k - ieeetsu

a m o c a n a #5
xaxunis Zalebi warmoadgenen tangencialur Zalebs,
romlebic mimarTuli arian sxeulebis (uZravi an moZravi)
moxaxune zedapirebis gaswvriv da abrkoleben maT
moZraobas erTmaneTis mimarT.
arsebobs xaxunis ori saxe: 1. mSrali, romelic warmoiqmneba
moxaxune sxeulebis mSrali zedapirebis xaxunis
dros; 2. blanti, romelic aRiZvreba myari sxeulis
moZraobisas siTxeSi an airSi.
ZiriTadi gansxvaveba maT Soris mdgomareobs imaSi,
rom pirvel SemTxvevaSi xaxunis Zalebi ar ispobian,
rodesac sxeulis moZraobis fardobiTi siCqare utoldeba
nuls, meore SemTxvevaSi ki es Zalebi qrebian.
mSrali xaxunis Zalas, romelic arsebobs uZrav sxeulebs
Soris uZraobis xaxunis Zala ewodeba.
rogorc cnobilia, Tu sxeuli devs horizontalur,
gluv zedapirze, masze modebuli mcire Zala ver daZmSrali
xaxunis koeficientis gansazRvra
- 5 -

avs mas adgilidan, radgan aRiZvreba am Zalis toli da
sawinaaRmdegod mimarTuli uZraobis xaxunis Zala.
magram, Tu gareSe Zala aRemateba garkveul mniSvnelobas,
sxeuli daiwyebs aCqarebul moZraobas, e.i. arsebobs
uZraobis xaxunis Zalis maqsimaluri mniSvneloba,
romlis miRwevamde sriali ar Cndeba.
kulonis kanonis Tanaxmad, uZraobis xaxunis Zalas
aqvs Semdegi saxe:
F kN
(1)
sadac k _ uZraobis xaxunis koeficientia, xolo N _
normaluri wnevis Zala.
k koeficienti damokidebulia moxaxune sxeulebis
gvarobaze da maT mdgomareobaze.
rodesac gareSe Zala aRemateba uZraobis xaxunis
Zalis maqsimalur mniSvnelobas, sxeuli iwyebs
moZraobas, romlis drosac adgili aqvs e.w. srialis
xaxuns.
rogorc uZraobis xaxunis Zala, ise srialis xaxunis
Zalac damokidebulia normalur wnevis Zalaze:
k N
F1
1
(2)
sadac k
1 srialis xaxunis koeficientia, romelic
damokidebulia rogorc sxeulis gvarobaze da damuSavebis
xarisxze, aseve srialis fardobiT siCqareze.
Tu moZraobis siCqare ar aris didi, maSin srialis
xaxunis koeficienti SegviZlia mudmivad CavTvaloT da
misi mniSvneloba uZraobis xaxunis koeficientis tolia
k k
1 .
siCqaris zrdasTan erTad srialis xaxunis koeficienti
odnav mcirdeba, aRwevs minimalur mniSvnelobas da
Semdeg ki izrdeba (nax. 1).
srialis garda arsebobs urTierTSemxebi sxeulebis
moZraobis kidev erTi saxeoba _ gorva. am SemTxvevaSi
sxeulebis Sexebis wertilebi yovel mocemul momentSi
uZravia da mgoravi sxeuli asrulebs brunvas am wertilebis
(an am wertilebSi gamavali RerZis) garSemo.
- 6 -

cxadia, rom gorvis dros yovel Semdgom momentSi
adgili eqneba sxva wertilebTan Sexebas da brunva
sruldeba maT mimarT.
srialis gareSe gorvis dros sxeulebis Sexebis
wertilebi an Sexebis wrfe yovel mocemul momentSi
uZravia, e.i. am wertilebSi moqmedebs uZraobis xaxunis
tangencialuri Zala.
k
1
u
nax. 1 nax. 2
F
R
u
amasTan erTad aRiZvrebian e.w. gorvis xaxunis Zalebi,
romelTa moqmedeba gamoixateba brunvis damatebiTi
momentis aRZvraSi.
ganvixiloT cilindruli formis sxeuli, romelic
migoravs horizontalur zedapirze srialis gareSe.
Tu haeris winaaRmdegobis Zalas ugulebelvyofT,
drois ganmavlobaSi cilindri anelebs Tavis moZraobas
da Cerdeba, rac gamowveulia im Zalebis arsebobiT,
romlebic amcireben cilindris gadataniT da brunviT
siCqares. e.i. aniWeben mas uaryofiT xazovan da kuTxur
aCqarebebs.
cilindris masaTa centris siCqaris Semcireba gamowveulia
xaxunis tangencialuri Zalis arsebobiT, romelic
mimarTulia moZraobis sawinaaRmdegod (nax. 2),
amitom
m x
F
(3)
sadac m _ cilindris masaa, x _ masaTa centris
aCqareba.
magram am Zalis moments SeiZleboda gaezarda cilindris
brunvis kuTxuri siCqare, radgan misi mimarTuleba
emTxveva brunvis mimarTulebas. e.i. rom arsebobdes
- 7 -

mxolod xaxunis tangencialuri Zala, igi erTdroulad
ver Seamcirebda cilindris gadataniT da brunviT siCqares
ise, rom ar warmoqmniliyo sriali.
maSasadame, arsebobs romeliRac Zalis momenti,
romelic mimarTulia xaxunis tangencialuri Zalis
momentis sawinaaRmdegod, aRemateba mas da anelebs brunvas.
am Zalis moments ewodeba gorvis xaxunis Zalis
momenti.
cilindris gorvis dros horizontalur zedapirze
simZimis Zalis gavleniT adgili aqvs cilindrisa da
sayrdenis deformacias.
Tu deformaciis Zalebi drekadia, isini simetriulia
vertikaluri ab sibrtyis mimarT, romelic gadis cilindris
brunvis RerZze (nax. 3a).
yovel f
Zalas Seesabameba misi toli da simetriulad
modebuli f Zala. drekadi deformaciis yvela
Zalis tolqmedi mimarTulia vertikalurad zeviT da am
Zalis momenti cilindris RerZis mimarT nulis tolia;
amitom drekadi deformaciis Zalebi ar moaxdenen
araviTar gavlenas cilindris gorvis siCqareze da moZraoba
iqneba iseTi, TiTqos araviTar deformacias adgili
ar hqonda, gorvis xaxunis Zalebi ki nulis tolia
(nax. 3b).
imisaTvis, rom avxsnaT gorvis xaxunis Zalebis
arseboba, saWiroa CavTvaloT, rom cilindris da sayrdenis
deformacia aradrekadia, rasac faqtiurad
yovelTvis aqvs adgili.
vTqvaT, cilindri deformacias ar ganicdis, xolo
gorvis sibrtyes gaaCnia narCeni deformacia, cxadia, rom
gorvis sibrtyidan cilindrze moqmedi Zalebi ar iqnebian
simetriuli ab sibrtyis mimarT, kerZod f Zala
f
f
f
f
u
- 8 -
u
nax. 3a
nax. 3b

aRemateba f Zalas, romelic modebulia simetriul
ubanze ab sibrtyis meore mxares (nax. 3g).
amitom, yvela modebuli Zalis tolqmeds
aucileblad eqneba horizontaluri mdgene-li, romelic
mimarTulia moZra-obis sawinaaRmdegod da am Za-lis
momenti cilindris RerZis mimarT nulisgan
gansxvavebulia.
davuSvaT, rom: 1) cilindri moZraobs haerTan
xaxunis gare-Se da anelebs Tavis moZraobas mxolod
gorvis xaxunis gamo; 2) cilindri moZraobs srialis
gareSe, e.i. cilindris zedapirze moTavsebuli
wertilebi gadian igive manZils,
rasac cilindris centri:
f
f
nax. 3g
sadac
x
R
(4)
d
aris cilindris
dt
kuTxuri aCqareba, R _
cilindris radiusia. amasTan
erTad cilindris xazo-vani da
kuTxuri aCqarebebi uaryofiTia.
pirveli pirobis gamo, cilindrze modebuli yvela
Zalis tolqmedi unda iyos mimarTuli moZraobis sawinaaRmdegod,
xolo meore pirobis gamo, tolqmedi Zalis
modebis wertili ar unda iyos ganlagebuli arc vertikalur
ab sibtrtyeSi da arc mis ukan (nax. 4a,b),
radganac am SemTxvevaSi igi mianiWebda cilindrs dadebiT
kuTxur aCqarebas.
- 9 -

b
N
N
a a) b) a
nax. 4
amasTan dakavSirebiT erTaderTi SesaZlebloba mdgomareobs
imaSi, rom sayrdenis reaqciis yvela Zalis
tolqmedi Zala mimarTulia ab sibrtyis win, amasTan
misi moqmedebis xazi unda gadiodes cilindris RerZis
zeviT (nax. 5).
maSasadame, gorvis dros sayrdenis reaqciis Zala ar
gadis cilindris simZimis centrze, aramed wanacvlebulia
win, moZraobis mimarTulebiT; es ki iwvevs sayrdenis
reaqciis Zalis momentis gaCenas cilindris
brunvis RerZis mimarT,
f f N romelic xels uSlis mis
brunvas. am moments ewodeba
gorvis xaxunis Zalis momenti
da igi Caiwereba Semdegnairad:
S
M SN k2N
(5)
sadac k
2 _ gorvis xaxunis
F
Zalis momentis koeficientia,
romelic faqtiurad warmonax.
5
adgens reaqciis Zalis S mxars
brunvis RerZis mimarT. igi mkveTrad gansxvavdeba k da
k koeficientebisagan, radgan mas aqvs ganzomileba.
1
- 10 -

ganvsazRvroT M gorvis xaxunis Zalis momentis
sidide cilindrisaTvis, romelic migoravs horizontalur
zedapirze. amisaTvis davweroT Semdegi gantoleba:
J M
FR
(6)
sadac J _ cilindris inerciis momentia, R _ misi radiusi,
F _ uZraobis xaxunis tangencialuri Zala. (3) da
(6) gantolebebis amoxsniT da (4)-is gamoyenebiT miviRebT
gamosaxulebebs M gorvis xaxunis Zalis momentisaTvis
da F ZalisaTvis
J
mR
2 M
da
J
mR
F
2
mR
uZraobis xaxunis tangencialuri Zala F yovelTvis
Rebulobs iseT mniSvnelobas, romlis drosac ar
warmoiSveba sriali. am Zalis mniSvneloba ar SeiZleba
aRematebodes uZraobis xaxunis Zalis udides mniSvnelobas,
amitom gorvis xaxunis Zalis momentis didi mniSvnelobisaTvis
F Zalis sidide ar aris sakmarisi cilindris
simZimis centris SenelebisaTvis. cilindris brunvis
siCqare ufro swrafad Semcirdeba M momentis moqmedebiT,
vidre misi simZimis centris moZraobis siCqare da
cilindris gorvasTan erTad gaCndeba sriali, romlis
mimarTuleba emTxveva moZraobis mimarTulebas.
M
(7)
(8)
- 11 -

R
O 2
k
N
y
F
r
x
N mgcos
nax. 6a
ganvixiloT k , k 1 da k 2 xaxunis koeficientebis gansazRvris
erT-erTi meTodi, romelic dakavSirebulia
burTulas moZraobasTan daxril RarSi.
I) mcire daxris kuTxis dros RarSi moTavsebuli bur-
Tula uZravi iqneba. maqsimaluri daxris kuTxe 1 , romlis
drosac burTula jer ar iwyebs Cagorebas, ganisaz-
Rvreba Semdegi pirobidan (nax. 6a):
mgsin 1
F 0
(9)
Fr k 2
mgcos
1
0
sadac m burTulas masaa, r _ F Zalis mxari. (9) gantolebaTa
sistemis amoxsniT miviRebT:
k rtg
(10)
2
1
Tu 1 kuTxe cnobilia, (10)-dan SegviZlia ganvsazRvroT
k .
2
- 12 -

N
2
R
r
II) Raris daxris kuTxis
zrdasTan erTad, dawyebuli
1 kuTxidan iwyeba
burTulas gorva srialis
gareSe.
marTkuTxa Raris SemTxvevaSi
burTulas moZraobis
gantolebebs aqvs Semdegi
saxe (nax. 6b):
m
x mgsin
F
mgcos
N 0
J Fr k2
x r
N mgcos
N
nax. 6b
N
2
sadac
2 mR
5
J
2
aris burTulas inerciis momenti, R
burTulas radiusi,
F
r
1
R . am gantolebebidan viRebT:
2
1 k2
mg4sin
5 cos
9 r
5 k2
x
gsin cos
9 r
(12) gantoleba gansazRvravs uZraobis xaxunis Zalas,
romelic kulonis kanonis Tanaxmad icvleba intervalSi
F kN kmgcos . Camogorebis dros yovelTvis myardeba
iseTi uZraobis xaxunis Zala, romlis drosac ar gaCndeba
sriali. amitom, uZraobis xaxunis Zalis maqsimaluri
mniSvneloba Fmaqs kmgcos gansazRvravs kidevac im
zRvrul kuTxes ( 2 ), romlis drosac jer kidev
SesaZlebelia burTulas moZraoba srialis gareSe,
maSasadame,
(12)
(13)
- 13 -

F
1 k2
kmgcos
2
mg4sin
2
S cos
9 r
2
(14) gantolebidan gamomdinareobs, rom
1 5 k2
k tg2
9 9 r
Tu 2 da k 2 cnobilia, (15)-dan SegviZlia ganvsazRvroT
k .
(13)-dan Cans, rom burTulas masaTa centri moZraobs
TanabaraCqarebulad.
Tu burTula moZraobs usawyiso siCqariT da gadis S
manZils t droSi, maSin
(13) da (16)-dan
S
1 x
t 2
9r
5 2S
1
k2 g sin
2
5g
9 t cos
5
sadac g sin j aris masaTa centris aCqareba gorvis
9
xaxunis gareSe.
zRvrul SemTxvevebSi, rodesac S 0 , xolo 1
(17)
gantoleba dadis (10) gantolebamde. (17)-dan SegviZlia
ganvsazRvroT k 2 , Tu cnobilia burTulas Camogorebis
dro Raris sxvadasxva daxris kuTxeebisaTvis.
III) Tu Raris daxris kuTxe
2 -ze, burTulas moZraoba
SegviZlia CavTvaloT rogorc wminda sriali.
burTulas masaTa centris moZraobis gantolebas aqvs
Semdegi saxe:
m x
mgsin k1mgcos
(18)
saidanac (16)-is gamoyenebiT SegviZlia miviRoT:
2
(15)
(16)
(17)
(14)
- 14 -

k
1
2S
g sin
2
t
1
g cos
(19) gvaZlevs saSualebas ganvsazRvroT srialis xaxunis
koeficienti Raris sxvadasxva daxris kuTxeebisaTvis.
danadgaris aRwera
danadgaris ZiriTad nawils warmoadgens marTkuTxa
kveTis liTonis Rari, romelic Tavisuflad brunavs mis
fuZeze gamaval horizontaluri RerZis garSemo.
Rari magrdeba sasurvel mdgomareobaSi Stativis
saSualebiT, xolo misi daxris kuTxe horizontis
mimarT aiTvleba kuTxemzomis saSualebiT 0,25
-is
sizustiT.
Raris zedapiri dafarulia maudiT, romelic advilad
deformirdeba foladis burTulis moZraobis dros. bur-
Tulas radiusi 2,69 sm-is tolia.
xaxunis koeficientis gansazRvra xorcieldeba Semdegi
wyvilisaTvis _ “maudi-foladi”. Raris zeda nawilSi
damagrebulia eleqtromagniti, romelic ikvebeba 6v
cvladi deniT da romlis daniSnulebaa burTulas
SeCereba zeda mdegomareobaSi.
Raris qveda nawilSi damagrebulia kontaqtebi, romlebic
CairTvebian burTulas dajaxebisas. Eeleqtromagniti
da kontaqtebi CarTulia eleqtrowamsazomis
wredSi, romlis saSualebiTac ganisazRvreba burTulas
moZraobis dro Raris gaswvriv.
CamrTvelis (eleqtromagniti_wamsazomi) gadarTvisas
eleqtromagniti gamoirTveba, ris Sedegadac burTula
iwyebs moZraobas da erTdroulad irTveba wamsazomi.
burTulas kontaqtebTan dajaxebis momentSi avtomaturad
irTveba rele, romelic CarTulia TviTblokirebuli
sqemis mixedviT, rac iwvevs wamsazomis wredis myisier
gamorTvas.
wamsazomis isrebis dabruneba nulovan mdgomareobaSi
xdeba Rilakze xelis mdovre daWeriT.
(19)
- 15 -

gazomvebi da Sedegebis damuSaveba
1. daayeneT Rari garkveul mdgomareobaSi da kuTxemzomis
saSualebiT gazomeT misi daxris kuTxe horizontis
mimarT.
2. gazomeT S manZili burTulas sawyis da saboloo
mdgomareobebs Soris, romlis gavlis dro izomeba
wamsazomis saSualebiT.
3. CarTeT eleqtromagnitis da wamsazomis kvebis
bloki. miadeT foladis burTula eleqtromagnitis
gulars Raris zeda nawilSi, CamrTveli
“eleqtromagniti_wamsazomi” gadaiyvaneT zeda
mdgomareobaSi, rac iwvevs eleqtromagnitis CarTvas.
4. CamrTveli “eleqtromagniti_wamsazomi” gadaiyvaneT
qveda mdgomareobaSi, burTula daiwyebs moZraobas Raris
mimarT da kontaqtebTan Sejaxebisas avtomaturad gamor-
Tavs wamsazoms.
Raris yoveli mdgomarobisTvis drois gazomva gaimeoreT
samjer da ipoveT saSualo ariTmetikuli.
Tanmimdevrulad cvaleT daxris kuTxe 0,5
-is
intervaliT da CaatareT gazomvebi 2-dan 10 gradusamde.
(16) formuliT sxvadasxva daxris kuTxisTvis gansaz-
RvreT burTulas aCqareba x a .
5. miRebuli Sedegebi warmoadgineT grafikis saxiT
milimetrebian qaRaldze; abscisTa RerZze gadazomeT
daxris kuTxe , xolo ordinatTa RerZze burTulas
aCqareba.
5
imave grafikze aageT j g sin damokidebulebis mrudi,
romelic warmoadgens burTulas aCqarebas gorvis
9
xaxunis gareSe.
daxris mcire kuTxeebisTvis j f
-s Sesabamisi
grafiki gadis eqsperimentuli mrudis zeviT, rac metyvelebs
imaze, rom gorvis xaxunis arseboba amcirebs bur-
Tulis masaTa centris aCqarebas /(13) gantoleba/. magram,
siCqaris zrdasTan erTad gorvis xaxunis Zala TandaTan
mcirdeba, rac iwvevs Sesabamisi mrudebis gadakveTas.
- 16 -

gadakveTis wertilSi eqsperimentulad miRebuli aCqareba
aris iseTive, rogorc burTulas moZraobisTvis
gorvis xaxunis gareSe.
didi siCqreebisaTvis burTulas aCqareba aRemateba im
mniSvnelobas, romelic gveqneboda mxolod Camomsrialebeli
da tangencialuri Zalis moqmedebiT gorvis xaxunis
gareSe. es SesaZlebelia mxolod srialis gaCenis
Semdeg.
maSasadame, Sesabamisi grafikebis gadakveTis wertili
gvaZlevs saSualebas ganvsazRvroT
2 kuTxe, romlis
drosac gaCndeba sriali.
avRniSnoT, rom gorvis xaxunis Zalis Semcireba
siCqaris zrdasTan erTad ZiriTadad damokidebulia
gorvis xaxunis koeficientis - k 2 -is SemcirebasTan, radgan
normaluri wnevis Zala amocanis pirobebSi umniSvnelod
icvleba.
Tavis mxriv k 2 -is Semcireba damokidebulia masalis
deformaciis SemcirebasTan, romelsac adgili aqvs siCqaris
zrdis dros.
2 -is miRebuli mniSvnelobebis saSualebiT SegviZlia
ganvsazRvroT k .
marTlac, Tu k
2
0
6. f
, (15)-dan miviRebT
4
9
k tg
2
(20)
a grafikis eqstrapolaciiT abscisTa RerZis
gadakveTamde gansazRvreT 1 kuTxe da (10)-is saSualebiT
gansazRvreT k 2 am kuTxisaTvis.
kuTxeebisaTvis, romlebic akmayofileben utolobas
1 2 , k 2 ganisazRvreba (17) formuliT.
Tu daxris kuTxeebi aRematebian
2 -s, magram gacilebiT
naklebi arin 90
-ze, k 1 gamoiTvleba (19)-iT.
miRebuli xaxunis koeficientebis ricxviTi mniSvnelobebi
SeadareT erTmaneTs.
- 17 -

g a z o m v a T a c x r i l i
1,65 1 Raris sigrZe S (m)
2; 2.5; 3; 3.5; 4; 4.5; 5;
5.5; 6; 7; 8; 9; 10
0.035; 0.044; 0.052; 0.061;
0.070; 0.075; 0.087;
0.096; 0.104; 0.122;
0.140
2 daxris kuTxe
3 burTulas moZraobis dro
t (wm)
burTulas aCqareba(gorvis
4 xaxunis gaTvaliswinebiT)
2
2
a 2S
t m
wm
5 sin
6
burTulas aCqareba gorvis
xaxunis gauTvaliswineblad
5
sin
9
7 2
8 uZraobis xaxunis koef_ti
2
j m
wm
k
4 tg
2
9
9 1
(grafikidan)
10 gorvis xaxunis koef_ti
k
rtg
2
1
11 gorvis xaxunis koef_ti
k
2 roca 1 2
12 srialis xaxunis koef_ti
k roca 90
1
2
- 18 -

danadgaris sqema
220 V
- 19 -

literatura:
1. m. mirianaSvili. zogadi fizikis kursi. I tomi, § 41, 1966.
2. С.П.Стрелков. Механика. § 38,41,42,72-75. М..Наука, 1975.
3. А.Н. Матвеев. Механика и теория относителности. §36. М., Высшая школа, 1986.
4. D. Halliday, R. Resnick, J. Walker. Fundamentals of Physics. § 6.1, 6.2, John Wiley &.
Sons. Inc. 1993.
- 20 -