi, Semdegdakide joxze imave adgilze da joxi dade skamis zurgzeigive sayrdeni wertiliT. ratom irRveva wonasworoba?

112atmosferuli wneva. sami cda WiqiT.1. aiRe Wiqa, Caasxi masSi wyali

(araa aucilebeli _ piramde) dadaxure qaRaldis naWriT. daikaveWiqa xelSi qveda nawiliT, meorexelis guliT daaweqi qaRalds daWiqa frTxilad gadmoapirqvave(sur. 115).

2. Semdeg moaSore xeli da dain-axav, rom qaRaldi darCeba adgilze,wyali ar gadmoiRvreba. ratom?

sur. 114

sur. 115

8 8

3. qaRalds akavebs ori Zala: atmosferuli wneviTgamowveuli da zedapiruli DdaWimulobis Zalebi. rode-sac Sen Wiqas gadmoabruneb, maSin wylis sveti odnav qveviTdaiwevs da haeris wneva Wiqis zeda nawilSi atmosfer-ulze naklebi gaxdeba (odnavi gafarToebis gamo). qvevidanatmosferul wnevasa da wylis zeviT wnevas Soris sxvao-ba qmnis Zalas, romelic siTxes Wiqidan gadmoRvris saSu-alebas ar aZlevs. meore Zala gamowveulia zedapirulidaWimulobiT siTxesa da qaRalds, wyalsa da Wiqis kedlebsSoris.

4. axla cade, Caatiro analogiuri cda erTi bolodandaxuruli grZeli minis miliT (sigrZiT 60 sm da di-ametriT 3-4 sm). daakvirdi: Tu mili TiTqmis carielia, anTiTqmis savsea, qaRaldi kargad Cerdeba da wyali ar gad-moiRvreba, xolo, Tu wyali mils daaxloebiT naxevramdeavsebs, maSin wyali misgan gadmoiRvreba. ratom?

5. aiRe wyliani taSti da Wiqa. CaZire Wiqa wyalSi da,gadayiravebuli, fskeriT zeviT amoswie. dainaxav, rom Wiqaswyali mohyveba. rodesac Wiqis napirebi gauswordeba taStSiwylis zedapirs, wyali Wiqidan taStSi CamoiRvreba. axse-ni es movlena.

6. Caasxi WiqaSi wyali, nebismieri raodenobiT. daxuretualetis qaRaldiT da daademinis naWeri (SeiZleba patarasarke). Semdeg yvela erTad gad-moabrune (sur. 116). axla aswieWiqa. mina aiwevs masTan erTad.Semdeg Wiqa daayene fskerze damina frTxilad aswie zeviT. minaadvilad ar moexsneba Wiqas. SeiZ-leba, Wiqam aiwios minasTan er-Tad. ratom?

sur. 116

8 9

113daamzade pulvelizatori.1. aiRe korpis sacobi an peno-

plastis naWeri da moaWeri mas erTimeoTxedi nawili. moamzade saweripastis ori plastmasis mili (suf-Ta) da gauyare korpSi (winaswargaxurebuli lursmniT gaukeTexvrelebi) ise, rogorc naCvenebiasur. 117-ze.

2. CauSvi qveda mili wylian WiqaSi, xolo zedas Seu-bere. Sen mier damzadebuli pulvelizatori ise imuSavebs,rogorc namdvili saparikmaxeroebSi an saRebavis Sesasx-urebeli pistoleti. axseni pulvelizatoris moqmedebisprincipi.

114ratom muSaobs pulvelizatori?1. am kiTxvaze pasuxi gagiadvildeba, Tu Caatareb Sem-

deg cdas: Txeli qaRaldisagan gamoWeri viwro zoli dadaikave erTi boloTi. cxadia, meore bolo Camoekideba.

2. aba, miitane xelebi pirTan da Zlierad SeubereqaRalds. dainaxav qaRaldi afrindeba, is gaiWimeba hori-zontulad, rogorc DdroSa haerSi. sanam uberav, qaRaldidgas.

aq SeiZleba iyos mxolod erTi mizezi: haeris Wavliqmnis Sewovas (nakadSi haeris wneva naklebia). qvevidanatmosferuli wneva metia, vidre WavlSi (zevidan). amitomqaRaldi maRla iwevs.

3. gairbens ra haeris nakadi pulvelizatoris ver-tikaluri milis Tavze, iq wneva Semcirdeba da atmosfer-uli wneva (gadaecema paskalis kanonis Tanaxmad) aiZulebswyals, avides milSi, Semdeg ki haeris nakadSi gaifrqveva.

sur. 117

9 0

115kovzi wylis nakadSi.koandis efeqti.1. onkanidan mouSvi wylis Wav-

li. miitane masTan axlos amozne-qili mxariT Cais (an sadilis)kovzi da Seaxe Wavls. dainaxav, romkovzi miekvreba (miezideba) amWavls (sur. 118).

2. Seecade, gawio gverdzekovzis zeda bolo ramdenime san-

timetriT. kovzi Wavlisagan mainc ar wydeba, miuxedavadimisa, rom is sakmao kuTxiTaa daxrili. TiTqos vardnilmawyalma kovzi gverdze unda gaagdos. ratom xdeba piri-qiT?

3. wylis nakadis fenaSi, romelic kovzs exeba, wnevanaklebia, vidre atmosferuli wneva kovzis meore mxridan.amitom kovzi awveba Wavls (am movlenas koandis efeqtiewodeba).

116kvercxi `amoxteba~ Wiqidan.1. wylian WiqaSi moaTavse kver-

cxi da dadgi Ria onkanis qveS (sur.119). rodesac wylis nakadis siC-qare gadaaWarbebs raRac kritikuls,maSin kvercxi aiwevs, TiTqos mas wy-lis Wavli izidavs. ratom xdebaes?

2. cxadia, wneva kvercxis qvev-idan da zevidan sxvadasxva iqneba.radgan zeviT iwevs; amitom wnevaqvevidan metia, e.i. siTxis nakadSisiCqare didia, wneva _ naklebi.

sur. 118

sur. 119

9 1

117liveris moqmedebis principi.1. aiRe samedicino Sprici (wvrili ufro

mosaxerxebelia). cilindridan amoaZvre dguSi.2. wvrili boloTi CauSvi wylian WiqaSi.

cxadia, masSi Seva wyali gareTa wylis donemde.Semdeg TiTiT daxure xvreli da amoiRe wyl-idan. mas milSi arsebuli wyalic amohyveba.

3. miitane cariel WiqasTan da xvrels TiTiauSvi. wyali WiqaSi CaiRvreba. anlogiurad mo-qmedebs liveri (sur. 120). axseni misi moqmede-bis principi.

118daamzade sifoni.1. aiRe rezinis an polipropilenis mili da erTi

bolo CauSvi wylian WiqaSi, meore ki iyos CamoSvebuli.2. meore bolodan gamowove haeri (an winaswar mili

wyliT aavse) da misgan gamova wyali. Seudgi mas ufroqveviT meore Wiqa. rodesac am WiqaSi dagrovdeba cotawyali da masSi iqneba CaSvebulimeore bolo, meore Wiqa maRla aswie,xolo pirveli dabla daswie (sur.121). axla wyali piriqiT meoreWiqidan gadaesxmeba pirvelSi. mils,romliTac erTi WurWlidan meo-reSi SeiZleba gadavasxaT wyali ansxva siTxe, sifoni ewodeba. sad darodis iyeneben sifons?

119rogor moqmedebs sifoni?1. kerZod, Tu misi moqmedeba dakavSirebulia atmos-

ferul wnevasTan, maSin ratom aris SesaZlebeli zogierTi

sur. 120

sur. 121

9 2

siTxis gadasxma sifonis saSualebiT vakuum-Si? damokidebulia Tu ara sifonis moqmede-ba simZimis Zalaze? ratom ar iwyeba sifo-nis moqmedeba maSinve, roca mili (sur. 122)CaeSveba siTxeSi? ra aiZulebs siTxes ai-wios ÀÂ muxlSi simZimis Zalis sawinaaRmde-god? riT SemoisazRvreba sifonis simaRle,kerZod, rodesac is muSaobs vakuumSi?

2. gavrcelebulia azri, rom sifoni mo-qmedebs atmosferuli wnevis gamo (dasawyis-Si, meore bolodan haeris gamowovis Semdeg

ÀÂ muxlSi siTxe atmosferuli wneviT iwevs maRla simZ-imis Zalis sawinaaRmdegod), magram sifoni xom vakuumSicmuSaobs! siTxes sifonis muxlSi ubiZgebs TviT siTxisatomebs Soris moqmedi Sinagani Zalebi. rodesac sifoniiwyebs moqmedebas, mis gamosaval CD milSi meti siTxea,vidre SesasvlelSi da warmoqmnili wnevaTa sxvaobis gamosiTxe iwevs maRla, gadaedineba milis moxril nawilSi dagamoedineba sifonidan. rac ufro maRla aiwevs siTxe si-fonis muxlSi, aq miT naklebi xdeba wneva siTxeSi. Tusifonis muxls avwevT sakmaod maRla, maSin siTxeSi wnevaSeiZleba iqamde Semcirdes, rom masSi moxdes kavitacia kavitacia kavitacia kavitacia kavitacia _buStulebma daiwyos (haeris an sxva gazis) gaCena. sworedamiT SemoisazRvreba sifonis simaRle, vinaidan buStulebiarRveven molekulebs Soris kavSirs. atmosferuli wnevi-sas sifoni ukeTesad muSaobs, vinaidan am SemTxvevaSi si-fonSi siTxis wneva izrdeba, am dros agreTve izrdebasimaRlec, romelzedac iwyeba buStulebis gaCena. magram,atmosferuli wnevisas sifonSi civi wylis awevis zRvru-li simaRle 6-7 metrs ar aRemateba.

1201. dadgi anTebuli sanTeli magidaze da gadaafare maRa-

li Wiqa. cota xnis Semdeg sanTeli Caqreba (sur. 123, a).ratom?

sur. 122

Â

A

C

D

9 3

2. axla sanTeli dadgisadilis TefSze an emalisjamze da TefSze daasxi wya-li. sanTeli aanTe da gadaa-fare maRali Wiqa. cota xnisSemdeg sanTeli Caqreba da Wiqa-Si wyali odnav maRla aiwevs(sur. 123, b). axseni movlena.

121kvercxi rZis boTlSi.1. aiRe rZis boTli an Cveulebrivi

Ggrafini. moxarSul kvercxs gaacalenaWuWi da garedan cota zeTi wausvi.

2. boTlSi Cade anTebuli qaRaldiszoli. daxure boTlis yeli kvercxiT(sur. 124, a). daakvirdi, rogor Seiwovebakvercxi boTlSi da davardeba mis fskerze(sur. 124, b) axseni dakvirvebuli movle-na.

122mkveTri dartyma da diqti gatydeba.1. aiRe 2_3 sm siganis da 50_60 sm sigrZis diqtis

zoli an xis Zveli saxazavi. gaawonaswore magidis kidezeise, rom igi susti dawoliT vardebodes. daafine zevidangaSlili gazeTi da kargad gaas-wore xelis gasmiT.

2. axla diqts magrad daartyimuSti (sur. 125). is adre odnavidawoliT vardeboda, axla ki al-baT, xeli getkina da mainc ar Camo-varda.

sur. 123A

A a A b

sur. 124A

A a A b

sur. 125

9 4

3. aiRe magari joxi da mTeli ZaliT daartyi diqts.dainaxav, rom diqti gatydeba, gazeTs ki araferi mouva.axseni dakvirvebuli movlena.

123mSrali wylidan.1. dadevi ganier TefSze liTonis fuli (mag. 10_20

TeTriani). daasxi cota wyali. fuli wyalSi aRmoCndeba.axla SesTavaze Sens amxanags, ise amoiRos wylidan moneta,rom TiTebi ar daisvelos da TefSidan wyali ar gadaR-varos. (ara mgonia, man moifiqros, rogor unda moiqces).

2. aiRe Txelkedliani Wiqa, gamoavle masSi mduRarewyali da gadaabrune TefSze monetasTan axlos (sur. 126).

daakvirdi, ra moxdeba.3. haeri WiqaSi daiwyebs gacive-bas. Sen, albaT ici, rom civi haeriikavebs ufro cota adgils, vi-dre _ cxeli. amitom Wiqa Tef-Sze arsebul wyals mTlianadSeiwovs. daicade, sanam moneta gaS-reba, da Semdeg aiRe.

124saocari boloki.1. aiRe wiTeli boloki da

moaWeri qveda naxevari. TeTrrbil nawils daaweqi, rom gauCndespatara Rrmuli ise, rom napirebsar Seexo. Semdeg magrad miaWireTefSze (sur. 127). bolo ki aswie,TefSic mihyveba. ratom?

sur. 126

sur. 127

9 5

laboratoriuli samuSaebilaboratoriuli samuSaebilaboratoriuli samuSaebilaboratoriuli samuSaebilaboratoriuli samuSaebi

aucilebeli Sesasrulebelia mxolod pirveli (anzogjer pirveli da meore) davaleba. danarCen davalebabsmsurvelebi xSirad saxlSi asruleben. es samuSao damate-biT fasdeba.

samuSao #1. patara sxeulebis zomebis gansazRvraspecialuri xelsawyoebis garda (magaliTad, mik-

rometri), patara sxeulebis zomebi SeiZleba gavzomoTCveulebrivi saxazaviT, magram im pirobiT, rom gvaqvs erT-nairi sxeulebis didi raodenoba.

davaleba 1. burTulas diametris gazomvadavuvSvaT, rom Tqven gindaT patara burTulas (mag.

burTulasakisaris) diametris gazomva. mravali aseTiburTula CaalageT RarSi ise, rom isini mWidroT exebod-nen erTmaneTs da maT orive boloSi miudgiT SemzRudveli(sur. l .1).

saxazaviT gazomeT l manZili da es ricxvi gayaviTburTulebis raodenobaze, ipoveT erTi burTulas di-ametri:

d = l/. radgan ricxvi zustia, amitom burTulas

diametris Δ d cdomileba l manZilis cdomilebaze -jernaklebi iqneba: Δ d = Δ l/.

analogiurad SeiZleba mavTulis, safantis, bardismarcvlis da sxv. diametris gansazRvra.

sur. l .1l

9 6

xelsawyoebi da masalebi: minis mili; saxazavi milime-trebiani danayofebiT; 10_20 erTnairi zomis burTula(safanti, bardis marcvali da a. S.).

miTiTeba muSaobisaTvisgazomvisa da gamoTvlis Sedegebi SeitaneT cxrilSi

l.1.

cxrili l .1.

CaatareT gazomvebi randenime sxeulze, gansazRvreTmaTi zomebi (diametrebi).

davaleba 2. gazomeT xraxnis bijixraxnis biji ewodeba kuTxvilis or uaxloes xveu-

las Soris manZils. vinaidan zogjer xraxnis biji pat-araa (Cveulebrivad is milimetris meaTed nawilebs Sead-gens), amitom am sididis gazomvisaTvis saWiroa imave me-TodiT visargebloT, rogoriTac burTulas diametris ga-zomvisas.

xelsawyoebi da masalebi: WanWiki an sWvali; saxazavimilimetrebiani danayofebiT.

miTiTeba muSaobisaTvisgazomeT WanWikis (an sWvalis) mTeli daWdeuli nawi-

lis sigrZe, Zalian akuratulad (zustad) daTvaleTxveulebis ricxvi. moxerxebulia WanWikis zedapirzewinaswar saRebavis an grafitis wasma da qaRaldze misianabeWdis miReba, xolo Semdeg am anabeWdze gazomvebisCatareba.

#

gamosakvlevisxeuli

nawilakebisricxvimwkrivSi

wkrivissigrZe

l, mm

diametri

d, mm

diametrisgazomviscdomilebaΔ d, mm

burTula

mavTuli

1

3

barda2

9 7

davaleba 3. giragis mamoZravebeli xraxnis bijisgazomva

xelsawyoebi da masalebi: magidis giragi; saxazavi mili-

metrebiani danayofebiT.

miTiTeba muSaobisaTvismoifiqreT, ramdeniT gadaadgildeba giragis moZravi

tuCi saxeluris erTi brunvisas; brunvisas. es mogex-marebaT, ipovoT giragis mamoZravebeli xraxnis bijis ga-

zomvis wesi, rom ar daSaloT giragi. Tqvens saxelosnoSi

gazomeT giragis xraxnis biji.

samuSao #2. moculobis gazomva sazomi cilind-ris gamoyenebiT

sazomi cilindri (menzura) gamoiyeneba siTxisa da

myari sxeulebis moculobis gasazomad.

sanam gazomvas SevudgebodeT, saWiroa ganvsazRvroT:

gazomvis zRvari — sididis maqsimluri

mniSvneloba (mocemul SemTxvevaSi moculo-

bis), romelic mocemuli xelsawyos gamoy-

enebiT gaizomeba;

danayofis fasi — skalis umciresi dan-

ayofis Sesabamisi moculobis mniSvneloba.

magaliTad, suraTze 1.26 gamosaxulia men-

zura, romlis gamoyenebiT SeiZleba gaizo-

mos 25 sm3 moculoba, xolo danayofis fa-

sia 1 sm3.

xelsawyoebi da masalebi: sazomi cilin-

dri; gadmosasxmeli Wiqa; wyliani WurWe-

li; myari sxeulebis nakrebi; patara boT-

li.

sur.1. 26

7 jemal kiknaZe

sm3

9 8

davaleba 1. gazomeT boTlis moculobamiTiTeba muSaobisaTvisgansazRvreT Tqveni sazomi cilindris danayofis fasi

da CawereT misi mniSvneloba. jer boTli gaavseT wyliT,

Semdeg es wyali gadaasxiT menzuraSi.

Tu aTvlis Catareba mouxerxebelia, ma-

Sin es procedura N-jer gaimeoreT,menzuris TiTqmis srul gavsebamde. mTe-

li moculobis gansazRvriTa da misi

N ricxvze gayofiT gaigebT boTlis

moculobas.

miaqcieT yuradReba siTxis mocu-

lobis aTvlisas Tvalis swor mde-

bareobas (sur. l.2). Tvali ise unda

moTavsdes, rom siTxis zedapiris axlo

da daSorebuli nawiburebi erT sxivze iyos.

davaleba 2. gazomeT myari sxeulis moculobaTu sazom cilindrSi CaasxamT siTxes da gansazRvravT

mis miculobas (sur. l.3, a), xolo Semdeg masSi myar sx-

euls CauSvebT, maSin siTxis done aiw-

evs (sur. l .3, b). am ori moculobis

sxvaoba udris myari sxeulis mocu-

lobas.

miTiTeba muSaobisaTvisaarCieT 3 _ 4 sxeuli, romlebic

Caetevian menzuraSi. dakideT isini Zafe-

bze, rom gaadvildes maTi wyalSi CaS-

veba da Semdeg amoReba. monacemebi Sei-taneT cxrilSi l .2.

sur. l.2

sur. l.3

ba

ml

1 ml=1 sm3

9 9

davaleba 3. gazomeT sxeulis moculoba, romelicsazom cilindrSi ar eteva

am mizniT saWiroa gadmosasxmeli Wiqis gamoyeneba,rogorc aris naCvenebi suraTze l .4.

cxrili l .2.

samuSao #3. qanqaras rxevis periodis gansazRvra. rxe-vis periodis Zafis sigrZeze damokidebulebis gamokv-leva

qanqarad gamoviyenebT l sigrZis Zafze dakidebul tvirTs(patara burTulas, qanCs, patara qvas da sxv.), (sur. l5). Tu mas gadavxriT C wertilidan, e. i. wonasworobismdgomareobidan, α kuTxiT da gauSvebT, maSin is daiwyebsrxevas, e.i. Tavdipiorvelad imoZravebs wertilisaken,Semdeg_ wertilisaken, da Semdeg_C wertilisaken. rogorcki gaivlis wonasworobis C mdebareobas, is kvlav dab-rundeba wertilSi. Semdeg yvelaferi es gameordeba. wertilidan gaSvebuli tvirTi, rodesac kvlav wertilSidabrundeba, maSin qanqara Seasrulebs srul rxevas.

dros, romlis ganmavlobaSi qanqara srul rxevas Sea-srulebs, rxevis periodi ewodeba. aRiniSneba T asoTi.

Zalian Znelia, wammzomis gamoyenebiT gavzomoT periodi,radgan, praqtikulad, is icvleba wamis meaTedi nawilidanerT-or wamamde; amitom vzomavT t dros, romlis ganmavlo-baSic qanqara Seasrulebs srul rxevas da ganvsazRvravTperiods formuliT: T=t/.

#

gasazomisxeuli

siTxissawyisi

moculobaV1 , sm

siTxismoculobasxeulTan

erTad V2 , sm

myarisxeulismoculoba

V=V2–V1 , sm

moculobisgazomviscdomileba

VΔ , sm

saSleli

qva

1

3

qanCi2

1 0 0

davaleba 1. rxevis periodis gansazRvraxelsawyoebi da masalebi: wammzomi (saaTi wamebiani

isriT); qanqaras dasamagrebeli (Stativi).

miTiTeba muSaobisaTvisgazomvisa da gamoTvlis Sedegebi mosaxerxebelia Seit-

anoT cxrilSi l.3. cxrili l.3.

gazomvebi CaatareT Zafis sigrZis sami mniSvnelobi-saTvis; magaliTad, 20 sm; 40 sm; 60 sm. upasuxeT kiTxvas:aris Tu ara periodi Zafis sigrZis proporciuli? Seamow-meT, gaizrdeba Tu ara rxevis periodi 2-jer an 3-jer,rodesac Zafis sigrZe gaizrdeba 2-jer da 3-jer.

sami wertiliT aageT rxevis T periodis Zafisl sigrZeze damokidebulebis grafiki (grafiki aageT mili-metrul qaRaldze).

davaleba 2. qanqaras rxevis periodis Zafis si-grZeze damokidebulebis gamokvleva

cdidan Tqven darwmundiT, rom qanqaras Zafis sigrZisgadidebiT misi periodi izrdeba, magram ara sigrZis propor-

sur. l.4 sur. l.5

Zafis sigrZel , sm

ricxvebisricxvi N

sruli drot, wm

periodi

T, wmperiodis kvad-rati y 2T=

1 0 1

ciulad, aramed ufro rTulad. erT-erTi cdis Sedegebimocemulia cxrilSi l.4 da pirveli sami gazomvis mixed-viT agebul grafikze (sur. l.6).

rogorc Cans, T=f(l) funqcia arawrfivia, e.i. periodiZafis l sigrZis proporciuli araa. wamovayenoT Semdegihi poTeza: periodis kvadrati Zafis sigrZis proporci-ulia, e.i. cvladi y=T2 proporciulia l sigrZis. es Sei-Zleba Semdegi saxiT CavweroT y=ql, sadac q_mudmivi sid-idea.

es hipoTeza, rom SevamowmoT CavweroT cxrilis bolosvetSi pirveli sami gazomvis periodis kvadratebi daavagoT Sesabamisi grafiki (sur. l.7). rogorc Cans, yvelasamive eqsperimentuli wertili dalagda wrfis maxlo-blad, rac Catarebuli gazomvebis sizustes Seesabameba.

cxrili l.4.

imaSi dasarwmuneblad, rom es SemTxveviTi damTxvevaaraa, Caatares kidev ori gazomva 60 sm da 100 sm sigrZisZafebis SemTxvevaSi (ix. me-4 da me-5 striqonebi cx. l. 4).miRebuli axali eqsperimentuli wertilebi_isini l. 7suraTze aRniSnulia varskvlavebiT_kvlav Zalian kargadmdebareoben wrfeze. es amtkicebs Cvens hipoTezas, rackanonis Camoyalibebis saSualebas iZleva:

qanqaras rxevis periodis kvadrati misi Zafis si-grZis proporciulia: T2 = ql.

es kanoni SeiZleba asec CamovayaliboT: qanqaras rxe-vis periodi misi Zafis sigrZidan kvdratuli fesvis

proporciulia: T=k l

Zafis sigrZel , sm

ricxvebisricxvi N

sruli drot, wm

periodi

T, wmperiodis kvad-rati y 2T=

30508060100

5050403020

5271724740

1,01,41,81,62,0

1,02,03,22,64,0

1 0 2

miTiTeba muSaobisaTvisTqveni gazomvebis Sesabamisad SeavseT cxrili l.3 da

milimetrul qaRaldze aageT grafiki, sur. l.7-ze gamosax-ulis analogiurad. CaatareT sakontrolo gazomvebi 50 smda 75 sm sigrZis Zafebis dros.

samuSao #4. Tanabari moZraobis SeswavlaTanabrad moZravi sxeulis saxiT gamoviyenebT wylian

milSi haeris buSts (ix. sur. 2.18). jer saWiroa Semow-mdes, rogor moZraobs haeris buSti milSi (Tanabrad, TuaraTanabrad), xolo Semdeg ganvsazRvroT misi moZraobissiCqare milis sxvadasxva daxrisas.

xelsawyoebi da masalebi: 20_25 sm sigrZis, 7_8 mmdiametris minis mili, orive mxridan darCiluli an plas-tilinis sacobiT daxuruli; 25 sm sigrZis saxazavi mili-metrebiani danayofebT, mcire zomis Zelaki an CveulebrivisaSleli; Sesabamisi zomis qaRaldis lenti; rezinis orirgoli; metronomi (erTi mTel klasze).

davaleba 1. daamtkiceT, rom haeris buSti TanabradmoZraobs

saxazavze dadeT qaRaldis lenti, xolo zemodan_wylianimili. (mili ise unda gaivsos wyliT, rom masSi aucile-blad unda darCes haeris buSti). daamagreT es sistema

l,sm l,sm

T,wm

sur. l.6 sur. l.7

1 0 3

(saxazavi, qaRaldis lenti, minis mili wyliT) rezinisrgolebiT. odnav daakakuneT saxazavze, miaRwieT buStisplastilinisagan moSorebas. Semdeg saxazavi moaTavseThorizontulad, daiwyeT erTi bolos odnav aweva. buStiam dros milis mopirdapire boloSi unda iyos (buStisplastilinTan miwebeba gamoricxulia). saxazavis aweuliTavi daadeT patara Zelakze an saSlelze, romelic brty-lad unda idos. rodesac sistema aRmoCndeba daxriladdawynarebul mdgomareobaSi, buSti daiwyebs nela gadaadg-ilebas (curvas) zeviT.

CarTeT metronomi da mis yovel dartymaze aRniSneThaeris buStis mdebareoba qaRaldis lentze

moxseniT qaRaldis lenti da mis gaswvriv gaatareTkoordinatTa RerZi (magaliTad, ox RerZi), winaswar air-CieT aTvlis saTave. gansazRvreT TiToeuli aRniSvnis koor-dinati. Sedegebi SeitaneT cxrilSi l.5.

cxrili l.5.

gaatareT sibrtyeze x da t koordinatTa RerZebi daaageT x(t) damokidebulebis_haeris buStis moZraobis grafi-ki. Tvalyuri adevneT imas, rom eqsperimentuli wertilebi,SeZlebisdagvarad, axlos iyos grafikTan. SeamowmeT, mocemulSemTxvevaSi sruldeba Tu ara Tanabari moZraobis gan-marteba (ix. $ 2.10). gamoTvaleT haeris buStis moZraobissiCqare.

davaleba 2. SeadareT haeris buStis moZraobis siGqa-reebi sistemis sxvadasxva daxrisas

CaatareT eqsperimenti, Zelaki dadeviT ara brtylad,aramed gverdiTi waxnagiT. dainaxavT, rom haeris buSti am

cdis#

1

2

t,wm

x, sm

x, sm

0

0

0 1 2 3 4 5 6 7 8 9 10

1 0 4

dros gadaadgildeba ufro Cqara. metronomis dartymebis

Sesabamisad qaRaldis lentze aRniSneT haeris buStis

mdebareobebi. Sedegebi SeitaneT cxrilSi l. 5.

imave koordinatTa RerZebze aageT moZraobis grafiki.

SeadareT grafikebis daxrebi pirvel da meore cdebSi.

gamoTvaleT haeris buStis siCqare. SeafaseT koordinate-

bisa da siCqareebis cdomilebebi.SeniSvna: am samuSaosaTvis avtoris mier damzadebulia xel-

sawyo, elastikuri polipropilenis milis gamoy-

enebiT _ `serelis xelsawyo~`serelis xelsawyo~`serelis xelsawyo~`serelis xelsawyo~`serelis xelsawyo~, romelic daculia

patentiT GE U 2004 1154 U (ix. Jurnali perpet-perpet-perpet-perpet-perpet-

uum mobileuum mobileuum mobileuum mobileuum mobile, 2005, #1, gv. 46).

samuSao #5. sxeulis masisa da misi simkvrivisgansazRvra

cnobilia, rom sxeulis masis gansazRvris erT-erTi

xerxia awonva. Cveulebrivad awonva warmoebs berketian an

zambarian sasworze. Tumca gazovis meTodika am saswore-

bis daxmarebiT sxvadasxvaa.

zambarian sasworze, Tu is dagraduirebulia masis er-

TeulebSi (ix. $ 3.8), mis skalaze pirdapir aviTvliT

Cvenebas (ix. sur. 3.16). berketian sasworze awonvisas

gamoiyeneba e.w. nulovani meTodi: sasworis erT pinaze

(marcxenaze) deben asawon sxeuls, meoreze (marjvenaze)

_sawonebs, amasTan, imdens, rom sasworis maCvenebeli dadges

nulze, an gaagrZelos rxeva ise, rom wonasworobis mdgo-

mareobidan orive mxares erTnairi kuTxiT gadaixaros.

mocemul samuSaoSi awonvisaTvis gTavazobT gamoiy-

enoT berketiani saswori.

sxeulis masisa da misi moculobis gazomvis Semdeg,

advilad gansazRvraven im nivTierebis simkvrives, romlis-

ganac damzadebulia sxeuli (ix. $ 3.2). moxerxebulia, ga-

zomvis Sedegebi SevitanoT cxrilSi l. 6.

1 0 5

cxrili l.6.

xelsawyoebi da masalebi: gamosakvlevi myari sxeule-bi; saswori; wvrilsawonebi; menzura; saxazavi milimetre-biani danayofebiT; qimiuri Wiqebi

miTiTeba muSaobisaTvisgamosakvlevad SeiZleba gamoiyenoT is sxeulebi, romelTa

moculoba gazomeT #2 samuSaoSi (an msgavsi sxeulebi).awonvamde SeafaseT, ra sizustemdea saWiro awonva,

Tu moculoba izomeba cdomilebiT araumciresi 0,5_1 sm3.

davaleba 1. gansazRvreT myari sxeulis masa dasimkvrive

gamosakvlev sxeulebad aiReT marTkuTxa paralelepi-pedis saxis Zelaki, patara cilindri, arawesieri formissxeuli. paralelepi pedis moculobis gansazRvrisaTvissaxazaviT gazomeT misi wiboebi, xolo Semdeg gamoTvaleTmoculoba; sxva sxeulebis moculoba gansazRvreT men-zuris gamoyenebiT.

davaleba 2. siTxis masisa da simkvrivis gansazRvraTavdapirvelad gansazRvreT carieli qimiuri Wiqis masa.

Semdeg menzuraSi CaasxiT gamosakvlevi siTxis raRac raodenoba(magaliTad, 50_60 sm3) da gansazRvreT misi moculoba. gada-asxiT es siTxe qimiur WiqaSi, awoneT siTxe WiqasTan erTad.cxadia, rom siTxis masa iqneba orive gazomvis Sedegissxvaoba.

gamosakvlevisxeuli

masam, g

moculobaV, sm3

simkvrive

p = m / VnivTiereba

g/sm3

1

3

2

cdis

#kg/sm3

1 0 6

davaleba 3. gansazRvreT wris farTobis Sefardebamisi radiusis kvadratTan

wris farTobis Sefardebas misi radiusis kvadratTanaRniSnaven π (pi) asoTi: S

wr/R2 = π. am ricxvis miaxloebiTi

mniSvnelobaπ ≈3,141592654... ≈3,14. arqimedem i pova mniSvneloba

π ≈22/7 ≈3,1428..., rac sakmaod zusti aRmoCnda (ix. savar-jiSo $1.12-is). SevecadoT es ricxvi miviRoT eqsperimen-tuli gziT.

am mizniT sqeli qaRaldisagan, Txeli Tunuqisagan anfolgisagan gamovWraT R radiusis wre da kvadrati, rom-lis gverdi am R radiusis toli iyos (sur. l.8). cxadia,radgan orive nakvTi erTi da igive masalisaganaa damzade-buli, agreTve aqvT erTnairi sisqe, amitom maTi masebimaTi farTobebis proporciulia:

mwr/m

kv = S

wr/S

kv = πR2/R2 =π.

amrigad, orive nakvTis awonviT da maTi masebis Sefardeb-iT SeiZleba eqsperimentulad ganvsazRvroT π ricxvi.

samuSao #6. drekadi deformaciis Seswavlamocemul samuSaoSi Tqven eqsperimentulad gamoikv-

levT drekadi sxeulis (rezinis Zafi, zambara) wagrZelebisdamokidebulebas moqmedi Zalisagan, e.i. SeamowmebT hukiskanonis samarTlianobas. Semdeg, miRebuli kanonzomiereb-is gamoyenebiT, unda darwmundeT, rom simZimis Zala masisproporciulia. es mogcemT dinamometris dagraduirebissaSualebas.

xelsawyoebi da masalebi: sadgari quroTi da TaTiT;oTxi erTnairi nimuSis wvrili rezinis nakrebi, TiToeu-li 20_30 sm sigrZis; 50 sm sigrZis TeTri muyaos zoli;sawonebisa da tvirTebis nakrebi meqanikaSi; mavTulis kakve-bi; danayofebiani saxazavi; saskolo dinamometri.

1 0 7

davaleba 1. daagraduireT dinamometridaagraduireT saskolo laboratoriuli dinamometri,

romlis drekadi elementia xveulebiani zambara.1 kg masis sxeulze moqmedebs 9,8 n-is toli simZimis

Zala. cxadia, rom meqanikaSi nakrebidan 100 g masis tvirTzeimoqmedebs 0,98 n-is toli simZimis Zala, rac 2 % cdom-lebiT 1 n-s udris.

dinamometris skalas daafareT qaRaldi da skalisboloebze daamagreT rezinis rgolebiT.

sadgarze TaTiT vertikalurad daamagreT dinamometri.horizontaluri xaziT aRniSneT dinamometris maCvenebe-lis sawyisi (nulovani) mdebareoba. kauWze CamokideT 100g, 200 g, 300 g da a.S. masis tvirTebi. aRniSneT 1 n, 2 n, 3 nZalebis Sesabamisi dinamometris maCveneblis mdebareoba.SeamowmeT, aris Tu ara skalaze graduireba Tanabari. amaveskalaze aRniSneT niutonis meaTedi nawilebi.

moxseniT TviTnakeTi skala, SeadareT is qarxanaSi da-graduirebul xelsawyos skalas. SeafaseT, rogori cdom-ileba dauSviT.

gansxvavdeba Tu ara is 2—3 %-isagan?

davaleba 2. SeamowmeT hukis kanonisuraTze l.9 gamosaxulia danadgari, romelic hukis

kanonis Semowmebis saSualebas iZleva.1. TiToeuli rezinis erT boloze SekariT liTonis

maryuJi. rezinebis meore boloebi muyaos zolTan erTaddaamagreT sadgaris TaTSi ise, rom yvela maryuJi erT

doneze iyos. es done aRniSneT muyaoze.

sur. l.8

R

R

R

1 0 8

2. erT-erT rezinze kauWiT dakideT 10_15

g tvirTi ise, rom rezini daaxloebiT 6_8

sm-ze gaiWimos. aRniSneT maryuJis mdebareo-

ba muyaoze. saxazaviT gazomeT rezinis l1

wagrZeleba da Sedegi SeitaneT cxrilSi l.7.

cxrili l.7.

3. igive tvirTi kauWiT erTdroulad dakideT or, Sem-

deg sam, oTx rezinze da TiToeul SemTxvevaSi aRniSneT

muyaoze maryuJis mdebareoba. gazomeT l2; l3; l4 wagrZeleba.

Sedegebi imave cxrilSi SeitaneT.

4. vertikalur RerZze (ordinatTa RerZi) gadazomeT

drekadobis Zala pirobiT erTeulebSi, horizontul RerZze

(abscisTa RerZi) wagrZeleba _ SerCeul maStabSi. aageT

drekadobis Zalis wagrZelebaze damokidebulebis grafi-

ki. SeamowmeT, eqsperimentis cdomilebis farglebSi srul-

deba Tu ara hukis kanoni.

rezinebis ricxvi,romlebzec tvirTi

kidia

drekadobis Zala

mocemul rezinSi(pirobiTi erTeuli)

wagrZelebal, mm

1

2

3

4

cdis

#

erTi

ori

sami

oTxi

1 =

2 = / 2

3 = / 3

4 = / 4

sur. l.9

1 0 9

davaleba 3. gamoikvlieT Tanafardoba masasa dasimZimis Zalas Soris

miTiTeba muSaobisaTvis1. imave danadgarze gamoiyeneT erTi rezina, SeamowmeT,

rogor icvleba simZimis Zala tvirTis masaze damokide-bulebiT. am mizniT m1=m; m2=2m; m3=3m masebis gamoy-enebiT gazomeT wagrZelebebi.

2 igive gazomvebi SeasruleT ori reziniT. SedegebiSeitaneT cxrilSi l. 8.

3. aageT tvirTebze moqmedi simZimis Zalis, maT masazedamokidebulebis grafiki. SeamowmeT, eqsperimentis cdom-ilebis farglebSi sruldeba Tu ara proporciuli damok-idebuleba simZimis Zalasa da sxeulis masas Soris. grafikisagebisas gaiTvaliswineT drekadobis Zalis damokidebulebarezinis wagrZelebisa da rezinebis ricxvisagan.

cxrili l.8.

samuSao #7. srialis xaxunis Zalis gazomva Tu horizontul zedapirze davdebT Zelaks da masze

horizontuli mimarTulebiT sakmarisi ZaliT vimoqmedebT,maSin Zelaki daiwyebs moZraobas. advilad davrwmundeb-

iT, rom am dros Zelakze oTxi Zala moqmedebs (sur. l.10):

#

rezinebisricxvi

tvirTismasa

(pirobiTerTeulebSi)

wagrZelebal, mm

drekadobisZala

(pirobiTerTeulebSi)

simZimisZala

(pirobiTerTeulebSi)

erTi

erTi

erTi

ori

ori

ori

1

2

3

4

5

6

m 1 = m

m 2 = 2 m

m 3 = 3 m

m 4 = m

m 5 = 2 m

m 6 = 3 m

1 = 1 =

1 1 0

vertikaluri mimarTulebiT moduliT toli da urTierT-sawinaaRmdegod simZimis Zala, sayrdenis reaqciisZala; horizontaluri mimarTulebiT— wevis Zala dasawinaaRmdego mimarTulebiT

xax xaxunis Zala. Zelakis

Tanabari moZraobisaTvis saWiroa, rom wevis Zalis modu-li xaxunis Zalis modulis toli iyos: |

wev| = |

xax|.

amazea damyarebuli xaxunis Zalis gazomvis meTodi.saWiroa Zelaks iseTi wevis Zala movdoT, romelic amsxeuls wrfivad da Tanabrad amoZravebs. am wevis ZaliTgansazRvraven xaxunis Zalis moduls.

xelsawyoebi da masalebi: tribometri, romelic Sedge-ba xis saxazavisa da samnaxvretiani xis Zelakisagan; saskolodinamometri; tvirTebis nakrebi meqanikidan.

davaleba 1. gansazRvreT xaxunis Zala Zelaksa dasaxazavs Soris

miTiTeba muSaobisaTvis1. gansazRvreT Zelakisa da nakrebidan tvirTebis masebi.2. Zelakis kauWs gamodeviT dinamometris kauWi da

moiyvaneT isini Tanabar moZraobaSi saxazavze (an magidiszedapirze), gazomeT wevis Zala. SeamCnevT, rom Zelakis moZrao-bisas dinamometris isari irxeva, amitom gazomvis SedegadaiReT dinamometris ori ganapira mdebareobis saSualomniSvneloba. gazomvis Sedegi SeitaneT cxrilSi l.9.

x a x

sur. l.10

1 1 1

3. datvirTeT Zelaki erTi, ori da sami tvirTiT, Ti-Toeul SemTxvevaSi gazomeT xaxunis Zala. monacemebi Seit-aneT cxrilSi.

davaleba 2. gansazRvreT xaxunis koeficientiadvilad darwmundebiT, rom horizontul zedapirze

sxeulis moZraobisas normaluri wnevis Zala am sxeulzemoqmedi simZimis Zalis tolia: =. es iZleva xaxuniskoeficientis gamoTvlis saSualebas: μ =

xax/ =

xax/.

cxrili l.9.

magram xaxunis Zalas zomaven didi cdomilebiT imisgamo, rom, rigi mizezebis gamo, dinamometris maCvenebeli ardgeba erT adgilze _ gazomvis procesSi irxeva. amitommizanSewonilia, gamoTvlebi Semdegnairad awarmooT.

1. eqsperimentuli wertilebiT (cx. l.9) aageT xaxunisZlis normaluri wnevis Zalaze damokidebulebis grafiki.radgan gamoricxuli araa eqsperimentuli wertilebis gabne-va,

xax xaxunis

Zalis simZimis

Zalaze wrfivi damokidebuleb-is grafiki (koordinatTa saTa-veze gamavali wrfe) ise undaaagoT, rom, SeZlebisdagvarad, isgadiodes yvela eqsperimentulwertilze (sur. l.11).

#

gamosakvlevisxeuli

masam , g

simZimisZala, n

xaxunisZala

xax , n

xaxuniskoeficienti

μ =xax

/

Zelaki erTitvirTiT

1

3

2Zelaki oritvirTiT

Zelaki samitvirTiT

xax, n

, n

sur. l.11

1 1 2

2. agebul grafikze aarCieT nebismieri wertili, gan-

sazRvreT misi Sesabamisi xax

da Zalebis mniSvnelobebi,

ipoveT maTi Sefardeba. es mogcemT xaxunis koeficientis

saSualo mniSvnelobas_μsaS.

3. eqsperimentuli wertilebisaTvis xaxunis koefici-

entis mniSvnelobebis gamoTvlis Semdeg, ipoveT saSualodan

gadaxris mniSvneloba. am mniSvnelobebis sxvaoba iZleva

cdis maqsimalur cdomilebas (absolutur cdomilebas):

Δμmaq=|μ

saS–μ|.

fardobiTi cdomileba: %100⋅μμΔ

=εmaq.

samuSao #8. momentebis wesis Semowmebamocemul samuSaoSi Tqven eqsperimentulad SeamowmebT

RerZze mbrunavi sxeulis wonasworobis pirobas, e.i. mo-

mentebis wess (ix. $ 4.10).

xelsawyoebi da masalebi: sadgari (Stativi) quroTida TaTiT; berketi-saxazavi; tvirTebis nakrebi meqanikidan;

danayofebiani saxazavi; dinamometri.

davaleba 1. SeamowmeT berketis wonasworobis pirobaori Zalis moqmedebisas

miTiTeba muSaobisaTvis1. aawyveT sur. 4.17_is Sesabamisi danadgari. SeamowmeT

Tavisuflad brunavs Tu ara berketi Tavisi RerZis garSemo.

2. berketis boloebze damagrebuli qanCebis brunviT

miaRwieT mis wonasworobas.

3. berketis marcxena nawilze dakideT ori tvirTi

brunvis RerZidan 10__15 sm-is manZilze. eqsperimentuli

gziT daadgineT, sad unda davkidoT erTi tvirTi RerZidan

marjvniv, rom berketi wonasworobaSi movides. monacemebi

SeitaneT cxrilSi l.10.

1 1 3

cxrili l.10.

4. SeafaseT, rogori sizustiT sruldeba momentebiswesi. amisaTvis ipoveT momentebis sxvaoba da misi modu-lis Sefardeba momentis saSualo mniSvnelobasTan.

%M

|MM|

.

10021 ⋅−

=εsaS

davaleba 2. SeamowmeT berketis wonasworobis pirobasxvadasxva wertilSi modebuli ramdenime Zalis moq-medebisas

am davalebis Sesasruleblad dakideT brunvis RerZ-idan marcxniv da marjvniv sxvadasxva kauWze ramdenimetvirTi da miaRwieT wonasworobas. SeafaseT, am eqsperi-mentSi rogori sizustiT sruldeba momentebis wesi.

davaleba 3. awoneT berketis gamoyenebiTsaskolo (laboratoriul) dinamometrs aqvs 4 n-is

toli Zalis gazomvis zRvari. moifiqreT, am dinamometriTda berketiT rogor gansazRvravT im sxeulis wonas, romel-ic gacilebiT metia am zRvarze. CaatareT Sesabamisi eqs-perimenti.

samuSao #9. SeadareT sxeulis wona haerSi dawyalSi

mocemuli samuSaos mizania arqimedes Zalis gazomva;myari sxeulisa da siTxis simkvrivis gansazRvra.

#

masam1 , g

1

2

3

mxaril1 , sm

Zala

1 , nmomenti

1 , n . m

RerZidan marcxniv RerZidan marjvniv

masam2 , g

mxaril2 , sm

Zala

1 , nZala

2 , nmomenti

2 , n . m

8 jemal kiknaZe

1 1 4

xelsawyoebi da masalebi: Stativi (sadgari) quroTida TaTiT; dinamometri; sqelkedliani Wiqa; menzura; ram-denime sxeuli Zafis maryuWiT; areometri; wyliani Wur-Weli; WurWeli sakvebi marilis koncetrirebuli xsnariTan gliceriniT.

davaleba 1. gazomeT wyalSi sxeulze moqmedi amomgde-bi Zala

miTiTeba muSaobisaTvis1. gazomeT menzuriT sxeulis moc-

uloba.2. daamagreT dinamometri Stativis

TaTSi, Zafis maryuJiT dakideT sxeu-li dinamometris kauWze da ipoveTsxeulis wona haerSi (sur. l.12).

3. sxeulis qveS dadgiT wylianiWiqa da dauSviT quro TaTiTa datvirTiani dinamometriT, sanam mTelisxeuli ar aRmoCndeba wyalSi. ipov-eT sxeulis wona wyalSi da gamoTva-leT amomgdebi Zalis mniSvneloba.

4. iciT ra sxeulis moculoba da wylis simkvrive,SeamowmeT, udris Tu ara amomgdebi Zala gamoZevebuli siTxiswonas.

5. CaatareT cda sxva sxeuliT. cdebis Sedegebi Cawer-eT cxrilSi l.11.

davaleba 2. gansazRvreT myari sxeulis simkvrivehidrostatikuri awonvis meTodiT

gaimeoreT $ 5.13 da amowereT formula, myari sxeulissimkvrivis gansazRvrisaTvis hidrostatikuri awonvis me-TodiT:

11 mmmρ

PPPρρ 00

−=

−=

.

sur. l.12

1 1 5

isargebleT cxrilis (l.11.) monacemebiT, gansazRvreTcdiT gamosakvlevi sxulis simkvrive.

cxrili l.10.

davaleba 3. gansazRvreT siTxis simkvrive hidrosta-tikuri awonvis meTodiT

isargebleT imave formuliT (ix. $ 5.13), myari sxeu-lis cnobili simkvriviT ipoveT sakvebi marilis xsnaris(an glicerinis) TqvenTvis ucnobi simkvrive. amisaTvis,damatebiT, ra gazomvebi unda SeasruloT?

davaleba 4. gansazRvreT siTxis simkvrive areome-tris gamoyenebiT

isargebleT areometriT, gazomeT marilis xsnaris (anglicerinis) simkvrive. areometris moqmedebis principisgarkvevisaTvis gaimeoreT $ 5.11.

laboratoriuli samuSaoebi aRebulia VII klasis sax-elmZRvanelodan _ ������ � ����������, ������� ��� 7������ ������������������� ����������, ������������ �. �. ��������, �. �. ������������, �.«�����������», 2002.

#

gamosakv-levi

sxeuli

1

2

sxeulismoculoba

V, sm3

sxeuliswona haerSi

, n

sxeuliswona

wyalSi

1, n

amomgdebiZala

a, n

gamoZevebu-li siTxis

wona

siTx., n

1 1 6

saSinao eqsperimentuli amocanebisaSinao eqsperimentuli amocanebisaSinao eqsperimentuli amocanebisaSinao eqsperimentuli amocanebisaSinao eqsperimentuli amocanebi

1. gansazRvre Saqris fxvnilis simkvrive mxolod say-

ofacxovrebo menzuris gamoyenebiT.2. 100 g-iani sawonis, samwaxnaga qlibiT da danayofe-

biani saxazaviT daadgine im sxeulebis masebi, romlebicsawonis masisagan Zalian ar gansxvavdebian.

3. berketian sasworze awoniT gansazRvre 20 TeTri-ani monetis masa, Semdeg mxolod am monetis gamoyenebiT

miaxloebiT gansazRvre danayofebiani saxazavis masa.4. gvaqvs: wyliani abazana, ganieryeliani patara qila,

ramdenime erT TeTriani moneta (erTi monetis masa cno-bili unda iyos), pipeti, feradi carci (an rbili fan-

qari). mxolod am sagnebis gamoyenebiT rogor ipovi erTiwveTis masas?

5. rogor gansazRvrav qvis simkvrives, berketiani sas-woriT, wvrilsawonebiT da wyliani WurWliT, Tu misi

moculobis gazomva pirdapir ar SegviZlia?6. sasworisa da wvrilsawonebis gamoyenebiT, rogor

gaigeb qvabis Siga moculobas?7. cilindruli WurWeli piramde avsebulia siTxiT.

rogor gayof am siTxes zustad or tol nawilad, Tugaqvs kidev erTi sxva formisa da odnav naklebi moculo-

bis WurWeli?8. gaqvs ori asanTis kolofi. erTSi naklebi raode-

nobis asanTis Reroebia. rogor daadgen, yuTis gauxsneladromelSia meti Reroebi?

9. rogor daadgen gluvi joxis masaTa (simZimis) cen-trs, xelsawyoebis gamouyeneblad?

10. gansazRvre fexburTis burTis diametri samasSta-bo saxazavis gamoyenebiT.

11. gansazRvre patara burTulas diametri menzurisgamoyenebiT.

1 1 7

12. gansazRvre wvrilimavTulis diametri ujrede-

biani rveulis furclisa dafanqris gamoyenebiT.

13. gaqvs nawilobrivwyliT avsebuli marTkuTxo-

vani kveTis WurWeli, romel-Sic curavs wyalSi CaZiruli

sxeuli. rogor gaigeb erTisaxazaviT am sxeulis masas?

14. rogor gaigeb fola-dis CxiriTa da wyliani menzu-

riT korpis (an penoplastisnaWris) simkrives?

15. minis sacobs SigniTaqvs siRruve. sasworis,

wvrilsawonebisa da wylianiWurWlis gamoyenebiT rogor

ipovi siRruvis moculobassacobis gautexavad?

16. rogor gaigeb gorgal-Si spilenZis mavTulis sigrZes,

gorglis dauSlelad?17. rogor gansazRvrav

onkanidan wylis gamodinebissiCqares, cilindruli WurW-

lis, wamzomisa da Stangenfarglis gamoyenebiT?18. ori erTnairi rezinis buSti erTi meoreze cota

metadaa gaberili da mokle miliT SeerTebulia erTmaneT-Tan, rogorc naCvenebia sur. 1-ze. Seni azriT, ra moxdeba?

gaibereba Tu ara patara buSti didis xarjze? Caatareeqsperimenti da Seamowme Seni varaudi (intuicias yovel-

Tvis nu endobi!).

sur. 1

sur. 2

1 1 8

19. rogor unda daalago wignebi yvelaze kargad, rommaTgan miiRo, rac SeiZleba, metad daxrili dasta (sur. 2)

SeiZleba Tu ara wignebi ise dalagdes, rom yoveliSemdegi wignis kide emTxveodes winas centrs?SeniSvna: irkveva, erTnairi wignebisagan Sedgenili dasta

erTi wignis siganeze, rom Camowves xuTi wignimaincaa saWiro. dasta sami wignis siganeze, romCamowves _ 227 wigni, xolo 10 wignis siganezedaxrisaTvis dasta unda Seicavdes 1,5.1044 wigns!aseT suraTs miviRebdiT maSin, dedamiwa brtye-li rom yofiliyo.

20. hidravlikuri wnexis modeli: aiRe ori, sxvadasxvazomis (mag. 2 ml da 20 ml moculobis) samedicino Spri-ci. SeaerTe polipropilenis wvrili (sisxlis gadasasxme-li) miliT. sistema aavse wyliT, Caatare cdebi da Sesabam-isi gaangariSebebi.

21. qila-bumerangi: aiRe yavis qila saxuraviT. fskerida saxuravi gaxvrite. gauyare rezinis zonariT, odnavdaWime da boloebi gaunaskve. gaxseni saxuravi da gaWimu-li rezinis SuaSi ZafiT an mavrTuliT daamagre tvirTi,TiTqmis qilis masis toli. miiReb qila-bumerangs. gaagoreiatakze igi ukan gamogordeba. ratom?

22. anTebuli sanTeli, spirtSi dasvelebuli bamba anqaRaldi moaTavse gadmobrunebul (fskeriT zeviT) WiqisSigniT. Semdeg swrafad, iseTive mdebareobaSi dade gaber-il sabavSvo sahaero buStis zedapirze. aRwere dakvirve-buli movlena.

23. atmosferuli wnevis moqmedeba safuZvlad udevssiTxis dguSiani tumbos muSaobas (ix. fizikis saxelmZR-vanelo _ VII kl. da Seiswavle misi moqmedebis principi).SegiZlia daamzado misi moqmedi modeli. gamoiyene orinaxevarlitriani polieTilenis boTli, samedicino Sprici(10-20 ml.), pipeti, sisxlis gadasasxmeli sistemis 10-15sm sigrZis mili, 15-18 mm diametris liTonis ori burTu-la, cilindruli formis saweri pastis korpusi da sax-uravi, webo (DAI-ICHI).

1 1 9

sarCevisarCevisarCevisarCevisarCevi

Sesavali ................................................................................................................................. 3umartivesi gazomvebiumartivesi gazomvebiumartivesi gazomvebiumartivesi gazomvebiumartivesi gazomvebi

sigrZis gazomva .................................................................................................................. 5farTobis gazomva ........................................................................................................... 1 1moculobis gazomva ....................................................................................................... 1 3vertikaluri da horizontuli mimarTuleba .............................................. 1 6Zalis gazomva. dinamometri ..................................................................................... 1 8saswori da wvrilsawonebi ...................................................................................... 1 9drois gazomva ................................................................................................................. 2 1Stangenfargali ............................................................................................................... 2 2mikrometri ........................................................................................................................ 2 3gazomvis Sedegebis damuSaveba. pirdapiri gazomviscdomilebis gansazRvra .............................................................................................. 2 4

meqanikameqanikameqanikameqanikameqanika

siCqare .................................................................................................................................. 2 6inercia ................................................................................................................................. 2 9rodis uxveven gverdze ............................................................................................... 3 2wona. uwonoba ................................................................................................................... 3 4ratom mifrinavs raketa ............................................................................................ 3 6simZimis centri. sxeulTa wonasworoba .......................................................... 3 9

myari, Txevadi da gazuri sxeulis Tvisebebimyari, Txevadi da gazuri sxeulis Tvisebebimyari, Txevadi da gazuri sxeulis Tvisebebimyari, Txevadi da gazuri sxeulis Tvisebebimyari, Txevadi da gazuri sxeulis Tvisebebi

nivTierebis drekadoba ................................................................................................ 6 1wneva. cdebi wnevis gadacemaze ............................................................................... 6 2curva da CaZirva ........................................................................................................... 7 3haeri da misi Tvisebebi ............................................................................................. 8 4

laboratoriuli samuSaoebilaboratoriuli samuSaoebilaboratoriuli samuSaoebilaboratoriuli samuSaoebilaboratoriuli samuSaoebi

samuSao #1. patara sxeulebis zomebis gansazRvra .................................. 9 5samuSao #2. moculbis gazomva sazomi

cilindris gamoyenebiT ............................................................. 9 7samuSao #3. qanqaras rxevis periodis gansazRvra ................................... 9 9samuSao #4 Tanabari moZraobis Seswavla .................................................. 102samuSao #5. sxeulis masisa da misi nivTierebis

simkvrivis gansazRvra ............................................................. 104samuSao #6. drekadi deformaciis Seswavla ........................................... 106samuSao #7. srialis xaxunis Zalisa gazomva da xaxunis

koeficientis gansazRvra ...................................................... 109samuSao #8. momentebis wesis Semowmeba ...................................................... 112samuSao #9. SeadareT sxeulis wona

haerSi da wyalSi ..................................................................... 113saSinao eqsperimentuli amocanesaSinao eqsperimentuli amocanesaSinao eqsperimentuli amocanesaSinao eqsperimentuli amocanesaSinao eqsperimentuli amocanebibibibibi ................................................................................................................................................................116

jemal simonis Ze kiknaZejemal simonis Ze kiknaZejemal simonis Ze kiknaZejemal simonis Ze kiknaZejemal simonis Ze kiknaZe

martivi da usafrTxo eqsperimentebi

fizika

redaqtori adelaida nikolaiSviliadelaida nikolaiSviliadelaida nikolaiSviliadelaida nikolaiSviliadelaida nikolaiSvili

kompiuteruliuzrunvelyofa lika sxirtlaZelika sxirtlaZelika sxirtlaZelika sxirtlaZelika sxirtlaZe

wigni gamodis avtoris xarjiT

gamomcemloba inteleqti

q. Tbilisi, WavWavaZis gamz. 17 b

tel.: 25 05 25, 8 99 55 66 54, 8 99 53 05 22