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giorgi gedeniZeeTer lazaraSvili

inteleqti XI

klasissaxelmZRvanelo

giorgi gedeniZe

eTer lazaraSvili

fizika

gamomcemloba inteleqti

Tbilisi 2012

XI klasis saxelmZRvanelo

grifi mieniWa 2012 wels ssip ganaTlebis xarisxis ganviTarebis

erovnuli centris (brZaneba ##375, 18.05.2012) mier

© gamomcemloba `inteleqti~, 2012ISBN 978-9941-439-67-4

giorgi gedeniZe, eTer lazaraSvili

fizika XI

Giorgi Gedenidze, Eter Lazarashvili

PHYSICS XI

INTELEKTI PUBLISHERSTbilisi 2012

redaqtorebi gvanca gedeniZe naTia mamulaSvili

Editor Gvantsa Gedenidze Natia Mamulashvili

gamomcemloba inteleqti

Tbilisi, ilia WavWavaZis gamziri 5

225-05-22, 599 55-66-54

faqsi: 225-05-22

[email protected] www.intelekti.ge

iNtELEKti Publishers

5 ilia Chavchavadze ave., tbilisi, Georgia. tel.: 225-05-22, 599 55-66-54

3

Sinaarsi

I Tavi. meqanikuri rxevebi da talRebi ................................................................6

1.1. ra da rogor iswavleT, SeamowmeT Tqveni codna ...............................................7

1.2. maTematikuri qanqara ........................................................................................................11

1.3. rxeviTi moZraoba. zambariani qanqara........................................................................14

1.4. harmoniuli rxeva ...............................................................................................................17

1.5. Tavisufali da iZulebiTi rxevebi. rezonansi .......................................................20

1.6. meqanikuri talRebi ...........................................................................................................23

1.7. bgeriTi talRa ....................................................................................................................26

1.8. amocanis amoxsnis nimuSi .................................................................................................29

1.9. SeamowmeT Tqveni codna ..................................................................................................31

II Tavi. eleqtromagnituri rxevebi da talRebi ............................................32

2.1. analogia meqanikur da eleqtromagnitur movlenebs Soris ............................33

2.2. cvladi deni. cvladi denis generatori. denis Zalisa da Zabvis

efeqturi mniSvneloba ......................................................................................................36

2.3. eleqtruli energiis gadacema ......................................................................................39

2.4. transformatori ................................................................................................................42

2.5. eleqtromagnituri talRebi ..........................................................................................44

2.6. eleqtromagnituri talRebis gamoyeneba. radiotalRebi ..................................48

2.7. eleqtromagnituri talRebis gamoye neba. optikuri diapazonis

eleqtromagnituri talRebi. rentgenis sxivebi ....................................................51



III Tavi. molekulur-kinetikuri Teoria da Termodinamika ...................56

3.1. molekulur-kinetikuri Teoriis ZiriTadi debulebebi. Termodinamika .....57

3.2. molekulebis raodenoba da masa. fardobiTi molekuluri masa.

nivTierebis raodenoba. moluri masa. avogadros mudmiva................................60

3.3. idealuri airi. molekulur-kinetikuri Teoriis ZiriTadi

gantoleba. temperatura .................................................................................................63

3.4. temperaturis absoluturi skala. temperatura _ molekulebis

saSualo kinetikuri energiis zoma .............................................................................65

3.5. idealuri airis mdgomareobis gantoleba ...............................................................68

3.6. airis kanonebi ......................................................................................................................70



4

3.9. Sinagani energia da misi Secvlis xerxebi ................................................................76

3.10. siTbos raodenoba. muSaoba airis moculobis cvlilebisas ..........................79

3.11. ra da rogor iswavleT SeamowmeT Tqveni codna ................................................81

3.12. najeri orTqli. duRili ...............................................................................................84

3.13. haeris tenianoba ...............................................................................................................87

3.14. Termodinamikis pirveli kanoni ..................................................................................91

3.15. Termodinamikis pirveli kanonis gamoyeneba sxvadasxva

procesisaTvis. adiabaturi procesi ........................................................................93

3.16. Seqcevadi da Seuqcevadi procesebi. Termodinamikis meore kanoni............95

3.17. siTburi Zravebi ................................................................................................................97

3.18. amocanis amoxsnis nimuSi ...............................................................................................100

3.19. SeamowmeT Tqveni codna ................................................................................................102

IV Tavi. birTvuli energiis miReba da gamoyeneba .......................................103

4.1. birTvuli kvlevebi ............................................................................................................105

4.2. radioaqtivoba .....................................................................................................................107

4.3. alfa (α), beta (b) da gama (g) .......................................................................................109

4.4. radioaqtiuri gamosxiveba ..............................................................................................111

4.5. atomis agebuleba. rezerfordis cdebi ....................................................................113

4.6. atomis planetaruli modeli ........................................................................................115

4.7. boris postulatebi ...........................................................................................................117

4.8. radioaqtiuri gardaqmnebi .............................................................................................119

4.9. naxevardaSlis periodi ....................................................................................................121

4.10. birTvuli reaqciebi. protonisa da neitronis aRmoCena.

atomis birTvis agebuleba ............................................................................................123

4.11. birTvuli Zalebi. atomuri birTvebis bmis energia ..........................................126

4.12. masis defeqti. birTvis bmis kuTri energiis masur

ricxvze damokidebuleba ...............................................................................................128

4.13. birTvuli reaqciebi protonebiT da neitronebiT ............................................130

4.14. jaWvuri birTvuli reaqciebi ......................................................................................132

4.15. TermobirTvuli reaqciebi. birTvuli reaqtori ................................................134

4.16. amocanis amoxsnis nimuSi ...............................................................................................137

4.17. SeamowmeT Tqveni codna ................................................................................................139

5

rogor vixelmZRvaneloT saxelmZRvaneloTi

3.12najeri orTqli. duRili

viciT, damokidebuleba absolutur tempe raturasa da molekulebis gadataniTi moZraobis saSualo kineti-

kur energias Soris gamoisaxeba formuliT: .E kT23

kin= (1)

10. aRwereT 77.1 suraTze gamo-sa xuli situacia. romeli energiis

xar jze xdeba sosisis Sewva?rogor icvleba sosisis Sina gani energia?

sur. 77.1

5. rogoria Tqveni varaudi, oTaxSi temperaturis Semcirebisas haerSi arsebuli wylis orTqli uaxlovdeba

Tu Sordeba najerobis mdgomareobas? pasuxi daasabuTeT magaliTebiT.

4. gamoiyofa Tu STainTqmeba ener-gia uranis birT-

vis gax leCisas meti bmis kuTri energiis birTvebis warmoqmnisas?

5. ra informacias iRebT 132.1 suraTi-dan?

neitroni

neitronebi

namsxvrevebi

sur. 132.1

I. ucvleli masis idealuri airis wnevisa da moculobis nam

ravlis Sefardeba absolutur tempe ratu ras Tan mudmivi sididea

.TPV const=

8. I winadadebis gamoyenebiT SeiZleba vTqvaT, rom rodesac mocemuli masis idealuri airis absoluturi temperatura

orjer izrdeba, maSin airis

a. wneva da moculoba ar icvleba;

b. wnevac da moculobac orjer izrdeba.

absoluturi tenianoba, fardobiTi tenianoba, namis wertili, higrometri, fsiqrometri

gavecaniT tenianobas. tenianobis gazomvis xerxebs. tenianobis mniSvnelobas yofacxovrebaSi.

Semdeg gakveTilze gavecnobiT energiis Senaxvisa da gardaqmnis kanons siTburi procesebisaTvis.

cdis mizani: meqanikur talRebze dakvirveba1. wyalSi CaagdeT qva an kenWi. daakvirdiT wylis

zedapirs. aRwereT da SeecadeT axsnaT SemC-neuli movlena.

2. ganier WurWelSi (abazanaSi), erT-maneTisagan daSorebiT, moaTavseT oTxi-xuTi msubuqi tivtiva _ korpis an asanTis Reris gadanaWeri. joxis perioduli Se xebiT

wyali rxeviT moZraobaSi moiyvaneT. daakvirdiT wyli s zedapirs da tiv-tivebs. ras amCnevT? gadaadgildeba Tu ara tivtivebi horizontalurad? aRwereT SemCneuli movlenebi.

saSinao cda

cdebisTvis saWiroa

• qva an kenWi

• wyliani abazana

• 4-5 tivtiva

• zonari

paragrafis nomeri

paragrafis

saxelwodeba

individualuri

samuSao

jgufebad

muSaoba

amocanebi logikuri

msjelobis gamoyenebiT

informacia suraTis

mixedviT

wyvilebad

muSaoba

saWiroa sifrTxile

saSinao cda

axali terminebi

daskvnebi

! dafiqrdiT da asanTis Reris Tavebi (sur. 136.1) ise ganalageT liTonis ta faze an kecze, rom cdiT SeZloT jaWvuri reaqciis demonstrireba.

6

I Tavi

meqanikuri

rxevebi da

talRebi

am TavSi gaixsenebT da gaecnobiT

meqanikur rxevas;

rxevis amplitudas, sixSires, fazas;

maTematikur da zambarian qanqarebs;

harmoniul rxevas da mis maxasiaTeblebs;

rezonanss;

meqanikur talRebs: ganivsa da grZivs;

bgeris warmoqmnas da gavrcelebas;

bgeris siCqares sxvadasxva

garemoSi;

adamianisa da cxovelebis mier

aRqmul bgerebs;

mocemul Temebze amocanebis amoxsnas.

7

testi

1. Tbilisidan quTaisSi mimavali TviTmfrinavi a. moZraobs Tbilisis mimarT, ar moZraobs quTaisis mimarT; b. moZraobs quTaisis mimarT, ar moZraobs Tbilisis mimarT; g. moZraobs orive qalaqis mimarT; d. ar moZraobs arc erTi qalaqis mimarT.

2. Tbilisidan quTaisSi mimavali datvirTuli TviTmfrinavi a. moZraobs Tbilisis da tvirTis mimarT; b. moZraobs Tbilisis mimarT, ar moZraobs tvirTis mimarT; g. ar moZraobs Tbilisis mimarT, moZraobs tvirTis mimarT; d. ar moZraobs arc Tbilisis, arc tvirTis mimarT.

3. Zafze dakidebuli wonasworobis mdebareobidan gadaxrili burTulis (sur. 7.1) gaTavisuflebis Semdeg misi moZraobis traeqtoriaaa

a. wrewiris rkali; b. wrfis monakveTi; g. wrewiri; d. wertili.

4. sxeuli, romelzec moqmedi Zalebis tolqmedi nuli ar aris

a. uZravia; b. moZraobs Tanabrad; g. moZraobs aCqarebulad; d. moZraobs mxolod RerZis Tanxvdenili mimarTulebiT.

5. Tu sxeulma 2 wTSi 120 m gaiara, maSin SISi misi saSualo siCqarea a. 60 m/wm; b. 240 m; g. 60 m/wT; d. 1 m/wm.

6. SISi muSaobisa da energiis erTeulebad, Sesabamisad, miRebulia a. 1 niutoni, 1 jouli; b. 1 jouli, 1 niutoni; g. 1 niutoni, 1 niutoni; d. 1 jouli, 1 jouli.

7. SISi siCqarisa da aCqarebis erTeulebad, Sesabamisad, miRebulia a. 1 m/wm, 1 m/wm2; b. 1 m/wm2, 1 m/wm; g. 1 km/sT, 1 m/wm2; d. 1 sm/wm, 1 m/wm2.

8. rodesac 7.2 suraTze gamosaxuli k sixistis zambara deformirebuli ar aris da m masis sxeuli moZraobs marjvniv v siCqariT, maSin mas gaaCnia (formulebSi x aris zambaris sigrZis cvlileba).

a. kinetikuri _ da potenciuri _ energiebi;

sur. 7.1

1.1ra da rogor iswavleT, SeamowmeT Tqveni codna

sur. 7.2

v1

www.physics.ge | saZiebo fraza k11t1p1

8

b. kinetikuri _ da potenciuri _ ;

g. mxolod kinetikuri _ energia;

d. mxolod potenciuri _ energia.

9. rodesac 8.1 suraTze gamosaxuli k sixistis zambara gaWimulia xiT da m masis sxeuli moZraobs marcxniv v siCqariT, maSin mas gaaCnia

a. kinetikuri _ da potenciuri _ energiebi;

b. kinetikuri _ da potenciuri _ ;

g. mxolod kinetikuri _ energia;

d. mxolod potenciuri _ energia.

10. erTnairi masalisa da ganivkveTis farTobis l da 2l sigrZis rezinidan l sigrZis rezinis sixiste

a. orjer metia 2l sigrZisaze; b. orjer naklebia 2l sigrZisaze; g. iseTivea, rogoric 2l sigrZis; d. oTxjer metia 2l sigrZisaze.

Tu testebze pasuxis gacema gagiWirdaT, maSin gaiRrmaveT codna qvemoT moyvanili winadadebebiT. miRebuli informaciiT, fiqriT da azrovnebiT aucileblad SeZlebT testebze swori pasuxebis gacemas.

drois ganmavlobaSi sxeulis mdebareobis cvlilebas sivrceSi sxva sxeulis mimarT meqanikuri moZraoba ewodeba.

sxeuls, romlis zomebi amocanis mocemuli pirobebiT SeiZleba ugulebelvyoT, nivTieri wertili ewodeba.

aTvlis sxeuli, masTan dakavSirebuli koordinatTa sistema da drois gasazomi xelsawyo erTad qmnis aTvlis sistemas, romlis mimarTac ganixileba sxeulis moZraoba.

warmosaxviT wirs, romelsac nivTieri wertili moZraobisas aRwers, am wertilis moZraobis traeqtoria ewodeba.

Tanabari moZraobis siCqare ewodeba mudmiv sidides, romelic tolia sxeulis S gadaadgilebis da drois im t Sualedis Sefardebisa, romlis

ganmavlobaSic man es gadaadgileba Seasrula: .vtS S tv &= =

TanabaraCqarebuli moZraobis aCqareba ewodeba mudmiv sidides, romelic tolia sxeulis siCqaris cvlilebis fardobisa drois im

SualedTan, romlis ganmav lobaSic es cvlileba moxda: ,v

a tv 0=- , (1)

sadac v0 aris sxeulis sawyisi siCqare, v _ siCqare drois t momentSi,

sur. 8.1 x

v1

9

a _ aCqareba.

sidides, romliTac xasiaTdeba erTi sxeulis moqmedeba meoreze, Zala ewodeba. Zalis moqmedebiT icvleba sxeulis siCqare.

niutonis meore kanoni _ aCqareba, romliTac moZraobs sxeuli,

tolia masze moqmedi Zalisa da sxeulis masis Sefardebis:

,a mF F ma&= = gegmilebiT Fx=max.

Zalis erTeulad SISi miRebulia 1 niutoni (1 n). es aris Zala, romelic 1 kg masis sxeuls 1 m/wm2 aCqarebas aniWebs. 1 n = 1 kg.m/wm2.

fizikur sidides, romelic axasiaTebs sxeulis an sxeulTa sistemis mier muSaobis Sesrulebis unars, meqanikuri energia ewodeba.

energias, romelic sxeuls moZraobis Sedegad aqvs, kinetikuri

energia ewodeba: ,vE m2

2

kin= sadac Ekin

aris v siCqariT moZravi m masis

sxeulis kinetikuri energia.

Tu sxeulze moqmedi Zala asrulebs dadebiT muSaobas, maSin sxeulis kinetikuri energia izrdeba. energiis erTeulad SISi miRebulia 1 jouli (1 j).

energias, romelic ganisazRvreba urTierTmoqmedi sxeulebis an erTi da imave sxeulis nawilebis urTierTmdebareobiT, potenciuri energia ewodeba.

potenciuri energia aqvs dedamiwis zedapiridan raime simaRleze aweul sxeuls da yvela drekadad deformirebul sxeuls.

potenciuri energiis aTvlis nulovani donidan h simaRleze aweuli m masis sxeulis Epot

potenciuri energia ganisazRvreba Epot

=mgh formuliT.

im zambaris potenciuri energia, romlis sixistea k, xolo

deformaciis sidide (wagrZeleba an SekumSva) _ x, ganisazRvreba

E kx2

2

pot= formuliT.

sixiste mocemuli zambarisTvis (rezinisTvis) mudmivi sidi dea. igi damokidebulia zambaris nivTierebis gvarobaze, pirdapir proporciulia zambaris ganivkveTis farTobis da ukuproporciulia zam

baris sawyisi sigrZis _ .klS`

10

cdis mizani: Zafze dakidebuli burTulis rxeviTi moZraobis gamokvleva.

grZel `uWimav~ da `umaso~ Zafze daki

debuli mcire zomis, magram didi masis

sxeuls maTematikur qan qaras uwodeben. grZel Zafze dakidebuli burTula

gadaxareT 5-80-iani kuTxiT, gauSviT xeli da daakvirdiT burTulis rxe vebs (sur. 10.1).

TanmimdevrobiT ganixileT qvemoT mocemuli sakiT xebi, upasuxeT SekiTxvebs da gamoitaneTY daskvnebi.

a. gansazRvreT qanqaras rxevis amplituda _ udidesi gadaxra wonasworobis mdebareobidan.

rodesac sxeuli oTxi amplitudis tol manZils gaivlis, maSin sruldeba erTi sruli rxeva.

erTi sruli rxevis xangrZlivobas rxevis periodi ewodeba. rxevis periodi aRvniSnoT TTi.

b. moifiqreT qanqaras rxevis periodis gansazRvris xerxi da gansazRvreT.

gegim qanqaras rxevis periodi Semdegnairad gansazRvra: qanqara gadaxara wonasworobis mdebareobidan. dainiSna drois is momenti, rodesac burTulas gauSva xeli (B Bmdebareoba) da gazoma drois is Sualedi _ rxevis periodi, romlis Semdegac burTula isev B mdebareobaSi mivida.

anastasiam gazoma drois τ Sualedi, romelSic qanqaram Seasrula n=20 sruli rxeva. drois es Sualedi gayo rxevaTa raodenobaze da miiRo

qanqaras rxevis periodis mniSvneloba .T nx=

g. Tqven rogor fiqrobT, romeli meTodiT miRebuli mniSvneloba iqneba ufro axlos qanqaras rxevis periodis namdvil mniSvnelobasTan?

d. jer ivaraudeT, Semdeg cdiT SeamowmeT, rogor Seicvleba qanqaras rxevis periodi amplitudis mcire sididiT gadidebisas?

gamoitaneT daskvna: rogor aris damokidebuli qanqaras rxevis periodi amplitudaze?e. jer ivaraudeT, Semdeg cdiT SeamowmeT, rogor Seicvleba qanqaras

rxevis periodi Zafze dakidebuli burTulis masis gadidebisas. gamoitaneT daskvna: rogor aris damokidebuli qanqaras rxevis periodi burTulis

masaze?v. jer ivaraudeT, Semdeg cdiT SeamowmeT, rogor Seicvleba qanqaras

rxevis periodi Zafis sigrZis Secvlisas? gamoitaneT daskvna: rogor aris damokidebuli qanqaras rxevis periodi qanqaras

sigrZeze?z. rogor moiqcevi Tu romelime SemTxvevaSi Tqveni varaudi ar gamarTlda?

ganmeorebiT CaatarebT cdebs, Tu miRebuli SedegiT maSinve gamoitan daskvnas?

miRebuli monacemebis mixedviT, samuSao rveulSi SeavseT cxrili.

sur. 10.1

CO

B

saSinao cda

cdebisTvis saWiroa• Zafi• burTula• danayofebiani saxazavi• wammzomi

11

maTematikuri qanqara 1.2

ratom maTematikuri da ara ubralod _ qanqara?

125-e a suraTze gamo saxulia grZel Zafze dakidebuli foladis bur-Tula. igi umartivesi qanqaraa. burTula uZravia.

gadavxaroT qanqara wonasworobis O mdebareobidan B mdebareobaSi da gavuSvaT xeli (sur. 11.1,b).

C mdebareobaSi meyseuli gaCerebis Semdeg igive Zalebis moqmedebiT burTula daiwyebs moZraobas O mdebareobisaken zrdadi siCqariT. procesi C mdebareobidan B mdebareobisken ise mimdinareobs, rogorc mimdinareobda B-dan C-sken. burTula O wertilis xan erT, xan meore mxares gadaixreba _ irxeva.

drois erTeulSi Sesrulebul rxevaTa ricxvs rxevis sixSire ewodeba. rxevis sixSire aRvniSnoT n-Ti.

rxevis periodi .T T1 1

& o= =o (1)

1. 11.1 a suraTze gamo saxeT burTulaze moqmedi Zalebi da

axseniT, ratom aris igi wonasworobaSi.

sur. 11.1a b

CO

B

2. 11.1 b suraTze B mdebareobaSi gamosaxeT burTulaze moqmedi Zalebi. awonasworebs Tu ara es Zalebi erTmaneTs? axseniT, ratom? ra mimarTulebiT

iwyebs burTula moZraobas B mdebareobidan?

3. gaCerda Tu ara burTula O wertilSi? axseniT, ratom?

4. SeadareT erTmaneTs O mdebareobis gavlis momentSi burTulaze moqmedi simZimisa da Zafis daWimulobis Zalebis modulebi. pasuxi daasabuTeT.

5. rogori mimarTuleba aqvs burTu laze moqmedi Zalebis tolqmeds O wertilis marcxena mxares? gamosaxeT suraTze samuSao rveulSi.

6. rogori moZraobaa rxeviTi? moiyvaneT rxeviTi moZraobis magaliTebi.7. ganmarteT rxevis amplituda da periodi. daasaxeleT

TiToeulis erTeuli SI-Si.

n _ `niu~ berZnuli asoa.


12

sixSiris erTeulad miRebulia 1 herci (1 hc).1 herci iseTi rxevis sixSirea, romlis drosac 1 wmSi erTi sruli

rxeva sruldeba.

CavataroT da gavaanalizoT saSinao cdebSi miRebuli Sedegebi. gamovitanoT daskv nebi:

wonasworobis mdebareobidan mcire gadaxrisas maTematikuri qanqaras rxevis periodi ar aris damokidebuli amplitudasa da burTulis masaze.

mcire amplitudiT rxevebisas maTematikuri qanqaras rxevis periodi pirdapirproporciulia kvadratuli fesvisa qanqaras sigrZidan.

mtkicdeba, rom maTematikuri qanqaras rxevis periodi ganisazRvreba formuliT

,T gl2= r (1)

sadac l aris qanqaras sigrZe _ manZili Zafis dakidebis wertilidan burTulis masaTa centramde.

8. qanqara 5 wm-Si asrulebs 10 rxevas. gansazRvreT rxevis periodi da sixSire.

9. aRwereT qanqaras rxeva energetikuli TvalsazrisiT.

10. bavSvebi erTsa da imave saqanelaze qanaoben (sur. 12.1). CaTvaleT, rom bavS ve bis masaTa centri erT donezea da SeadareT maTi rxevis periodebi erTmaneTs.

11. moifiqreT, dagegmeT da Sin CaatareT cda, romlis meSveobiTac gansazRvravT Tavisuflad vard nili sxeulis aCqarebas.

sur. 12.1

maTematikuri qanqara, rxevis periodi, sixSire, herci

13

cdis mizani: zambaraze damagrebuli burTulis rxeviTi moZraobis gamokvleva.

zambaris (rezinis) erTi bolo daamag-reT. meore boloze dakideT sxeuli. sxeuli wonasworobis mdebareobidan 2-3 sm-iT CamoswieT da gauSviT xeli.

moiyvaneT rxeviT moZraobaSi (sur. 13.1). sxeulis masa ise SearCieT, rom rxevebi swrafad ar Sewzydes.

TanmimdevrobiT ganixileT qvemoT mocemuli sakiTxebi, upasuxeT SekiTxvebs da gamoitaneT daskvna.

a. gazomeT rxevis amplituda;

b. gazomeT drois Sualedi, romlis ganmavlobaSic sxeulma Seasrula 20 an 30 rxeva. gansazRvreT rxevis periodi.

g. jer ivaraudeT, Semdeg cdiT SeamowmeT, rogor Seicvaleba rxevis periodi amplitudis 1-1,5 sm-iT gadidebisas? daadgineT rxevis periodis damokidebuleba amplitudaze.

d. jer ivaraudeT, Semdeg cdiT SeamowmeT, rogori gaxdeba zambaraze dakidebuli oTxjer meti masis sxeulis rxevis periodi? rogor Seicvala igi?

gamoitaneT daskvna: rogor aris damokidebuli zambariani qanqaras rxevis periodi masze damagrebuli sxeulis masaze?

e. CaatareT cdebi sxvadasxva sigrZis reziniT. romeli rezinis sixistea meti _ grZelis Tu moklesi?

rogor icvleba rxevis periodi rezinis sixistis gazrdiT? gamoi-taneT daskvna da CawereT samuSao rveulSi cxrilSi.

v. rogor moiqceviT, Tu romelime SemTxvevaSi Tqveni varaudi ar gamarTlda: ganmeorebiT CaatarebT cdebs, Tu miRebuli SedegiT maSinve gamoitanT daskvnas?

z. rogor fiqrobT, erTnair pirobebSi cdis mxolod erTxel Catareba sakmarisia saboloo daskvnis gamosatanad? axseniT, ratom fiqrobT ase.

saSinao cda

cdebisTvis saWiroa

• zambara an rezini

•    danayofebiani saxazavi

• wammzomi

• saswori

• sxvadasxva masis burTulebi

sur. 13.1

14

rxeviTi moZraoba. zambariani qanqara

CavataroT cdebi:gluv horizonta lur RerZze Camocmuli ara defor mirebuli zambaris

erTi bolo damagrebulia. meore boloze mimagre bulia RerZuli nax vre-tis mqone sxeuli (sur. 14.1, a). zam ba raze moqmedi simZimis Zala gawo naswo rebulia RerZis reaqciis ZaliT. sxeuli wonaswo-robaSia.

SevkumSoT zambara. sxeuli davaci-loT wonasworobis O mdebareobas. gav-wioT mar cxniv A manZilze, gadaviyvanoT B mdebareobaSi, gavuSvaT xeli da dava k vir deT (sur.14.1,b). x sxeulis koo r dinatia. O wertilis mar jvniv koor dina ti dadebiTia, marcxniv _ uaryofiTi.

C mdebareobaSi sxeuli meyseulad Cerdeba. zambara gaWimulia, rogorc cda gviCvenebs, TiTqmis A-s toli maqsimaluri manZiliT (sur. 14.1, g).

am mdebareobaSi sxeulze moqmedebs marcxniv mimarTuli drekadobis Zala, romlis moduli maqsimaluria. SeCerebis Semdeg sxeuli marcxniv amoZravda. man xelaxla gaiara O mdebareoba (axla marjvnidan marcxniv) da kvlav gadaixara misgan TiTqmis A manZiliT anu dabrunda wertilSi, saidanac daiwyo moZraoba. amis Semdeg procesi meordeba. sxeuli O wertilis mimarT xan erT, xan meore mxaresaa.

`sxeuli _ zambaras~ erTobliobas xSirad zambarian qanqaras uwo deben.

sur. 14.1

g

O

b

a

x=0

x=-A

x=A

B

C

X

X

X

zambarac maTematikuri qanqaras msgavsad `iqceva~

1.3

1. daasaxeleT da gamosaxeT 14.1 suraTze Zala, romliTac zambara B mdebareobaSi moqmedebs sxeulze.

2. jer ivaraudeT, Semdeg cdiT SeamowmeT, ra moxdeba sxeulze xelis gaSvebis Semdeg?

3. rogor icvleba sxeulis siCqare O wertilisken moZrao bisas?

4. ra moxdeba sxeulis O wertilSi misvlis Semdeg?

ra emarTeba zambaras? axseniT, ratom?

5. rogor icvleba sxeulze moqmedi drekadobis Zala O wertilidan marjvniv moZraobisas? sxeulis siCqare? aCqareba? pasuxi daasabuTeT.

6. rogor moZraobas asrulebs sxeuli?


15

7. ra saxis energia aqvs deformirebul zambaras?

deformirebuli zambaris potenciuri energia ganisazRvreba formuliT

,E kx2

2

pot= (1)

sadac k zambaris sixistea, x _ deformaciis sidide.

Tu sistema Caketilia da rxe visas xa xu ni mcirea, garkveuli drois ganmav-lo baSi misi moqmedebis Sedegi TiTqmis ar gamo v lindeba da sistemis sruli meqa ni ku ri energia SeiZleba mudmivad CaiTvalos.

SekumSuli zambaris maqsimaluri potenciuri energia kA2

2

wonaswo robis

mdebareobaSi gavlisas sxeulis kinetikuri energiis mv

2

2

maqs -is tolia, e. i.

⇒=⇒=km

v

AmvkA2

22

22 maq

2maqs

.km

vA

=⇒maq

(2)

roca sxeuli ukidures marjvena mdebareobaSi aRmoCndeba, misi kineti kuri energia kvlav nuls gautoldeba, xolo sruli energia _ maqsimalur poten-ciur energias. wonasworobisa da maqsimaluri gadaxris mdebareobebs Soris sxeuls aqvs rogorc kinetikuri, ise poten ciuri energia, maTi jami _ sruli

meqanikuri energia mudmivia da nebismier mdebareobaSi kA2

2

-is to lia.

amrigad, merxevi sxeulis sruli meqani kuri energia rxevis amplitudis kvadratis pro por ciulia.

gavaanalizoT saSinao cdebSi miRebuli Sedegebi da gamovitanoT daskvnebi.

wonasworobis mdebareobidan mcire gadaxrisas zambariani qanqaras rxevis periodi ar aris damokidebuli amplitudaze. igi pirdapirproporciulia kvadratuli fesvisa sxeulis masidan da ukuproporciulia kvadratuli fesvisa zambaris sixistidan, e.i.

.Tkm+

Semdeg paragrafSi davamtkicebT, rom zambariani qanqaras rxevis periodi ganisazRvreba formuliT

Tkm2= r , (3)

sadac m sxeulis masaa, k _ zambaris sixiste.

8. ra saxis energiad gardaiqmneba SekumSuli zambaris gaSlisas misi potenciuri energia?

9. cxrili samuSao rveulSi gadaxazeT da SeavseT. rogor icvleba cxrilSi miTiTebuli TiToeuli sididis moduli 14.1 suraTze gamosaxuli zambariani qanqaras rxevisas?

16

zambariani qanqara

sxulis moZraobis

mimarTuleba

drekadobisZala

siGqare aGqarebapotenciuri

energiakinetikuri

energia

sruli meqanikuri energia

realur pirobebSi

idealur pirobebSi

B-dan O-sken

O-dan C-sken

C-dan O-sken

O-dan B-sken

Zabri (SeiZleba gamoiyenoT polieTi-lenis patara boTlis gadanaWeri) ZafiT CamokideT (sur.16.1). Zabris xvrelSi CadeT qaRaldi da gaukeTeT iseTi xvreli, rom masSi Cayrili sila (an marili) wvril nakadad gamovides.

Zabris qveviT magidaze dadeT qaRaldi. ZabrSi CayareT sila.

a. jer ivaraudeT, Semdeg cdiT SeamowmeT, rogori iqneba qaRaldze dafenili silis forma, Tu qanqaras Sveuli mdebareobidan gadaxris mcire kuTxiT da xels gauSvebT?

daakvirdiT, qanqaras rxevisas rogor efineba sila qaRal dze.gamarTlda Tqveni varaudi?

b. jer ivaraudeT, Semdeg cdiT SeamowmeT, rogori iqneba furcelze dayrili silis forma, Tu qanqaras rxevis sibrtyis marTobulad qaRalds Tanabrad amoZ ravebT?

daakvirdiT qaRaldze dafenil silas. rogori forma aqvs mas?gamarTlda Tqveni varaudi?

saSinao cda

sur. 16.1

17

harmoniuli rxeva1.4

rxevebi gansakuTrebiT TvalsaCino maSin xdeba, rodesac mer xevi sxe-ulis koordinatis droze da mo ki de bu lebas grafikis saxiT war movad genT.

CavataroT cda: merxev sxeulze davamagroT flomaste ri, mis win _ muyao (sur. 17.2). sxeulis rxevisas flo masteri muyaoze gaavlebs wrfis AB monakveTs (sur. 17.3, a), romlis yovel wertils flomasteris wveri peri odis ganmav lo baSi orjer gaivlis _ zeviT da qveviT moZra obisas.

magram, Tu gvinda davafiq siroT merxevi sxeulis mdebareoba drois sxvadasxva momentSi, saWiroa flomasteri muyaos erTsa da imave wertils mxolod erTxel Seexos. amisaTvis muyaos zoli flomaste ris rxevis sibrtyis mar Tobulad mudmivi siCqa riT vamoZ raoT. davina xavT, muyaoze gaC ndeba mrudi, rom lis yoveli wertili Seesa bameba flomasteris, maSasadame, mer xevi sxeulis mdeba reobas drois mo cemul momen tSi (sur. 17.3, b). su raTze gamosaxul mruds mivi RebT, Tu muyaos ava-moZravebT im momentSi, roca sxeuli wonasworobis mdebare obas gadis. am mruds sinuso ida hqvia.

fizikuri sididis droze damokidebul periodul cvli lebas, romelic sinusis an kosi nusis kanoniT sruldeba, harmoniuli rxeva ewodeba.

zambaraze damagrebuli sxeulis rxevis gamomwvevi mizezi zambaris deformaciisas aRZruli drekadobis Zalaa, romlis gegmili Fx=-kx. (1)

(1)⇒ drekadobis Zalis gegmili pir dapir-pro porciulia wonasworobis mdebareo bi dan gadaxris da mis sapirispi rodaa mimar Tuli. aqedan gamomdinareobs, rom harmoniul rxe viT moZraobas iwvevs iseTi Zala, romlis moduli

pirdapirproporciulia wonasworobis mdeba reobidan gadaxris da mis sapirispirod aris mimarTuli.

SeadareT saSinao cdaSi qaRaldze dafenili silis forma 17.3 suraTze gamosaxul mruds.

1. ra aris saWiro,

rom Zafze daki debulma

(sur. 17.1,a) an zamba raze mimagrebulma

(sur. 17.1,b) sxe ulma rxeva daiwyos? sur. 17.1ab

sur. 17.2

sur. 17.3

aB

A

b

2. hgavs Tu ara mrudebi erTmaneTs?3. SegviZlia Tu ara vTqvaT, rom zambaraze damagrebuli

sxeulis rxevisas misi koordinati drois mixedviT ise icvleba, rogorc Zafze dakidebuli sxeulis koordinati?


18

cdebiT miRebuli grafikebis msgavseba gvaZlevs uflebas vTqvaT, rom zambaraze mimagrebuli burTulasa da qanqaras koordinati drois mixedviT icvleba erTi da imave kanoniT, miuxedavad imisa, rom rxevebis gamomwvev Zalebs gansxvavebuli fizikuri buneba aqvT. pirvel SemTxvevaSi es zambaris drekadobis Zalaa, xolo meoreSi _ simZimis Zalis da Zafis daWimulobis Zalis tolqmedi.

ganvixiloT A radiusian wrewirze moduliT mudmivi v siCqariT moZravi nivTieri wertilis gegmilis moZraoba erT-erT diametrze gavlebul X RerZze (sur. 18.1). vTqvaT t=0 momentSi sxeuli C wertilSia, xolo t1 momentSi _ B wertilSi. radiusis Semobrunebis kuTxe aRvniSnoT j-Ti. suraTidan ⇒ sxeulis koordinati x=Asinj. (2)

kuTxuri siCqare .t t& {= =~{

~ (3) 2 ,Tr~ =

(4) sadac T garSemovlis periodia.

(4) (3) (2)⇒ 2 .sin sinx AT

t A t2r ro= = (5)

wrewirze moduliT mudmivi siCqariT moZravi nivTieri wertilis X RerZze gegmilis koordinatis droze damokidebulebis grafiki sinusoidaa (sur. 18.2). es imas niSnavs, rom misi rxevebi harmoniulia.

amgvarad, maTematikuri qanqaras da zambaraze damagrebuli sxeulis rxevisas maTi koordinatis drois mixedviT cvlileba gamoisaxuleba (5)

formuliT, sadac A rxevis amplitudaa, T _ rxeviT periodi, T1=o rxevis

sixSire, w _ 2p wamSi Sesrulebuli rxevaTa raodenoba, mas cikluri an wriuli sixSire ewodeba, t _ drois aTvlis dawyebidan gasuli dro.

wrewirze moZravi nivTieri wertilis siCqaris moduli v=wA. (6).

(4) (6)⇒ T

A2v =r ⇒ .v

A T2r= (7)

O wertilSi (sur. 18.1) merxevi sxeulis siCqaris moduli udidesia,

amitom (7)⇒ .A T2vmaqs = r

(8) wina paragrafSi davadgineT .Akm

vmaqs = (9)

(9)∧(8)⇒ .Tkm2= r (10) miviReT formula, romelic saSinao cdebis

analiziT ukve miRebuli gvqonda.harmoniuli rxeviTi moZraobisas wonasworobis mdeba reobidan x

gadaxrasa da drois t Sualeds Soris damoki debulebis grafiki sinusoidaa (sur. 18.2).

4. amplitudis meSveobiT gamosaxeT harmoniulad

merxevi sxeulis koordinatebi drois nul, , ,T T T4 2 4

3 da T momentebSi.

5. gaimeorebs Tu ara merxevi sxeuli drois meore periodSi im gzas rac pirvel periodSi gaiara?

6. romel wertilebSia merxevi wertilis siCqaris gegmilis moduli udidesi? umciresi (sur. 18.1)?

O

CB

A

jj

E x X

v1

v2

v3

v4

sur. 18.1

x

tT

sur. 18.2

2T

4T

19

roca wonasworobis mdebareobidan gadaxra mcirea, ma Sin zambaraze an Zafze dakidebuli sxeulis rxevebi har moniulia.

sinusis arguments j=w0t= Tt2r (11) rxevis faza ewodeba.

Tt Sefardeba miuTiTebs, periodis ra nawili gavida rxeviTi moZraobis

dawyebidan. periodis nawilebiT gamosaxul drois nebismier mniSvnelobas

radianebiT gamosaxuli fazis mniSvneloba Seesabameba. magaliTad, sruli

T periodis gasvlas Seesabameba j=2p faza, T/2-is gasvlas _ j=p.

19.1 suraTze gamosaxulia har-mo niulad mer xevi sxeulis koor-dinatis fazaze damoki debulebis grafiki.

Tu muyaos moZraobas (sur. 17.2) da viwyebT drois im momentSi, ro -desac sxe uli ukidures zeda wer-tilSi imyofeba, maSin muyaoze mi-Rebul su raTs eqneba II mru dis Sesa -bamisi sa xe (sur. 19.2). es kosinu-so idaa, romelic sinuso idisgan gans xvavdeba mxolod p/2 faziT.

.sin cost t20 0~+ =~ rb l

7. fazis ra mniSvneloba Seesabameba periodis meoT-xeds? pasuxi daasabuTeT.

harmoniuli rxeva, rxevis faza.

x,sm

j

sur. 19.1

p2

p 2p 3p 4p

x,sm

t,wm

I II

4T

sur. 19.2

cdis mizani: ori qanqaras rxevaze dakvirveba erTerTis sigrZis cvlilebisas.

aawyveT 19.3 suraTze gamosaxu li da-nadgari. zonarze dakideT ori qan qara. pirveli zonarze gadadeT ZafiT, romlis sigrZis cvlileba SegiZ liaT Zafis Tavisu-fali bolos moZraobiT, meore _ ucvle li sigrZis ZafiT.

pirveli qanqara wonas worobis mde-bareobidan gamoiyvaneT da xeli gauSviT.

daakvirdiT da daafiqsireT meore qanqa-ras rxevis maqsimaluri amplituda. Semdeg pirveli qanqaras sigrZe odnav SeamcireT da cda gaimeoreT _ kvlav daafiqsireT meore qanqaras rxevis maqsimaluri amplituda. cdebi CaatareT pirveli qanqaras sxvadasxva sigrZisas, im SemTxvevaSidac, rodesac orive

qanqaras sigrZe erTmaneTis tolia.gamoitaneT daskvna: pirveli qanqaras rogori sigrZisas aRwevs meoris

rxevis amplituda udides mniSvnelobas? dakvirvebis Sedegi rveulSi CawereT.Tqveni azriT, sakmarisia Tu ara monacemebi daskvnis gamosatanad?saWirod xom ar TvliT, dagegmoT da CaataroT damatebiTi cdebi?

III

sur. 19.3

saSinao cda

cdebisTvis saWiroa• polieTilenis ori

wyliani boTli• Zafi• ori burTula

gavecaniT harmoniul rxevas, mis gantolebas.

20

iseT rxevas, romelsac wonasworobis mdeba-reobidan gadaxrili sxeuli gaTavisuflebis Semdeg TavisTavad, gare zemoqmedebis gareSe asrulebs, Tavisufali rxeva hqvia. Zalebs, romlebic Tavisufal rxevebs aRZravs, Siga Zalebi ewodeba. Tavisufali rxevebi sruldeba erTxel miniWebuli energiis xarjze (sur. 20.1).

sxeulTa sistemas, romelsac aqvs Tavisufali rxevebis unari, rxeviTi sistema ewodeba. Tavisufali rxevebis sixSires ki _ sistemis sakuTari rxevebis sixSire.

maTematikur qanqaraSi sxeulze moqmedi simZimis Zalis `wyaro~ dedamiwaa, amitom aseTi qanqaras sistemaSi Sedis dedamiwac.

ganxiluli magaliTebidan SeiZleba gamovitanoT daskvna: Tavisufali rxevebis aRZvrisaTvis saWiroa, sistemis wonasworobis mdebareobidan gamoyvanisas aRiZras Zala, romelic wonasworobis mdebareobisken aris mimarTuli da xaxuni iyos Zalian mcire.

iseT rxevebs, romelTa amplituda drois ganmavlobaSi mcirdeba, milevadi ewodeba. yovel axal periodSi amplituda sul ufro da ufro mcirdeba.

Tu xaxuni ar aris, qanqaras sruli meqanikuri energia ar icvleba da im energiis tolia, romelic sistemas dasaw yis Si mivaniWeT. am SemTxvevaSi rxevis amplituda ar icvleba (sur. 20.2).

Tavisufali da iZulebiTi rxevebi. rezonansi

1.5

rogor aZlierebs yuTi kamertonis xmas?

1. SesaZlebelia saqanelam TavisTavad, gare zemoqmedebis gareSe daiwyos rxeva?

2. daasaxeleT maTematikuri da zambariani qanqarebis rxeviTi moZraobis gamomwvevi Zalebi.

3. Tavisufalia Tu ara maTematikuri da zambariani qanqarebis rxevebi? axseniT, ratom?

4. ra sidideebiT ganisazRvreba maTematikuri da zambariani qanqarebis Tavisufali rxevebis sixSire? dawereT maTi gamosaTvleli formulebi.

5. rogor icvleba Tavisuflad merxevi sxeulis sruli meqanikuri energia? amplituda? axseniT, ratom?

6. rodis ufro swrafad mcirdeba amplituda _ mcire Tu didi xaxunisas? axseniT, ratom?

sur. 20.2

X, m

T

TA

t, wm

sur. 20.1


21

merxevi sistemis energiis Sevseba SeiZleba masze periodulad cvalebadi gare Zalis moqmedebiT. am Zalas maiZulebeli Zala ewodeba, xolo rxevebs _ iZulebiTi. sistemis energia aRdgeba gare Zalis muSaobis xarjze.

iZulebiTi ewodeba iseT rxevas, romelsac sxeuli asrulebs periodulad cvladi gare Zalis moqmedebiT. aseT rxevebs asrulebs qanqara, rodesac masze periodulad cvladi gare Zala moqmedebs. am dros qanqara irxeva maiZulebeli Zalis sixSiriT. iZulebiT rxevas asrulebs sakeravi manqanis nemsi moZraobisas, Cveni xeli fanjris wmendisas.

iZulebiTi rxevis sixSire maiZulebeli Zalis sixSiris tolia.gavaanalizoT saSinao cdaSi miRebuli Sedegebi:

iZulebiTi rxevis amplituda maqsimalur mniSvnelobas maSin aRwevs, roca maiZulebeli Zalis n sixSire emTxveva merxevi sistemis sakuTar n0 sixSires (n=n0). xaxunis Zala aq did rols asrulebs. swored igi ar aZlevs saSualebas amplitudas, miaRwios Za lian did mniSvnelobas. magram maiZulebeli Zalisa da sistemis saku Tari rxevebis sixSireTa tolobisas SeiZleba amplituda sakmaod didi aRmoCndes.

iZulebiTi rxevis amplitudis mkveTrad gazrdis movlenas, rode sac maiZulebeli Zalis sixSire sis temis sakuTari rxevis sixSires em Txveva, rezonansi ewodeba.

21.1 suraTze gamosaxulia iZu lebiTi rxevis am-plitudis maiZu lebeli Zalis n sixSireze damo ki-debu lebis grafiki. suraTidan Cans, rom amplituda maqsimums aRwevs sixSiris raRac n=n0 mniSvnelobaze, sadac n0 merxevi sistemis sakuTari sixSirea. (1) mruds mcire xaxuni Seesabameba, am SemTxvevaSi maqsi-mumi Zalian mkveT ria. rodesac xaxunis Zala didia, maqsimumi mkveTri ar aris (me-2 mrudi).

rezonanss farTo gamoyeneba aqvs eleqtro gam zom xelsawyoebSi, ra-dioteqnikaSi, medicinaSi.

saWiroebis mixedviT SegviZlia maqsimalurad gavzardoT saqanelas rxevis ampli tuda modu liT mcire ZaliT.

rezonansi SeiZ leba saziano da saSiSic aRmoCndes. iyo xidis dangrevis, avtomobilisa da TviTmfrinavis damsxvrevis SemTxvevebi.

7. ra hqvia 20.2 suraTze gamosaxul mruds da rxevebs, romelic am kanoniT mimdinareobs?

8. daxazeT wonasworobis mdebareobidan gadaxris droze damokidebulebis grafiki milevadi rxevebisas.

9. ra aris saWiro imisaTvis, rom rxeva miulevadi iyos?

10. romeli qanqaras rxevaa iZu lebiTi da ra iwvevs mas (sur. 19.3)?

11. icvleba Tu ara pirveli qanqaras rxevis sixSire misi sigrZis SecvliT?

12. ras amCnevT, icvleba Tu ara meore qanqaras rxevis amplituda pirvelis sigrZis SecvliT?

13. pirveli qanqaras rogori sig rZisas xdeba meore qanqaras rxevis amplituda udidesi?

sur. 21.1

nn00

1

2

X

22

rezonansis movlenas bgeriT rxevebzec Sei-Zleba davak virdeT.

CavataroT cda: er Tmane TTan axlos movaTav-soT ori erTnairi A da B kamer toni ise, rom maTi Ria nawi lebi erT ma neTisaken iyos mimar-Tuli. B kamertonis Reros msubuqi burTula exeba (sur. 22.1). SemovkraT A kamertons rezinis CaquCi (avaJReroT igi) da Semdeg TiTebis SexebiT CavaxSoT rxevebi.

B kamertonis fexze mivaweboT plastilini da amiT SevcvaloT rxevis sakuTari sixSire. gavimeoroT cda; Sevam CnevT, B

kamertoni aRar exmaureba A kamertonis rxe vas.rezonansis movlenas farTod iyeneben musikalur instrumentebSi.

sur. 22.1

BA

Tavisufali rxeva, iZulebiTi rxeva, rezonansi

moipoveT dawvrilebiTi informacia sasargeblo da saziano rezonansis

magaliTebis Sesaxeb. moamzadeT masala gakveTilze warsadgenad.

davaleba

14. gesmiT Tu ara bgerebi?15. ra emarTeba burTulas, romelic B kamertonis Re-

ros exeba?16. ras miuTiTebs es faqti?

17. ratom aJRerda B kamertoni pirvel cdaSi da ar aJRerda, roca masze plastilini iyo mikruli?

cdis mizani: meqanikur talRebze dakvirveba1. wyalSi CaagdeT qva an kenWi. daakvirdiT wylis

zedapirs. aRwereT da SeecadeT axsnaT SemC-neuli movlena.

2. ganier WurWelSi (abazanaSi), erT-maneTisagan daSorebiT, moaTavseT oTxi-xuTi msubuqi tivtiva _ korpis an asanTis Reris gadanaWeri. jer ivaraudeT, Semdeg cdiT SeamowmeT, joxis perioduli Se xebiT wyali

rxeviT moZraobaSi rom moiyvanoT, gadaadgildeba Tu ara tivtivebi hori-zontalurad? gamoikvlieT da aRwereT SemCneuli movlenebi.

3. Sveul kedelze erTi bo loTi damagrebuli, odnav gaWimuli, grZeli zonris me ore bolo rxeviT moZraobaSi moiy va neT (sur. 22.2). amoZraveT jer zeviT da qveviT, Sem deg marcxniv da marjvniv; SemCne uli movlena aRwereT rveulSi.

saSinao cda

cdebisTvis saWiroa• qva an kenWi• wyliani abazana• 4-5 tivtiva• joxi• zonari

sur. 22.2

23

gavaanalizoT saSinao cdebSi SemCneuli movlenebi. wyalSi qvis Cavard-nis adgilas qvam gamodevna wyali da am adgilTan gaCnda Cazneqiloba. gamodevnilma wyalma CazneqilobasTan gaaCina rgolisebri amozneqiloba. Semdeg amozneqilobam war-moqmna ufro didi radiusis Cazneqiloba, romelmac war-moqmna meore amozneqiloba. Semdeg warmoiqmna mesame, meo-Txe da a. S. amozneqilobebi da Cazneqilobebi, qvis Ca-vardnis adgilidan ufro da ufro Sors _ wylis zedapirze `garbis~ talRa (sur. 23.1).

talRa ewodeba rxevas, romelic sivrceSi drois ganmavlobaSi vrcel deba.

saSinao cdaSi SeamCnieT, rom, Tu zonris bolos ganuwyvetliv vamoZ-ravebT zeviT da qveviT, maSin zonris gaswvriv garbis talRa (sur. 23.2).

talRebi SeiZleba iyos ganivi da grZivi.

talRas, romelSic merxevi sxeulis nawilakebi talRis gavrcelebis marTobulad irxeva, ganivi talRa ewodeba.

talRas, romelSic merxevi sxeulis nawi lakebi talRis gavrcelebis mimarTulebis gaswvriv irxeva, grZivi talRa ewodeba.

grZivi talRis warmoqmnas SeiZ leba davakvirdeT grZeli, didi diamet-ris mqone rbili zambaris meSveobiT. Tu zambaris erT bolos SevarxevT masze xelis mirtymiT, Sedegad warmoiqmneba xviebis Sesqeleba, romelic

sur. 23.1

1.6

ratom Cndeba talRebi wyalSi qvis Cavardnisas?

sur. 23.2

1. urTierTqmedeben Tu ara nebismier sxeulSi (myari, Txevadi, airadi) nawilakebi erTmaneTTan?

2. Tu sxeulis romelime nawilaki rxeviT moZraobas daiwyebs, maSin ra emarTeba am nawilakis maxloblobaSi myof nawilakebs?

3. talRasTan erTad gadaadgildeba Tu ara wylis zedapirze mimobneuli tivtivebi?

4. aRwereT, rogor moZraoben tivtivebi.

5. Tqveni azriT, ganivia Tu grZivi zonarSi aRZruli talRa? axseniT, ratom fiqrobT ase?

meqanikuri talRebi


24

`garbis~ zam baris gas wvriv. Tanmimdevruli dartymebiT zam baraSi aRvZ raT talRa. igi zambaris xviebis erTimeoris mim devar Sesqele bebs da SeTxe-lebebs warmoadgens (sur. 24.1, a).

talRuri moZraobisas yoveli nawilaki imeorebs wina nawilakis rxe vebs odnav nak lebi amplitudiT da dagvi-anebiT. cal keuli nawilakebis wonasworo-bis mde bareoba am dros ar icvleba, e. i. niv Tiereba, ro melSic talRa vrceldeba, Tavad ar gadaadgildeba, magram tal-Ris gavrcelebisas energia nawilakidan nawilaks gadaecema. es energia moedineba wya rodan, romelsac rxeviT moZra obaSi mohyavs pirveli nawilaki.

gamovitanoT daskvna: nebismieri talRis ZiriTadi Tvisebaa energiis gadatanis unari nivTierebis gadatanis gareSe.

manZils, romelzec vrceldeba talRa nawilakebis rxevis periodis ganmavlobaSi, talRis sigrZe ewodeba.

SemoviRoT aRniSvnebi: talRis sig-rZe ≡ λ, rxevis periodi ≡ T, sixSire ≡ n (sur. 24.1, b da g).

talRis gavrcelebis siCqare talRis sigrZisa da rxevis sixSiris namravlis tolia.

v=ln. (1) daskvna marTebulia rogorc ganivi, ise grZivi talRebisTvis.airSi, myar sxeulsa da siTxeSi meqa-

nikuri talRa drekadi Za lebiT Cndeba. drekadi Zalebis aRZvras iwvevs sxe-

ulis formis an moculobis cvlileba. sxeulis forma icvleba nivTierebis fenebis erTimeoris mimarT wanacvlebi-sas. am dros xdeba Zvris deformacia (sur. 24.2). sxeulis moculoba ki icv-leba misi SekumSvisas an gafarToebisas.

ganivi talRa warmoiqmneba mxolod myar sxeulSi. ganivi talRa siTxis zedapirzec warmoiqmneba, magram ara mis SigniT.

sur. 24.2

B C

A D

ac

bd

A

g

B C

D

ac

bd

a b

sur. 24.1

bλ

λ

g

λ

a

6. gamosaxeT talRis siCqare talRis sigrZiT da pe-riodiT.

7. iwvevs Tu ara drekadi Zalebis gaCenas myar sxeulSi fenebis erTimeoris mimarT wanacvleba?

8. iwvevs Tu ara drekadi Zalebis gaCenas airsa da siTxeSi fenebis erTimeoris mimarT wanacvleba?

9. SesaZleblad migaCniaT Tu ara airsa da siTxeSi ganivi talRebis arseboba? pasuxi daasabuTeT.

25

grZiv talRaSi SesaZlebelia kumSvis deformacia.

myar garemoSi grZivi talRac vrceldeba da ganivic. es faqti miuTiTebs, rom myar garemoSi SesaZlebelia maTi erTdroulad arseboba. magaliTad, miwisZvrisas orive talRa erTdroulad warmoiqmneba.

dedamiwis qerqSi grZivi talRis siCqarea 3 km/wm.ganivi talRis ki _ 2 km/wm.

cdebis mizani: bgeris warmoqmnasa da sxvadasxva garemoSi mis gavrcelebaze dakvirveba.

1. simebiani instru mentis (mag. violino, Celo, Conguri, gi tara) gaWimul sims daak virdiT aJRere-bamde da JRe ris pro cesSi. amCnevT gansxvavebas?

Sem Cneuli mov lena CawereT rveulSi.

2. yuri mWidrod miadeT magidis erT bolos. megobarma meore boloze daakakunos. magidas yuri odnav mo aSoreT da cda gaime oreT. Semdeg megobarma daados yuri magidas da Tqven daakakuneT. Sem Cneuli mov lenebi CawereT rveulSi.

cdebisTvis saWiroa

simebiani

instrumenti magida

saSinao cda

meqanikuri talRebi, ganivi talRa, grZivi talRa,

talRis sigrZe

10. warmoiSoba Tu ara kumSvis deformaciasTan da-kavSirebuli drekadobis Zalebi myar, Txevad da airad sxeulebSi?

11. iwvevs Tu ara es Zalebi garemos calkeuli ubnebis rxevebs?

12. romel garemoSi vrceldeba grZivi talRa? pasuxi daasabuTeT.

13. seismur sadgurSi romeli talRa registrirdeba pirvelad? axseniT, ratom?

14. SesaZleblad migaCniaT Tu ara seismuri sadguridan miwisZvris keramde manZilis gansazRvra? axseniT, rogor?

26

1.7 bgeriTi talRa

fizikis nawils, romelic bge riT movlenebs Seiswavlis, akus tika ewodeba.

gavaanalizoT saSinao cdebSi SemCneuli movlenebi: musika-luri instru mentebis mJRer si-mebze dakvirvebisas vxedavT, rom xmis gamocemisas isini irxe vian.

aseTi cdac CavataroT: dava-kvir deT xis yuTze damagrebul U-s msgav sad moRunul Reros – kamertons (sur. 26.1, a). rezinis patara CaquCi davartyaT Reros.

mJReri kamertonis Reros frTxilad mivuaxlooT msu bu qi bur Tula ise, rom odnav Seexos (sur. 26.1, b).

Catarebuli cdebiT vrwmun debiT: bgeris wyaro yovelTvis merxevi sxe ulia. sanam simi (an kamertonis totebi) irxeva, gvesmis bge ra; gava-CerebT sims da bge rac Sewydeba.

ra xdeba haerSi an sxva garemoSi, rodesac iq moTav sebuli sxeuli irxeva?

merxevi sxeuli (firfita) ubiZ gebs haers da gadaanac vlebs mis nawi-lakebs adrin deli mdebareobi dan. igi mis erT mxares kumSavs ha eris fe-nas – qmnis haeris nawila kebis siWarbes (Sesqelebas). erT dro ulad iwvevs haeris gaiS viaTebas meore mxares. Semdgom imave ad gilas Sesqelebas cv-lis SeTxeleba. es SekumSvebi da gaiSviaTebebi drois mixedviT erTmaneTs rigrigobiT cvlis da vrceldeba drekadi grZivi talRis saxiT (sur. 26.2). haeris wneva nebismier adgilas xan metia, xan ki naklebi im wnevaze, romelic bgeris gaCenamde iyo. wnevis am namats an danakliss bgeris wneva ewodeba. talRa aRwevs Cvens yurs da iwvevs mis maxloblad wnevis periodul rxevas, romelic smenis aparatze moqmedebs.

sur. 26.2

sur. 26.1a b

yuri imitom aqvs adamians, rom moisminos

1. ra aris bgera?2. risi xma gvesmis?

3. ra gvesmis?

4. ras amCnevT? ras miuTiTebs SemCneuli movlena?


27

haerSi bgeris wneva haeris normaluri wne-vis umniSvnelo nawils Seadgens.

Cveni yuri bgeris saxiT aRiqvams rxevas, romlis sixSirec 17-dan 20 000-mde hercis farg lebSia. aseT rxevas akustikuri rxeva ewodeba.

bgeriTi rxeva SeiZleba warmoiSvas da gavr-celdes nebis mier nivTier gare moSi.

nebismieri talRa, rogorc meqanikuri, ise eleqtromagnituri, imis mixedviT, rogoria dabrkoleba, misgan nawilobriv airekleba, gardatydeba da STainTqmeba.

iseve, rogorc sinaTlisTvis, meqanikuri talRebisTvisac mar Tebulia arekvlisa da gardatexis kano nebi.

gavrcelebisas, Tu bge ra Sexvdeba raime zRudes, mTas, tyes, kedels, maSin is misgan airekleba da Cven SeiZleba gavigonoT areklili bgera, romelsac eqo ewodeba. yvela areklil bgeras ver aRviqvamT, rogorc eqos, radganac ori bgera cal-calke SegviZlia ga vigonoT mxolod im Sem TxvevaSi, Tu maTi aRqmis momentebs Soris drois Sualedi 1/15 wm-ze naklebi ar aris.

SenobebSi bgeriTi talRebi ramdenime aTeuljer airekleba Senobis kedle bidan, Weridan, avejidan da sxva sagnebidan, vidre maTi energia mTlianad STainTqmeba. amitom bgeris wyaros rxevis Sewyvetis Semdeg, maTi mravaljeradi arekvlis gamo, SenobaSi bgera ismis ramdenime wamis gan mav lo baSi.

CavataroT cda: magidis erT bolosTan dadeT isrebiani saaTi (sur. 27.1). Tqven dadeqiT magidis mopirdapire boloSi, sadac saaTis wikwiki TiTqmis ar ismis. magidis am bolos miadeT yuri da gamoitaneT daskvna.

drekadi sxeulebi _ liTonebis umetesoba, xe, airebi, siTxeebi _ bgeris kargi gamtarebia.

rbili da forovani sxeulebi _ nabadi, xaliCa, dawnexili korpi, naxerxi, forovani qvebi _ bgeris cudi gamtarebia.

bgeriTi rxevebi, miaRweven ra aseT fenas, swrafad miilevian da qrebian. rxeviTi moZraobis energia gardaiqmneba Sinagan energiad _ sxeulebi Tbeba.

vaku umSi bgera ar vrceldeba. bgeris gavrcelebis siCqare siTxeSi metia, vidre haerSi da kidev uf ro metia myar sxeulSi.

sur. 27.1

6. haeri ufro kargad atarebs bgeriT rxevebs Tu magidis zedapiri?

7. aRwereT, rogor moiqceviT xmaurisagan oTaxis dasa-cavad.

8. rogoria Tqveni varaudi, miileva Tu ara bgerebi gavrce lebisas? moiyvaneT varaudis damadasturebeli magaliTi.

5. ra minimaluri manZili unda iyos dabrkolebamde, rom eqo gavigonoT?

28

mag. haerSi bgeris gavrcelebis siCqarea 340 m/wm, wyalSi _ ≈1400 m/wm,

rkinaSi _ ≈5850 m/wm. garemos temperaturis gadidebiT masSi bgeris siCqare izrdeba.

zogierT garemoSi bgeris gavrcelebis siCqare ixileT cxrilSi gv. 140.

bgerebi, romlebsac yoveldRi urad vismenT, metad mravalferovania.bgeras, romelsac rxevis gan sa z Rvruli sixSire aqvs, musi ka luri bgera,

anu toni ewodeba.musikaluri tonebi gansxvavdebian xmamaRlobiT da simaRliT.tonis xmamaRloba ganisazRvreba rxevis amplitudiT. rac ufro

didia rxevis amplituda, miT ufro xmamaRalia toni.magaliTad, rac ufro Zlierad vurtyamT CaquCs kamertons, miT ufro

metia kamertonis fexis rxevis amplituda da miT ufro xmamaRla JRers igi.

tonis simaRle ganisazRvreba rxevis sixSiriT. rac ufro didia rxe vis sixSire, miT ufro metia tonis simaRle (maRalia toni). amas SeiZleba davakvirdeT simis rxevisas. si-mis daWimulobis zrda iwvevs misi Tavisufali rxevis sixSiris zrdas. amitom, roca vWimavT gitaris an sxva instrumentis sims, vzrdiT bgeris simaRlesac.

adamianis xmis bgerebis sazRvrebi moTavse-bulia 70 hc-sa (dabali sabaso noti) da ≈1400 hc-s (maRali sopranos noti) Soris.

xmauri musikaluri tonisagan imiT gansxvavdeba, rom mas ar Seesabam-eba rxevis raime gansazRvruli sixSire. igi sxvadasxva sixSi ris rxevebis erTobli obaa.

grZiv talRebs, romelTa sixSire 16 hc-ze naklebia, infrabgerebi ewodeba, xolo talRebs, romelTa sixSire 20 000 hc-ze metia _ ultrabgerebi.

samyaroSi infrabgerebi da ultrabgerebi iseve farTodaa gavrcele-buli, rogorc bgeriTi talRebi. aRmoCnda, rom maT asxivebs da iRebs cocxali organizmebi ro gorc xmeleTze, ise wyalsa da haerSi da iyenebs TavisianebTan `salaparakod~ an sivrceSi orientirebisaTvis.

sur. 28.1

akustika, musikaluri bgera, tonis simaRle,

tonis xmamaRloba

davaleba

moipoveT informacia cxovelebisa da adamianebis mier aRqmuli bgeris sixSiris Sesaxeb da warmoadgineT svetovani diagramis saxiT.

moamzadeT masala prezentaciisTvis.

8. moipoveT informacia, sxvadasxva garemoSi bgeris gavrcelebis siCqaris Sesaxeb. SeadareT erTmaneTs da gamoTqviT varaudi maT Soris arsebul gansxvavebaze.

29

1.8amocanis amoxsnis nimuSi

1. gansazRvreT, ra simaRleze iyo aweuli maTematikuri qanqaras

burTula wonasworobis mdebareobidan, Tu xelis gaSvebis Semdeg man

es mdebareoba 1,4 m/wm siCqariT gaiara.

amoxsna

potenciuri energiis aTvlis nulovan doned avir-

CioT burTulis udablesi mdebareoba (sur. 29.1).

meqanikuri energiis mudmivobis kanonis Tanaxmad,

Epot.1

+Ekin.1

=Epot.2

E+Ekin.2

, (1)

sadac Epot.1

=mgh, (2) Ekin.1

=0, (3) Epot.2

=0 (4) .E mv2

2

kin.2= (5)

(2),(3),(4),(5) (1) Þ (*)

(*): m.

2. gansazRvreT maTematikuri qanqaras sigrZe, Tu misi sixSire

1 hercia.

amoxsna

maTematikuri qanqaras rxevis periodi

T gl l

gT2

4 2

2

&= =rr

(1) .T 1= o (2)

(2) (1) Þ .lg

4 2 2r=

o (*) (*): l=0,25 m.

3. dinamometrze dakidebuli sxeulis rxevis sixSire 2 hcia.

gansazRvreT rxevebis Sewyvetis Semdeg zambaris wagrZeleba.

amoxsna

rxevebis Sewyvetis Semdeg sxeuli wonasworobaSia.

sxeulze moqmedi mg simZimis da F drekadobis Zalebi

erTmaneTs awonasworebs F=mg. (1)

hukis kanonis Tanaxmad, F=k∆l. (2) (1)(2) Þ .lkmg

=D (3)

zambariani qanqaras rxevis periodi .Tkm2= r (4) aseve .T 1= o (5)

(4)(5) Þ .km

412 2=

r o (6) (6) (3) Þ .l

g4 2 2r o

=D (*)

(*): ∆l ≈ 6 .10-2 m.

sur. 29.1

? l

2moc.: hc

D

=o

? lmoc.: n=1 hc.


30

4. zambaraze dakidebul firfitaze drois toli Sualedebis Semdeg ecema wylis wveTebi, ris gamoc zambara irxeva maqsimaluri amplitudiT. firfitis sakuTari rxevis sixSire n

0ia. wveTebi swydeba

raRac simaRlidan.gansazRvreT manZili or uaxloes vardnil wveTs Soris. haeris

winaaRmdegoba umniSvneloa.

amoxsnaradgan haeris winaaRmdegoba umniSvneloa, wveTebis

aCqareba SeiZleba CavTvaloT g-s tolad. wveTebi erTmaneTis mimarT Tanabrad moZraoben. ris

gamoc vardnis procesSi wveTebs Soris manZili ar icvleba. manZili or vardnil wveTs Soris

.hg2

2

=x

(1)

sadac τ aris drois Sualedi wveTis mowyvetidan momdevno wveTis mowyvetamde. wveTebis dacemis gamo firfitis rxevebi iZulebiTia. radganac firfitis rxevis amplituda maqsimaluria da ar icvleba, amitom damyarebulia rezonansi. e. i. gare Zalis sixSire (am SemTxvevaSi vardnili wveTebis sixSire) emTxveva firfitis sakuTari rxevis sixSires n=n0

. (2)

aqedan gamomdinareobs, rom t drois Sualedi firfitis rxevis t0 periodis

tolia.

.10

0

x x o= = (3) (3) (1) Þ .hg

2 0

2o

= (*)

5. Tqveni varaudiT, did darbazSi oratoris xma rodis ufro kargad ismis, roca darbazi xalxiTaa savse, Tu roca msmenelTa raodenoba mcirea?

amoxsna

did darbazSi, roca msmenelTa raodenoba mcirea, oratoris sityva naklebad garkveviT ismis. bgerebi ramdenjerme irekleba kedlebidan, Weridan. radgan es zRudeebi msmenelTagan sxvadasxva manZilze mdebareobs, amitom oratoridan wamosuli da areklili bgerebi msmenelebTan sxvadasxva dros midis. amitom oratoris sityva garkveviT ar ismis.

magram imave darbazSi, roca is msmenelebiTaa savse, tansacmeli STanTqavs bgeriT rxevebs, amitom aseTi darbazis akustikuri (bgeriTi)

Tvisebebi umjobesdeba da oratoris xma ukeTesad ismis.

? h

g

moc.: o

31

1.9SeamowmeT Tqveni codna

amoxseniT amocanebi

1. qanqaras rxevis erTi periodis ganmavlobaSi ramdenjer gardaiqmneba potenciuri energia kinetikurad da, piriqiT, kinetikuri _ potenciurad?

2. gansazRvreT maTematikuri qanqaras sigrZe, Tu misi rxevis periodi 1 wm-ia.

3. gansazRvreT zambaraze damagrebuli sxeulis rxevis periodi da sixSire, Tu igi 16 wm-Si 20 rxevas asrulebs.

4. 400 n/m sixistis zambara 10 sm-iT gaWimes. gansazRvreT zambaris maqsimaluri potenciuri energia. zambara horizontalur mdebareobaSia.

5. gitarebiaT Tu ara wyliani vedro? migiqceviaT yuradReba, rom wyliani vedros tarebisas zogjer misgan wyali gadmoaSxefebs? ratom xdeba ase? rogor moiqceviT gadmoSxefebis SesaCereblad?

6. zRvaSi talRis sigrZe 150 m-ia, rxevis periodi _ 15 wm-i. gansaz-RvreT talRis gavrcelebis siCqare.

7. grZiv talRasTan SedarebiT granitis masivSi seismuri signali ganivi talRiT 2,8 wm-is dagvianebiT dafiqsirda. gansazRvreT manZili seismografidan miwisZvris epicentramde, Tu grZivi talRis siCqare 5,40 km/wm-ia, xolo ganivis _ 3,85 km/wm.

8. haeri metad STanTqavs bgeras, vidre mina. quCis xmauri ki Ria fan-jaraSi ufro metad ismis, vidre daxurulSi. axseniT, ratom?

testi

1. zambaraze damagrebuli sxeulis masis oTxjer gazrdiT rxevis periodi a. oTxjer gaizarda; b. oTxjer Semcirda; g. orjer gaizarda; d. orjer Semcirda; e. ar Seicvala.

2. zambaris sixistis oTxjer gazrdiT masze damagrebuli sxeulis rxevis periodi

a. oTxjer gaizarda; b. oTxjer Semcirda; g. orjer gaizarda; d. orjer Semcirda; e. ar Seicvala.

3. maTematikuri qanqaras sigrZis oTxjer gadidebiT rxevis periodi a. oTxjer gaizarda; b. oTxjer Semcirda; g. orjer gaizarda; d. orjer Semcirda; e. ar Seicvala.

4. Zafze dakidebuli sxeulis masis oTxjer gadidebiT rxevis periodi a. oTxjer gaizarda; b. oTxjer Semcirda; g. orjer gaizarda; d. orjer Semcirda; e. ar Seicvala.


32

II Tavi

eleqtromagnituri

rxevebi da

talRebi

am TavSi gaixsenebT da gaecnobiT

analogias meqanikur da ele-

qtrul rxevebs Soris;

cvlad dens;

cvladi denis efeqtur mniSvnelobas;

cvladi denis simZlavres;

cvladi denis generators;

transformators;

sinaTles, rogorc eleqtromagnitur talRas;

eleqtromagnitur skalas;

mocemul Temebze amocanebis amoxsnas.

33

2.1analogia meqanikur da eleqtromagnitur movlenebs Soris

33.1, a suraTze gamosa xulia SekumSuli zambara, 33.2, a-ze mimdevrobiT SeerTebuli kondensatori da induqciurobis koWa _ rxeviTi konturi.

ganxilul SemTxvevebSi meqanikuri da eleqtromagnituri energiebis sxva saxis energiad gardaqmna ar gaviTvaliswinoT.

burTulis gaTavisuflebis t0= momentidan inertulobis gamo Fx drekado-bis Zalis moqmedebiT burTulis siCqare TandaTan iwyebs gadidebas.

t T41= momentSi burTulas aqvs maqsimaluri kinetikuri energia. am mo-

mentSi zambaris potenciuri energia nulis tolia. meqanikuri energiis

mudmivobis kanonis Tanaxmad: kA m

2 2

v2 2maqs

= (sur. 33.1,b).

analogiurad, K gadamrTvelis meore mdebareobaSi gadayvanis momenti-dan U Zabvis moqmedebiT kondensatori iwyebs ganmuxtvas. TviTinduqciis gamo wredSi deni TandaTan iwyebs gadidebas. kondensatoris eleqtruli velis energia mcirdeba, igi denis magnituri velis energiad gardaiqmneba.

sur. 33.2

sur. 33.1

a

a

b

b

g

g

d

d

e

e

t0=0

t0=0

Im Im

t4=T

t4=T

v vF F F

t T41=

t T41=

t T22=

t T22=

t T343=

t T343=

1. ra saxis energia aqvs gaWimul (SekumSul) zambaras? damuxtul kondensators (sur. 33.2,a)? dawereT energiis

ganmsazRvreli formulebi?

2. rogor icvleba zambaris potenciuri energia? rad gardaiqmneba igi?


34

t T41= momentSi denis magnituri velis energia maqsimaluria. am momentSi

kondensatoris energia nulis tolia. rodesac wredis R winaRoba umniS-vneloa, maSin energiis mudmivobis kanonis Tanaxmad, SegviZlia davweroT:

(sur. 33.2,b)

b mdebareobaSi burTulaze drekadobis Zala ar moqmedebs.

inertulobis gamo burTula agrZelebs moZraobas marjvniv. zambara iWimeba. drekadobis Zala mimarTulia marcxniv. burTulis siCqare mcirdeba.

t T22= momentSi potenciuri energia maqsimaluria, kinetikuri _ nuli

(sur. 33.1, g).analogiurad, magnituri velis energiis xarjze eleqtruli muxtebi

iwyeben kondensatoris Semonafenebze dagrovebas da t T22= momentSi

magnituri velis energia kondensatoris eleqtruli velis energiadaa gardaqmnili (sur. 33.2, g).

amis Semdeg burTula iwyebs moZraobas wonasworobis mdebareobisaken _ kondensatori iwyebs ganmuxtvas. wredSi deni gadis Tavdapirvelis sapi-rispiro mimarTulebiT (sur. 33.2,d) da periodis bolos sistema ubrundeba sawyis mdgomareobas (sur. 33.2, e).

amis Semdeg procesi meordeba. sistemaSi _ kondensatori da mis SemonafenebTan mierTebuli koWa _ aRiZvreba Tavisufali eleq tru li rxe vebi. aseT sis temas rxeviTi konturi ewodeba.

xaxunis gamo Tavisufali meqanikuri rxevebi garkveuli drois Semdeg Sewydeba.

aseve, gamtarebis winaRobisa da energiis gamosxivebis gamo, kontu rSi eleqtromagnituri rxevebi Sewydeba. meqanikuri da eleqtruli energia Sinagan energiad gardaiqmneba. es rom ase ar iyos, maSin meqanikuri da eleqtromagnituri rxevebi usasrulod gagrZeldeboda.

drois im umcires Sualeds, romlis Semdegac denis Zalis an Zabvis mniSvnelobis moduli da mimarTuleba meordeba, denis Zalisa da Zabvis rxevis periodi ewodeba.

Cveni msjelobidan Cans, rom arsebobs msgavseba meqanikur da ele-qtromagnitur rxevebs Soris. magram msgavsebaa ara periodulad cvladi sidideebis bunebas Soris, aramed am sidideebis perioduli cvlilebis

procesebs Soris. magaliTad, kondensatoris damuxtva _ misTvis

eleqtruli energiis miniWeba _ analogiuria zambaraze damagrebuli

3. gaCerdeba burTula am mdebareobaSi? axseniT, ratom fiqrobT ase?

4. rad gardaiqmneba burTulis kinetikuri energia? pasuxi daasabuTeT.

35

sxeulis wonasworobis mdebareobidan gamoyvanis da misTvis energiis

miniWebis. kondensatoris q muxtis cvlileba analogiuria x koordinatis cvlilebis da a. S. analogia meqanikur da eleqtromagnitur rxevebs So-ris gamovsaxoT cxrilis saxiT.

meqanikuri sidideebi eleqtruli sidideebi

koordinati x

siCqaris gegmili vx

masa m

zambaris sixiste k

kinetikuri energia mv2/2

potenciuri energia kx2/2

muxti q

denis Zala I

induqciuroba L

tevadobis Sebrunebuli sidide 1/C

magnituri velis energia LI2/2

eleqtruli velis energia q2/2C

radgan zambaraze damagrebuli sxeulis rxevis periodi amitom

meqanikur da eleqtrul rxevebs Soris analogiis safuZvelze, SeiZleba davweroT rxeviT konturSi sakuTari eleqtruli rxe vebis periodis

gamosaxuleba: es formula pirvelad ingliselma fizikosma

tomsonma gamoiyvana, amitom tomsonis formulis saxelwodebiTaa cnobili.

gavecaniT analogias meqanikur da eleqtromagnitur rxevebs Soris.analogiis safuZvelze, davwereT eleqtruli rxevebis periodis

ganmsazRvreli formula.

5. rxeviTi konturis induqciuroba 2 hn-ia, konden-satoris tevadoba ki _ 0,5 mkf. gansazRvreT konturSi

eleqtromagnituri rxevebis sakuTari sixSire.

6. rogor Seicvleba rxeviTi konturis sakuTari sixSire, Tu koWas induqciurobas orjer gavadidebT, xolo kondensatoris tevadobas orjer SevamcirebT? pasuxi daasabuTeT.

rxeviTi konturi, tomsonis formula

36

2.2 cvladi deni. cvladi denis generatori. denis Zalisa da Zabvis efeqturi mniSvneloba

rxeviT konturSi Tavisufali eleqtruli rxevebi swrafad miileva. ara-milevad iZulebiT rxevebs ki udidesi praqtikuli mniSvneloba aqvs. mis misaRebad daxarjuli energia rxeviT konturSi ganuwyvetliv unda Sevav-soT. ganaTebis qselSi cvladi deni iZulebiTi eleqtruli rxevebia. rogor miviRoT igi?

CavataroT cda: magnitur velSi movaTavsoT Sveul RerZze Camoc-muli ABCD marTkuTxa CarCo, rome-lic izolaciiT dafaruli mavTulis ramdenime aTeuli xviisagan Sedgeba. gamtaris boloebi rgolebisa (r) da musebis (m) meSveobiT galvanometrTa-naa SeerTebuli (sur. 36.1).

cda gviCvenebs, rogori mdebare-obac unda hqondes CarCos magnitur velSi. Tu igi uZravia, galvanometri dens ar gviCvenebs.

vabrunoT CarCo mudmivi kuTxuri siCqariT saaTis isris brunvis mimarTulebiT im damkvirveblisaTvis, romelic CarCos zemodan uyurebs. CarCos im mdebareobas, rodesac misi sibrtye magnituri velis daZabulobis wirebis marTobulia, neitraluri vuwodoT. t=0 momentSi am mdebareobis gavlisas CarCos AB da CD gverdebi daZabulobis wirebis paralelurad moZraoben. ar xdeba am wirebis gadakveTa, ar icvleba CarCos gamWoli magnituri nakadi, ris gamoc masSi deni ar aRiZvreba. am mdebareobis gavlis momentidan CarCos gamWoli magnituri nakadi icvleba, amitom konturSi aRiZvreba deni. Semobrunebis kuTxis gadidebasTan erTad izrdeba CarCos gamWoli magnituri nakadis cvlilebis siCqare.

2. rogor icvleba am dros konturSi gamavali denis moduli? pasuxi daasabuTeT.

3. gansazRvreT CarCoSi gamavali denis mimarTuleba

drois t T41= momentSi, rodesac igi 900-iTaa Semobrunebuli.

4. jer ivaraudeT, Semdeg cdiT daadgineT, drois am momentidan dawyebuli rogor icvleba deni konturSi. gansazRvreT deni drois t

T22=

momentSi, rodesac CarCo 1800-iT Semobrundeba.

1. Tqveni azriT, SeiZleba Tu ara praqtikulad gamoviyenoT iseTi deni, romelic swrafad miileva?

asxeniT, ratom fiqrobT ase?

sur. 36.1

mm

r

A

B C

D


37

am mdebareobis gavlisas deni Seicvlis mimarTulebas, misi moduli

izrdeba da aRwevs maqsimums t T343= momentSi.

Semdeg isev mcirdeba. t4=T momentSi CarCo ubrundeba sawyis mdebareobas. masSi gamavali deni nuli xdeba, kvlav icvlis mimarTulebas da procesi meordeba.

damtkicebulia, rodesac CarCo brunavs mudmivi kuTxuri siCqariT erTgvarovan magnitur velSi, ma-Sin CarCoSi aRiZvreba si nusoiduri kanoniT cvla di

em Zala da deni. (sur. 37.1).

E=Emaqs

sinwt, I=Imaqs

sin(wt+j0), sa dac j0 fazaTa sxvaobaa denis rxevasa da Zabvas Soris.

mowyobilobas, sadac ama Tu im sa xi s energia gardaiqmneba cvladi denis eleq-trul energiad, cvladi denis generatori ewodeba.

cvla di denis generatoris modelia (sur. 36.1) danadgari, romelic Sedgeba magnitisa da gamtari CarCosagan, ori rgo-liTa da ori musiT.

mZlavri generatorebiT SeiZleba mivi-RoT aTeul aTasobiT amperi deni 10 000 v rigis Zabvis dros.

moZravi kontaqtebis meSveobiT aseTi maRali Zabvis denis gamoyvana, praqti-kulad, SeuZlebelia, vinaidan moZrav kontaqtebSi Zlieri naperwklebi Cndeba. amitom cvladi denis TiTqmis yvela gen-eratorSi gragnils (Ruza), romelSic in-duqciiT aRiZvreba em Zala, uZravad dgamen, magnituri sistema (induqtori) ki brunavs. manqanis uZrav nawils statori ewodeba, moZravs ki _ rotori.

generatoris rotori brunavs romelime ZravaTi _ hidro turbi niT, orTqlis turbiniT, Sigawvis ZravaTi an sxva.

erT agregatad SeerTebul ele q trul generators da orTqlis turbinas turbogeneratori ewo deba (sur. 37.2).

hidroeleqtrul sadgurSi (he si) generatorebis rotorebis sabrune-blad gamoiyeneba kaSxliT aweuli wylis potenciuri energia (sur. 38.1, a). eleqtruli generatoris rotori brunavs hidravlikuri turbiniT (sur. 38.1, b).

cvladi denis mniSvnelobis dadgenisas sargebloben misi iseTi moq-medebiT, romelic denis mimarTulebaze damokidebuli ar aris, magaliTad, denis siTburi moqmedeba.

E

t

sur. 37.1

sur. 37.2

38

sur. 38.1

eleqtruli energia

a b

5. SesaZleblad migaCniaT Tu ara, rom mocemuli winaRobis gamtarSi mocemul droSi mudmivma denma

iseTive siTbos raodenoba gamoyos, rasac gamoyofs cvladi deni imave droSi? pasuxi daasabuTeT.

6. rodesac ganaTebis qselSi Zabvis efeqturi mniSvneloba 220 v-ia, maSin rogoria Zabvis amplituduri

mniSvneloba?

cvladi denis generatori, statori, rotori, turbogeneratori, Zabvisa da denis efeqturi mniSvneloba.

mudmivi denis im mniSvnelobas, romelic gamtarSi siTbos imdenive raodenobas gamoyofs, ramdensac cvladi deni imave droSi, cvladi denis moqmedi (efeqturi) mniSvneloba ewo deba.

mtkicdeba, rom sinusoiduri cvladi denisaTvis misi I efeqturi mniSvneloba

mis Imaqs

amplitudur mniSvnelobaze -jer naklebia, e. i. . msgavsad amisa,

Zabvis U efeqturi mniSvneloba naklebia mis amplitudur mniSvnelobaze -jer, e. i.

, E.

2E maqs

=

saqarTveloSi ganaTebis qselSi denis sixSire 50 hercia. es imas niSnavs, rom deni gamtarebSi 1 wm-Si 50-jer erTi mimarTulebiT gadis da 50-jer sapirispiro mimarTulebiT.

gavecaniT cvladi denis generatoris models. cvladi denis generatoris mowyobilobas da misi moqmedebis princips. agreTve, cvladi denis da Zabvis moqmed anu efeqtur mniSvnelobas.

39

2.3eleqtruli energiis gadacema

eleqtrosadgurebs ageben im adgilebSi, sadac sawvavisa da hidrore-sursebis wyaroebia. momxmareblebi ki yvelganaa. didi masStabiT eleq-troenergiis Senaxva SeuZlebelia. igi miRebisTanave unda gamoiyenon. amitom iqmneba eleqtroenergiis did manZilze gadacemis aucilebloba. deni gadamcem sadenebs aTbobs.

eleqtroenergiis gadacema ekono miurad xelsayreli rom iyos, aucile-blad saWiroa, sadenebis gaTbobaze danakargi rac SeiZleba Semcirdes. rogor movaxerxoT es?

gamtarSi denis gavlisas gamoyofili siTbo ganisazRvreba joul-lencis kanoniT.

Q = I2Rt, (1)

sadac I gamtarSi gamavali denia, (2) gamtaris winaRoba, l _ gam-

taris sigrZe, S _ ganivkveTis farTobi, ρ _ kuTri winaRoba, t _ drois Sualedi, romlis ganmavlobaSic gamtarSi deni gadioda.

(1) ⇒ energiis danakargis Semcirebis ramdenime gza arsebobs. erT-erTi gadamcemi xazis sadenebis winaRobis Semcirebaa.

SevecadoT, problemebis gadawyvetis gzebi amocanis amoxsniT, etapobrivad, vaCvenoT.

vTqvaT, eleqtrosadguris generatoris simZlavrea 220 kvt, Zabva _ 220 v. eleqtroenergia unda gadavceT 40 kmze spilenZis mavTuliT. ganvsazRvroT, rogori unda iyos mavTulis ganivkveTis farTobi da masa, rom sadenebSi danakargi ar aRematebodes gadasacemi simZlavris 10%s?

amoxsna

xazis winaRoba . (3)

(3) ⇒ (4)

simZlavris danakargi

P1=I2R, (5) da P1=kP. (6)

2. rogor SevamciroT energiis danakargi gadamcem xazSi? varaudi CawereT samuSao rveulSi.

1. dakargulia Tu ara denis mier gadamcem xazSi gamoyofili siTburi energia? axseniT, ratom fiqrobT

ase?

3. ramdenad misaRebia mcire winaRobis sadenebis gamo-yeneba eleqtruli energiis gadacemisas? varaudi Cawe reT samuSao rveulSi.

? S, m

moc.: P=220kvt=22.104 vt

U=220v

l=40 km= 4.104 m

ρ=1,7.10–2 omi.mm2/m

D=9800 kg/m3

K=0,1


40

generatoris simZlavre (7)

(6) (7) (5): ⇒ (8)

(8) (4) ⇒ (*) (*): S=31 000 mm2 = 0,031 m2.

m=DSl. (**) (**): m=11 036 000kg.

mavTulis TiToeuli metris masa

energiis danakargis mkveTrad Semcireba SeiZleba gadamcem xazSi denis SemcirebiT.

vTqvaT, igive 220 kvt simZlavre unda gadavceT 100-jer meti 22000 v ZabviT.

gamoTvlebi gviCvenebs, Tu eleqtrul energias 100-jer meti ZabviT gadavcemT, SesaZlebelia, gadamcemi xazis winaRobis 1002-jer gadideba da, Sesabamisad, xazis masis 1002-jer Semcireba. amis Sedegad, TiToeuli metris masa toli iqneba ≈0,0276 kg-is da energiis gadacema, praq tikulad, SesaZ lebeli gaxdeba.

amgvarad, eleqtroenergiis did man Zilze gada cemisas aucileblad maRali ZabviT unda visa rgebloT.

amis gamo, generatoridan miRebul Zabvas amaR-leben transformatoriT. umartivesi tran sfo-rmatori, misi mowyobilobis sqema da pirobiTi aRniSvna gamosaxulia 40.1 a, b da g suraTebze. transformatoris muSaobas safuZvlad udevs eleqtromagnituri induqciis movlena.

4. praqtikulad, SesaZleblad migaCniaT Tu ara eleq-truli energiis gadacema aseTi didi masis mavTulebiT? axseniT, ratom fiqrobT ase?

5. mocemuli P=IU simZlavris Seucvlelad, rogor SeiZ leba denis Semcireba?

6. gansazRvreT, Tu Zabvas 100-jer gavadidebT, maSin ramdenjer Semcirdeba deni gadamcem xazSi?

7. P1=I2R formulidan daadgineT, simZlavris imave danaka rgisaTvis ramdenjer ufro didi winaRobis gadamcemi xazis gamo yenebaa SesaZle-beli?

transformatori (laT.) _ aparati, romelic eleq-truli denis Zabvas zrdis

an amcirebs.

sur. 40.1

a

b g

41

gadamcemi xazis boloebze _ momxmarebelTan Zabva unda SevamciroT. amas axorcieleben sadab lebeli transformatoriT. Cveulebriv, Zabvis dadableba da, Sesabamisad, denis gazrda xorcieldeba ramdenime etapad. yovel etapze Zabva xdeba sul ufro mcire, eleqtruli qselis mier Semo-fargluli teritoria _ sul ufro farTo.

eleqtroenergiis gadacemisa da ganawilebis sqema mocemulia 41.1 suraTze.

Tu adamiani SeZlebs iseTi gamtaris Seqmnas, romelsac bunebriv piro-bebSi winaRoba ar eqneba, maSin (1) ⇒ aseT gamtarSi (zegamtarSi) denis gavlisas siTbo ar gamoiyofa da eleqtrul energias, ragind did manZilze, udanakargod gadavcemT.

davadgineT, rom eleqtrosadgurebidan momxmareblamde eleqtruli energiis gadacemisas aucileblad maRali ZabviT unda visargebloT. amisaTvis generatoridan miRebul Zabvas jer amaRleben, Sor manZilze gadacemis Semdeg ki adableben transformatoris meSveobiT. Semdeg gakveTilze gavecnobiT transformatoris moqmedebis princips.

ramdenad saWiroa iseTi gamtaris Seqmna, romelsac bunebriv pirobebSi winaRoba ar eqneba.

sakiTxi ganixileT etapebis mixedviT.

1. CamoayalibeT Tqveni pozicia, am sakiTxTan dakavSirebiT.

2. moiyvaneT magaliTebi, romliTac daasabuTebT oTaxis tempera-turaze zegamtaris Seqmnis aucileblobas.

3. ra Seicvleboda eleqtruli energiis gadacemisas, Tu zegamtarebs gamoviyenebdiT?

4. ratom aris es mniSvnelovani?

davaleba

cvladi denis generatori

11 kv samaRlebeli transforma-

tori

110 kv

gadacemis xazi

sadablebeli transfor-

matori

35 kv

gada-cemis xazi

sadablebeli transforma-

tori

6 kv

6 kv

gadacemis xazi

6 kv sadablebeli transforma-

tori

220 v

220 v

220 v

220 v

220 vmomxmareblisken

35 kv

35 kv

sur. 41.1

42

2.4 transformatori

transformatori Sedgeba Sekruli fo-ladis gularisagan, ro melzec Camocmulia ori (an meti) mavTulis gragniliani koWa. erT-erT gragnils, romlis boloebze mode bulia gardasaqmneli cvladi U1 Zabva, ewodeba pirveladi gragnili. gragnils, rom-lis boloebi SeerTebulia momxmarebelTan, ewodeba meoreuli.

transformatoris moqmedebis principi damyarebulia eleq tromagnituri induqciis movlenaze. pirvelad koWaSi cvladi denis gavlisas, gularSi Cndeba cvladi magnituri nakadi, romelic, praqtikulad, mxolod gula-ris SigniT arsebobs da erTnairia yvela kveTaSi. amis gamo induqciis em Zalis myisi mniSvneloba pirveladi Tu meoreuli gragnilis nebismier xviaSi erTnairia.

sur. 42.2

a b

4. ra aris gamosaxuli 42.2 suraTze?

1. ra aris saWiro eleqtroenergiis Sor manZilze naklebi dana-kargebiT gadasacemad?

2. ra informacias iRebT 42.1 suraTebidan?

3. ris meSveobiT xorcieldeba Zabvis amaRleba?

e. CamrTvelis gamorTvidan

1-2 wm-is Semdeg

a. CamrTveli gamorTulia b. CamrTvelis CarTvisas g. CamrTvelis CarTvidan

1-2 wm-is Semdeg

d. CamrTvelis gamorTvisas

denis wyaro

sur. 42.1


43

cxadia, rac metia koWas xviaTa ricxvi, miT metia masSi aRZruli induqciis em Zala da Zabva am koWas boloebze.

dasabuTebulia, rom ,

sadac U1 da U2 Zabvis moqmedi mniSvnelobebia, Sesabamisad, pirveladi da meoreuli gragnilebis boloebze. n1 da n2 pirveladi da meoreuli grag-nilebis xviaTa ricxvia.

K sidides ewodeba transformaciis koeficienti. Tu K>1, transfor-matori aris sadablebeli, xolo Tu K<1, samaRlebeli.

Tanamedrove transformatorebSi energiis danakargebi Zalian mcirea. igi ar aRemateba 2-3%, amitom SegviZlia vTqvaT, rom meoreul wredSi gadacemuli energia tolia cvladi denis wyarodan moxmarebuli energiisa, e. i. denis simZlavre pirvelad wredSi miaxloebiT tolia simZlavrisa

meoreul wredSi: U1I1 U2I2, aqedan ,UU

II

2

1

1

2. e. i. ramdenjerac izrdeba

transformatoris meSveobiT Zabva, imdenjer mcirdeba deni meoreul gragnilSi (da piriqiT).

gularis arasasurveli gaxurebis Sesamcireblad mas amzadeben ara masiuri foladisagan (Tumca, es gacilebiT advili da iafia), aramed specialuri foladis furclebisagan, romlebic erTmaneTisagan izolaciis Txeli feniTaa ganmxoloebuli. aseTi gularis winaRoba gacilebiT didia masiuri gularis winaRobaze.

gavecaniT transformatoris agebulebis da moqmedebis princips. davad gineT, rodis aris transformatori samaRlebeli da rodis _ sadablebeli.

5. rogoria Tqveni varaudi, ra daniSnuleba aqvs transformatoris gulars?

6. transformatoris gulari foladisaa. Tqveni varaudiT, aRiZvreba Tu ara induqciuri deni gularSi? pasuxi daasabuTeT.

7. gaxurdeba Tu ara foladis gulari denis gavlisas? ramdenad sasurvelia gularis gaxureba?

8. Tqveni varaudiT, ratom iqcevian ase?

9. transformatoris gragnilebi sxvadasxva sisqis mavTulisganaa damzadebuli. axseniT, romel gragnils aqvs xviaTa meti raodenoba?

10. Tu transformatoris gragnilSi erT-erTi xvia rgolad Caiketeba, trans formatori gamodis mwyobridan. axseniT, ratom?

transformatori, transformaciis koeficienti, samaRlebeli da sadablebeli transformatorebi.

44

2.5 eleqtromagnituri talRebi

miveCvieT, rom cnoba msoflios sxvadasxva adgilas momxdari ambis Sesaxeb sul ramdenime wuTSi aRwevs Cvenamde. rogorc xSirad vambobT xolme, SevigrZnobT samyaros majiscemas. yovelive amas ki, uzrunvelyofs radiokavSiris erTiani sistema.

radiokavSirs safuZvlad udevs jeimz klerk maqsvelis eleqtromagnituri velis Teoria.

maqsvelma Teoriulad daasabuTa, rom eleqtrul da magni tur velebs Soris mWidro kavSiri arsebobs: magnituri velis yoveli cvlileba garemomcvel sivrceSi iwvevs cvla di eleqtruli velis gaCenas. eleq truli velis yoveli cvlileba ki _ cvla di magnituri velis gaCenas.

cvladi eleqtruli velis da mas Tan uwyvetad dakav Sirebuli cvla di magnituri velis erTo bliobas eleq tromagnituri veli ewo deba.

swrafad cvladi eleqtromag nituri veli vakuum-Si vrceldeba sinaTlis gavrcelebis _ 300 000 km/wm siCqariT da gavrcelebisas gadaaqvs energia.

periodulad cvla di eleqtro mag nituri ve lis gavrcelebis pro cesi warmoadgens ta lRur pro cess _ ele qtromagnitur ta l Ras.

44.1 suraTze gamosa xu lia ase Ti procesis `momentaluri su ra Ti~. eleqtruli da mag-ni tu ri velebi warmoiqmne ba ur TierT marTob sibrtyeebSi. ma T marTobulad vrceldeba eleqtro magnituri talRa.

maqsvelma daamuSava sinaT-li s eleq tromagnituri Teoria da amiT gaaerTiana manamde erT ma neTisagan gan calkevebuli eleq trobis, magniti zmisa da optikis dargebi. maqsvelis varaudi, rom sinaTle eleqtromagnituri tal Raa, daadastura henrix hercma (1857-1894). man eqsperimentulad miiRo sinaTleze naklebi sixSiris ele-qtromagnituri talRebi da gazoma maTi siCqare. aRmoCnda, rom sinaTlis msgavsad, isic ganivi talRebia da gavrcelebisas imave Tvi sebebs avlens, rasac sinaTlis tal Rebi: arekvla, gardatexa, da sxva.

Tu eleqtromagnitur talRebs ganvalagebT talRis sigrZis klebis mixedviT, miviRebT skalas, romelsac eleqtromagnitur talRaTa skala ewodeba.

1. daasaxeleT mowyobilobebi, romelTa meSveobiT swrafad SeiZleba informaciis mopoveba.

sur. 44.1

eleqtruli veli

magnituri veli

jeimz klerk maqsveli(18311879)


45

radiotalRebioptikuri diapazonis

gamosxivebarentgenis

sxivebi

sur. 45.1

gama sxivebibgeriTi da infrabgeriTi

sixSiris

eleqtromagnituri gamosxivebis mTeli speqtri gamosaxulia 45.1 suraTze.

eleqtromagnituri talRebi talRis sigrZe, m

sixSire, hc

eleqtromagnituri talRebis klasifikacia

bgeriTi da infrabgeriTi sixSiris 1011-105 3.10-3-3.103

radiotalRebi

zegrZeli 105-104 3.103-3.104

grZeli ? 3.104-3.105

saSualo 103-102 3.105-3.106

mokle 102-10 3.106-3.107

metruli 10-1 ?

decimetruli 1-10-1 3.108-3.109

santimetruli 10-1-10-2 3.109-3.1010

milimetruli 10-2-10-3 3.1010-3.1011

decimilimetruli 10-3.10-4 3.1011-3.1012

optikuri diapazonis gamosxiveba

infrawiTeli 10-3-7,6.10-7 3.1011-7,0.1014

wiTeli 7,6.10-7-6,2.10-7 ?

narinjisferi 6,2.10-7-5,9.10-7 4,8.1014-5,1.1014

yviTeli 5,9.10-7-5,6.10-7 5,1.1014-5,4.1014

mwvane 5,6.10-7-5,0.10-7 5,4.1014-6,0.1014

cisferi ? 6,0.1014-6,2.1014

lurji 4,8.10-7-4,5.10-7 6,2.1014-6,7.1014

iisferi 4,5.10-7-3,8.10-7 6,7.1014-8,0.1014

ultraiisferi gamosxiveba 3,8.10-7-10-8 8.1014-3,0.1015

rentgenis gamosxiveba 8.10-8-10-12 3,7.1015-3.1020

gama gamosxiveba 10-11 da naklebi 3.1019 da meti

ultramokle

xiluli

gamosxiveba

46

gamosxivebaTa skalis cal keul ubnebs Soris sazRvrebi sakmaod pi-robiTia. prin cipuli ga nsxvaveba cal keul gamosxi ve bebs Soris ar aris. yoveli maT gani warmoadgens eleqtro mag nitur talRas, romelic va ku umSi vrceldeba 300 000 km/wm siCqariT. sxvadasxva sigrZis talRis gamos xivebebs erT maneTisagan asxvaveben maTi miRebis xerxisa (antenis gamos xiveba, siTburi gamosxiveba, gamosxi veba swrafi eleqtro nebis damuxruWe bisas da sxva) da regist raciis meTo diT. gamosxivebis talRis sigrZis Sem ci rebasTan erTad, talRis sigrZeebs So ris raodenobrivi gansxvavebani iw vevs mniS vnelovan Tvisebriv gansxva vebebs. maga liTad: radiotalRebi, romelTa talRis sigrZe

10 m-ze metia, airekleba iono sfe rodan. maSin, rodesac ul tra mokle talRebi, romelTa tal-Ris sigrZe 10 m-ze nak lebia, gadis iono sferoSi (sur. 46.2).

sagnebidan ultramokle radiotalRebis arekvlis movlena safuZvlad daedo e. w. ra-diolokacias.

sur. 46.2

mowyobiloba, romelSic swrafi eleqtro nebis damuxruWe bisas gamosxivdebarentgenis sxivebi

sur. 46.1

2. 45-e gv.-ze cxrilSi kiTxviTi niSnebis adgilas Cas-viT Sesabamisi mniS vnelobebi.

3. radiotalRebis, xiluli sinaTlis da rentgenis sxivebidan, romels aqvs yvelaze grZeli talRis sigrZe? yvelaze mokle? romeli eleqtromagnituri talRis sixSirea yvelaze meti? icvleba Tu ara eleqtro magnituri talRis siCqare talRis sigrZis SemcirebiT?

47

lokatori gagzavnili impulsi

areklili impulsiekrani

obieqtamde manZili

mimRebi

gadamcemi

antenis gad-amrTveli

impulsebisgeneratori

gamaZlierebeli

sur. 47.1

eleqtromagnituri veli, elemagnituri talRa, eleqtromagnituri talRebis klasifikacia, radiolokacia.

obieqtis aRmoCenas da maTi adgilsamyofelis zustad gansazRvras radiotalRebis meSveobiT radiolokacia ewodeba. radiolokatoris moqmedebis principi gamosaxulia 47.1 suraTze.

optikuri diapazonis tal Re bisaTvis gaum Wvir vale nivTierebani rent-genisa da gan sa kuTrebiT g sxi vebisaTvis gamWvir valea. magram mTavari gan-sxvaveba grZe l tal Rian da mokletalRian gamos xivebebs Soris isaa, rom mokle tal Riani gamosxiveba nawilakebis Tvi sebebs avlens.

eleqtromagnituri talRebis cal keul ubnebs, maTi Tvisebebis Sesabami-sad, sxvadasxva praqtikuli gamoyeneba aqvs.

gavecaniT eleqtromagnituri talRebis skalas. Semdeg gakve Tilze ki gave cnobiT eleqtromagnituri talRebis, kerZod, radiotalRebis ga moyenebas.

48

2.6 eleqtromagnituri talRebis gamoyeneba. radiotalRebi

1. daasaxeleT TqvenT-vis cnobili ra diota l-

Rebi.2. ra aris radio kavSiris safuZve-

li?

radiokavSiris fizikuri safuZvlebi Zalian rTulia. SemovifargloT mxolod aRweriT. radiokav Siri xor-cieldeba radiogadamcemiT da radiomimRebiT.

daakvirdiT 48.2 suraTs.

radiotal-Rebis

ultramokleradiotal-

Rebis

dabalsixSi-ruli

mikrotalRebis

maRalsixSirulimikrotalRebis

a

b g

gadamcemi antenis meSveobiT maRali si xSiris moduli-rebuli eleqtromagnituri talRebi (radio tal Rebi) gamosxivdeba sivrceSi.

modulirebul eleqt ro-magnitur talRebs iW-ers mimRebi antena.

gadamcemi radiosadguris sixSireze awyobili radio mimRebi maRali sixSiris cvlad dens gardaqmnis ise Tsave eleqtrul denad, romelic mikrofonSi warmoiqmneba.

eleqtruli mowyobilobebi aZlierebs bgeriTi six-Siris dens, romelic gadis xmamaRla molaparakis koWaSi da qmnis cvlad magnitur vels. igi aiZulebs koWas, rxeva daiwyos mudmivi magnitis mimarT. rxevebi gadaecema membra-nas, difuzori aZlierebs rxevebs da gamosxivdeba bgeriTi talRebi.

mikrofons ecema bgeriTi talRebi.

mikrofoni bgeriT tal-Rebs gardaqmnis imave formis eleq trul rxe-vebad.

bgeriTi sixSiris ele q t ruli rxeve-biT xde ba maRa li sixSiris eleqtro-magnituri rxevebis modu lireba.

konusuri difuzori

membranamagniti

koWa

d

e v

z

gamoyeneba

3. imsjeleT radiogadacemisa da miRebis principebze.

modulacia _ maRali sixSiris rxevebis Secvla dabali (bgeriTi)

sixSiris eleqtruli rxevebiT.

sur. 48.1. radiotalRebis gamoyeneba

sur. 48.2


49

pirveli radiogadacema eTerSi ga vida 1906 wlis 24 dekembers. es gax-ldaT kanadeli profesoris, fesen deris, mravalwliani Sromis Sedegi. mauwyebloba, ZiriTadad, reklama da musika, 128 m simaRlis anZis meSve obiT ganxorcielda. am movlenis Sem deg radiomauwyebloba saocari sis wra fiT ganviTarda. amitom 1927 wels pirvelad moaxdines sixSireebis centrali-zebuli danawi leba. es imas niSnavda, rom yvela radiosadgurs mxolod misTvis gamo yofil sixSireze unda emuSava, raTa erTmaneTTan ax los mde-bare gadam cemebs erTmane TisaTvis xeli ar SeeSa laT eTerSi.

radiotalRebis meSveobiT gamosaxulebis manZilze gadacema 1923 wels pirvelad ganaxorciela Sotlandielma inJinerma jon lodji berdma (1888-1946).

regularuli telegadacemebi did britaneTSi 1936 wels daiwyo, aSS-Si _ 1941 wels, xolo saqarTveloSi _ 1956 wlis 30 dekembridan.

am patara saocrebis Semyureni, albaT, maSin verc warmoidgendnen, rom sul mcire xanSi televizori (sur. 49.1) Cveni cxovrebis yoveldRiuri, ganuyreli atributi gaxdeboda, masobrivi komunikaciis yvela sxva saSuale-bas ajobebda sazoga doebaze Tavisi gavleniT da namdvil socialur-fsiqologiur fenomenad iqceoda.

dRes msoflioSi, sxvadasxva monacemebiT, ramdenime aTeuli aTasi satelevizio gadam-cemi sadguri muSaobs. televizia masobrivi komunikaciis grandiozuli sistemaa, romelsac adamianebze zemoqmedebis simZlavriT, albaT, veraferi Seedreba.

gamosaxulebis manZilze gadacemis principi ki aseTia: gadamcem sadgurSi gamosaxuleba Tanamimdevrulad gardaiqmneba eleq trul sig-nalebad. Semdeg am signa lebiT axdenen maRali sixSiris generatoris mier warmoq mnili rxevebis modulacias. modulirebul eleqt ro m agnitur talRas informacia did manZilze gadaaqvs. mimRebSi xdeba uku gardaqmna, maRali sixSiris moduli rebuli rxevebi modulirdeba, xolo miRe buli signali gardaiqmneba xilul gamo saxulebad. moZrao-baTa gada sa cemad gamoiyeneba kinos principi: moZravi obieqtis erTmaneTisagan mci red gan-sxvavebuli gamosaxulebebi (kadrebi) wamSi ramdenime aTeul jer gadaicema.

TiTqmis 30 weliwadia, rac mobiluri kav-Sirgabmuloba mTel msoflioSi intensiurad viTardeba. manamde ki, didi xniT adre, ukve arsebobda idea, rom erTsa da imave adamians hqonoda ara ramdenime tele foni, misi adgilsamyofelis mixedviT, aramed erTi, romelic mas mudam Tan eqneboda.

1977 wels CikagoSi mwyobrSi Cadga pirveli sacdeli fiWuri sadguri, romelic ori aTas abonents emsa xureboda. male mobiluri tele fonizaciis tempma yovelgvar molo dinsa Tu prognozs gadaaWarba.

ramdenad usafrTxoa mobiluri telefoni? amboben, rom antenis maRali sixSiris gamosxiveba iwvevs simsivnes, fsiqikur moSlilobas, uSvilobas,

modulireba (ing.) _

maRali sixSiris rxevebis

dabali sixSiris (bgeriT)

rxevebad gardaqmna.

sur. 49.1

50

genetikur daavadebebs... sinamdvileSi, dRes konkretulad aravin icis, ras iwvevs adamianis organizmSi maRali sixSiris aramai onizirebeli gamosxiveba. es radiacia ar aris. amgvari gamosxi vebis moqme debis konkretuli Sedegebi jerac ucnobia, Tumca, yvela aRiarebs erTs: aucilebelia elementaruli normebis dacva, namdvilad ar Rirs fiWuri telefoniT uzomod didxans saubari iseve, rogorc kompi uterTan Seusveneblad muSaoba. cnobisaTvis: sa qar Tve loSi mobi luri telefoniT erTi adamianis saubris sa-Sualo xangrZlivoba msoflio maCve nebels TiTqmis orjer aWarbebs.

mobiluri telefonebis (sur. 50.1) wya lobiT, aRar arsebobs ganSo rebis saf rTxe, maT gaauqmes manZili da distancia, maT marTlac Secvales msoflio da, bunebrivia, Segvcvales Cven _ adamianebi, Cveni azrovneba da mentaliteti, gemovneba da cxovrebis wesi. es cvlile-bebi ki Zalian swrafi da radikaluria.

gavecaniT radiotalRebis praqtikul gamoyenebas. Semdeg gakveTilze gavecnobiT sxva diapazonis eleqtromagnituri talRebis gamoyenebas.

SearCieT da moamzadeT erT-erTi Tema:

1. radiotalRebis miReba da gamoyeneba.

2. radiolokatorebi.

am Temis Sesaswavlad gamoiyeneT TqvenTvis xelmisawvdomi sainformacio wyaro (beWdviTi, audiovizualuri, interneti).

damuSavebuli masala warmoadgineT seminarze.

davaleba

sur. 50.1

51

2.7eleqtromagnituri talRebis gamoye neba. optikuri diapazonis eleqtromagnituri

talRebi. rentgenis sxivebi

ultramokle radiotalRebze meti sixSirisa da wiTel ferze naklebi sixSiris eleqtromag-nitur talRebs infrawiTeli ewodeba. mas asxi-vebs nebismieri gaxurebuli sxeuli maSinac ki, rodesac ar anaTebs. magaliTad, gaxurebuli Rumeli an binis gamaTbobeli asxivebs infrawiTel sxivebs, romlebic garemomcvel sxeulebs aTboben. amitom infrawiTel talRebs xSirad siTbur talRebs uwodeben. varvaris naTuras gamosxivebis maqsimumi infrawiTel sxivebze modis.

infrawiTel sxivebs didi gamoyeneba aqvs. igi gamoiyeneba bostneulis, xilis da sxvaTa gamosaSrobad. Seqmnilia xelsawyoebi, romelTa meSveo-biTac obieqtis TvaliT uxilavi infrawiTeli gamosaxuleba xilul gamo-saxulebad gardaiqmneba. damzadebulia binoklebi da optikuri samizneebi, romlebiTac sibneleSic vxedavT.

iisfer sinaTleze meti sixSiris eleqtromagnitur talRebs ultraiis-feri ewodeba. ultraiisferi sxivebi gamoirCeva didi qimiuri aqtivobiT. amaSi davrwmundebiT, Tu sibneleSi ultraiisfer sxivebs davasxivebT fotoqa Raldze. gamJRavnebis Semdeg aRmovaCenT, rom ultraiisferi sxivebi ufro metad aSavebs qaRalds, vidre xiluli sinaTle. mzis ultraiisfer gamosxivebas atmosfero nawilobriv STanTqavs. mcire dozebiT ultraiis-feri sxivebi samkurnaloa, amitom mzeze zomieri yofna sasargebloa, gan-sakuTrebiT patarebisaTvis. ultraiisferi sxivebi xels uwyobs organizmis zrdasa da ganviTarebas, kanis qsovilze moqmedebiT iwvevs damcveli pig-mentis gaSavebas da vitamin D2-is warmoqmnas, gavlenas axdens centralur nervul sistemaze, astimulirebs organizmis bevr sasicocxlo funqcias.

ultraiisferi sxivebis didi doziT moqmedeba Tvalis badurasa da kanze Zalian sazianoa. amitom maRalmTian adgilebSi Tovlze minis muqi saTvalisa da tanisamosis gareSe didxans yofna ar aris rekomendebuli. mina Zlier STanTqavs ultraiisfer sxivebs.

sur. 51.1. optikuri diapazonis gamosxivebis gamoy

eneba

1. daasaxeleT opti kuri di-apazonis eleq tro magnituri talRebi.

2. romel eleqtromagnitur tal Rebs iyenebs adamiani yvelaze me tad?

3. SeadareT erTmaneTs wiTeli da infrawiTeli sxivebis talRis sigrZe.

4. ratom aris mTaSi tansacmlis gareSe mzeze didxans yofna ufro mavnebeli, vidre zRvaze?


52

diagnozis dasmaSi eqimebs exmareba specialuri diagnostikuri aparatebi.

1895 wels gamoCenilma germanelma fizi kosma vilhelm rentgenma (1845-1923) aRmo aCina sxivebi, romlebsac sinaTlisaTvis gaumWvirvale sxeulebSi SeRwevis unari aRmoaCndaT. am sxivebs Semdeg rent genis sxivebi uwodes. sxi-vebis STan Tqmis unari nivTierebis simkvrivis propo rciuli aRmoCnda. aRmoCenis mniSvne loba Zalian swrafad Seafases medikosebma da dRemde ren tgenis aparats praqtikulad yvela kli nika iyenebs.

rentgenis sxivebis meSveobiT SeiZ leba miviRoT adamianis sxvadasxva orga nos suraTi (sur. 52.2).

rentgenis sxivebs zianis motanac SeuZ liaT. maTi moqmedebiT irRveva cocxali organizmis cxovelmoqmedeba, amitom xSirad gaSuqeba re komende buli ar aris. mis Sesac vle lad ukanasknel wlebSi ufro da ufro xSirad gamoiyeneba ultrabgeriTi tomografi.

rentgenis sxivebi gamosxivdeba swra-fad moZravi eleqtronebis mkveTri da mux ruWebis dros. isini rom eleq-tromagnituri talRebia, daamtkices misi aRmoCenidan 15 wlis Semdeg. rentgenis sxivebis sixSire miT metia, rac metia damuxruWebuli eleqtronebis energia.

avxsnaT rentgenis sxivebis gamosxivebis meqanizmi.

5. ra unda vicodeT avadmyofis mosarCenad?6. ra iciT rentgenis sxivebis Sesa xeb?

9. ra saxis energia aqvT eleqtronebs damuxruWebamde?10. romeli saxis energia icvleba eleqtronebis

damuxruWebisas?

7. Tqveni varau-diT, ra Cans araTi-Tze (sur. 52.2,b)?

8. 52.2 b suraTis mixedviT gaa-keTeT komentari.

diagnozi (berZnuli) _ daavadebis ga-

mocnoba avadmyofis gamokvlevis Sedegad.

sur. 52.2

1895 wels rentgenis mier miRebuli erTerTi rentgenograma

a

b

rentgenis da gama sxivebis gamoyenebasur. 52.1

53

teqnologiuri procesebis ganviTarebam SesaZlebeli gaxada Seqmniliyo xelsawyo tomografi (sur. 53.1), romelsac kompiu-teris gamoyenebiT SeuZlia Seqmnas sxe-ulis an misi romelime nawilis sivrculi gamosaxuleba (sur. 53.1).

eleqtromagnituri talRebidan yvelaze didi sixSire g sxivebs aqvs. maT Tvisebebs Semdeg gavecnobiT.

gavecaniT optikuri diapazonis eleqtromagnituri talRebisa da rentgenis sxivebis praqtikul gamoyenebas. gavecaniT rentgenis sxivebis miRebis meqanizms.

tomografis marTvis pulti

rentgenis sxivebis wyaro

skaneri brunavs gamosakvlevi obieqtis irgvliv

rentgenis sxivebi gan Wolavs Tavs

deteqtorebi aRricxaven sxvadasxva ubnidan ga mosul sxivebs

tvinis gamosaxulebasur. 53.1

tomografi (berZnuli) _ tomos

`fena~ da `grafi~ _ vwer.

survilis mixedviT, SearCieT da moamzadeT erT-erTi Tema:1. infrawiTeli sxivebi da maTi gamoyeneba.2. ultraiisferi sxivebi. maTi dadebiTi da uaryofiTi mxareebi.3. rentgenis sxivebis miReba da gamoyeneba. misi dadebiTi da uaryo-

fiTi mxareebi.am Temis Sesaswavlad gamoiyeneT TqvenTvis xelmisawvdomi sainfor-

macio wyaroebi (beWdviTi, audiovizualuri, interneti).damuSavebuli masala warmoadgineT seminarze.

davaleba

11. ras iwvevs magnituri velis cvlileba?12. ras iwvevs cvladi eleqtruli veli?13. ra xdeba swrafad moZravi eleqtronebis mkveTri

damuxruWebisas? icvleba Tu ara eleqtronebis mier Seqmnili magnituri veli? ra xdeba Semdeg?

54

2.8 amocanis amoxsnis nimuSi

1. rxeviT konturSi deni icvleba I = 0,8sin628t kanoniT. ganvsazRvroT denis Zalis amplituda, Tavisufali rxevebis periodi da denis Zala 0,01 wm momentSi.

amoxsna

mocemuli I = 0,8sin628t (1) gantolebisa da harmoniuli rxeviTi moZ-

raobis (2) zogadi gantolebis SedarebiT vadgenT:

Imaqs

=0,8 a;

(*): I=0,8sin628.0,01=0,8sin6,28=0,8sin2p=0.

2. rxeviTi konturis induqciuroba 0,5 mhnia, kondensatoris Semonafenebze maqsimaluri Zabva _ 200 v, xolo konturSi maqsimaluri deni _ 0,2 a. ganvsazRvroT konturis Tavisufali rxevebis periodi.

amoxsna

rxeviT konturSi Tavisufali rxe vebis pe-

riodi (1)

energiis mudmivobisa da gardaqmnis kanonis Tanaxmad,

(2)

(2) (1) ⇒ (*) (*): T=3,14 mkwm.

3. ramdenjer Semcirdeba gadamcem xazSi eleqtruli energiis danakargebi, Tu transformatorSi Semavali Zabva 11 kvia, xolo gamomavali _ 110 kv.

amoxsna

joul-lencis kanonidan (1)

energiis mudmivobis kanonis safuZvelze:

I1U1=I2U2 ⇒ (2)

(2) (1) ⇒ (*) (*):

e. i. siTburi dana kargebi gadamcem xazSi 100-jer Semcirdeba.


55

2.9SeamowmeT Tqveni codna

amoxseniT amocanebi

1. rxeviT konturSi Tavisufali rxevebisas denis Zalis amplituda 100 ma-ia. gansazRvreT Zabvis amplituda 1 mkf tevadobis kondensatorze, Tu koWas induqciuroba 1 hn-ia, xolo aqtiuri winaRoba _ umniS-vnelo.

2. rxeviTi konturis kondensatoris tevadoba 2,0 pkf-ia, koWas in-duqciuroba _ 0,50 mkhn. gansazRvreT konturSi eleqtruli rxevebis sixSire.

3. magnitur velSi Tanabrad mbrunav CarCoSi maqsimaluri em Zala 100 v-ia. gansazRvreT em Zalis myisi mniSvnelobebi, rodesac CarCo brun-vis procesSi neitraluri mdgomareobidan gadaxrilia 300 da 600-iani kuTxiT.

4. dasaSvebia Tu ara 220 v Zabvis cvladi denis wredSi iseTi kondensa-toris CarTva, romlis garRvevis Zabva 250 v-ia? pasuxi daasabuTeT.

5. transformatoris pirvelad gragnilSi 20 xviaa. ramdeni xvia unda iyos meorad gragnilSi, rom Zabva 220 v-dan gaizardos 11000 v-mde? gansazRvreT transformaciis koeficienti.

testi

1. rxeviTi konturis kondensatoris tevadobis oTxjer gadidebiT eleqtromagnituri rxevebis periodi

a. oTxjer gaizarda; b. oTxjer Semcirda; g. orjer gaizarda;

d. orjer Semcirda; e. ar Seicvala.

2. rxeviTi konturis induqciurobis oTxjer gadidebiT da kondensatoris tevadobis oTxjer SemcirebiT konturis eleqtromagnituri rxevis periodi

a. oTxjer gaizarda; b. oTxjer Semcirda; g. orjer gaizarda;

d. orjer Semcirda; e. ar Seicvala.

3. Tu rxeviTi konturis kondensators paralelurad mivuerTebT 3jer meti tevadobis kondensators, maSin konturSi eleqtromagnituri rxevebis sixSire

a. gaizrdeba orjer; b. gaizrdeba samjer; g. Semcirdeba orjer;

d. Semcirdeba samjer; e. ar Seicvleba; v. Semcirdeba -jer.

4. Tu idealuri rxeviTi konturis 4mkf tevadobis kondensatorze

Zabvis amplituda 10 via, maSin am konturis koWas maqsimaluri magnituri velis energiaa

a. 2.10-4 j; b. 2.10-3 j; g. 2.10-2 j; d. 200 j.

5. Tu rxeviTi konturis kondensatoris eleqtrotevadoba 2 mkfia,

koWas induqciuroba _ 2 hn, xolo Tavisufali miulevadi rxevebis

denis amplituda _ 0,1 a, maSin kondensatoris Zabvis amplitudaa

a. 10 v; b. 3 v; g. 80 v; d. 100 v.


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