fizikis kursi
fizikis kursi fizikis kursi
v. melaZe fizikis kursi (I nawili) `teqnikuri universiteti”@
- Page 2 and 3: saqarTvelos teqnikuri universiteti
- Page 4 and 5: sarCevi Sesavali 5 fizikuri sididee
- Page 6 and 7: Sesavali fizikis sagani, misi kavSi
- Page 8 and 9: TavsarTi 7 cxrili 1. mamravli aRniS
- Page 10 and 11: fizikuri sidide farTobi S moculoba
- Page 12 and 13: meqanikis fizikuri safuZvlebi 1. ki
- Page 14 and 15: drois aTvla daviwyoT A mdebareobida
- Page 16 and 17: araTanabari (cvladi) moZraobis dama
- Page 18 and 19: 3) a τ = f (t), a = 0 - wrfivi aCq
- Page 20 and 21: nax. 8. kuTxuri gadaadgileba: Δϕ
- Page 22 and 23: unviTi moZraobis maxasiaTeblebi, wr
- Page 24 and 25: Zala veqtoruli sidide _ Zala, warmo
- Page 26 and 27: niutonis meore da mesame kanonebis
- Page 28 and 29: gravitaciuli Zalebi gansazRvrven pl
- Page 30 and 31: aCqarebis tolobebi am sistemebSi ni
- Page 32 and 33: cda gviCvenebs, rom drekadi deforma
- Page 34 and 35: xolo nax. 19 b SemTxvevisTvis : 33
- Page 36 and 37: Soris. Δ r simciris gamo F Zala Se
- Page 38 and 39: SualedebSi erTnairi muSaoba sruldeb
- Page 40 and 41: Zalur vels erTgvarovani ewodeba, Tu
- Page 42 and 43: • Mmaterialuri wertilis (nawilaki
- Page 44 and 45: impulsis momenti fsevdoveqtoria. mi
- Page 46 and 47: zogierTi erTgvarovani m masis sxeul
- Page 48 and 49: nax. 28. sadac vi = ωRi materialur
- Page 50 and 51: energiis Senaxvis kanoni da drois e
v. melaZe<br />
<strong>fizikis</strong> <strong>kursi</strong><br />
(I nawili)<br />
`teqnikuri universiteti”@
saqarTvelos teqnikuri universiteti<br />
v. melaZe<br />
<strong>fizikis</strong> <strong>kursi</strong><br />
(I nawili)<br />
damtkicebulia stu-s<br />
saredaqcio-sagamomcemlo sabWos<br />
mier. 02.07.2009, oqmi #6<br />
Tbilisi<br />
2009
<strong>fizikis</strong> <strong>kursi</strong>s pirveli nawili _ meqanika,<br />
rxevebi da talRebi, molekuluri fizika, Termo-<br />
dinamika _ Sedgenilia umaRlesi teqnikuri saswavleblis<br />
studentebisaTvis. masSi mocemulia moqmedi<br />
programiT gaTvaliswinebuli yvela sakiTxi sakmao<br />
siRrmiT, amasTan, im varaudiT, rom mkiTxvels SeeZlos<br />
wignze damoukidebeli muSaoba. igi sargeb-<br />
lobas moutans sxva specialobis studentebsac.<br />
recenzenti sr. prof. k. cxakaia<br />
© sagamomcemlo saxli ,,teqnikuri universiteti’’, 2009<br />
ISBN 978-9941-14-707-4 (yvela nawili)<br />
ISBN 978-9941-14-708-1 (pirveli nawili)<br />
http://www.gtu.ge/publishinghouse/<br />
yvela ufleba daculia. am wignis arc erTi nawili (iqneba es teqsti, foto,<br />
ilustracia Tu sxva) aranairi formiT da saSualebiT (iqneba es eleqtronuli Tu<br />
meqanikuri), ar SeiZleba gamoyenebul iqnas gamomcemlis werilobiTi nebarTvis<br />
gareSe.<br />
saavtoro uflebebis darRveva isjeba kanoniT.
sarCevi<br />
Sesavali 5<br />
fizikuri sidideebi. erTeulTa sistemebi 6<br />
1. kinematika<br />
1.1. aTvlis sxeuli. aTvlis sistema 11<br />
1.2. materialuri wertilis kinematika 11<br />
1.3. absoluturad myari sxeulis kinematika 17<br />
1.4. kuTxuri gadaadgileba, kuTxuri siCqare, kuTxuri aCqareba 18<br />
2. dinamika<br />
2.1. materialuri wertilis dinamika 22<br />
2.2. bunebis Zalebi 25<br />
2.3. muSaoba, simZlavre, energia 34<br />
2.4. myari sxeulis dinamika 41<br />
2.5. meqanikuri sistema. Senaxvis kanonebi 48<br />
2.6. sxeulTa wonasworobis pirobebi 52<br />
3. relativisturi meqanika<br />
3.1. fardofiTobis Teoriis safuZvlebi. ainStainis<br />
postulatebi<br />
3.2. lorencis gardaqmnebi da maTi Sedegebi 54<br />
3.3. relativisturi dinamika 56<br />
4. rxevebi da talRebi<br />
4.1. rxevebi. harmoniuli rxevebi 58<br />
4.2. siCqare da aCqareba harmoniuli rxevis 59<br />
4.3. harmoniuli rxevis energia 60<br />
4.4. harmoniuli rxevebis Sekreba 61<br />
4.5. milevadi rxevebi 63<br />
4.6. talRebi. ZiriTadi cnebebi 64<br />
4.7. brtyeli talRis gantoleba 65<br />
4.8. talRuri gantoleba 66<br />
4.9. talRebis interferencia 67<br />
3<br />
52
molekuluri fizika 68<br />
5. idealuri airebis kinetikuri Teoria<br />
5.1. idealuri airi. molekulur-kinetikuri<br />
Teoriis ZiriTadi gantoleba 71<br />
5.2. idealuri airis Sinagani energia 74<br />
5.3. molekulebis siCqareTa ganawilebis kanoni 75<br />
5.4. barometruli formula.<br />
bolcmanis ganawilebis kanoni 76<br />
5.5. molekulaTa dajaxebaTa ricxvis da<br />
saSualo Tavisufali ganarbenis gamoTvla 78<br />
6. Termodinamika<br />
6.1. Termodinamikuri sistema, damaxasiaTebeli parametrebi 78<br />
6.2. Termodinamikis pirveli kanoni 80<br />
6.3. airebis siTbotevadoba. maieris gantoleba 81<br />
6.4. adiabaturi procesi 83<br />
6.5. wriuli procesi. Seqcevadi da Seuqcevadi procesebi 84<br />
6.6. siTburi manqana. margi qmedebis koeficienti 85<br />
6.7. karnos cikli. karnos ciklis mqk 86<br />
6.8. Termodinamikis meore kanoni 88<br />
6.9. entropia. Termodinamikis gaerTianebuli kanoni 89<br />
7. realuri airebi<br />
7.1. realuri airebi. molekuluri Zalebi 90<br />
7.2. van-der-vaalsis gantoleba 92<br />
7.3. realuri airis izoTermebi 93<br />
damateba 95<br />
4
Sesavali<br />
<strong>fizikis</strong> sagani, misi kavSiri teqnikasTan<br />
fizika aris mecniereba, romelic Seiswavlis materiis moZraobis<br />
umartives da uzogades formebs da maT urTierTgardaqmnas. cnobilia<br />
materiis ori saxe: nivTiereba da veli. materiis pirvel saxes _<br />
nivTierebas miekuTvnebian atomebi, molekulebi da maTgan agebuli<br />
sxeulebi. materiis meore saxes qmnian gravitaciuli, eleqtromagnituri<br />
da sxva velebi.<br />
adre fiqrobdnen, rom nivTierebas diskretuli agebuleba aqvs, veli<br />
ki uwyvetia. Semdgom aRmoCnda, rom materiis orive saxes erTdroulad<br />
axasiaTebs rogorc diskretuloba, ise uwyvetoba _ rac materiis<br />
ZiriTadi Tvisebaa. nebismieri movlena, materiis yoveli cvlileba<br />
warmoebs sivrcesa da droSi. sivrce da dro materiis arsebobis<br />
formebia.<br />
fizika SeiZleba gavyoT or nawilad _ klasikurad da kvanturad.<br />
klasikuri fizika Seiswavlis sinaTlis siCqaresTan SedarebiT mcire<br />
siCqareebis mqone makroskopiuli sxeulebis moZraobas. sinaTlis<br />
siCqaresTan maxlobeli siCqareebis mqone makroskopuli sxeulebis<br />
moZraobis kanonebs Seiswavlis relativisturi fizika. mikroskopiuli<br />
sxeulebis (atomebis da elementaruli nawilakebis) moZraobis<br />
Sesaswavlad klasikuri fizika (meqanika) ar gamodgeba, is icvleba<br />
kvanturi meqanikiT.<br />
<strong>fizikis</strong> aRmoCenebis safuZvelze warmoiSva da ganviTarda teqnikis<br />
mravali dargi. Tavis mxriv teqnika xels uwyobs <strong>fizikis</strong> ganviTarebas,<br />
aiaraRebs ra fizikas axali, srulyofili xelsawyoebiT da<br />
danadgarebiT.<br />
amgvarad, praqtikul moTxovnebs mivyavarT axal fizikur<br />
aRmoCenebamde da es aRmoCenebi xels uwyobs teqnikis winsvlas.<br />
fizika _ eqsperimentaluri mecnierebaa. eqsperimentaluri<br />
dakvirvebebi, gazomvebi da winaswar gamoTqmuli Teoriebi sabolood<br />
daiyvanebian fizikur sidideebsa da ricxvebs Soris<br />
urTierTdamokidebulebebze. amitom <strong>fizikis</strong> enaa maTematika.<br />
5
fizikuri sidideebi, ganzomileba, erTeulTa sistemebi<br />
fizikuri sididis erTeuli ewodeba pirobiT SerCeul fizikur<br />
sidides, romelsac gaaCnia gansaxilveli obieqtis fizikuri Tvisebebi.<br />
erTeulTa sistema ewodeba fizikur sidideTa erTeulebis erTobliobas,<br />
romlebic SeirCevian dadgenili wesiT. mocemuli sistemis ZiriTadi<br />
erTeulebi ewodebaT sxvadasxvagvari fizikuri sidideebis erTeulebs,<br />
romlebic nebismierad airCevian am sistemis Sedgenisas, erTeulTa<br />
sistemas ewodeba absoluturi, Tu misi ZiriTadi erTeulebia sigrZis,<br />
masis da drois erTeulebi.<br />
warmoebuli erTeulebi iseT erTeulebs ewodebaT, romlebic<br />
dadgenilebi arian mocemuli sistemis sxva erTeulebiT fizikuri<br />
kanonebis safuZvelze da warmoadgenen ZiriTadi erTeulebis<br />
ganzomilebaTa xarisxebis namravls.<br />
fizikuri sidideebis ganzomileba ewodeba gamosaxulebas, romelic<br />
axasiaTebs fizikuri sididis kavSirs mocemuli sistemis ZiriTad<br />
erTeulebTan. es gamosaxuleba warmoadgens erTwevrs ZiriTadi<br />
erTeulebis simboloebis namravlis saxiT Sesabamis xarisxebSi. sidides<br />
ewodeba uganzomilebo (ganyenebuli), Tu mis ganzomilebaSi yvela<br />
ZiriTadi sidideebi Sedian nulovan xarisxebSi. magaliTad,<br />
Tanabarwrfivi moZraobis siCqarisTvis<br />
s<br />
v = ,<br />
t<br />
ganzomileba Caiwereba<br />
dim<br />
−1<br />
= LT , sididis erTeuli [v] = m . wm-1 .<br />
fizikuri sidideebis ZiriTadi erTeulebis garda SeiZleba<br />
gamoviyenoT jeradi da wiladi erTeulebi, romlebic miiRebian ZiriTadi<br />
erTeulebis 10-is romelime xarisxSi gamravlebiT an gayofiT. mamravlebi<br />
da TavsarTebi aTis jeradi da wilobrivi erTeulebis misaRebad (maTi<br />
dasaxelebebi) mocemulia cxrilSi 1.<br />
1960 wels zoma-wonis I generalurma konferenciam miiRo<br />
dadgenileba erTeulTa saerTaSoriso (SI) sistemis SemoRebis Sesaxeb.,<br />
1971 wlidan zoma-wonis XIX konferenciaze miiRes axali ZiriTadi<br />
(meSvide) erTeuli moli da ori damatebiTi erTeuli radiani da<br />
steradiani.<br />
6
TavsarTi<br />
7<br />
cxrili 1.<br />
mamravli aRniSvna mamravli aRniSvna<br />
dasaxeleba dasaxeleba<br />
qarTuli saerTaSoriso<br />
qarTuli saerTSoriso<br />
10 18<br />
10 15<br />
10 12<br />
10 9<br />
10 6<br />
10 3<br />
10 2<br />
10 1<br />
eqsa<br />
peta<br />
tera<br />
giga<br />
mega<br />
kilo<br />
heqta<br />
deka<br />
e<br />
p<br />
t<br />
g<br />
m<br />
k<br />
h<br />
da<br />
E<br />
P<br />
T<br />
G<br />
M<br />
K<br />
h<br />
da<br />
10 -1<br />
10 -2<br />
10 -3<br />
10 -6<br />
10 -9<br />
10 -12<br />
10 -15<br />
10 -18<br />
deci<br />
santi<br />
mili<br />
mikro<br />
nano<br />
piko<br />
femto<br />
atto<br />
amgvarad, saerTaSoriso SI (Sistem International) sistemas safuZvlad<br />
daedo Svidi ZiriTadi erTeuli. ZiriTadi da damatebiTi sidideebi, maTi<br />
aRniSvnebi da erTeulebi mocemulia cxrilSi 2.<br />
sidide erTeuli<br />
d<br />
s<br />
ml<br />
mk<br />
n<br />
p<br />
f<br />
a<br />
aRniSvna<br />
d<br />
c<br />
m<br />
M<br />
n<br />
p<br />
f<br />
a<br />
cxrili 2.<br />
dasaxeleba ganzomileba dasaxeleba saerTaSoriso qarTuli<br />
sigrZe L metri m m<br />
masa M kilogrami kg kg<br />
dro T wami S wm<br />
denis Zala I amperi A a<br />
Termodinamikuri<br />
temperatura<br />
nivTierebis<br />
raodenoba<br />
θ kelvini K K<br />
NN moli mol moli<br />
sinaTlis Zala J kandela cd kd<br />
brtyeli kuTxe _ radiani rad rad<br />
sxeulovani<br />
kuTxe<br />
_ steradiani sr sr
ZiriTadi erTeulebis gansazRvra<br />
sigrZis erTeuli _ metri tolia vakuumSi brtyeli eleqtromagni-<br />
turi talRis gavlili manZilis wamis 1 , nawilSi.<br />
299792458<br />
masis erTeuli _ kilogrami aris kilogramis saerTaSoriso proto-<br />
tipis masa, damzadebuli platina-iridiumis Senadnobisgan (Pl 90%, Ir 10%)<br />
cilindruli sawonis formiT, diametriT da simaRliT toli 39 mm.<br />
drois erTeuli _ wami drois Sualedia, romelic tolia cezium-<br />
133-is atomis ZiriTadi mdgomareobis zenazi urTierTqmedebis or dones<br />
Soris gadasvlis Sesabamisi gamosxivebis 9192631770 periods.<br />
denis Zalis erTeuli _ amperi aris iseTi mudmivi denis Zala,<br />
romelic vakuumSi erTmaneTisagan 1 metriT daSorebul or paralelur,<br />
usasrulod grZel da mcire diametris gamtarebSi gavlisas, sigrZis<br />
7<br />
yovel metrze iwvevs 2⋅10<br />
niutonis tol urTierTqmedebis Zalas.<br />
temperaturuli erTeuli _ kelvini tolia wylis sammagi wertilis<br />
Termodinamikuri temperaturis<br />
1 nawilis.<br />
273,<br />
16<br />
nivTierebis raodenobis erTeuli _ moli aris sistemis nivTierebis<br />
raodenoba, romelic Seicavs imdenive struqturul elements (molekulas,<br />
ions, atoms) ramdeni atomicaa 0,012 kg C 12 naxSirbadSi.<br />
sinaTlis Zalis erTeulia _ kandela. kandela tolia sinaTlis<br />
Zalis mocemuli mimarTulebiT sinaTlis wyarodan, romelic uSvebs<br />
12<br />
monoqromatul gamosxivebas 540⋅10 hc sixSiriT da sinaTlis<br />
1 3t<br />
energetikuli Zala am mimarTulebiT Seadgens .<br />
683 sr<br />
SI sistemis damatebiTi erTeulebia: brtyeli kuTxis _ radiani,<br />
romelic tolia wris or radiuss Soris kuTxis, romlis momWimavi<br />
rkalis sigrZe radiusis tolia.<br />
sxeulovani kuTxis _ steradiani, romelic iseTi sivrculi kuTxea,<br />
romlis wvero moTavsebulia sferos centrSi da sferos zedapirze<br />
amokveTs misi radiusis kvadratis tol farTs.<br />
8
fizikuri sidide<br />
farTobi S<br />
moculoba V<br />
siCqare v<br />
simkvrive ρ<br />
aCqareba a<br />
inerciis momenti I<br />
warmoebuli erTeulebi<br />
meqanikuri sididis erTeulebi<br />
ganmsazRvreli<br />
gantoleba<br />
9<br />
sididis<br />
erTeuli<br />
sididis<br />
ganzomileba<br />
2<br />
S = a kvadr. metri m2 2<br />
L<br />
3<br />
V = a kuburi metri m3 3<br />
L<br />
s<br />
metri<br />
v = , m/wm<br />
t<br />
wm<br />
m<br />
=<br />
V<br />
ρ 3<br />
a<br />
Δv<br />
Δt<br />
−1<br />
LT<br />
kg<br />
L M<br />
m<br />
3 −<br />
m<br />
= −2<br />
2<br />
wm<br />
2<br />
I = mV<br />
kg . m2 sxeulis impulsi P P = mV<br />
kg<br />
wm<br />
m<br />
impulsis momenti L L = mV<br />
kg<br />
wm<br />
2<br />
LT<br />
L M<br />
2<br />
m<br />
−1<br />
LMT<br />
L MT<br />
2 −1<br />
Zala F F = ma niutoni (n) −2<br />
LMT<br />
Zalis momenti M M = F�<br />
n . m 2 −2<br />
L MT<br />
muSaoba, energia A A = FS<br />
jouli (j) 2 −2<br />
L MT<br />
simZlavre N<br />
kuTxuri aCqareba ω<br />
rxevis sixSire υ<br />
kuTxuri aCqareba ε<br />
A<br />
j<br />
N = vati= (vt)<br />
t<br />
wm<br />
ϕ<br />
ω =<br />
t<br />
wm<br />
1<br />
υ =<br />
wm<br />
t<br />
dω<br />
dt<br />
L MT<br />
2 −3<br />
rad<br />
−1<br />
T<br />
-1 1 −<br />
rad<br />
−2<br />
ε = 2<br />
T<br />
wm<br />
T
laTinuri anbani berZnuli anbani<br />
A, a _ a Α, α − alfa<br />
B, b _ b Β, β − beta<br />
C, c _ ce Γ, γ − gama<br />
D, d _ de Δ, δ − delta<br />
E, e _ e E, ε − efsilon<br />
F, f _ ef Ζ, ζ − Zeta<br />
G, g _ Je Η, η − eta<br />
H, h _ haS Θ, ϑ − Teta<br />
I, i _ i Ι, ι − iota<br />
J, j _ Ji Κ, κ − kapa<br />
K, k _ ka Λ, λ − lambada<br />
L, l _ el Μ, μ − miu<br />
M, m _ em Ν, ν − niu<br />
N, n _ en Ξ, ξ − qsi<br />
O, o _ o Ο, ο − omikroni<br />
P, p _ pe Π, π − pi<br />
Q, q _ qu Ρ, ρ − ro<br />
R, r _ er ∑, σ −sigma<br />
S, s _ es Τ, ι − tau<br />
T, t _ te Φ, ϕ − fi<br />
U, u _ u Χ, χ − xi<br />
V, v _ ve Υ, υ − ifsilon<br />
W, w _ dubl-ve Ψ, ψ − fsi<br />
X , x _ iqs Ω, ω − omega<br />
Y, y _ igrek<br />
Z, z _ zet<br />
10
meqanikis fizikuri safuZvlebi<br />
1. kinematika<br />
materiis moZraobis umartivesi saxea meqanikuri moZraoba. am<br />
moZraobis dros xdeba materialuri sxeulebis, an maTi nawilebis<br />
mdgomareobis Secvla (gadanacvleba) sivrceSi da droSi. klasikur<br />
(niutonis) meqanikaSi miRebulia, rom sivrces gaaCnia sami ganzomileba da<br />
masSi samarTliania evklides geometria.<br />
1.1. aTvlis sxeuli. aTvlis sistema<br />
sxeulis mdebareobis gansazRvra SesaZlebelia mxolod sxva<br />
sxeulebis mimarT. sxeuls, romlis mimarTac ganisazRvreba mocemuli<br />
sxeulis mdebareoba, aTvlis sxeuli ewodeba. aTvlis sxeuli, masTan<br />
xistad dakavSirebuli koordinatTa sistema da drois gamzomi xelsawyo<br />
(saaTi), Seadgenen aTvlis sistemas. fizikaSi sargebloben dekartes<br />
marTkuTxa koordinatTa sistemiT (nax.1), romelSic nebismieri A wertili<br />
xasiaTdeba x,y,z koordinatebiT an radius _ veqtoriT. r = OA.<br />
radius-<br />
veqtori aerTebs erTmaneTTan O koordinatTa saTaves A wertilTan.<br />
nax. 1.<br />
1.2. materialuri wertilis kinematika. traeqtoria<br />
meqanikis nawils, romelic Seiswavlis sxeulebis moZraobas<br />
gamomwvevi mizezebisagan damoukideblad, kinematika ewodeba.<br />
11
sxeulis umartivesi fizikuri modelia materialuri wertili.<br />
materialuri, anu nivTieri wertili ewodeba iseT sxeuls, romlis zoma<br />
SeiZleba ugulvebelvyoT mocemuli amocanis pirobebSi. materialuri<br />
wertilis moZraobisas misi koordinatebi icvlebian drois ganmavlobaSi<br />
da drois yovel moments Seesabameba x, y, z-is garkveuli mniSvneloba, e.i.<br />
koordinatebi warmoadgenen drois funqciebs, rac Semdegnairad Caiwereba:<br />
x=f1(t), y=f2(t), z=f3(t), (1)<br />
radius-veqtori agreTve drois funqciaa<br />
r = r(t)<br />
(2)<br />
Tu cnobilia (1) funqciebis, an veqtoruli (2) funqciis saxe, maSin<br />
cnobili iqneba wertilis mdebareoba drois yovel momentSi, rac<br />
meqanikis ZiriTadi amocanaa. (1) sam gantolebas, an maT eqvivalenturs (2)<br />
kinematikuri gantolebebi ewodebaT. (1) gantolebebidan SeiZleba miviRoT<br />
traeqtoriis gantoleba, e.i. im mrudis gantoleba, romelsac aRwers<br />
materialuri wertili moZraobisas. traeqtoriis formis mixedviT<br />
moZraoba SeiZleba iyos wrfivi an mrudwiruli.<br />
damoukidebel koordinatTa ricxvs, romlebic gansazRvraven<br />
wertilis mdebareobas sivrceSi, Tavisuflebis xarisxi ewodeba. Tu<br />
materialuri wertili sivrceSi Tavisuflad moZraobs, maSin mas gaaCnia<br />
sami Tavisuflebis xarisxi (koordinatebi x,y,z), sibrtyeze moZraobisas _<br />
ori, xolo wrfis gaswvriv moZraobisas _ erTi. ganvixiloT materialuri<br />
wertilis moZraoba nebismier traeqtoriaze, mag. (AB) (nax. 2).<br />
nax. 2<br />
12
drois aTvla daviwyoT A mdebareobidan. ΔS _ gavlili manZili (gza)<br />
ewodeba traeqtoriis AB monakveTis sigrZes da warmoadgens drois<br />
skalarul funqcias: S = ΔS(t)<br />
Δ . r = r − r0<br />
Δ veqtors, romelic gaivleba<br />
wertilis sawyisi mdebareobidan sabolooSi, Δt droSi Sesrulebuli<br />
gadaadgildeba ewodeba. cxadia, wrfivi moZraobisas gadaadgilebis<br />
veqtori emTxveva Sesabamisi traeqtoriis monakveTs da misi moduli [ Δ r]<br />
toli iqneba Δ S gavlili gzis.<br />
siCqare<br />
materialuri wertilis moZraobis dasaxasiaTeblad ganixileba<br />
veqtoruli sidide _ siCqare, romelic gansazRvravs sxeulis moZraobis<br />
siswrafes da mis mimarTulebas drois mocemul momentSi. DdavuSvaT,<br />
materialuri wertili moZraobs raime mrudze (nax. 2). drois t momentSi<br />
igi A mdebareobaSia, xolo t + Δt<br />
momentSi _ B-Si. gadaadgilebis veqtori<br />
r r r − = Δ , sididiT is udris AB qordas da gansxvavdeba gavlili<br />
iqneba 0<br />
gzisgan (AB rkali). es gansxvaveba miT ufro mcirea, rac ufro mcirea Δ t .<br />
drois Sualedis _ Δ t SemcirebiT mrudwiruli moZraoba daiyvaneba<br />
wrfiv moZraobaze. wrfivi moZraobis saSualo siCqare tolia gavlili<br />
gzis Sefardebisa Sesabamis drosTan (nax. 3).<br />
v<br />
ΔS<br />
= ,<br />
Δt<br />
13<br />
v<br />
nax. 3.<br />
Δr<br />
=<br />
Δt
es gamosaxulebebi gansazRvraven saSualo siCqaris sidides da<br />
mimarTulebas. Tu gadavalT zRvarze, roca Δt → 0,<br />
miviRebT siCqares<br />
drois momentSi, anu myis siCqares (saSualo da myisi siCqaris<br />
mimarTulebebi naCvenebia nax.3)<br />
Δr<br />
dr<br />
v = lim =<br />
Δt<br />
dt<br />
e.i. myisi, anu namdvili siCqare tolia radius-veqtoris pirveli<br />
rigis warmoebulisa droiT. rodesac Δt → 0 , maSin Δ S → Δr<br />
, amitom<br />
rogorc wrfivi, aseve mrudwiruli moZraobisaTvis gveqneba:<br />
Δr<br />
Δr<br />
ΔS<br />
ds<br />
v = v = lim = lim = lim =<br />
Δt→0 Δt<br />
Δt→0<br />
Δt<br />
Δt→0<br />
Δt<br />
dt<br />
e.i. myisi siCqaris ricxviTi mniSvneloba tolia gzis pirveli rigis<br />
warmoebulisa droiT.<br />
araTanabari, anu cvladi moZraobis SemTxvevaSi, radgan myisi<br />
siCqaris mniSvneloba droSi icvleba, ganmartaven saSualo siCqares:<br />
v<br />
ΔS<br />
=<br />
Δt<br />
nax.3-dan Cans, rom v > v , radgan Δ S > Δr<br />
, mxolod wrfivi<br />
moZraobisas Δ S = Δr<br />
sxeulis mier gavlili gza t1 -dan t 2 drois SualedSi zogadi saxiT<br />
gamoiTvleba integraliT:<br />
S =<br />
t<br />
2<br />
∫<br />
t<br />
1<br />
v(<br />
t)<br />
dt<br />
Tanabari moZraobis SemTxvevaSi v = const ( t − t = Δt)<br />
da miviRebT:<br />
S =<br />
t<br />
2<br />
14<br />
, 2 1<br />
∫vdt = v∫dt<br />
= vΔ<br />
t<br />
1<br />
aCqareba, aCqarebis mdgenelebi<br />
t<br />
t<br />
2<br />
1<br />
fizikur sidides, romelic axasiaTebs siCqaris cvlilebis<br />
siswrafes moduliT da mimarTulebiT, aCqareba ewodeba. aCqareba<br />
t
araTanabari (cvladi) moZraobis damaxasiaTebeli mniSvnelovani<br />
veqtoruli sididea.<br />
davuSvaT, (1) wertilSi t drois momentSi wertilis siCqarea v 1 ,<br />
xolo t + Δt<br />
momentSi (2) wertilSi v v + Δv<br />
saSualo aCqareba Δ t droSi<br />
2 = 1 (nax.4), v = v2<br />
− v1<br />
15<br />
nax. 4<br />
a<br />
Δ ,<br />
Δv<br />
= , xolo myisi aCqareba<br />
Δt<br />
a = lim a<br />
Δt→0 Δv<br />
dv<br />
= lim = .<br />
Δt→0<br />
Δt<br />
dt<br />
mrudwiruli moZraobis dros aCqareba icvleba<br />
rogorc sididiT, aseve mimarTulebiT. imisaTvis, rom davaxasiaToT<br />
TiToeulis cvlileba cal-calke, gamovTvaloT Δv da warmovadginoT is<br />
ori mdgenelis saxiT. nax. 4-dan Cans, rom n v v v Δ + Δ =<br />
amitom sruli aCqareba a iqneba:<br />
Δv<br />
Δvτ<br />
Δvn<br />
a = lim = lim + lim ,<br />
Δt→0 Δt<br />
Δt→0<br />
Δt<br />
Δt→0<br />
Δt<br />
dv dvτ<br />
dvn<br />
a = = + ,<br />
dt dt dt<br />
Δ τ da v = v2<br />
− v1<br />
Δ ,<br />
dvτ sadac = a τ tangencialuri (mxebi) aCqarebaa da axasiaTebs siCqaris<br />
dt<br />
dv n sididis cvlilebas, xolo = an<br />
_ normaluri aCqarebaa da axasiaTebs<br />
dt<br />
siCqaris mimarTulebis cvlilebas.
2<br />
dv<br />
v1<br />
a τ = τ , an = n<br />
dt<br />
R<br />
τ da n erTeulovani veqtorebia, a τ mimarTulia siCqaris gaswvriv<br />
traeqtoriis mxebad, xolo an _ radiusis gaswvriv centrisken.<br />
R_simrudis radiusia (nax. 5). amgvarad, mrudwiruli moZraobisas sruli<br />
aCqareba:<br />
a a +<br />
misi moduli<br />
a<br />
= τ n , an a = τ + n,<br />
2 2<br />
a = aτ<br />
+ an<br />
nax. 5.<br />
16<br />
dv<br />
dt<br />
=<br />
⎛<br />
⎜<br />
⎝<br />
dv<br />
dt<br />
dv<br />
dt<br />
2<br />
⎞<br />
⎟<br />
⎠<br />
2 ⎛ v ⎞<br />
+ ⎜<br />
⎟<br />
⎝ R ⎠<br />
aCqarebis tangencialuri da normaluri mdgenelebis gamoyenebiT<br />
SeiZleba movaxdinoT moZraobis klasificireba:<br />
1) a = 0,<br />
a = 0 _ wrfivi Tanabari moZraobaa,<br />
τ<br />
n<br />
2) a τ = a = const,<br />
a n = 0 _ wrfivi Tanabarcvladi moZraoba da<br />
Δv<br />
v2<br />
− v1<br />
aτ<br />
= a = = , Tu aTvla iwyeba 1 0<br />
Δt<br />
t − t<br />
= t momentidan, maSin t = t<br />
2<br />
1<br />
2<br />
2 da v 2 = v,<br />
xolo v 1 = v0<br />
- sawyisi siCqarea, gveqneba<br />
v − v0<br />
a = ,<br />
t<br />
saidanac v = v0<br />
+ at,<br />
gavlili gza<br />
S =<br />
t t<br />
2<br />
at<br />
( ,<br />
2<br />
∫vdt = ∫ v0<br />
+ at)<br />
dt = v0t<br />
+<br />
0 0
3) a τ = f (t),<br />
a = 0 - wrfivi aCqarebuli moZraobaa,<br />
n<br />
4) a = 0,<br />
an = const - Tanabari moZraoba wrewirze,<br />
τ<br />
5) a = 0,<br />
an = f (t)<br />
- Tanabari mrudwiruli moZraoba,<br />
τ<br />
6) a = const,<br />
a ≠ 0 - Tanabarcvladi mrudwiruli moZraoba,<br />
n<br />
7) a τ = f (t),<br />
a n ≠ 0 - aCqarebuli mrudwiruli moZraoba.<br />
mxedvelobaSi unda miviRoT, rom Cvens mier ganxilul sidideebs<br />
Soris adgili aqvs Semdeg Tanafardobebs:<br />
r ( t)<br />
= x(<br />
t)<br />
i + y(<br />
t)<br />
j + Z(<br />
t)<br />
k,<br />
dr dx dy i j dzk<br />
v(<br />
t)<br />
= = i + j + k,<br />
siCqaris modulisaTvis:<br />
dt dt dt dt<br />
v = v = v + v + v<br />
2<br />
x<br />
dv dv x y dvz<br />
( t)<br />
= i + j + k = axi<br />
+ ay<br />
j + a k,<br />
dt dt dt<br />
a z<br />
2<br />
dv d r<br />
a = = aCqarebis modulisaTvis<br />
2<br />
dt dt<br />
2<br />
2 2 2<br />
dv d r<br />
a = a = ax<br />
+ ay<br />
+ az<br />
, magram a ≠ ≠ 2<br />
dt dt<br />
1.3. absoluturad myari sxeulis kinematika<br />
absoluturad myari sxeuli iseTi sxeulis fizikuri modelia,<br />
romelic ar ganicdis deformacias mocemul konkretul amocanaSi. myari<br />
sxeulis nebismieri moZraoba SeiZleba dayvanil iqnas gadataniT da<br />
brunviT moZraobaze. gadataniTi ewodeba iseT moZraobas, romlis drosac<br />
sxeulSi gavlebuli yoveli wrfe Tavisi paraleluri rCeba (nax.6).<br />
nax. 6<br />
17<br />
2<br />
4<br />
2<br />
z
unviTi moZraobis dros sxeulis yvela wertili imoZravebs wrewirze,<br />
romelTa centrebi ganlagdebian erT da igive wrfeze, romelsac brunvis<br />
RerZi ewodeba. brunvis RerZi SeiZleba moTavsebuli iyos rogorc<br />
sxeulSi, aseve mis gareT (nax. 7 a da b).<br />
a b<br />
nax. 7 a da b.<br />
sxeulis gadataniTi moZraoba aRiwereba misi erTi wertilis<br />
moZraobiT, romelsac masaTa centri ewodeba.<br />
materialuri wertilebis sistemis (sxeulis) masaTa centri _<br />
wertilia romlis mdebareoba ganisazRvreba r c radius veqtoriT.<br />
mr1<br />
+ m2<br />
r2<br />
+ .... + mk<br />
r<br />
r c =<br />
m + m + ..... + m<br />
sadac m _ mTliani sxeulis masaa.<br />
masaTa centris siCqare<br />
1<br />
v<br />
c<br />
2<br />
drc<br />
= =<br />
dt<br />
18<br />
∑<br />
k<br />
k<br />
mi<br />
r<br />
m<br />
k<br />
∑<br />
=1<br />
m1ri<br />
i =<br />
m<br />
,<br />
1.4. kuTxuri gadaadgileba, kuTxuri siCqare, kuTxuri aCqareba<br />
wrewirze moZravi wertilis mdgomareoba ganisazRvreba<br />
Semobrunebis kuTxis ( Δ ϕ ) mniSvnelobiT (nax. 8).<br />
i
nax. 8.<br />
kuTxuri gadaadgileba:<br />
Δϕ - veqtoria, romlis sigrZe<br />
tolia Semobrunebis kuTxis modulis Δ ϕ , xolo mimarTuleba aiReba<br />
brunvis RerZis gaswvriv marjvena burRis wesiT. aseT veqtorebs _<br />
fsevdoveqtorebi (aksialurebi) ewodebaT.<br />
kuTxuri siCqare<br />
Δϕ<br />
dϕ<br />
ω = lim =<br />
Δt→0 Δt<br />
dt<br />
kuTxuri siCqare warmoadgens RerZis garSemo mbrunavi sxeulis<br />
maxasiaTebels (nax.9).<br />
ω - fsevdoveqtoria, mimarTuli brunvis RerZis gaswvriv marjvena<br />
burRis wesiT.<br />
nax. 9.<br />
rad<br />
ω = = wm<br />
wm<br />
-1 , dimω = T-1 Tu ω = const brunva Tanabaria. brunvis periodi T – droa, romlis<br />
2π<br />
ganmavlobaSi sxeuli asrulebs erT srul bruns, T = .<br />
ω<br />
brunvis sixSire υ − drois erTeulSi Sesrulebuli brunvaTa<br />
ricxvia.<br />
19
1 ω<br />
υ = =<br />
T 2π<br />
1<br />
[ ] =<br />
wm<br />
υ =wm -1 ,<br />
dim<br />
= T<br />
−1<br />
υ .<br />
Tu ω ≠ const − brunva araTanabaria. kuTxuri aCqareba tolia<br />
Δω<br />
dω<br />
ε = lim =<br />
Δt→0 Δt<br />
dt<br />
kuTxuri aCqareba warmoadgens siCqaris cvlilebis maxasiaTebels. ε _<br />
fsevdoveqtoria, mimarTuli brunvis RerZis gaswvriv (nax.10).<br />
nax. 10<br />
aCqarebuli moZraobisas ε veqtoris mimarTuleba paraleluria ω<br />
veqtoris mimarTulebis (nax. 11), xolo Senelebuli moZraobisas<br />
mimarTulia sawinaaRmdegod (nax. 12).<br />
nax.11 nax. 12.<br />
wrewirze Tanabari moZraobis SemTxvevaSi ( ε = const)<br />
2<br />
εt<br />
ω = ω0<br />
± εt,<br />
ϕ ω0t<br />
± ,<br />
2<br />
= sadac 0<br />
ω -sawyisi kuTxuri siCqarea.<br />
20
unviTi moZraobis maxasiaTeblebi, wrfivi da kuTxuri sidideebi,<br />
dakavSirebuli arian erTmaneTTan Semdegi TanafardobiT<br />
ds = Rdϕ<br />
, v = [ ω × r]<br />
, v = ωR<br />
,<br />
[ r]<br />
2<br />
2<br />
a τ = ε × , a τ = ε R , an = −ω<br />
R , an = ω R .<br />
aq r radius-veqtoria, gavlebuli brunvis RerZze mdebare<br />
koordinatTa saTavidan. is gansazRvravs materialuri wertilis<br />
mdebareobas. R veqtori gavlebulia gansaxilvel wertilSi da<br />
marTobulia brunvis RerZis.<br />
uZravi RerZis garSemo mbrunavi sxeulis da gadataniTi moZraobis<br />
Sesabamisi (analogiuri) sidideebis da gantolebebis cxrili:<br />
@ gadataniTi moZraoba brunviTi moZraoba<br />
1 masa<br />
2 gavlili manZili _ gza<br />
3 siCqare<br />
4 aCqareba<br />
m<br />
S<br />
d r<br />
v =<br />
dt<br />
dv<br />
a =<br />
dt<br />
21<br />
inerciis<br />
momenti<br />
Semobrunebis<br />
kuTxe<br />
5 Zala F Zalis<br />
6 impulsi<br />
7 dinamikis ZiriTadi<br />
gantoleba<br />
8 muSaoba<br />
9 kinetikuri energia<br />
p = mv<br />
F = ma<br />
d p<br />
F =<br />
dt<br />
dA = F ⋅ d s<br />
W =<br />
2<br />
mv<br />
2<br />
kuTxuri<br />
siCqare<br />
dϕ<br />
ω =<br />
dt<br />
kuTxuri<br />
aCqareba<br />
dω<br />
ε =<br />
dt<br />
momenti<br />
impulsis<br />
momenti<br />
dinamikis<br />
ZiriTadi<br />
gantoleba<br />
I<br />
ϕ<br />
M an Mz<br />
L = Iω<br />
M = Iε<br />
d L<br />
M =<br />
dt<br />
muSaoba<br />
M = Mdϕ<br />
kinetikuri<br />
energia<br />
W =<br />
2<br />
Iω<br />
2
2. dinamika<br />
2.1. materialuri wertilis dinamika<br />
klasikuri dinamika Seiswavlis sinaTlis siCqaresTan SedarebiT<br />
mcire siCqareebiT moZravi makroskopuli sxeulebis moZraobis kanonebs,<br />
sxeulTa urTierTqmedebis gaTvaliswinebiT.<br />
dinamikas safuZvlad udevs niutonis sami kanoni, romlebic<br />
samarTliania yvela saxis nivTieri makroskopiuli obieqtebisTvis.<br />
radgan movlenebs vswavlobT sivrcesa da droSi, amitom unda<br />
movnaxoT iseTi aTvlis sistema, romelSic sivrce da dro erTgvarovani<br />
da izotropulia. aseT sistemebSi Tavisufali izolirebuli sxeulis<br />
sivrceSi sxvadasxva mdebareoba da orientacia meqanikis TvalsazrisiT<br />
erTmaneTis eqvivalenturia. igive samarTliania droisaTvisac, e.i. misi<br />
sxvadasxva momentebi erTmaneTis eqvivalenturia. sistema, romlis mimarT<br />
sivrce da dro erTgvarovani da izotropulia sxva sistemebisgan<br />
gansxvavdeba imiT, rom, Tu am sistemaSi izolirebuli materialuri<br />
sxeuli drois erT momentSi aris uZravi, an moZraobs mudmivi siCqariT,<br />
is am mdgomareobas SeinarCunebs usasrulod didi drois ganmavlobaSi.<br />
aTvlis aseT sistemas ewodeba inerciuli.<br />
niutonis pirveli kanoni: aTvlis inerciul sistemaSi yoveli<br />
izolirebuli (Tavisufali) sxeuli inarCunebs uZraobis an Tanabari<br />
wrfivi moZraobis mdgomareobas.<br />
sxeulis Tvisebas, SeinarCunos uZraobis an Tanabari wrfivi<br />
moZraobis mdgomareoba, uwodeben inercias. aqedan warmosdgeba niutonis<br />
kanonis saxelwodeba _ inerciis kanoni.<br />
sxeulis Tvisebas, SeinarCunos Tavisi mdgomareoba, ewodeba<br />
inertuloba. sxeulis inertulobis zomaa _ masa. klasikur (niutonis)<br />
meqanikaSi, masa sididea:<br />
• skalaruli<br />
• dadebiTi (m>0),<br />
• aditiuri ( m = ∑ m1<br />
),<br />
• mudmivi ( m = const)<br />
[m]=kg<br />
22
Zala<br />
veqtoruli sidide _ Zala, warmoadgens sxeulze sxva sxeulebis an<br />
velebis zemoqmedebis zomas, romlis Sedegad sxeuli iZens aCqarebas an<br />
deformacias.<br />
mocemulia F Zala niSnavs, rom viciT misi moduli, mimarTuleba<br />
sivrceSi da modebis wertili. wrfes, romlis gaswvrivac mimarTulia<br />
Zala, ewodeba Zalis moqmedebis wrfe.<br />
sxeulebs Soris meqanikuri urTierTqmedeba SeiZleba<br />
ganxorcieldes rogorc manZilze (mzis mier planetebis mizidva), aseve<br />
uSualo kontaqtisas (xaxuni, Sexla).<br />
ZalTa superpoziciis principi<br />
materialur wertilze Zalebis erTdrouli moqmedeba eqvivalenturia<br />
erTi Zalis moqmedebis, romelsac tolqmedi (marezultirebeli) Zala<br />
ewodeba F da tolia maTi geometriuli jamis<br />
[ F ]= n (niutoni), dimF = LMT -2<br />
F =<br />
23<br />
n<br />
∑ Fi<br />
i=<br />
1<br />
materialuri wertilis impulsi<br />
P = m v<br />
sadac mi -materialuri wertilis masaa, vi - misi siCqare.<br />
materialur wertilTa sistemis (sxeulis) impulsi<br />
i<br />
p =<br />
n<br />
∑<br />
i=<br />
1<br />
i<br />
pi<br />
materialur wertilTa sistemis impulsi tolia sistemis sruli<br />
masis namravlis masaTa centris siCqareze = m v<br />
[ p]= kg m/wm, dim =LMT-1 .<br />
i<br />
p c
niutonis meore kanoni. sxeulze momqmedi Zala tolia sxeulis impulsis<br />
cvlilebis siCqaris da gaaCnia Zalis moqmedebis mimarTuleba.<br />
d p<br />
F =<br />
dt<br />
Tu m = const,<br />
meore kanoni gamoiTqmeba: sxeulis aCqareba<br />
F<br />
pirdapirproporciulia Zalis da ukuproporciulia masis: a = , sadac:<br />
m<br />
2<br />
dv<br />
d r<br />
a = = , 2<br />
dt dt<br />
2<br />
d r<br />
sxeulis moZraobis gantolebaa: m = F 2<br />
dt<br />
koordinatTa RerZebze proeqciebSi:<br />
2<br />
2<br />
2<br />
d x<br />
d y<br />
d z<br />
m = F 2 x , m = Fy,<br />
m = F ,<br />
2<br />
2 z<br />
dt<br />
dt<br />
dt<br />
sadac x,y,z, moZravi wertilis koordinatebia.<br />
niutonis mesame kanoni. sxeulebis nebismieri moqmedeba erTmaneTze<br />
yovelTvis urTierTqmedebis xasiaTs atarebs. Zalebi, romliTac<br />
urTierTmoqmedeben sxeulebi sididiT tolia, mimarTulebiT sapirispiro<br />
da modebulia sxvadasxva sxeulebze. mokled asec gamoiTqmeba _ qmedebis<br />
Zala tolia ukuqmedebis Zalis, sawinaaRmdegoa niSniT da mdebareoben<br />
erT wrfeze. (nax.13)<br />
F12 = −F<br />
21 , N<br />
p =<br />
nax. 13<br />
sadac p - sxeulis wonaa, modebulia sayrdenze, N - normaluri<br />
wnevis Zalaa, modebulia sxeulze, e.i. p da N qmedebis da ukuqmedebis<br />
Zalebia.<br />
24
niutonis meore da mesame kanonebis Sedegebi:<br />
1. nebismier meqanikur sistemaSi Sinagani Zalebis geometriuli jami<br />
nulis tolia<br />
n<br />
n<br />
∑∑<br />
i=<br />
1 k=<br />
1<br />
25<br />
F<br />
sadac n-sistemaSi Semavali urTierTmomqmedi materialuri wertilebis<br />
in<br />
= 0<br />
gare<br />
raodenobaa. gare Zalebis mTavari veqtori ( F )<br />
sadac<br />
tolqmedia.<br />
gare<br />
F =∑ gare<br />
i<br />
F<br />
gare<br />
F - i-ur materialur wertilze modebuli gare Zalebis<br />
2. impulsis warmoebuli droiT tolia sistemaze modebuli gare<br />
Zalebis mTavari veqtoris (impulsis cvlilebis kanoni).<br />
d p<br />
=<br />
dt<br />
gare<br />
F<br />
3. meqanikuri sistemis masaTa centris moZraobis kanoni:<br />
d<br />
dt<br />
( mv<br />
c ) =<br />
an mac<br />
=<br />
gare<br />
F ,<br />
gare<br />
F<br />
Tu meqanikuri sistema _ myari sxeulia, maSin gadataniTi moZraobis<br />
ZiriTadi gantoleba iqneba:<br />
ma<br />
=<br />
gare<br />
F ( a = ac<br />
)<br />
2.2. bunebis Zalebi<br />
Tanamedrove fizikaSi miRebulia urTierTqmedebis 4 saxe:<br />
1. Zlieri anu birTvuli;<br />
2. eleqtromagnituri;<br />
3. susti;<br />
4. gravitaciuli.
klasikur (niutonis) meqanikaSi ganixilaven fundamentalur-<br />
eleqtromagnitur da gravitaciul Zalebs. drekadi da xaxunis Zalebi<br />
Tavisi bunebis gamo, miekuTvnebian eleqtromagnitur Zalebs.<br />
gravitaciuli Zalebi<br />
msoflio mizidulobis kanoni. gravitaciuli Zala, romliTac<br />
miezidebian erTmaneTs materialuri wertilebi (an ori sxeuli),<br />
pirdapirproporciulia maTi masebis namravlisa da ukuproporciulia<br />
maT Soris manZilis kvadratis (nax. 14).<br />
m m2<br />
F = G ⋅ 2<br />
R<br />
26<br />
R<br />
1 ,<br />
sadac m 1 da m 2 - materialuri wertilebis masebia,<br />
R _ maT Soris manZili,<br />
2<br />
−11 n ⋅m<br />
G _ gravitaciuli mudmiva toli 6,67 ⋅10<br />
, 2<br />
kg<br />
R - erTeulovani veqtori, romelic gviCvenebs gravitaciuli Zalis<br />
R<br />
mimarTulebas.<br />
na.x 14<br />
pirvel miaxloebaSi dedamiwa sferuli formisaa da masa<br />
ganawilebulia masSi sferuli simetriiT. dedamiwis mizidulobis Zala m<br />
masis sxeulze mimarTulia dedamiwis centrisaken, misi moduli ki<br />
tolia:<br />
mM<br />
F =<br />
G<br />
2<br />
R<br />
R
gravitaciuli Zalebi gansazRvrven planetebis, varskvlavebis da sxva<br />
makroobieqtebis moZraobas. mikroobieqtebis moZraobaSi isini<br />
praqtikulad ar monawileoben.<br />
simZimis Zala da wona.<br />
uwonadoba<br />
simZimis Zala aris msoflio mizidulobis gravitaciuli Zalis kerZo<br />
gamovlineba. igi aris Zala, romliTac dedamiwa izidavs sxeulebs, amitom<br />
P simZimis Zala moqmedi m masis sxeulze<br />
mM<br />
P = mg = F = G , 2<br />
R<br />
sadac M – dedamiwis masaa.<br />
simZimis Zalis aCqareba g gamoiTvleba niutonis meore kanoniT:<br />
F M<br />
g = = G , 2<br />
m R<br />
e.i. g simZimis Zalis aCqareba ar aris damokidebuli sxeulis masaze da<br />
yvela sxeulisaTvis erTnairia. mas xSirad Tavisufali vardnis aCqarebas<br />
uwodeben. simZimis Zala da Sesabamisad simZimis Zalis aCqareba icvleba<br />
geografiuli ganedis mixedviT, rasac ganapirobebs ori faqtori _ erTia<br />
dedamiwis dReRamuri brunva, meore ki _ dedamiwis elifsuri forma.<br />
ekvatorze simZimis Zalis aCqarebis sidide g ( ϕ = 0)<br />
=9,78 m/wm2 . xolo<br />
polusze 0<br />
( ϕ = 90 )<br />
g = 9,83 m/wm<br />
g aCqareba mimarTulia simZimis Zalis veqtoris mimarTulebiT, amitom<br />
p = mg<br />
sxeulis wona ewodeba Zalas, romliTac sxeuli gravitaciuli Zalis<br />
gavleniT moqmedebs sayrdenze.<br />
sxeulis mdgomareobas, rodesac is moZraobs mxolod simZimis Zalis<br />
gavleniT, uwonadoba ewodeba.<br />
27
inerciuli da arainerciuli sistemebi<br />
iseT sistemas, romelSic sruldeba niutonis pirveli kanoni,<br />
inerciuli sistema ewodeba. nebismieri sistema iqneba inerciuli, Tu is<br />
inerciuli sistemis mimarT uZravia, an moZraobs Tanabrad da wrfivad.<br />
sistema arainerciulia, Tu is moZraobs aCqarebulad nebismieri<br />
inerciuli sistemis mimarT (nax. 15). vTqvaT, sistema K (koordinatebiT<br />
x,y,z) inerciulia, xolo sistema K 1 (koordinatebiT x 1 y 1 z 1 ) moZraobs K-s<br />
mimarT v 0 siCqariT, ise rom x 1 y 1 z 1 RerZebi K sistemis Sesabamisi RerZebis<br />
paraleluria.<br />
nebismieri Tavisufali A wertilis radius-veqtori K sistemaSi<br />
aRvniSnoT r , xolo<br />
sistemaSi aRvniSnoT 0<br />
1) Tu<br />
nax. 15<br />
1<br />
K sistemaSi 1<br />
r -iT. 01 wertilis radius-veqtori K<br />
1<br />
r -iT. naxazidan miviRebT: r r + r0<br />
28<br />
= (1).<br />
1<br />
K sistema moZraobs K-s mimarT mudmivi v siCqariT, is xdeba<br />
inerciuli, radgan misi moZraoba K-s mimarT iqneba Tanabari da wrfivi.<br />
(1)-is droiT gawarmoeba mogvcems:<br />
1<br />
dr dr<br />
dr<br />
0<br />
1<br />
= + , anu v = v + v 0<br />
dt dt dt<br />
rac warmoadgens siCqareTa Sekrebis (galileis) kanons klasikur<br />
meqanikaSi. Tu miRebuls kvlav gavawarmoebT v = const)<br />
, miviRebT:<br />
1<br />
a = a<br />
( 0
aCqarebis tolobebi am sistemebSi niSnavs A wertilze moqmedi<br />
Zalebis tolobas:<br />
1<br />
F = F , rac koordinatTa sistemis arCevaze ar aris<br />
damokidebuli, anu K da K 1 sistemebi tolfasia. e.i. yvela inerciul<br />
sistemaSi meqanikis kanonebs erTnairi saxe aqvs. maSasadame, meqanikuri<br />
movlenebi inerciul sistemebSi erTnairad mimdinareoben. galileis mier<br />
miRebul am debulebebs fardobiTobis meqanikuri principi ewodeba.<br />
2) Tu v ≠ const,<br />
K1 sistema arainerciulia, amitom (1)-is meore<br />
warmoebuli mogvcems:<br />
anu aCqareba<br />
0<br />
d<br />
dt<br />
2 2 2<br />
1<br />
r d r d r<br />
1<br />
0<br />
= + , anu a = a + a<br />
2 2 2<br />
0<br />
dt<br />
dt<br />
1<br />
1<br />
a − K sistemaSi gansxvavebulia K-Si a aCqarebisagan<br />
1<br />
= a a0<br />
miRebulis gamravleba A wertilis masaze mogvcems:<br />
a −<br />
1<br />
1<br />
= ma<br />
ma<br />
0 , anu F = F − ma<br />
0<br />
ma −<br />
e.i. K 1 sistemaSi Zalac gansxvavebulia, amitom niutonis meore kanonic<br />
samarTliani ar iqneba. unda davuSvaT, rom K 1 sistemaSi garda<br />
garemomcveli sxeulTa moqmedebisa (F 1 Zala), A materialur wertilze<br />
moqmedebs agreTve Zala:<br />
F i = m −<br />
29<br />
( a 0<br />
gamowveuli K 1 sistemis aCqarebuli moZraobiT. F i Zalas inerciis Zala<br />
ewodeba. im damatebiT Zalas, romelic sxeulze moqmedebs arainerciul<br />
sistemaSi myofi damkvirveblis TvalsazrisiT, inerciis Zala ewodeba.<br />
drekadobis Zalebi<br />
drekadobis Zalebi warmoiqmnebian myar sxeulSi deformaciis dros da<br />
eqvemdebarebian hukis kanons.<br />
hukis kanoni: mcire deformaciis dros, deformaciis gamomwvevi Zalis<br />
sidide pirdapirproporciulia deformaciis sididis da gamoisaxeba<br />
formuliT (nax 16) F = −kx<br />
,sadac x- deformaciaa (wanacvleba),<br />
)
nax. 16.<br />
k- drekadobis koeficientia, damokidebuli sxeulis gvarobaze,<br />
sxeulis deformacia ganisazRvreba misi geometriuli zomebis<br />
cvlilebiT. grZivi deformaciis dros<br />
sadac<br />
Δ �<br />
- fardobiTi wagrZelebaa;<br />
� 0<br />
0<br />
Δ�<br />
ε = ,<br />
�<br />
Δ � = � − � - absoluturi wagrZelebaa.<br />
� 0 - sxeulis sawyisi sigrZea. F 1 = F2<br />
= Fn<br />
nax.17<br />
30<br />
0<br />
.
cda gviCvenebs, rom drekadi deformaciis dros Reros wagrZeleba<br />
Δ � gamWimavi F normaluri Zalis da Reros sawyisi sigrZis<br />
pirdapirproporciulia da ukuproporciulia misi ganivkveTis S farTisa.<br />
sadac α drekadobis, anu<br />
F�<br />
Δ � = α ,<br />
S<br />
grZivi gaWimvis koeficientia da<br />
damokidebulia nivTierebis gvarobaze.<br />
wina formulidan<br />
Δ�<br />
� 0<br />
F<br />
= α<br />
S<br />
, anu ε = α ,<br />
S<br />
Fn _ farTobis erTeulze moqmedi gamWimavi Zala, anu normaluri<br />
S<br />
Zabvaa σ , miviRebT:<br />
ε = ασ<br />
miRebuli gantoleba saSualebas gvaZlevs hukis kanoni Semdegnairad<br />
CamovayaliboT:<br />
fardobiTi deformacia deformaciis gamomwvevi Zabvis<br />
pirdapirproporciulia.<br />
grZivi gaWimvis koeficientis Sebrunebul sidides iungis moduli<br />
ewodeba:<br />
1 σ<br />
E = da ε =<br />
α E<br />
amgvarad, normaluri meqanikuri Zabva<br />
F Δ�<br />
σ<br />
σ = da = .<br />
S � E<br />
e.i. iungis moduli iseTi meqanikuri Zabvis tolia, romlis drosac<br />
fardobiTi deformacia udris erTs. myari sxeulis deformacia hukis<br />
kanons eqvemdebareba garkveul zRvrul mniSvnelobamde, rac<br />
dakavSirebulia masalis gvarobaze.<br />
[ E ]<br />
=<br />
-2<br />
n ⋅m<br />
31<br />
dimE<br />
F n<br />
−1<br />
−2<br />
= ML T
xaxunis Zalebi<br />
xaxunis Zalebi warmoiSvebian erTmaneTis mimarT raime siCqariT<br />
moZravi myari sxeulebis Sexebis zedapirze an sxeulebis garemoSi<br />
(siTxeSi, gazebSi) moZraobis Sedegad da Tavisi bunebiT gansxvavdebian<br />
meqanikuri Zalebisagan. winaaRmdegobis F Zalas, romelic mimarTulia<br />
sxeulebis moZraobis sawinaaRmdegod, xaxunis Zala ewodeba.<br />
maqsimaluri uZraobis xaxunis Zala (srialis xaxunis Zalac), ar aris<br />
damokidebuli Semxebi zedapirebis farTze da proporciulia normaluri<br />
wnevis Zalis<br />
F xax = μΝ<br />
,<br />
sadac N - normaluri wnevis Zalaa,<br />
μ _ xaxunis koeficienti, damokidebulia Semxebi zedapirebis<br />
gvarobaze da mdgomareobaze.<br />
srialis dros xaxunis koeficienti siCqaris funqciaa.<br />
uZraobis xaxuni mJRavndeba uZravi sxeulis amoZravebisas. misi<br />
koeficientia μ 0<br />
nax. 18.<br />
srialis xaxuni mJRavndeba sxeulis moZraobisas; μ < μ0<br />
.<br />
ganvixiloT xaxunis Zalebi sxeulebis srialis dros:<br />
1. Tu wevis Zala emTxveva gadaadgilebis mimarTulebas (nax. 18)<br />
F = μmg<br />
2. Tu wevis Zala gadaadgilebasTan adgens α kuTxes (nax. 19 a)<br />
xax<br />
F =<br />
( mg − F sinα<br />
)<br />
xax<br />
μ wv<br />
32
xolo nax. 19 b SemTxvevisTvis :<br />
33<br />
nax. 19.<br />
F xax = μ( mg + Fwev<br />
sinα<br />
)<br />
3. Tu sxeuli moZraobs daxril sibrtyeze, xaxunis Zala tolia (nax.<br />
20):<br />
F xax = μmg cosα<br />
am dros xaxunis koeficienti μ = tgα<br />
nax. 20
4. Tu sxeuli raRac ZaliT ekroba vertikalur zedapirs, xaxunis<br />
Zala tolia (nax. 21):<br />
F = μF<br />
xax<br />
k<br />
nax. 21<br />
transportis moZraobisas unda gaviTvaliswinoT xaxuni ara marto<br />
borblebsa da gzas Soris, aramed xaxuni burTulsakisrebSic. am dros<br />
orive xaxunis koeficienti gaiTvaliswineba moZraobis winaaRmdegobis<br />
koeficientSi.<br />
2.3. muSaoba, simZlavre, energia<br />
meqanikuri muSaoba<br />
fizikur sidides, romelic tolia Zalisa da gadaadgilebis<br />
skalaruli namravlis, muSaoba ewodeba. F Zalis elementaruli muSaoba<br />
ΔAmcire Δr gadaadgilebaze, ganmartebis Tanaxmad, iqneba (nax. 22):<br />
ΔA = ( FΔr)<br />
= FΔr<br />
cosα<br />
= FrΔr<br />
nax. 22<br />
sadac Fr = F cosα<br />
_ F Zalis proeqciaa gadaadgilebis<br />
mimarTulebaze. α _ kuTxea Zalisa da gadaadgilebis mimarTulebebs<br />
34
Soris. Δ r simciris gamo F Zala SeiZleba mudmivad CavTvaloT, xolo<br />
Δ r → dr<br />
.<br />
elementaruli gzis sigrZe, romelsac gadis Zalis modebis<br />
wertili dt drois SualedSi<br />
maSin elementaruli muSaoba<br />
ds =<br />
35<br />
d r<br />
dA = Fds cosα<br />
aq d simbolo aRniSnavs mcire sidideebs.<br />
meqanikuri muSaoba _ skalaruli sididea, aditiuri. Tu:<br />
• 90 ,<br />
°<br />
α < dA > 0,<br />
muSaoba dadebiTia.<br />
• 90 ,<br />
°<br />
α = dA = 0,<br />
muSaoba tolia nulis.<br />
• 90 ,<br />
°<br />
α > dA < 0,<br />
muSaoba uaryofiTia.<br />
n<br />
n<br />
n<br />
⎛ ⎞<br />
E dA = ∑ dAi<br />
= ⎜∑<br />
F i ⎟d<br />
r i = ∑ F i v idt<br />
,<br />
i=<br />
1 ⎝ i=<br />
1 ⎠ i=<br />
1<br />
sadac r i da v i radius-veqtori da siCqarea Zalis modebis wertilSi.<br />
materialuri wertilis moZraobis dros<br />
sadac p - wertilis impulsia.<br />
dA = vd<br />
myari sxeulis gadatanis da moZraobis dros<br />
dA c<br />
p<br />
= v d p<br />
sadac p = mv<br />
c - myari sxeulis impulsia, romlis masaTa centri<br />
moZraobs v c siCqariT. m – myari sxeulis masaa.<br />
cvladi Zalis muSaoba<br />
davuSvaT, nawilakze (sxeulze) moqmedebs cvladi Zala, romlis<br />
sidide damokidebulia koordinataze kanoniT Fr = F(r<br />
) . aseTi Zalis<br />
elementaruli muSaoba Δ Ai = FrΔr<br />
i ricxobrivad toli iqneba naxazze<br />
daStrixuli zolis farTis, xolo 1<br />
r -dan 2<br />
r gzaze is tolia farTis,
omelic SemosazRvrulia Fr (r)<br />
mrudiT, vertikaluri wrfeebiT r 1 da r 2<br />
da r RerZiT (nax. 23)<br />
∑<br />
A =<br />
Δr<br />
→0<br />
i<br />
i<br />
r<br />
2<br />
12 lim Fr<br />
Δri<br />
= ∫ Fr<br />
( r)<br />
dr = f( r112r2<br />
)<br />
r<br />
cvladi Zalis meqanikuri muSaoba<br />
A<br />
= 2<br />
12<br />
1<br />
∫ dA = ∫<br />
r<br />
r<br />
1<br />
2<br />
1<br />
F ( r)<br />
dr<br />
[ A ] = n ⋅m<br />
= j(jouli)<br />
,<br />
r<br />
dim A<br />
nax. 23<br />
2 −2<br />
= L MT<br />
simZlavre<br />
skalarul fizikur sidides, romelic tolia elementaruli<br />
muSaobis dA Sefardebis dt drosTan, romlis ganmavlobaSic sruldeba<br />
mocemuli muSaoba dA, myisi simZlavre ewodeba<br />
dA<br />
N =<br />
dt<br />
Tu dA muSaobas asrulebs F Zala, maSin N simZlavre SeiZleba<br />
warmovadginoT Semdegi skalaruli namravliT:<br />
dA d r<br />
N = = F ⋅ = ( F ⋅ v)<br />
dt dt<br />
e.i. namdvili (myisi) simZlavre udris Zalisa da siCqaris veqtorebis<br />
skalarul namravls. Tu muSaoba Tanabrad sruldeba, e.i. drois tol<br />
36
SualedebSi erTnairi muSaoba sruldeba, maSin namdvili simZlavre<br />
saSualo simZlavris toli iqneba da miviRebT:<br />
amitom<br />
A<br />
N =<br />
Δt<br />
es gantoleba gamosadegi iqneba drois nebismieri SualedisaTvis,<br />
A<br />
N =<br />
t<br />
e.i. simZlavre udris drois erTeulSi Sesrulebul muSaobas.<br />
j<br />
2 −3<br />
[ N] = = vt(vati),<br />
dim N = L TM<br />
wm<br />
energia, kinetikuri energia<br />
energia _ universaluri raodenobrivi zomaa yvela saxis materiis<br />
moZraobis da urTierTqmedebis. materiis moZraobis sxvadasxva saxeebTan<br />
dakavSirebulia energiis sxvadasxva formebi: meqanikuri, siTburi,<br />
eleqtromagnituri, birTvuli da sxva.<br />
sxeulze (nawilakze) momqmedi tolqmedi Zalis muSaoba d r<br />
gadaadgilebaze SeiZleba warmovadginoT Semdegnairad:<br />
2<br />
dv<br />
d r<br />
mv<br />
dA = ( F ⋅ d r)<br />
= m d r = mdv<br />
= mvd<br />
v = d(<br />
)<br />
dt dt<br />
2<br />
frCxilebSi gamosaxulebas kinetikuri energia ewodeba.<br />
sxeulis kinetikuri energia warmoadgens meqanikuri moZraobis<br />
zomas, romelic unda SevasruloT, rom gamoviwvioT mocemuli moZraoba.<br />
kinetikuri energia _ energiaa, romelic gaaCnia moZrav sxeulebs,<br />
e.i. is aris moZravi sistemis mdgomareobis funqcia.<br />
k<br />
W =<br />
Teorema kinetikuri energiis Sesaxeb: tolqmedi Zalis<br />
Sesrulebuli muSaoba nawilakze (sxeulze) tolia misi kinetikuri<br />
energiis cvlilebis:<br />
37<br />
mv<br />
2<br />
2
2 2<br />
k mv 2 mv1<br />
A = ΔW<br />
= −<br />
2 2<br />
sadac sxvaobis pirveli wevri Seesabameba nawilakis saboloo<br />
mdgomareobas, xolo meore _ sawyiss.<br />
kavSiri energiasa da impulss Soris<br />
W<br />
38<br />
k<br />
2<br />
p<br />
=<br />
2m<br />
sadac p = mv<br />
nawilakis impulsia, m - misi masa.<br />
[ W ] = j,<br />
dimW<br />
2 −2<br />
= L MT<br />
Zaluri veli, konservatoruli Zalebi<br />
sxeulTa urTierTqmedeba SeiZleba ganxorcieldes maTi uSualo<br />
SexebiT, an Tu sivrcis yovel wertilSi masze moqmedebs garkveuli Zala,<br />
romelic kanonzomierad icvleba. aseT SemTxvevaSi vambobT, rom sxeuli<br />
(nawilaki) moTavsebulia Zalur velSi (mag. gravitaciuli veli).<br />
Zalur vels potencialuri ewodeba, Tu masSi raime sxeulis<br />
gadaadgilebaze Sesrulebuli muSaoba damokidebuli araa traeqtoriis<br />
formaze da srulad ganisazRvreba sawyisi da saboloo mdgomareobiT.<br />
potencialur velSi momqmed Zalebs konservatoruli (potencialuri)<br />
Zalebi ewodebaT. cxadia, potencialur velSi Caketil konturze sxeulis<br />
gadaadgilebaze muSaoba ar sruldeba _ A=0. aseTive Tviseba gaaCnia<br />
centralur vels. vels centraluri ewodeba, Tu sivrcis nebismier<br />
wertilSi nawilakze momqmedi Zalis mimarTuleba gadis uZrav wertilSi<br />
(centrSi), xolo Zalis sidide damokidebulia mxolod am centramde<br />
manZilze. centraluri velis magaliTia dedamiwis zedapiris<br />
maxloblobaSi gravitaciuli veli, uZravi wertilovani muxtebis mier<br />
Seqmnili eleqtruli veli.<br />
gravitaciuli, kulonuri, drekadi Zalebi _ konservatoruli<br />
Zalebia. drekadi Zalebis muSaobaa<br />
kx1<br />
Adr =<br />
2<br />
kx2<br />
−<br />
2<br />
,<br />
sadac k _ drekadobis koeficientia, x 1 da x 2 nawilakis sawyisi da<br />
saboloo mdebareobebia.<br />
2<br />
2
Zalur vels erTgvarovani ewodeba, Tu velis nebismier wertilebSi<br />
nawilakze momqmedi Zalebi erTnairia sididiT da mimarTulebiT.<br />
⎛ dF ⎞<br />
droSi ucvlel-mudmiv vels ⎜ = 0⎟<br />
⎝ dt ⎠<br />
⎛ dF ⎞<br />
cvlads ⎜ ≠ 0⎟<br />
−<br />
⎝ dt ⎠<br />
arastacionaruli.<br />
disipatiuri Zalebi<br />
39<br />
stacionaruli ewodeba, xolo<br />
Zalebs ewodebaT disipatiuri, Tu maTi Sesrulebuli muSaoba,<br />
Caketil sistemaSi nebismieri moZraobisas uaryofiTia. aseTia<br />
winaaRmdegobis, xaxunis Zala. aseTi Zalebis sidide damokidebulia<br />
rogorc sxeulebis konfiguraciaze, aseve sxeulebis fardobiT siCqareze.<br />
isini yovelTvis mimarTulia nawilakebis (sxeulebis) siCqaris<br />
sawinaaRmdegod da iwveven maT damuxruWebas.<br />
potenciuri energia<br />
sxeulebis (nawilakebis) sistemis potenciuri energia ganisazRvreba<br />
maTi urTierTmdebareobiT da damokidebulia sxeulebs (wertilebs)<br />
Soris momqmedi konservatoruli Zalebis xasiaTze. ganmartebis Tanaxmad,<br />
is warmoadgens wertilTa koordinatebis funqcias u = u(<br />
x,<br />
y,<br />
z)<br />
.<br />
Tu Cven velis yovel wertils SevusabamebT aseT funqcias u(x,y,z) =<br />
u(r), maSin velis Zalebis mier Sesrulebuli muSaoba toli iqneba am<br />
funqciis Semcirebis. aseT funqcias uwodeben da utoleben potenciur<br />
energias. amgvarad, sxeulis (nawilakis) gadaadgilebisas X RerZis<br />
gaswvriv X 1 wertilidan X 2 –Si, Sesrulebuli muSaoba Cveni ganmartebis<br />
Tanaxmad, iqneba<br />
x2<br />
p<br />
p<br />
A12 = ∫ F(<br />
x)<br />
dx = −(<br />
W ( x2)<br />
−W<br />
( x1)<br />
)<br />
x<br />
1<br />
potencialuri energia _ sxeulis (nawilakebis) urTierTqmedebis<br />
energiaa konservatorul velTan. is damokidebulia am velSi nawilakis<br />
mdebareobaze.
Zala da potenciuri energia<br />
davuSvaT, urTierTqmedebis konservatoruli F Zalis moqmedebiT<br />
nivTieri wertili asrulebs dr gadaadgilebas, F Zalis Sesrulebuli<br />
muSaoba Caiwereba<br />
dA =<br />
40<br />
( Fd<br />
r<br />
meores mxriv, potenciuri energia Semcirdeba imave sididiT.<br />
amitom<br />
p<br />
( Fdr) = Fdrcosα<br />
= Frdr<br />
= −dW<br />
, ( Fr = F cosα<br />
)<br />
p<br />
p<br />
dW<br />
Frdr = −dW<br />
da Fr = −<br />
dr<br />
e.i. Zalis gegmili dr mimarTulebaze udris potenciuri energiis<br />
warmoebuls imave mimarTulebiT. skalaruli W funqciis warmoebuls im<br />
mimarTulebiT, romliskenac warmoebuli udidesia, am funqciis gradienti<br />
ewodeba _ grad W.<br />
funqciis gradienti aris veqtori, romlis gaswvriv am funqciis<br />
zrdis siCqare maqsimaluria da sididiT tolia am mimarTulebiT<br />
funqciis cvlilebisa manZilis erTeulze, veqtorulad:<br />
)<br />
p<br />
F = −gradW<br />
niSani minusi aCvenebs, rom Zala mimarTulia potencialuri<br />
energiis Semcirebis mimarTulebiT. simbolo<br />
(ortebi).<br />
p<br />
p<br />
p<br />
p ∂W<br />
∂W<br />
∂W<br />
grad W = i + i + k<br />
∂x<br />
∂y<br />
∂z<br />
p<br />
gradW -Ti aRniSnulia jami:<br />
sadac i , j,<br />
k − koordinatTa RerZebis erTeulovani veqtorebia<br />
w funqciis gradientis gegmilebi RerZebze konservatoruli<br />
p<br />
∂W<br />
Zalebis SemTxvevaSi iqnebian ,<br />
∂x<br />
dagegmilebiT miviRebT:<br />
F x<br />
∂W<br />
= −<br />
∂x<br />
p<br />
,<br />
F x<br />
∂W<br />
= −<br />
∂y<br />
p<br />
,<br />
F x<br />
∂ p<br />
W<br />
∂y<br />
∂W<br />
= −<br />
∂z<br />
p<br />
∂W<br />
,<br />
∂z<br />
p<br />
,<br />
amitom<br />
F −gradW<br />
p<br />
= RerZebze
• Mmaterialuri wertilis (nawilakis)<br />
potencialuri energia erTgvarovan Zalur velSi<br />
dedamiwis zedapiris maxloblobaSi simZimis Zalis veli miviRoT<br />
erTgvarovnad. maSin nawilakis potencialuri energia<br />
p<br />
p<br />
W ( z)<br />
= mgz + W ( 0)<br />
.<br />
sadac m nawilakis masaa (z RerZi mimarTulia vertikalurad maRla,<br />
p<br />
Fz= _ (mg). W ( 0)<br />
nawilakis potencialuri energiis mniSvnelobaa z=0 dros.<br />
nawilakis potencialuri energia centraluri Zalebis velSi _<br />
W<br />
p<br />
∞<br />
= ∫<br />
r<br />
p<br />
( r)<br />
F ( r)<br />
dr + W ( ∞)<br />
41<br />
r<br />
sadac Fr − F Zalis proeqciaa r veqtoris mimarTulebaze, r _<br />
radius-veqtoria, gavlebuli ZalTa centridan gansaxilvel nawilakamde,<br />
p<br />
W ( ∞ ) - potencialuri energiaa usasrulobaSi, romelic nulad miiCneva.<br />
2.4. myari sxeulis dinamika<br />
myari sxeulis moZraoba SeiZleba dayvanil iqnas or martiv<br />
moZraobaze: masaTa centris gadataniT moZraobaze da uZravi RerZis<br />
garSemo brunviT moZraobaze.<br />
Zalis momenti<br />
veqtorul sidides, romelic tolia F Zalis veqtoruli namravlis 0<br />
uZravi wertilidan Zalis modebis wertilSi gavlebul radius-veqtorze<br />
r , ewodeba F Zalis momenti 0 uZravi wertilis mimarT (nax. 24)<br />
nax. 24<br />
[ r F ]<br />
M = ×
Zalis momenti _ fsevdoveqtoria, misi mimarTuleba ganisazRvreba<br />
marjvena burRis wesiT misi mobrunebisas r -dan F -sken. Zalis momentis<br />
moduli<br />
M = r ⋅ F sin α = � ⋅ F<br />
aq α _ kuTxea r da F veqtorebs Soris, � = r sinα<br />
-Zalis mxari 0<br />
wertilis mimarT.<br />
Tu adgili aqvs ramdenime Zalis, an ZalTa sistemis zemoqmedebas,<br />
maSin ZalTa sistemis momenti _ mTavari an tolqmedi momenti _<br />
geometriuli jamia am wertilis mimarT sistemis n Zalebis:<br />
M<br />
=<br />
n<br />
∑<br />
i−1<br />
42<br />
[ r1<br />
× Fi<br />
]<br />
sadac ri - radius-veqtoria, gavlebuli 0 wertilidan F i Zalis<br />
modebis wertilamde.<br />
[ ] = n ⋅m<br />
M ,<br />
dimM<br />
2 −2<br />
= L MT<br />
impulsis momenti<br />
materialuri wertilis impulsis momenti 0 uZravi wertilis mimarT<br />
ewodeba L i veqtors, romelic tolia r i . radius-veqtoris veqtoruli<br />
namravlis impulsis Pi � veqtorze. ri � radius veqtori gaivleba 0<br />
wertilidan materialur wertilamde (nax. 25)<br />
nax. 25<br />
[ r i ]<br />
L ×<br />
i = pi
impulsis momenti fsevdoveqtoria. misi mimarTuleba ganisazRvreba<br />
marjvena burRis wesiT, i r -dan p i -sken brunvisas. impulsis momentis<br />
moduli tolia:<br />
mxaria.<br />
L = r ⋅ p sin α = � ⋅ p<br />
i<br />
i<br />
43<br />
i<br />
sadac α kuTxea r da p veqtorebs Soris, xolo � = r sinα<br />
Zalis<br />
materialur wertilTa sistemis (sxeulis) impulsis momenti uZravi 0<br />
wertilis mimarT, ewodeba L veqtors, romelic tolia igive 0 wertilis<br />
mimarT wertilebis impulsebis L i momentTa geometriuli jamis:<br />
L =<br />
n<br />
∑<br />
i=<br />
1<br />
[ r i × p i ]<br />
sxeulis impulsis momenti uZravi z RerZis mimarT ewodeba<br />
skalarul sidides, romelic tolia amave RerZze mdebare 0 wertilis<br />
mimarT L impulsis momentis veqtoris gegmilisa imave RerZze:<br />
L<br />
z<br />
=<br />
n<br />
∑<br />
i=<br />
1<br />
2<br />
m<br />
L = kg = j ⋅wm,<br />
wm<br />
n<br />
[ r i × p i ] = ∑<br />
i−1<br />
i<br />
i<br />
m v r<br />
dim L<br />
inerciis momenti<br />
i<br />
i<br />
2 −1<br />
= L MT<br />
materialuri wertilis (m) masis namravls brunvis RerZidan<br />
manZilis kvadratze ewodeba inerciis momenti I igive brunvis RerZis<br />
mimarT (nax. 26)<br />
RerZamde.<br />
I = m<br />
i<br />
sadac mi _ materialuri wertilis masaa, ri - manZili brunvis<br />
nax. 26<br />
2<br />
iri<br />
i
mTeli sxeulis inerciis momenti I udris sxeulis Semadgeneli n<br />
materialuri wertilebis (an elementebis) inerciis momentebis jams:<br />
I<br />
=<br />
2 [ I ] = kg ⋅m<br />
,<br />
44<br />
n<br />
∑<br />
i=<br />
1<br />
i i r m<br />
2<br />
2<br />
dim I = ML<br />
inerciis momenti warmoadgens sxeulis inertulobis zomas brunvis<br />
procesSi, iseve rogorc masa gadataniTi moZraobisas.<br />
masis uwyveti ganawilebis SemTxvevaSi<br />
Δmi<br />
→0<br />
2 2<br />
∑ Δmir<br />
= ∫ r dm = ∫<br />
2<br />
I = lim i<br />
ρ r dV<br />
sadac ρ -sxeulis simkvrivea, dV − moculobis elementi.<br />
Teorema brunvis RerZis gadatanis Sesaxeb _ Steineris Teorema: Tu<br />
m masis sxeulis inerciis momenti 0 I 0 I RerZis mimarT I , xolo C masaTa<br />
centrSi gamavali da 0I0I RerZis paraleluri 00 RerZis mimarT I c , maSin<br />
(nax. 27) maT Soris Semdegi damokidebulebaa:<br />
I = Ic<br />
+<br />
2<br />
ma<br />
sadac a manZilia 00 da 0 I 0 I RerZebs Soris<br />
nax. 27
zogierTi erTgvarovani m masis sxeulebis<br />
inerciis momentebis tabula<br />
sxeuli RerZebis mdebareoba inerciis momenti<br />
Rru Telkedliani R<br />
radiusiani cilindri<br />
mTliani cilindri an<br />
R radiusiani diski<br />
simetriis RerZi<br />
simetriis RerZi<br />
l sigrZis Txeli Rero RerZi marTobia Rerosi<br />
da gadis mis Sua<br />
wertilSi<br />
l sigrZis Txeli Rero RerZi marTobTa Rerosi<br />
da gadis mis boloSi<br />
R radiusiani sfero RerZi<br />
centrSi<br />
gadis sferos<br />
mR 2<br />
1<br />
mR<br />
2<br />
1<br />
ml<br />
12<br />
1<br />
ml<br />
3<br />
siCqariT, maSin misi inerciis momenti I z igive RerZis mimarT<br />
45<br />
2<br />
2<br />
mR<br />
5<br />
myari sxeulis brunviTi moZraobis dinamikis ZiriTadi gantoleba<br />
brunviTi moZraobis dros dinamikis ZiriTadi sidideebia Zalis<br />
momenti M , impulsis momentis L da inerciis momenti I .<br />
dinamikis ZiriTadi kanoni warmoadgens urTierTkavSirs maT Soris.<br />
• Tu materialuri wertili brunavs uZravi 0 RerZis mimarT,<br />
maSin impulsis momentis droiT warmoebuli 0 wertilis<br />
mimarT tolia amave 0 wertilis mimarT Zalis momentis:<br />
d L<br />
=<br />
dt<br />
M<br />
i<br />
• Tu myari sxeuli brunavs uZravi RerZis garSemo, maSin<br />
dinamikis ZiriTadi kanoni Rebulobs saxes:<br />
d L<br />
dt<br />
∑<br />
gare<br />
= M i<br />
sadac ∑ i M -gare Zalebis momentebis jamia (mTavari momenti).<br />
• Tu myari sxeuli brunavs Oz uZravi RerZis garSemo ω kuTxuri<br />
2<br />
2<br />
2
ar icvleba droSi ( I z = const).<br />
impulsis momenti am RerZis<br />
mimarT L z = I ω<br />
z<br />
uZravi RerZis garSemo mbrunavi sxeulis myari sxeulis dinamikis<br />
ZiriTadi kanoni miiRebs saxes:<br />
I z<br />
an<br />
dω<br />
=<br />
dt<br />
ε =<br />
46<br />
gare<br />
M<br />
1 <br />
M<br />
sadac ε − sxeulis kuTxuri aCqarebaa.<br />
I z<br />
uZravi sxeulis garSemo mbrunavi sxeulis brunvis diferencialuri<br />
gantolebaa:<br />
I z<br />
2<br />
d ϕ<br />
=<br />
dt<br />
gare<br />
gare<br />
M<br />
sadac I z - inerciis momentia igive RerZis mimarT, ϕ - kuTxuri<br />
gadaadgileba,<br />
gare<br />
M _ gare Zalebis mTavari momenti.<br />
zogad SemTxvevaSi Tavisufali myari sxeulis moZraoba<br />
akmayofilebs or diferencialur gantolebas:<br />
siCqare,<br />
d<br />
dt<br />
gare<br />
( mvc<br />
) = F ,<br />
d L<br />
=<br />
dt<br />
gare<br />
M<br />
sadac m sxeulis masaa, v c − masaTa centris gadataniTi moZraobis<br />
gare<br />
F - sxeulze modebuli gareSe ZalTa mTavari veqtori, gare<br />
M _<br />
gare Zalebis mTavari momenti brunvis wertilis mimarT, L − sxeulis<br />
impulsis momenti imave wertilis mimarT.<br />
mbrunavi myari sxeulis kinetikuri energia<br />
m i masis materialuri wertilis kinetikuri energia, romelic<br />
brunavs ω = const mudmivi kuTxuri siCqariT, tolia (nax. 28):<br />
2<br />
i<br />
k miv<br />
1 2<br />
W =<br />
= miω<br />
R<br />
R 2<br />
2<br />
i
nax. 28.<br />
sadac vi = ωRi<br />
materialuri wertilis wiriTi siCqarea.<br />
Ri − manZili m i wertilidan brunvis RerZamde.<br />
mbrunavi absoluturad myari sxeulis nebismieri wertilisaTvis<br />
ω = const,<br />
amitom misi kinetikuri energia Caiwereba<br />
mimarT.<br />
sadac ∑<br />
2<br />
miRi = I<br />
k<br />
k 1 2<br />
2 1 2<br />
W = ∑Wi= ω ∑miRi=<br />
ω I.<br />
2<br />
2<br />
_ sxeulis inerciis momentia brunvis RerZis<br />
miRebuli gamosaxuleba<br />
k 1 2<br />
( W = ω I )<br />
2<br />
gviCvenebs, rom brunviTi<br />
moZraobis dros inerciis momenti asrulebs masis magivrobas, kuTxuri<br />
siCqare ki _ wiriTi siCqaris. Tu sxeuli monawileobas Rebulobs<br />
erTdroulad rogorc gadataniT, aseve brunviT moZraobaSi, maSin misi<br />
sruli kinetikuri energia iqneba:<br />
1<br />
= ω<br />
2<br />
2<br />
W Ic<br />
+<br />
47<br />
1<br />
mv<br />
2<br />
1 2<br />
sadac I cω<br />
_ mbrunavi sxeulis kinetikuri energiaa, Ic − inerciis<br />
2<br />
momenti masaTa centrSi gamavali RerZis mimarT<br />
1 2<br />
mv c − gadataniTi moZraobis kinetikuri energia, vc -masaTa centris<br />
2<br />
siCqare, m – sxeulis masaa.<br />
2<br />
c
dros.<br />
iqneba:<br />
am formuliT gamoiTvleba sxeulis kinetikuri energia gorvis<br />
muSaoba brunviTi moZraobisas<br />
gare Zalebis elementaruli muSaoba sxeulis brunvisas dt droSi<br />
dA = Mωdt<br />
= Mdϕ<br />
= Mωdϕ<br />
( M = M cosα)<br />
ω<br />
sadac M - Zalis momentia wertilis mimarT dϕ = ωdt<br />
da dϕ = ωdt<br />
Sesabamisad mobrunebis kuTxe da kuTxuri gadaadgilebis veqtoria dt<br />
droSi.<br />
Mω − M veqtoris gegmilia ω veqtoris mimarTulebaze.<br />
sruli muSaoba ϕ1 -dan ϕ2 -mde gadaadgilebisas<br />
A<br />
48<br />
∫<br />
ϕ<br />
= 2<br />
ϕ<br />
1<br />
Mdϕ<br />
2.5. meqanikuri sistema. Senaxvis kanonebi<br />
yoveli myari sxeuli SeiZleba ganvixiloT rogorc materialuri<br />
wertilebis sasrulo ricxvisgan Semdgari meqanikuri sistema, e.i.<br />
meqanikuri sistema materialuri wertilebis erTobliobaa.<br />
meqanikur sistemaSi Semaval materialur wertilebs (sxeulebs)<br />
Soris momqmed Zalebs Sinagani Zalebi ewodebaT, xolo sistemaze momqmed<br />
yvela sxva Zalas _ gareSe Zala.<br />
Tu meqanikur sistemaze gareSe Zalebi ar moqmedeben, mas Caketili<br />
(izolirebuli) ewodeba.<br />
sistemaSi Semavali urTierTmomqmedi sxeulebis koordinatebi,<br />
siCqareebi da aCqarebebi ganicdian mudmiv cvlilebas. arseboben iseTi<br />
fizikuri sidideebi, romlebic Caketil sistemaSi ar icvlebian. aseTi<br />
sidideebia energia, impulsi da impulsis momenti. am sidideebis Senaxvis<br />
kanonebi dakavSirebulni arian sivrce _ drois ZiriTad TvisebebTan.
energiis Senaxvis kanoni da drois erTgvarovneba<br />
sxeulebis (nawilakebis) sruli meqanikuri energia konservatorul<br />
ZalTa velSi gamoisaxeba Semdegnairad:<br />
sadac<br />
W +<br />
k p p<br />
= W + W W gare ,<br />
k<br />
W _ sistemis kinetikuri energiaa<br />
p<br />
W _ sxeulebis (nawilakebis) urTierTqmedebis energia erTmaneTTan,<br />
k<br />
W g _ nawilakebis (sxeulebis) urTierTqmedebis potenciuri energia<br />
gare sxeulebTan.<br />
davuSvaT, sistemaSi Semaval sxeulebze garda konservatoruli<br />
Zalebisa, moqmedeben agreTve arakonservatoruli Zalebic.<br />
arakonservatoruli Zalebis muSaoba tolia sruli energiis cvlilebis:<br />
dA = dW ,<br />
sadac dA - arakonservatoruli Zalebis muSaobaa,<br />
dW − sruli energiis cvlileba.<br />
rodesac dA = 0 , dW = 0 da miviRebT:<br />
k p p<br />
W + W + W = const<br />
p<br />
Tu sistema Caketilia, W = 0 da energiis Senaxvis kanoni miiRebs<br />
k p<br />
saxes W = W + W = const<br />
gare<br />
da gamoiTqmeba: Caketilis sistemis sruli meqanikuri energia<br />
mudmivi sididea _ ar icvleba droSi.<br />
energiis mudmivobis kanoni bunebis fundamentaluri kanonia,<br />
dakavSirebulia drois erTgvarovnebasTan. magaliTad, Tavisufali<br />
vardnis dros simZimis ZalTa velSi, sxeulis siCqare da Tavisufali<br />
vardnis xangrZlivoba damokidebulia sxeulis sawyis siCqareze da ara im<br />
drois momentze, roca is iwyebs vardnas (diliT Tu saRamos).<br />
impulsis Senaxvis kanoni da sivrcis erTgvarovneba<br />
sxeulebis (nawilakebis) sistemis moZraobis gantolebas, romelzec<br />
moqmedeben gareSe Zalebi, aqvs saxe<br />
49<br />
gare
d p<br />
dt<br />
=<br />
50<br />
∑<br />
sadac p sistemis impulsia, ∑ gare<br />
i<br />
Zalebis tolqmedi.<br />
∑ gare<br />
i<br />
F<br />
gare<br />
i<br />
F - sistemaze momqmedi gareSe<br />
Tu sistema Caketilia, F = 0,<br />
p = const , rac warmoadgens<br />
impulsis Senaxvis kanons, romelic Semdegnairad gamoiTqmeba:<br />
Caketili sistemis impulsi mudmivi sididea. impulsis mudmivobis<br />
kanoni bunebis fundamentaluri kanonia. is Sedegia sivrcis<br />
erTgvarovnebis, rac dakavSirebulia im faqtTan, rom Caketili sistemis<br />
fizikuri Tvisebebi da misi moZraobis kanonebi ar aris damokidebuli<br />
koordinatTa sistemis saTavis mdebareobis arCevaze.<br />
reaqtiuli moZraoba<br />
impulsis mudmivobis kanonis damtkicebas teqnikaSi warmoadgens<br />
reaqtiuli moZraoba. sxeulis moZraobas, romelic aRiZvreba misgan<br />
gamotyorcnili nawilakebis reaqciis xarjze, reaqtiuli moZraoba<br />
ewodeba. gamotyorcnili nawilakebis (gazebis) nakadis reaqciis Zala<br />
sxeuls (raketas) aniWebs aCqarebas, romelic mimarTulia gamotyorcnili<br />
gazebis moZraobis sawinaaRmdegod.<br />
meSCerskis mier miRebuli cvladi masis sxeulis moZraobis<br />
gantolebaa:<br />
sadac F - gareSe Zalaa, xolo<br />
Tu F = 0,<br />
vRebulobT<br />
m a = F +<br />
dv dm<br />
m = −u<br />
,<br />
dt dt<br />
saidanac reaqtiuli moZraobis siCqare<br />
Fn<br />
dm<br />
F n = −u<br />
-s reaqtiuli Zala ewodeba.<br />
dt<br />
dm<br />
v = −u∫<br />
= −u<br />
ln m + c<br />
m<br />
sawyisi pirobebis gamoyenebiT C = u lnm0<br />
( m0 − sastarto masaa), da
miRebuls ciolkovskis<br />
m0<br />
v = u ln<br />
m<br />
formula ewodeba. is miRebulia<br />
ararelativisturi moZraobisTvis.<br />
∑ i<br />
impulsis momentis mudmivobis kanoni da<br />
sivrcis izotropiuloba<br />
dinamikis ZiriTadi kanonis Tanaxmad,<br />
d L<br />
= ∑ M<br />
dt<br />
sadac L- sistemis impulsis momentia. Caketili sistemisTvis<br />
M = 0,<br />
miviRebT:<br />
d L<br />
= 0,<br />
dt<br />
51<br />
i<br />
L = const,<br />
an I ω = const<br />
miRebuli warmoadgens impulsis momentis mudmivobis kanons:<br />
Caketili sistemis impulsis momenti mudmivi sididea, rac bunebis<br />
fundamentaluri kanonia. is dakavSirebulia sivrcis<br />
izotropiulobasTan, anu fizikuri kanonebis invariantobasTan<br />
koordinatTa sistemis RerZebis mimarTulebis mimarT (Caketili sistemis<br />
SemobrunebasTan sivrceSi nebismieri kuTxiT).<br />
amgvarad, Caketil sistemebSi sami fizikuri sidide _ energia,<br />
impulsi da impulsis momenti – mudmivi sidideebia. isini koordinatebis<br />
da siCqareebis funqciebia da maT moZraobis integralebi ewodebaT.<br />
impulsis mudmivobis kanoni<br />
SeiZleba SevamowmoT mbrunavi skamis<br />
saSualebiT, romelzec zis adamiani,<br />
Tu brunvis dros adamiani xelebs<br />
gaSlis, misi inerciis momenti<br />
gaizrdeba da kuTxuri siCqare<br />
Semcirdeba. xelebis daSvebis dros<br />
inerciis momenti Semcirdeba, xolo<br />
kuTxuri siCqare imatebs.
2.6 sxeulTa wonasworobis pirobebi.<br />
myari sxeulis moZraoba aRiwereba Semdegi gantolebebiT:<br />
d � � gare dL � gare<br />
( mvc<br />
) = ∑ F , = ΣM<br />
dt<br />
dt<br />
sadac – m sxeulis masaa, vc � - misi masaTa centris siCqarea.<br />
myari sxeulis wonasworobis pirobebia:<br />
1. sxeulze modebuli gareSe ZalTa tolqmedi unda iyos nuli:<br />
gare<br />
Σ F = 0<br />
�<br />
2. gareSe ZalTa momentebis tolqmedi sxeulis nebismieri wertilis<br />
mimarT unda iyos nuli<br />
ΣM = 0<br />
�<br />
es veqtoruli pirobebi eqvivalenturia sami skalarulis:<br />
gare<br />
ΣM<br />
= 0 , ΣM<br />
= 0 ΣM<br />
= 0<br />
x<br />
y<br />
gare<br />
52<br />
z<br />
gare<br />
3. relativisturi meqanika<br />
3.1. fardobiTobis Teoriis safuZvlebi. ainStainis postulatebi<br />
Tanamedrove fizika Camoyalibda mas Semdeg, rac ainStainis mier<br />
Seiqmna fardobiTobis specialuri Teoria. es Teoria warmoadgens<br />
sivrce-droze Tanamedrove Sexedulebebs, romelic niutonis Teoriis<br />
msgavsad varaudobs, rom dro erTgvarovania, xolo sivrce erTgvarovani<br />
da izotropiulia. amasTan erTad is uaryofs klasikuri <strong>fizikis</strong> ZiriTad<br />
daSvebebs eTeris Teoriis, sivrcisa da drois absoluturobis Sesaxeb.<br />
fardobiTobis principi, urTierTqmedebis gavrcelebis maqsimaluri<br />
siCqaris debuleba da sinaTlis siCqaris invariantoba _ warmoadgens<br />
ainStainis fardobiTobis specialuri Teoriis, relativisturi Teoriis<br />
ZiriTad principebs. mas safuZvlad udevs ainStainis mier<br />
formulirebuli ori postulati:
1. fardobiTobis principi: bunebis kanonebi invariantulia inerciuli<br />
sistemebis mimarT, anu bunebis kanonebi erTnairad mimdinareoben<br />
sxvadasxva inerciul sistemebSi.<br />
2. sinaTlis siCqaris invariantobis principi: sinaTlis siCqare<br />
vakuumSi, erTnairia yvela inerciul sistemebSi da ar aris<br />
damokidebuli damkvirveblis an sinaTlis wyaros siCqareze.<br />
ainStainis pirveli postulati warmoadgens galileis fardobiTobis<br />
principis ganzogadoebas nebismier fizikur procesze. gantolebebi,<br />
romlebic gamosaxaven fizikur kanonebs, inarCuneben TavianT saxes yvela<br />
aTvlis inerciul sistemaSi.<br />
meore postulatis Tanaxmad, nebismieri urTierTqmedebis gavrcelebis<br />
siCqare sasruloa. maqsimaluri urTierTqmedebis (signalis) gavrcelebis<br />
dasaSvebi siCqare aris sinaTlis gavrcelebis siCqare vakuumSi.<br />
ainStainamde miRebuli iyo msoflio eTeris arsebobis hipoTeza,<br />
romelic ganWolavda msoflio sivrces da warmoadgenda<br />
urTierTqmedebis gadamcem garemos. warmodgenebi aseT substanciaze<br />
arsebobda jer kidev antikuri xanidan. magaliTad, demokrites<br />
koncefciis mixedviT, nivTiereba Sedgeboda nawilakebisgan, romelTa<br />
Soris sicarielea. aristoteles koncefciis mixedviT ki, samyaroSi ar<br />
aris iseTi adgili, sadac `araferia~. es hipoTeza gamoiyeneboda<br />
mecnierebis mier movlenebis asaxsnelad gasuli saukunis dasawyisSic,<br />
xolo hipoTezur garemos, romelic unda arsebobdes sxeulis nawilakebs<br />
Soris da ganWolavdes msoflio sivrces, ewodeba eTeri.<br />
gansakuTrebiT gaizarda interesi eTeris bunebis Sesaxeb gamoCenili<br />
Teoretikosis, maqsvelis mier eleqtromagnituri velis aRmoCenis Semdeg.<br />
eleqtruli da magnituri velebis erTmaneTSi TanmimdevrobiTi<br />
monacvleoba aucilebels xdida procesebis ganxilvas gansakuTrebul<br />
drekad garemoSi. mas unda uzrunveleyo gravitaciuli Zalebis<br />
urTierTqmedeba, sinaTlis talRebis gamtarebloba-gavrceleba da<br />
saerTod pasuxi unda gaeca bunebis nebismier movlenebze. yvela am<br />
funqciebis Sesasruleblad eTers unda hqonoda Zalian gansxvavebuli da<br />
xSirad urTierTsawinaaRmdego Tvisebebi. magaliTad, misi drekadoba unda<br />
yofiliyo foladze bevrad meti da amave dros winaaRmdegoba ar unda<br />
53
Seeqmna masSi sinaTlis gavrcelebisaTvis da amave dros ciuri sxeulebis<br />
(varskvlavebis da planetebis) moZraobisaTvis.<br />
ainStainis fardobiTobis TeoriiT eTeri uaryofil iqna,<br />
fardobiTobis Teoriis paralelurad Seqmnilma velis kvanturma Teoriam<br />
ki ainStainis sivrceSi aRmoaCina specifikuri materialuri garemo<br />
eTeris Semcvleli _ romelsac fizikuri vakuumi ewoda.<br />
marTalia, fizikuri vakuumis realuri arseboba dasturdeba cdebiT,<br />
magram misi struqtura dRemde daudgenelia. fizikuri vakuumis<br />
struqturis da Tvisebebis dadgena warmoadgens Tanamedrove <strong>fizikis</strong><br />
erT-erT mniSvnelovan mecnierul mimarTulebas.<br />
3.2. lorencis gardaqmnebi<br />
lorencis gardaqmnebi. koordinatebis da drois gardaqmnis<br />
formulebi, romlebic akmayofilebs ainStainis fardobiTobis princips,<br />
Semdegia:<br />
1<br />
x + v t<br />
x =<br />
1− β<br />
t<br />
t =<br />
1<br />
0<br />
2<br />
54<br />
x<br />
1<br />
x − v0t<br />
=<br />
2<br />
1− β<br />
1<br />
1<br />
y = y<br />
y = y<br />
1<br />
1<br />
z = z<br />
z<br />
1<br />
x<br />
+ v0<br />
2<br />
c<br />
2<br />
1− β<br />
sadac C _ sinaTlis siCqarea vakuumSi,<br />
1<br />
v0 − k sistemis siCqarea k-s mimarT.<br />
t<br />
1<br />
v0 β =<br />
c<br />
z =<br />
x<br />
t − v0<br />
2<br />
=<br />
c<br />
2<br />
1− β<br />
v 0
nax. 29<br />
lorencis gardaqmnebis Sedegebi<br />
1. wrfivi zomebis fardobiToba. lorencis gardaqmnebis formulebidan<br />
gamomdinareobs, rom inerciuli sistemis mimarT moZravi sxeulis wrfivi<br />
zoma mcirdeba moZraobis mimarTulebis gaswvriv (lorencis Semokleba):<br />
= � �<br />
0<br />
55<br />
2<br />
1 β −<br />
sadac � 0 sxeulis wrfivi zomaa im inerciul sistemaSi, romlis<br />
mimarTac is uZravia, xolo � zomaa moZravi inerciuli sistemis mimarT.<br />
sxeulis wrfivi zomebi udidesia uZravi sistemis mimarT, maT sakuTari<br />
zomebi ewodebaT. sxeulis sxva zomebi, romlebic ar emTxveva moZraobis<br />
mimarTulebas, ucvlelni rCebian.<br />
2. movlenis xangrZlioba sxvadasxva sistemebSi.<br />
davuSvaT k sistemis mimarT uZrav wertilSi koordinatiT x, adgili<br />
1<br />
aqvs movlenas, romlis xangrZliobaa δ . 2 1<br />
xangrZlioba k 1 sistemaSi aRvniSnoT<br />
gardaqmnis formulebidan<br />
1<br />
δ =<br />
saidanac gamomdinareobs, rom<br />
v0x<br />
t1<br />
− 2<br />
1<br />
t 1 = c ,<br />
2<br />
1− β<br />
1.<br />
δ = t − t<br />
t<br />
− t<br />
1<br />
2<br />
1 1 2 1<br />
t 2 − t1<br />
= = ,<br />
2<br />
2<br />
1− β 1−<br />
β<br />
1<br />
δ = t − t . amave movlenis<br />
v0<br />
x<br />
t2<br />
− 2<br />
1<br />
t 2 =<br />
c , miviRebT:<br />
2<br />
1− β<br />
δ<br />
1<br />
δ < δ , anu wertilSi momxdari movlenis<br />
xangrZlioba umciresia im inerciul sistemaSi, romlis mimarTac<br />
aRniSnuli wertili uZravia.
3. siCqareTa Sekrebis kanoni. galileis siCqareTa Sekrebis<br />
kanonis Tanaxmad,<br />
v = v1<br />
+ v0<br />
fardobiTobis specialur TeoriaSi siCqareTa Sekrebis kanons aqvs<br />
Semdegi saxe:<br />
v′<br />
+ v0<br />
v =<br />
v′<br />
v<br />
1+<br />
c<br />
mcire siCqareebis SemTxvevaSi ( v ′<br />
v′<br />
v0<br />
inerciuli m masa, romelic axasiaTebs sxeulis reaqcias gare Zalaze.<br />
Tu v
4. rxevebi da talRebi.<br />
4.1. rxeva. harmoniuli rxevebi<br />
rxeva ewodeba iseT moZraobas an process, romelic zustad an<br />
raime miaxloebiT meordeba drois erTsa da imave SualedSi. fizikuri<br />
procesebis xasiaTis mixedviT ansxvaveben meqanikur da eleqtromagnitur<br />
rxevebs da maT kombinaciebs. droze damokidebulebiT ansxvaveben<br />
periodul (nax. 30 a,b,g) da araperiodul rxevebs (nax. 30 d)<br />
periodulobis pirobaa:<br />
nax. 30<br />
x ( t + T)<br />
= x(<br />
t)<br />
)<br />
sadac T - rxevis periodia, x − droSi cvladi fizikuri sidide.<br />
perioduli rxevis mniSvnelovani saxea harmoniuli (sinosoidaluri)<br />
rxevebi (nax. 30 a). merxevi sistemis mixedviT arCeven martiv (erTi<br />
Tavisuflebis xarisxiT), Tavmoyrili parametrebiT (Tavisuflebis<br />
xarisxis sasrulo raodenobiT) da ganawilebuli parametrebiT,<br />
romelTac gaaCniaT sakuTari sixSireebis usasrulo raodenoba.<br />
periodul rxevebs, romlis drosac merxevi sidide icvleba sinusis<br />
an kosinusis kanoniT, harmoniuli rxevebi ewodeba (nax. 31).<br />
x = A ω t + ϕ),<br />
an x = A ω t + ϕ)<br />
cos( 0<br />
nax. 31.<br />
sin( 0<br />
58
sadac x merxevi sistemis fizikuri sididis (parametris) garkveuli<br />
gadaxraa (wanacvleba) wonasworobis mdebareobidan – x =0 -dan.<br />
A - rxevis amplitudaa, udidesi gadaxra wonasworobis<br />
mdebareobidan.<br />
ω 0 t + ϕ - rxevis fazaa,<br />
ϕ − rxevis sawyisi fazaa.<br />
rxevis periodi T – erTi sruli rxevis droa.<br />
ω t + T)<br />
+ ϕ = ( ω t + ϕ)<br />
+ 2π<br />
, saidanac<br />
0 ( 0<br />
2π<br />
T =<br />
ω<br />
rxevis sixSire υ -rxevaTa ricxvia drois erTeulSi<br />
[ ]<br />
υ = hc(herci ), dimυ<br />
= T<br />
−1<br />
ω −wriuli<br />
(cikluri) sixSire – rxevaTa ricxvia 2π wamSi:<br />
0<br />
2π<br />
ω 0 = , ω0 = 2πυ<br />
T<br />
4.2. siCqare da aCqareba harmoniuli rxevis dros<br />
59<br />
0<br />
harmoniuli oscilatori _ sistemaa (sxeuli), romelic asrulebs<br />
harmoniul rxevebs mdgradi wonasworobis maxloblobaSi ω 0 sakuTari<br />
rxevis sixSiriT. sistemis merxevi sididis x wanacvleba (gadaxra) iqneba<br />
x = A ω t + ϕ)<br />
,<br />
cos( 0<br />
romlis gawarmoebiTac miviRebT rxevis siCqares<br />
dx<br />
v =<br />
dt<br />
⎛ π ⎞<br />
= −Aω<br />
0 sin( ω0t<br />
+ ϕ)<br />
= Aω0<br />
cos⎜ω0t<br />
+ ϕ + ⎟<br />
⎝ 2 ⎠<br />
2<br />
d x<br />
2<br />
rxevis aCqareba a = = −Aω<br />
0 cos( ω0t<br />
+ ϕ + π ) (nax. 32)<br />
2<br />
dt<br />
nax. 32.
mocemulia wanacvlebis, siCqaris da aCqarebis damokidebuleba droze.<br />
harmoniuli rxevebi sruldebian drekadi (an kvazidrekadi) F d = −k<br />
x<br />
Zalis gavleniT. Tu visargeblebT niutonis me-2 kanoniT da am Zalebs<br />
gavutolebT erTmaneTs, martivi gardaqmnebiT miviRebT harmoniuli rxevis<br />
diferencialur gantolebas:<br />
k 2<br />
= ω0<br />
m<br />
2<br />
2<br />
d x<br />
d x k<br />
F = m F = −kx<br />
2 d da + = 0<br />
2<br />
dt<br />
dt m<br />
- oscilatoris sakuTari rxevis sixSirea. gantoleba Caiwereba<br />
2<br />
d x 2<br />
+ ω 0 x = 0<br />
2<br />
dt<br />
miRebuli diferencialuri gantolebis amoxsnaa:<br />
x = A ω t + ϕ)<br />
cos( 0<br />
4.3. harmoniuli rxevis energia.<br />
merxev sxeuls wonasworobis mdebareobaSi gaaCnia mxolod<br />
kinetikuri energia, maqsimaluri gadaxrisas ki _ mxolod potencialuri.<br />
potencialuri energia gaizomeba F = −kx<br />
drekadi Zalis<br />
sawinaaRmdegod x manZilze sxeulis gadasaadgileblad Sesrulebuli<br />
muSaobiT. elementaruli Sesrulebuli muSaoba iqneba<br />
sruli muSaoba<br />
A =<br />
dA = Fdx =<br />
x<br />
∫<br />
0<br />
x<br />
60<br />
kxdx<br />
kx<br />
Fdx = ∫ kxdx =<br />
2<br />
2 2<br />
kx kA 2<br />
e.i. potenciuri energia W ( t)<br />
= = cos ( ω 0t<br />
+ ϕ)<br />
2 2<br />
p<br />
kinetikuri energia wonasworobidan x manZilze<br />
W k<br />
2<br />
mω<br />
A 2<br />
( t)<br />
= sin ( ω0t<br />
+<br />
2<br />
sruli energiisTvis gveqneba ( k = mω<br />
)<br />
0<br />
2<br />
0 ϕ<br />
2<br />
0<br />
2<br />
2<br />
2<br />
mω<br />
0 A<br />
[ cos ( ω t + ϕ)<br />
+ sin ( ω t + ϕ)<br />
] = const.<br />
2 2<br />
mω<br />
0 A<br />
W =<br />
0<br />
0<br />
=<br />
2<br />
2<br />
2<br />
)
e.i. harmoniuli rxevis dros sruli energia mudmivia, rac imis Sedegia,<br />
rom garda wonasworobisadmi damabrunebeli drekadi (kvazidrekadi)<br />
Zalisa, sxva Zala ar moqmedebs.<br />
4.4. harmoniuli rxevebis Sekreba<br />
erTnairi sixSiris da mimarTulebis rxevebis veqtoruli Sekreba<br />
ori harmoniuli rxevis x 1 da x 2 Sekrebisas, romlebic ganisazRvrebian<br />
gantolebebiT:<br />
x = A cos( ω t + ϕ ) da x = A ω t + ϕ )<br />
1<br />
, 0 1<br />
miviRebT igive sixSiris harmoniul rxevas:<br />
x = x + x = A ω t + ϕ)<br />
jamuri rxevis amplituda iqneba (nax. 33)<br />
A<br />
2<br />
2<br />
1<br />
1<br />
2<br />
2<br />
2<br />
2 cos( 0 2<br />
x = Acosωt,<br />
y<br />
= Bcos(<br />
ω t + ϕ)<br />
61<br />
2<br />
cos( 0<br />
= A + A + A cos( ϕ −ϕ<br />
)<br />
xolo faza ϕ gamoisaxeba gantolebiT:<br />
a) Tu − ϕ = 0<br />
ϕ 2 1 , maSin 1 2 A A A +<br />
1<br />
2A1 2 1 2<br />
A1<br />
sinϕ1<br />
+ A2<br />
sinϕ<br />
2<br />
tgϕ<br />
=<br />
A cosϕ<br />
+ A cosϕ<br />
1<br />
nax. 33<br />
2<br />
= amplituda udidesia<br />
b) Tu ϕ 2 − ϕ1<br />
= ± π , maSin A = A1<br />
− A2<br />
, rxevebi sawinaaRmdego fazebSia<br />
da amplituda minimaluria.<br />
urTierTmarTobi harmoniuli rxevebis Sekreba.<br />
Tu materialuri wertili erTdroulad irxeva OX da OY koordinatTa<br />
RerZebis gaswvriv kanoniT:<br />
2
sadac A da B sawyisi amplitudebia,<br />
ω _ maTi sixSireebi,<br />
ϕ − erT-erTi rxevis sawyisi fazaa.<br />
SedegiTi rxeva warmoadgens elifss, romlis gantolebaa (nax. 34):<br />
a) Tu ϕ = 0<br />
x<br />
A<br />
2<br />
2<br />
y<br />
+<br />
B<br />
2<br />
2<br />
2xy<br />
− cosϕ<br />
= sin<br />
AB<br />
nax. 34<br />
⎛ x y ⎞<br />
⎜ − ⎟ = 0,<br />
⎝ A B ⎠<br />
traeqtoria _ wrfea, romlis gantolebaa<br />
B<br />
Y = X<br />
A<br />
wertili gairxeva gantolebidan miRebuli wrfis gaswvriv ω sixSiriT da<br />
2 2<br />
A + B amplitudiT.<br />
B<br />
b) Tu ϕ = ± π , traeqtoria isev wrfea, gantoleba iqneba Y = − X<br />
A<br />
π<br />
g) Tu ϕ = ± , traeqtoria elifsia<br />
2<br />
x<br />
A<br />
2<br />
2<br />
Y<br />
+<br />
B<br />
62<br />
2<br />
2<br />
2<br />
= 1<br />
2<br />
ϕ
Tu A = B , elifsi gadadis wrewirSi<br />
iwarmoebs saaTis isris mimarTulebiT, xolo<br />
sawinaaRmdegod.<br />
4.5. milevadi rxevebi<br />
63<br />
π<br />
ϕ = + SemTxvevaSi moZraoba<br />
2<br />
π<br />
ϕ = − SemTxvevaSi _ mis<br />
2<br />
Tavisufal rxevebs, romelTa amplituda droSi mcirdeba energiis<br />
kargvis gamo, milevadi rxevebi ewodeba. energiis Semcireba ori mizeziT<br />
aris gamowveuli: winaaRmdegobis Zalebis arsebobiT da gamosxivebiT.<br />
milevadi meqanikuri rxevis aRmweri diferencialuri gantolebaa:<br />
2<br />
d x dx 2<br />
+ 2β<br />
+ ω 0 x = 0,<br />
2<br />
dt dt<br />
sadac x -droSi cvladi fizikuri sididea<br />
β − milevis koeficienti,<br />
ω − sistemis sakuTari sixSirea<br />
0<br />
mocemuli gantolebis amonaxsnia<br />
x = A e<br />
0<br />
sadac<br />
−βt<br />
cos( ωt<br />
+ ϕ)<br />
ω −<br />
2 2<br />
= ω0<br />
β - milevadi rxevis sixSirea<br />
dx<br />
A 0 da ϕ - mudmivi sidideebia, damokidebuli t = 0 momentSi x − is da<br />
dt<br />
mniSvnelobebze _ anu sawyis pirobebze. milevadi rxevis grafiki<br />
mocemulia nax. 35.<br />
nax. 35.<br />
milevadi rxevis amplituda icvleba eqsponencialuri kanoniT:<br />
A(<br />
t)<br />
=<br />
Aoe<br />
−βt
sadac A 0 sawyisi amplitudaa<br />
milevis siCqare ganisazRvreba milevis koeficientiT: β =<br />
sadac r -xaxunis koeficientia<br />
m - merxevi wertilis masa.<br />
relaqsaciis dro δ drois Sualedia, romlis ganmavlobaSi milevadi<br />
rxevis amplituda mcirdeba е-jer.<br />
milevadi rxevis periodi<br />
1<br />
δ =<br />
β<br />
2π<br />
T = =<br />
ω<br />
64<br />
2π<br />
2<br />
ω − β<br />
milevis logariTmuli dekrementi _ λ ewodeba rxevis ori momdevno<br />
amplitudebis naturaluri logariTmebis Sefardebas<br />
2<br />
0<br />
A(<br />
t)<br />
T 1<br />
λ = � n = βT<br />
= =<br />
A(<br />
t + T ) δ N<br />
sadac Ne - rxevaTa ricxvia, romlis ganmavlobaSi amplituda mcirdeba<br />
е-jer.<br />
4.6. talRebi<br />
talRebi _ garemoSi (an vakuumSi) gavrcelebuli SeSfoTebaa _<br />
talRebs gadaaqvs energia nivTierebis gadatanis gareSe. SeiZleba iTqvas,<br />
rom talRa _ garemos rxevaa.<br />
fizikuri bunebiT ansxvaveben meqanikur (drekad, bgeriT) talRebs,<br />
eleqtromagnitur talRebs talRgamtarebSi da sxvadasxva garemoSi<br />
(sinaTle, radiotalRebi, rentgenis gamosxiveba).<br />
SeSfoTebis orientaciis mixedviT ansxvaveben ganiv da grZiv<br />
talRebs. iseT talRas, romelSic rxeva warmoebs gavrcelebis<br />
mimarTulebis marTobulad, ganivi talRa ewodeba. grZivi talRa ewodeba<br />
iseT talRas, romelSic rxeva warmoebs talRis gavrcelebis<br />
mimarTulebiT.<br />
e<br />
r<br />
m
drekadi talRebi. ZiriTadi cnebebi. drekadi talRebi drekad<br />
garemoSi gavrcelebuli meqanikuri SeSfoTebaa (deformaciebi) talRis<br />
wyaroebad gvevlinebian sxeulebi, romlebic garemoze zemoqmedebiT masSi<br />
aRZraven SeSfoTebebs.<br />
talRebia.<br />
bgeriTi (akustikuri) talRebi mcire intensivobis drekadi<br />
adamianis yuri aRiqvams bgerebs, romelTa sixSire moTavsebulia 20<br />
hc-dan 20 khc-mde. 20 hc dabali sixSiris rxevebs infrabgera ewodeba, 20<br />
khc maRals ki ultrabgera.<br />
garemo erTgvarovania, Tu misi fizikuri Tvisebebi ucvlelia<br />
wertilidan wertilSi, xolo izotropiulia Tu fizikuri Tvisebebi<br />
erTnairia yvela mimarTulebiT (sawinaaRmdegoa anizropuli).<br />
msrboli talRa _ talRaa, romelsac gadaaqvs energia sivrceSi.<br />
talRis fronti _ im wertilebis geometriuli adgilia, romlebsac<br />
talRa garkveul momentSi miaRwevs.<br />
talRis zedapiri _ im wertilebis geometriuli adgilia, romlebic<br />
erTnair fazebSi irxevian.<br />
talRis gavrcelebis mimarTulebas sxivi ewodeba, xolo manZils,<br />
romelzedac sinosoidaluri talRuri moZraoba vrceldeba erT<br />
periodSi, talRis sigrZe ewodeba.<br />
4.7. brtyeli talRis gantoleba<br />
talRuri zedapirebis mixedviT ganixilebian brtyeli, sferuli da<br />
cilindruli talRebi. talRuri zedapirebis raodenoba talRaSi<br />
usasruloa, gansxvavebiT talRuri frontisgan. isini gadaadgilebas ar<br />
ganicdian. talRuri fronti ganicdis mudmiv gadaadgilebas da drois<br />
yoveli momentisTvis erTaderTia.<br />
brtyeli sinosoidaluri, x RerZis dadebiTi mimarTulebis gaswvriv<br />
gavrcelebuli talRis gantolebaa<br />
⎡ ⎛ x ⎞ ⎤<br />
ξ ( x, t)<br />
= Acos⎢ω⎜<br />
t − ⎟ + α ⎥<br />
⎣ ⎝ v ⎠ ⎦<br />
sadac A − talRis amplitudaa;<br />
ω − talRis cikluri (wriuli) sixSire;<br />
65
α − talRis sawyisi faza<br />
⎛ x ⎞<br />
ω⎜t<br />
− ⎟ + α − talRis fazaa<br />
⎝ v ⎠<br />
v − talRis gavrcelebis siCqare<br />
x t droSi talRis gavlili gzaa.<br />
2π<br />
ω<br />
talRuri ricxvi k = = ,<br />
λ v<br />
sadac λ talRis sigrZea, ω − wriuli sixSire, v − talRis siCqare.<br />
talRuri veqtoria k , romlis moduli tolia talRuri ricxvis,<br />
mimarTulia talRuri zedapiris marTobulad.<br />
brtyeli talRis gantoleba, romelic vrceldeba k veqtoriT<br />
gansazRvruli mimarTulebiT, iqneba:<br />
ξ ( r , t)<br />
= Acos(<br />
ωt<br />
− kr<br />
+ α).<br />
sadac r − dakvirvebis wertilis radius veqtoria;<br />
α − rxevis faza r = 0 wertilSi, rodesac t = 0,<br />
anu rxevis faza<br />
koordinatTa saTaveSi.<br />
4.8. talRuri gantoleba<br />
talRuri gantoleba _ meore rigis diferencialuri gantolebaa da<br />
aRwers talRebis gavrcelebas erTgvarovan da izotropiul garemoSi:<br />
an<br />
2 2 2<br />
2<br />
∂ ξ ∂ ξ ∂ ξ 1 ∂ ξ<br />
+ + =<br />
2 2 2 2 2<br />
∂x<br />
∂y<br />
∂z<br />
v ∂t<br />
Δξ<br />
=<br />
66<br />
1<br />
2<br />
∂ ξ<br />
2 2<br />
v ∂t<br />
sadac ξ -fizikuri sididea, axasiaTebs SeSfoTebis gavrcelebas<br />
garemoSi v siCqariT, Δ- laplasis operatori<br />
∂<br />
Δ =<br />
∂<br />
2<br />
∂<br />
+<br />
∂<br />
2<br />
2<br />
∂<br />
+<br />
z<br />
2 2<br />
x y ∂<br />
brtyeli talRisTvis talRuri gantoleba Caiwereba:<br />
2<br />
2<br />
∂ ξ<br />
1 ∂ ξ<br />
= 2 2 2<br />
∂x<br />
v ∂t<br />
2
sadac x − talRis gavrcelebis mimarTulebaa,<br />
v - gavrcelebis siCqare<br />
talRuri gantolebis amoxsnaa:<br />
sadac k - talRuri veqtoria,<br />
α − rxevis sawyisi faza<br />
ξ ( r , t)<br />
= Acos(<br />
ωt<br />
− kr<br />
+ α)<br />
4.9. talRebis interferencia<br />
koherentuli talRebi erTnairi sixSiris talRebia, romelTa<br />
fazaTa sxvaoba drois mixedviT mudmivia ( Δϕ = const)<br />
koherentuli talRebis zeddebas interferencia ewodeba.<br />
interferenciis Sedegad rxevebi sivrcis zogierT wertilebSi<br />
Zlierdebian, zogierTSi ki _ asusteben erTmaneTs.<br />
ori erTnairi sixSiris da amplitudis Semxvedri sinusoidaluri<br />
talRebis zeddebis Sedegs mdgari talRa ewodeba (nax. 36)<br />
mdgari talRis gantolebaa<br />
amplituda<br />
burcobebi<br />
kvanZebi<br />
nax. 36.<br />
⎛ x ⎞<br />
ξ = ⎜2<br />
Acos 2π<br />
⎟ ⋅ cosωt<br />
⎝ λ ⎠<br />
x<br />
Amd = 2 Acos<br />
2π<br />
= 2Acos<br />
kx<br />
λ<br />
wertilebisTvis, romlebSic kx = 0, π... Ak<br />
= 0 − warmoadgenen mdgari<br />
talRis kvanZebs, xolo wertilebisaTvis, romlebSic kx = π ,<br />
2<br />
67
3π A = 2A<br />
2...<br />
md amplituda maqsimaluria _ mdgari talRis burcobebia<br />
(nax. 36).<br />
umokles manZils mezobel kvanZebs (an burcobebs Soris mdgari<br />
talRis sigrZe ewodeba<br />
sadac λ − msrboli talRis sigrZea.<br />
λ =<br />
md<br />
mdgar talRaSi nawilakebis siCqare ganisazRvreba gantolebiT:<br />
68<br />
λ<br />
,<br />
2<br />
� ∂ξ<br />
⎛<br />
x ⎞<br />
ξ = = −⎜2<br />
Aω<br />
cos 2π<br />
⎟sinωt<br />
= −(<br />
2Aω<br />
cos kx)<br />
⋅sinωt<br />
∂t<br />
⎝<br />
λ ⎠<br />
garemos deformacia ki toli iqneba:<br />
∂ξ<br />
⎛ 2π<br />
x ⎞<br />
ε = = −⎜2<br />
A cos 2π<br />
⎟ ⋅cosωt<br />
= −(<br />
2Ak<br />
cos kx)<br />
cosωt<br />
∂x<br />
⎝ λ λ ⎠<br />
mdgari talRis SemTxvevaSi adgili ar aqvs energiis gadatanas.<br />
energia periodulad (2ω sixSiriT) burcobebidan, sadac kinetikuri<br />
energia<br />
k<br />
W maqsimaluria, gadaiqaCeba kvanZebSi potenciur<br />
molekuluri fizika<br />
p<br />
W energiad.<br />
molekuluri fizika (molekulur-kinetikuri Teoria) <strong>fizikis</strong><br />
nawilia, romelic Seiswavlis sxeulTa fizikur Tvisebebs sxvadasxva<br />
agregatul mdgomareobaSi maTi molekuluri aRnagobis ganxilvis<br />
safuZvelze. molekulur-kinetikuri Teoria Camoyalibda XIX saukuneSi<br />
daltonis, klauziusis, maqsvelis da bolcmanis Sromebis ganviTarebiT.<br />
nivTierebis molekulur-kinetikur Teorias safuZvlad udevs Semdegi<br />
debulebebi:<br />
1. nivTierebas gaaCnia diskretuli agebuleba, is Sedgeba<br />
molekulebisagan (atomebisagan). nivTierebis erTi moli agregatuli<br />
mdgomareobisgan damoukideblad Seicavs molekulas ( -s<br />
avogadros ricxvi ewodeba).<br />
2. molekulebi nivTierebaSi imyofebian ganuwyvetel siTbur-qaosur<br />
moZraobaSi.
3. molekulebis siTburi moZraobis xasiaTi damokidebulia<br />
molekulebs Soris urTierTqmedebis bunebaze da icvlebian nivTierebis<br />
erTi agregatuli mdgomareobidan meoreSi gadasvlisas.<br />
4. siTburi moZraobis intensivoba damokidebulia sxeulis gaTbobis<br />
xarisxze, rac xasiaTdeba absoluturi (Termodinamikuri) temperaturiT<br />
.<br />
5. molekulur-kinetikuri TeoriiT sxeulis sruli energia<br />
warmoadgens Semdeg SesakrebTa jams:<br />
sadac da warmoadgenen sxeulis, rogorc mTlianis kinetikur<br />
da potencialur energiebs, xolo warmoadgens sxeulis Semadgeneli<br />
molekulebis (atomebis) energias. mas Sinagani energia ewodeba.<br />
debulebebis irib mtkicebulebebs warmoadgenen brounis moZraoba da<br />
difuziis movlena, xolo pirdapirs _ atomebze dakvirveba eleqtronuli<br />
da ionuri mikroskopebiT.<br />
makroskopiuli sistema. mdgomareobis parametrebi. sistemas (sxeuls)<br />
ewodeba makroskopiuli, Tu is Sedgeba molekulebis didi<br />
raodenobisagan. makroskopiuli sistemis Tvisebebis damaxasiaTebel<br />
sidideebs _ parametrebi ewodebaT. ZiriTad parametrebs warmoadgenen<br />
sistemis wneva , moculoba da temperatura .<br />
wneva _ fizikuri sididea, is ricxobrivad tolia farTobis<br />
erTeulze moqmedi marTobi Zalis:<br />
sadac _ marTobi (normaluri) Zalis ricxviTi mniSvnelobaa,<br />
moqmedi sxeulis zedapiris mcire farTobze.<br />
pa (paskali),<br />
temperatura _ fizikuri sididea, axasiaTebs sxeulis gaTbobis<br />
xarisxs. Termodinamikuri wonasworobis pirobebSi sistemis Semadgeneli<br />
sxeulebis temperaturebi erTnairia.<br />
_ kelvinis skaliT, _ celsiusis skaliT.<br />
wneva da temperatura statistikuri sidideebia, amitom am cnebebs<br />
erTi an ramdenime molekulisTvis azri ara aqvs.<br />
69<br />
,
sxeulis simkvrive _ ewodeba sxeulis masis Sefardebas mis<br />
moculobasTan.<br />
xvedriTi wona _ ewodeba sxeulis wonis Sefardebas mis<br />
moculobasTan.<br />
avogadros ricxvi warmoadgens nivTierebis erT molSi<br />
nawilakebis (molekulebis) raodenobas.<br />
moli -1 .<br />
molis masa _ molaruli masaa, xolo erTi molis moculobas<br />
molaruli moculoba ewodeba.<br />
molekuluri <strong>fizikis</strong> meTodebi.<br />
makrosistemebis Tvisebebis Seswavlis ori meTodi arsebobs:<br />
statistikuri da Termodinamikuri.<br />
mTeli sxeulis mdgomareobis damaxasiaTebeli sidideebi miiReba<br />
calkeuli molekulebis damaxasiaTebel sidideTa gasaSualoebiT.<br />
magaliTad, sxeulis temperatura warmoadgens molekulebis saSualo<br />
kinetikuri energiis proporciul sidides; gazis wneva gaizomeba im<br />
saSualo impulsiT, romelsac molekulebi gadascemen kedlis erTeul<br />
farTobs drois erTeulSi; idealuri gazis Sinagani energia warmoadgens<br />
misi Semadgeneli molekulebis saSualo kinetikuri energiebis jams.<br />
sxeulis makroskopiuli Tvisebebis Sesaswavlad saWiroa molekuluri<br />
warmodgenebidan gamomdinare, gamoviyvanoT is zogadi kanonzomierebani,<br />
romlebic mTel sxeuls axasiaTebs. aseTi Seswavla xorcieldeba e.w.<br />
statistikuri meTodis saSualebiT. statistikuri meTodi emyareba<br />
albaTobis Teorias. mas gamoyavs is zogadi kanonzomierebani, romlebsac<br />
emorCileba SemTxveviTi movlenaTa erToblioba.<br />
Termodinamikuri meTodi _ aqsiomaturi meTodia. aqsiomebad<br />
gamoiyenebian is fundamentaluri kanonebi, romelTa samarTlianoba<br />
70
emyareba eqsperimentebs. maT Termodinamikis principebi ewodebaT. am<br />
principebze dayrdnobiT, Termodinamika Seiswavlis energiis gardaqmnis<br />
movlenebs sistemebSi maTi molekuluri aRnagobis gaTvaliswinebis<br />
gareSe.<br />
Termometruli xelsawyoebis dasagraduireblad gamoiyeneba e.w.<br />
`reperuli wertilebi~ _ zogierTi nivTierebis dnobis da duRilis<br />
temperaturebi, romlebic mudmivi moculobis pirobebSi ar icvlebian.<br />
5. idealuri airebis kinetikuri Teoria<br />
airebis kinetikuri Teoria _ Seiswavlis airebis aRnagobas, maT<br />
fizikur Tvisebebs da efuZneba kvlevis statistikur meTods.<br />
5.1. idealuri airi. molekulur-kinetikuri Teoriis<br />
ZiriTadi gantoleba<br />
iseT airs, romlis molekulebs Soris ugulvebelyofilia<br />
urTierTqmedebis energia da romelSiac molekulebis zoma SeiZleba<br />
ugulebelvyoT, idealuri airi ewodeba. es fizikuri modelia.<br />
urTierTqmedeba idealuri airis molekulebs Soris warmoebs mxolod<br />
dajaxebisas. molekulebis uamravi dajaxebebis Sedegia airis warmoebuli<br />
wneva WurWlis kedlebze, romelSic is moTavsebulia.<br />
airebis molekulur-kinetikuri Teoriis ZiriTadi gantolebaa:<br />
airis wneva tolia erTeul moculobaSi moTavsebuli molekulebis<br />
gadataniTi moZraobis kinetikuri energiis -is,<br />
sadac _ airis molekulebis gadataniTi moZraobis saSualo<br />
kinetikuri energiaa, _ siCqaris kvadratis saSualo mniSvnelobaa.<br />
71
_ molekulebis saSualo kvadratuli siCqarea,<br />
kv _ molekulebis koncentraciaa, _ airis<br />
moculobaa, _ molekulebis raodenoba mocemul moculobaSi.<br />
kavSiri temperaturasa da molekulebis<br />
saSualo kinetikur energias Soris<br />
siTburi movlenebi gvarwmunebs, rom molekulebis saSualo<br />
kinetikuri energia izrdeba temperaturis gazrdiT. rodesac gazs<br />
vaTbobT, misi wneva izrdeba, rac aisaxeba imiT, rom gaTbobis dros<br />
izrdeba molekulebis kinetikuri energia, amitom izrdeba dajaxebisas<br />
molekulebis mier kedlisadmi gadacemuli impulsi. uamravi<br />
dakvirvebidan gamomdinare, airis temperatura proporciulia<br />
molekulebis saSualo kinetikuri energiis (warmoadgens energiis zomas)<br />
. molekulis gadataniTi moZraobis saSualo kinetikuri energia<br />
gad gad<br />
sadac gadamyvani koeficientia energiis erTeulebidan<br />
temperaturis erTeulebSi. _ bolcmanis universaluri<br />
mudmivaa, absoluturi temperaturaa, is aiTvleba kelvinis skalaze,<br />
sadac nulad aRebulia , romelsac absoluturi nuli ewodeba.<br />
es is temperaturaa, romelzec molekulaTa gadataniTi moZraoba wydeba.<br />
igi dakavSirebulia celsiusis skalaze aTvlil temperaturasTan<br />
formuliT .<br />
Tu gaviTvaliswinebT wina formulebs, miviRebT, rom idealuri airis<br />
wneva dakavSirebulia temperaturasTan TanafardobiT, rac agreTve<br />
ZiriTad gantolebas warmoadgens _ .<br />
Tu , wneva damokidebulia mxolod koncentraciaze da ar<br />
aris damokidebuli molekulis (atomis) gvarobaze.<br />
idealuri airis gantoleba.<br />
airebis kinetikuri Teoriis ZiriTadi gantolebidan vRebulobT:<br />
72
es gantoleba amyarebs kavSirs airis mdgomareobis da<br />
parametrebs Soris, amitom faqtiurad warmoadgens idealuri airis<br />
gantolebas. am gantolebiT sargebloba praqtikulad mouxerxebelia,<br />
radgan is Seicavs molekulebis saerTo ricxvs airSi _ .<br />
aRvniSnoT airSi molebis raodenoba -iT, maSin , amitom<br />
, miviRebT da , rac warmoadgens<br />
klapeironis gantolebas idealuri airisaTvis, sadac airis masaa, _<br />
molaruli masa, xolo warmoadgens airis universalur<br />
mudmivas.<br />
idealuri airis kanonebi.<br />
idealuri airis gantolebidan SesaZlebelia miviRoT idealuri<br />
airebis yvela kanoni.<br />
1. izoTermuli procesi _ boil-mariotis kanoni:<br />
izoTermis gantolebaa.<br />
nax. 37<br />
nax. 1. naCvenebia -s damokidebulebis grafiki -ze.<br />
2. , izobaruli procesi _ gei-lusakis kanoni: _<br />
izobaris gantolebaa.<br />
-s damokidebuleba -ze mocemulia nax. 2. .<br />
3. , izoqoruli procesi _ Sarlis kanoni: _<br />
izoqoris gantolebaa.<br />
73
-s damokidebuleba -ze mocemulia nax. 3. .<br />
nax. 38 nax. 39<br />
4. avogadros kanoni. erTnairi wnevisa da temperaturis pirobebSi<br />
nebismieri airis tol moculobebSi molekulebis erTnairi ricxvi<br />
imyofeba, radgan<br />
maSin<br />
sadac _ molekulebis raodenobaa airis nebismier tol<br />
moculobebSi.<br />
5. daltonis kanoni. airebis narevis wneva tolia narevSi Semavali<br />
airebis parcialuri wnevebis jamis:<br />
parcialuri wneva ewodeba narevis erT-erTi komponentis wnevas, Tu<br />
marto is Seavsebda narevis mTel moculobas.<br />
5.2. idealuri airis Sinagani energia<br />
Sinagani energia moicavs airis Semadgeneli nawilakebis Sinagani<br />
moZraobis da urTierTqmedebis energiis yvela saxeobas. mravalatomiani<br />
airis Sinagani energiis Semadgenlebia:<br />
1. molekulebis siTburi da brunviTi moZraobebis kinetikuri<br />
energiebi.<br />
74
2. molekulebSi atomebis rxeviTi moZraobis kinetikuri da<br />
potencialuri energiebi.<br />
3. molekulebSorisi urTierTqmedebis potencialuri energia.<br />
4. atomebis da ionebis garsebis energia.<br />
5. atomebis birTvebSi nuklonebis kinetikuri da urTierTqmedebis<br />
potencialuri energiebi.<br />
energiis Tanabari ganawilebis kanoni<br />
Tavisuflebis xarisxTa ricxvi ewodeba im damoukidebel<br />
koordinatTa ricxvs, romlebic gansazRvraven sxeulis mdebareobas<br />
sivrceSi. magaliTisTvis, wrfeze moZrav materialur wertils gaaCnia<br />
Tavisuflebis xarisxi, sibrtyeze xolo sivrceSi rac<br />
Seesabameba moZraobis ganmsazRvrel koordinatebs.<br />
energiis Tanabari ganawilebis kanoni Tavisuflebis xarisxebis<br />
mixedviT. nebismieri saxis moZraobisas erT Tavisuflebis xarisxs<br />
eTanadeba energiis raodenoba. Tu molekulas gaaCnia Tavisuflebis<br />
xarisxTa raodenoba, maSin misi saSualo energia<br />
masis airis Sinagani energia iqneba<br />
5.3. molekulaTa siCqareTa ganawilebis kanoni<br />
maqsvelis kanoni molekulebis siCqareebis ganawilebis mixedviT,<br />
gansazRvravs molekulebis raodenobas saerTo raodenobidan,<br />
romelTa siCqareebi moTavsebulia SualedSi mocemul<br />
temperaturaze<br />
sadac _ molekulis siCqaris absoluturi<br />
mniSvnelobaa, _ molekulis masaa.<br />
molekulebis ganawilebis funqcia , romlis maTematikuri<br />
gamosaxuleba miiRo maqsvelma, Semdegia:<br />
75
ganawilebis funqcia eqvemdebareba normirebis pirobas<br />
integrireba warmoebs 0-dan -mde, radgan siCqareebi moTavsebulia am<br />
intervalSi.<br />
grafikulad maqsvelis ganawilebis kanoni gamosaxulia nax. 4.,<br />
siCqares, romelsac ganawilebis mrudis maqsimumi Seesabameba ( -s RerZze<br />
1), ualbaTesi siCqare ewodeba. ualbaTesi siCqaris maxlobeli siCqareebi<br />
gaaCnia molekulebis umetes nawils,<br />
nax. 40 nax. 41<br />
grafikze daStrixuli farTi ricxobrivad tolia molekulebis im<br />
fardobiTi raodenobis, romelTa siCqareebi moTavsebulia da<br />
intervals Soris.<br />
temperaturis gazrdiT mrudis maqsimumi inacvlebs didi<br />
siCqareebisken, magram siCqareebis absoluturi mniSvneloba klebulobs<br />
(nax. 5).<br />
5.4. barometruli formula. bolcmanis ganawilebis kanoni<br />
dedamiwis mizidulobis velSi airis (haeris) molekulebi imyofebian<br />
ganuwyvetel siTbur-qaosur moZraobaSi da ganicdian simZimis Zalis<br />
moqmedebas. mizidulobis da siTburi moZraobis moqmedeba iwvevs airis<br />
stacionalur mdgomareobas, ris gamoc atmosferuli wneva da simkvrive<br />
mcirdeba dedamiwis zedapiridan manZilis gazrdiT.<br />
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gantoleba, romelic gansazRvravs airis wnevis damokidebulebis<br />
kanons simaRlesTan, aris barometruli formula da aqvs Semdegi saxe:<br />
sadac _ airis wnevaa simaRleze, _ wnevaa simaRleze,<br />
_ molekulis masaa,M _ molaruli masaa.<br />
wnevis damokidebuleba simaRlesTan mocemulia nax. 6-ze.<br />
nax. 42<br />
radgan koncentraciis ganawilebis kanoni simaRlis<br />
cvlilebasTan, iqneba<br />
sadac da _ molekulaTa koncentraciaa im wertilebSi,<br />
romelTa Soris simaRleTa sxvaoba -is tolia.<br />
_ molekulis potencialuri energiaa simaRleze.<br />
Tu , adgili aqvs koncentraciis gaTanabrebas airis<br />
dakavebul moculobaSi.<br />
Tu dedamiwis atmosferos yvela molekula unda daeSvas<br />
dedamiwis zedapirze.<br />
bolcmanis ganawileba sruldeba nebismier Zalovan velSi<br />
sadac molekulis potencialuri energiaa.<br />
5.5. molekulaTa dajaxebaTa ricxvis da saSualo<br />
77
Tavisufali gadarbenis gamoTvla<br />
martivi cdebi (brounis moZraoba, difuzia) aCveneben, rom molekulis<br />
moZraoba airis erTi nawilidan meoresken ar aris Tavisufali, igi<br />
ganicdis mraval dajaxebas sxva molekulebTan. manZils _ , romelsac<br />
gaivlis molekula erTi dajaxebidan meoremde, Tavisufali ganarbeni<br />
ewodeba. radgan molekulaTa dajaxeba (Sexla) SemTxveviTi xasiaTisaa,<br />
amitom gansazRvraven Tavisufali ganarbenis saSualo mniSvnelobas _<br />
sadac dajaxebaTa raodenobaa,<br />
molekulis efeqturi diametri _ minimaluri manZilia,<br />
romelzedac uaxlovdebian molekulebis centrebi Sexlisas. es xdeba<br />
maSin, roca maTi urTierTganzidvis potenciuri energia gadaaWarbebs<br />
maTi fardobiTi moZraobis kinetikur energias.<br />
gamoTvlebis Tanaxmad, drois erTeulSi TiToeuli molekula<br />
ganicdis dajaxebaTa saSualo raodenobas, rac tolia<br />
sadac _ molekulis saSualo ariTmetikuli siCqarea, _<br />
koncentraciaa.<br />
mudmivi temperaturis pirobebSi airis koncentracia wnevis<br />
pirdapirproporciulia ( ) da molekulis saSualo Tavisufali<br />
ganarbeni tolia:<br />
formula aCvenebs, rom izrdeba temperaturis gazrdiT da wnevis<br />
SemcirebiT: da .<br />
6. Termodinamika<br />
6.1. Termodinamikuri sistema, damaxasiaTebeli parametrebi<br />
makroskopiuli sxeulebis Tvisebebis Seswavla SeiZleba<br />
ganxorcieldes maTi molekuluri aRnagobis gaTvaliswinebis gareSe.<br />
78
amisaTvis sakmarisia ganvixiloT energiis gardaqmnis movlenebi,<br />
romlebsac adgili aqvs fizikuri procesebis dros.<br />
<strong>fizikis</strong> im nawils, romelic Seiswavlis energiis gardaqmnis<br />
movlenebs, Termodinamika ewodeba.<br />
Termodinamikuri sistema _ makroskopiuli obieqtebia (sxeulebi da<br />
velebi), romlebsac SeuZliaT energocvla, rogorc erTmaneTTan, aseve<br />
gareSe sxeulebTan.<br />
Termodinamikuri sistemebis mdgomareoba calsaxad ganisazRvreba<br />
sami parametriT: wneviT P, moculobiT V da Termodinamikuri<br />
(absoluturi) temperaturiT T.<br />
Termodinamikuri sistemis mdgomareobas, romlis drosac misi<br />
mdgomareobis ganmsazRvreli parametrebi ucvlelia, ucvleli garemo<br />
pirobebisas, wonasworuli mdgomareoba ewodeba. am mdgomareomaSi<br />
sistemis temperatura mudmivia da warmoadgens molekulebis moZraobis<br />
intensivobis zomas. sistema arawonasaworul mdgomareobaSia, Tu mis<br />
Termodinamikur parametrebs sxvadasxva wertilebSi sxvadasxva<br />
mniSvnelobebi gaaCnia.<br />
relaqsacia iseTi procesia, rodesac sistema arawonasaworuli<br />
mdgomareobidan gadadis wonasworulSi.<br />
Termodinamikuri sistema stacionalur mdgomareobaSia, Tu misi<br />
mdgomareobis ganmsazRvreli parametrebi, droSi mudmivi rCebian sistemis<br />
nebismier wertilSi.<br />
process wonasworuli ewodeba, rodesac sistemis mdgomareobis<br />
cvlileba imdenad nela mimdinareobs, rom is uwyvetad gaivlis<br />
usasrulod maxlobel Termodinamikur wonasworul mdgomareobebs.<br />
procesebi, romlebic ar akmayofileben am moTxovnebs _<br />
arawonasworulia.<br />
Termodinamikuri sistemis Sinagani energia<br />
sistemis Sinagani energia U damokidebulia mxolod mis<br />
Termodinamikur mdgomareobaze. is calsaxa funqciaa sistemis<br />
mdgomareobis: misi cvlileba dU-Ti sistemis gadasvlisas 1<br />
mdgomareobidan 2-Si ar aris damokidebuli procesis gvarobaze da<br />
tolia<br />
79
sadac da Sinagani energiis mniSvnelobebia 1 da 2<br />
mdgomareobebSi. Tu sistema asrulebs wriul process (cikls), anu<br />
ubrundeba Tavis sawyis mdgomareobas, maSin Sinagani energiis cvlileba<br />
iqneba nuli.<br />
muSaoba da siTbo<br />
nebismieri Termodinamikuri sistemis mdgomareobis cvlilebas Tan<br />
axlavs muSaoba, romelsac is asrulebs _ an muSaoba, romelsac masze<br />
asruleben gare Zalebi. cxadia, muSaoba gamoisaxeba sistemis<br />
parametrebiT da nebismieri maTi cvlileba dakavSirebulia Sesrulebul<br />
muSaobasTan.<br />
Tu sistemis elementarul Sesrulebul muSaobas gare sxeulebze<br />
aRvniSnavT -Ti, maSin niutonis me-3 kanonis Tanaxmad<br />
sadac gare sxeulebis Sesrulebuli muSaobaa sistemaze.<br />
sistemis mier Sesrulebuli muSaoba gare wnevis Zalis sawinaaRmdegod<br />
(gafarToebis muSaoba), gamoisaxeba formuliT<br />
sadac p _ gare wnevaa, dV _ moculobis cvlileba.<br />
sruli muSaoba gafarToebaze<br />
sistemis mdgomareobis cvlilebas procesi ewodeba. muSaoba da<br />
siTbo _ procesis funqciebia. amitom dA da dQ aRniSnaven muSaobis da<br />
siTbos mcire sidideebs, xolo dU warmoadgens srul diferencials.<br />
6.2. Termodinamikis pirveli kanoni<br />
80
Termodinamikuri sistemis Sinagani energiis Secvlis ori gza<br />
arsebobs:<br />
a) siTbos miReba an gacema,<br />
b) muSaobis Sesruleba.<br />
Termodinamikis I kanoni (principi), warmoadgens energiis Senaxvis<br />
kanons siTburi procesebisaTvis: sistemis mier miRebuli siTbos<br />
raodenoba (dQ) ixarjeba am sistemis Sinagani energiis gazrdaze da mis<br />
mier Sesrulebul muSaobaze gare Zalebis sawinaaRmdegod: . Tu<br />
Sinagani energiis cvlileba usasrulod mcirea, maSin formula aseT<br />
saxes miiRebs<br />
Tu sistema periodulad ubrundeba sawyiss mdgomareobas, misi<br />
Sinagani energiis cvlileba da Termodinamikis I kanonis Tanaxmad<br />
e.i. ar SeiZleba avagoT periodulad momqmedi siTburi manqana,<br />
romelic met muSaobas Seasrulebda, vidre Sesabamisi miwodebuli<br />
energiaa. sxva sityvebiT, pirveli gvaris mudmivi Zravi (perpetuum mobile)<br />
SeuZlebelia.<br />
6.3. airebis siTbotevadoba. maieris gantoleba<br />
sistemis (sxeulis) siTbotevadoba fizikuri sididea da tolia<br />
sistemisTvis gadacemuli siTbos raodenobis Sefardebis mis<br />
temperaturis cvlilebasTan:<br />
kuTri siTbotevadoba ( ). nivTierebis kuTri siTbotevadoba<br />
ewodeba skalarul fizikur sidides, romelic tolia sxeulis<br />
siTbotevadobis Sefardebis amave sxeulis masasTan:<br />
81
e.i. kuTri siTbotevadoba siTbos is raodenobaa, romelic saWiroa<br />
sxeulis erTi kilogramis gasaTbobad erTi kelvinis gradusiT.<br />
iqneba<br />
sxeulis gasaTbobad kelviniT, saWiro siTbos raodenoba ,<br />
da kuTri siTbotevadobebia Sesabamisad mudmivi wnevis da<br />
mudmivi moculobis pirobebSi.<br />
molaruli siTbotevadoba ( ). nivTierebis molaruli<br />
siTbotevadoba ewodeba fizikur sidides, romelic tolia sistemis<br />
siTbotevadobis fardobis masSi Semaval nivTierebis raodenobasTan.<br />
ansxvaveben siTbotevadobebs mudmivi moculobis da wnevis pirobebSi.<br />
sadac molaruli siTbotevadobaa mudmivi moculobis pirobebSi,<br />
2.<br />
_Sinagani energiis cvlilebaa temperaturis cvlilebisas,<br />
_ molekuluri masaa, _ nivTierebis masa.<br />
sadac _ molaruli siTbotevadobaa mudmivi wnevis pirobebSi,<br />
_ sxeulisadmi gadacemuli siTbos raodenobaa temperaturis<br />
cvlilebisas. maieris gantoleba akavSirebs molarul siTbotevadobebs<br />
da erTmaneTTan:<br />
kuTri siTbotevadobebisTvis maieris gantolebaa:<br />
sadac _ airebis universaluri mudmivaa.<br />
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airebis universaluri mudmiva ricxobrivad tolia im muSaobis,<br />
romelic sruldeba airis nivTierebis erTi molis gasaTbobad erTi<br />
kelviniT mudmivi wnevis pirobebSi.<br />
gazebis siTbotevadoba da Tavisuflebis xarisxi<br />
Taviseflebis xarisxTa mixedviT, Sinagani energiis ganawilebis<br />
kanonis da maieris gantolebis gaTvaliswinebiT, vRebulobT:<br />
sadac da molaruli siTbotevadobebia mudmivi moculobis da<br />
wnevis pirobebSi. Termodinamikuri procesebis ganxilvisas, sargebloben<br />
gamosaxulebiT<br />
erTatomiani molekulisTvis Tavisuflebis xarisxi = 3,<br />
oratomianisTvis = 5, xolo sam da mravalatomiani airebisTvis = 6.<br />
6.4. adiabaturi procesi<br />
process, romelic mimdinareobs garemosTan siTbocvlis gareSe,<br />
adibaturi procesi ewodeba _ = 0.<br />
imisaTvis, rom airi adiabaturad gafarTovdes, is unda movaTavsoT<br />
siTbos aragamtar WurWelSi. gafarToebisas airi siTbos ar miiRebs, e.i.<br />
muSaobas asrulebs Sinagani energiis xarjze da civdeba. adiabaturi<br />
kumSvisas muSaobas gareSe Zala asrulebs da, radgan airi siTbos ar<br />
gascems, misi Sinagani energia izrdeba, e.i. airi gaTbeba.<br />
maSasadame, adiabaturi gafarToebis dros airi civdeba, xolo<br />
adiabaturi kumSvis dros _ Tbeba.<br />
ewodeba:<br />
adiabaturi procesis gamomsaxvel gantolebas puasonis gantoleba<br />
83
adiabaturi gafarToebis muSaoba<br />
sadac _ adiabaturi gafarToebis muSaobaa, da procesis<br />
sawyisi da saboloo temperaturebia.<br />
6.5. wriuli procesi. Seqcevadi da Seuqcevadi procesebi<br />
wriuli procesi anu cikli _ Termodinamikuri procesebis<br />
erTobliobaa, romlis Sesrulebis Semdeg sxeuli ubrundeba sawyis<br />
mdgomareobas (nax. 7)<br />
nax. 43<br />
gamovTvaloT ciklis dros Sesrulebuli muSaoba. aRvniSnoT ACB<br />
procesis dros Sesrulebuli muSaoba -iT. is dadebiTia da ACB<br />
farTobiT gamoisaxeba. kumSvis procesis dros Sesrulebuli<br />
muSaoba uaryofiTia da ADB farTobiT gamoisaxeba. amitom, ciklis<br />
dros Sesrulebuli sruli muSaoba toli iqneba<br />
ACB ADB ACB<br />
e.i. ciklis dros Sesrulebuli muSaoba cikliT SemosazRvruli<br />
farTobiT gamoisaxeba. ciklis dros Sinagani energiis cvlileba nulis<br />
tolia:<br />
cikls pirdapiri ewodeba, Tu sistema asrulebs dadebiT muSaobas<br />
84
da Seqceulia (ukucikli), Tu sistemis Sesrulebuli muSaoba<br />
uaryofiTia<br />
Seqcevadi ewodeba iseT Termodinamikur process, romelic SeiZleba<br />
warmoebdes rogorc pirdapiri, ise Sebrunebuli mimarTulebiT;<br />
Sebrunebuli procesis dros sistema TanmimdevrobiT gaivlis yvela im<br />
saSualedo mdgomareobas, romlebic man gaiara pirdapiri procesis dros<br />
da ise dabrunda sawyis mdgomareobaSi,rom gareSe sxeulebSi araviTari<br />
cvlileba ar moxda. winaaRmdeg SemTxvevaSi cikli Seuqcevadia.<br />
saerTod, nebismieri wminda meqanikuri procesi (xaxunis gareSe<br />
mimdinare), Seqcevadia. praqtikulad Seqcevadi procesebi ar<br />
xorcieldeba.<br />
6.6. siTburi manqana. margi qmedebis koeficienti<br />
nebismieri siTburi manqanis Semadgeneli sami nawilia gamaxurebeli,<br />
macivari da muSa sxeuli.<br />
muSa sxeuli _ Termodinamikuri sistemaa, romelic asrulebs wriul<br />
process da siTbocvlaSia sxva sxeulebTan. Cveulebriv is airia.<br />
gamaxurebeli (siTbogadamcemi) _ sxeulia, romelic Termodinamikur<br />
sistemas gadascems energias siTbos saxiT.<br />
macivari (siTbos mimRebi) _ sxeulia, romelic Termodinamikuri<br />
sistemidan Rebulobs energias siTbos saxiT.<br />
siTburi manqanis Termodinamikuri margi qmedebis koeficienti<br />
ewodeba sasargeblo muSaobaze daxarjul siTbos raodenobis<br />
Sefardebas gamxureblidan miRebul siTbos raodenobasTan<br />
sadac _ muSa sxeulis mier gamaxureblidan miRebuli siTbos<br />
raodenobaa temperaturisas,<br />
_ macivris mier muSa sxeulisgan miRebuli siTbos raodenobaa<br />
temperaturisas,<br />
85
ciklis dros.<br />
_ siTburi manqanis mier Sesrulebuli sasargeblo muSaobaa erTi<br />
_ margi qmedebis Termodinamikuri (mqk) koeficientia.<br />
6.7. karnos cikli. karnos ciklis mqk<br />
karnos cikli pirdapiri wriuli procesia, romlis drosac sistemis<br />
Sesrulebuli muSaoba maqsimaluria. vTqvaT cilindrSi dguSis qveS<br />
moTavsebulia idealuri airis erTi moli (nax. 8). cilindris kedlebi da<br />
dguSi siTbos aragamtarebia, xolo fskeri atarebs siTbos. mivadgaT<br />
cilindris fskers gamaxurebeli , maSin airi miiRebs gamaxureblis<br />
temperaturas, rac iqneba airis sawyisi temperatura. aRvniSnoT sawyisi<br />
moculoba , sawyisi wneva _ . airis sawyisi mdgomareoba diagramaze<br />
gamoisaxeba 1 wertiliT (nax. 9).<br />
nax. 44 nax. 45<br />
Tu airis sawyisi wneva metia gareSe wnevaze, maSin is<br />
gafarTovdeba da Seasrulebs muSaobas, masTan, airis temperatura ar<br />
Seicvleba, radganac is iRebs siTbos gamaxureblisgan. Tu gafarToeba<br />
sakmaod nela iwarmoebs, procesi izoTermuli iqneba da 2 mdgomareobaSi<br />
airis parametrebi iqneba da . 1-2 izoTermuli gafarToebis dros<br />
muSa sxeulis miRebuli siTbos raodenoba aRvniSnoT -iT. 2<br />
86
mdgomareobaSi movaciloT cilindrs gamaxurebeli da mivadgaT siTbos<br />
aragamtari firfita, maSin airi gafarTovdeba da is siTbos arc<br />
miiRebs da arc gascems e.i. procesi adiabatauri iqneba. airi Seasrulebs<br />
muSaobas Sinagani energiis xarjze, misi temperatura Semcirdeba da<br />
gafarToebas SevwyvetT, rodesac airis temperatura macivris<br />
temperaturas gautoldeba. adiabaturi procesi 2-3 mrudiT gamoisaxeba da<br />
3 mdgomareobaSi airis parametrebi iqnebian da . am mdgomareobaSi<br />
firfitis nacvlad cilindrs mivadgaT macivari da daviwyoT airis<br />
kumSva. am dros muSaobas gareSe Zala asrulebs, airi ar Tbeba, radgan<br />
gamoyofili siTbo macivars gadaecema e.i. kumSva izoTermulad<br />
iwarmoebs, procesi gamoisaxeba 3-4 izoTermiT. aRvniSnoT am procesis<br />
dros macivrisadmi gadacemuli siTbos raodenoba -iT. me-4<br />
mdgomareobaSi airis parametrebia da . me-4 mdgomareobaSi<br />
movaciloT cilindrs macivari da mivadgaT siTbogaumtari firfita.<br />
radganac, exla gazi izolirebulia siTbos mxriv, kumSva adiabaturad<br />
iwarmoebs da, Tu meoTxe mdgomareoba saTanadod aris SerCeuli, airi<br />
daubrundeba sawyis 1 mdgomareobas. Sesruldeba erTi cikli, romelic<br />
Sedgeba ori izoTermuli da ori adiabaturi procesisgan.<br />
mTeli ciklis dros muSa sxeulis mier miRebuli siTbos raodenoba<br />
iqneba . radgan airi asrulebs wriul process _ cikls,<br />
energiis cvlileba da Termodinamikis I kanonis Tanaxmad<br />
A .<br />
karnos Teorema. gamxureblis da macivris erTi da igive<br />
temperaturebisas, verc erTi siTburi manqanis mqk ver gadaaWarbebs<br />
karnos Seqcevadi ciklis mqk-s.<br />
karnos ciklis mqk ar aris damokidebuli muSa sxeulis gvarobaze<br />
da warmoadgens mxolod gamaxureblis da macivris temperaturebis<br />
funqcias<br />
es formula gviCvenebs agreTve mqk gazrdis gzas. karnos Seqcevadi<br />
ciklisaTvis sruldeba Sefardeba<br />
87
nebismieri ciklisaTvis Termodinamikuri mqk<br />
sadac tolobis niSani Seqcevad cikls Seesabameba, utolobis ki _<br />
Seuqcevads.<br />
6.8. Termodinamikis meore kanoni<br />
Termodinamikis I kanoni faqtiurad energiis mudmivobis kanonia<br />
siTburi procesebisaTvis da amitom yvela procesSi sruldeba, magram is<br />
ar aCvenebs procesis mimarTulebas. magaliTad, siTbo TavisTavad<br />
arasodes ar gadadis civi sxeulidan cxelze, Tumca am process<br />
Termodinamikis I kanoni ar ewinaaRmdegeba.<br />
Termodinamikis II kanoni (principi) gansazRvravs Termodinamikuri<br />
procesis mimarTulebas da amiT pasuxs cems kiTxvas, Tu romeli<br />
procesebi SeiZleba ganxorcieldes bunebaSi.<br />
ganvixiloT meore kanonis ramdenime formulireba:<br />
a) SeuZlebelia procesi, romlis erTaderTi Sedegi iqneba siTbos<br />
gadacema civi sxeulidan cxelze.<br />
b) SeuZlebelia iseTi perioduli procesi, romlis erTaderTi<br />
Sedegi iqneboda siTburi energiis gardaqmna mis eqvivalentur muSaobad.<br />
g) SeuZlebelia avagoT iseTi periodulad momqmedi manqana, romlis<br />
moqmedebis erTaderTi Sedegia muSaobis Sesruleba siTbos erTi wyaros<br />
gacivebis xarjze.<br />
davuSvaT, rom sxeuli vardeba dedamiwaze. vardnis procesSi<br />
meqanikuri potenciuri energia siTbod gardaiqmneba _ Tbeba sxeulic da<br />
miwac. Sebrunebuli procesi _ siTburi energiis xarjze (miwis gacivebis),<br />
sxeulis asvla imave simaRleze arasodes ganxorcieldeba.<br />
Termodinamikis I kanonis TvalsazrisiT es procesi ar aris SeuZlebeli,<br />
magram igi ewinaaRmdegeba Termodinamikis meore kanons, radgan<br />
Sesruldeba muSaoba mxolod erTi wyaros _ dedamiwis gacivebis xarjze.<br />
88
6.9. entropia. Termodinamikis gaerTianebuli kanoni<br />
siTburi procesebis Seswavlidan gamomdinareobs, rom unda<br />
arsebobdes iseTi funqcia , romlis cvlileba 1-dan 2 mdgomareobaSi<br />
raime Seqcevadi procesis gadasvlisas, toli iqneba<br />
funqcias entropia ewodeba. da entropiis mniSvnelobebia 1 da<br />
2 mdgomareobebi. -s dayvanili siTbo ewodeba.<br />
amgvarad, entropia warmoadgens mdgomareobis funqcias, romlis<br />
cvlileba Seqcevadi procesis dros, gvaZlevs dayvanil siTbos<br />
raodenobaTa jams.<br />
Tu sistema izolirebulia, maSin , Seqcevadi procesisTvis<br />
gveqneba , xolo nebismierisTvis e.i. izolirebul<br />
sistemaSi procesebi ise warmoebs, rom sistemis entropia mudmivi rCeba,<br />
an izrdeba. es debuleba warmoadgens Termodinamikis meore kanonis<br />
uzogades formulirebas.<br />
Tu 1 da 2 wertilebi usasrulod axlosaa erTmaneTTan e.i. sistemis<br />
mdgomareoba usasrulod mcired icvleba, maSin entropiis sasrulo<br />
cvlilebis magivrad gveqneba usasrulod mcire nazrdi da<br />
Termodinamikis meore kanoni Semdeg saxes miiRebs (entropiis zrdis<br />
kanoni):<br />
xolo, Tu sistema araizolirebulia, maSin<br />
kavSiri entropiasa da informacias Soris mogvca bolcmanma<br />
sadac _ bolcmanis mudmivaa, _ Termodinamikuri albaToba. am<br />
formulidan gamomdinareobs entropiis fizikuri arsi kinetikuri<br />
TeoriiT _ entropia warmoadgens fizikuri sistemis mouwesrigeblobis<br />
zomas.<br />
89
entropiis warmodgena, rogorc damoukidebeli parametris ucnauri<br />
Canda, radgan ar arsebobda misi gazomvis pirdapiri meTodi. es problema<br />
moxsna nerstis siTburma Teoriam, romlis Tanaxmadac Tu , maSin<br />
, e.i. absolutur nulze entropiac nuls utoldeba. amgvarad,<br />
nerstis TeoremiT moxda entropiis kalibreba.<br />
cnobilia, rom nebismier energetikul kontaqts Seesabameba<br />
parametrebis wyvili. Termodinamikis meore kanonidan , e.i.<br />
temperatura da entropia parametrTa wyvilia. radgan siTbocvla<br />
proporciulia entropiis zrdis, is miCneulia eqstenciur parametrad,<br />
xolo temperatura intensiurad.<br />
Termodinamikis I da II kanonebis ( ) SerwymiT miviRebT<br />
Termodinamikis gaerTianebul kanons:<br />
es formula saSualebas gvaZlevs srulad miviRoT Termodinamikuri<br />
Tanafardobebi nebismieri konkretuli fizikuri sistemisaTvis.<br />
7. realuri airebi<br />
7.1. realuri airebi. molekuluri Zalebi<br />
realuri airebis Tvisebebis gansxvaveba idealurebTan gansakuTrebiT<br />
SesamCnevia didi wnevebisa da dabali temperaturebis dros. didi wnevebis<br />
dros airis molekulebs Soris manZili imdenac mcirdeba, rom aRar<br />
SeiZleba molekulebis sakuTari moculobisa da maTi urTierTqmedebis<br />
ugulvebelyofa, xolo temperaturis Semcirebis dros, molekulebis<br />
saSualo kinetikuri energia mcirdeba, amitom dabal temperaturaze<br />
molekulebis urTierTqmedebis energiebs veRar ugulvebelvyofT maT<br />
kinetikur energiebTan SedarebiT.<br />
realuri iseT airebs ewodebaT, romlis molekulebs Soris<br />
moqmedebs mizidva-ganzidvis Zalebi. es Zalebi sxvadasxvanairad arian<br />
damokidebulni molekulebs Soris manZilebze. atomis zomis tol<br />
manZilebze (10 -10 m) Warbobs ganzidvis Zalebi, xolo 10 -9 m manZilebze _<br />
ki urTierTmizidvis Zalebi (nax. 10). tolqmedi Zala<br />
90
Tu<br />
Tu xolo Tu<br />
_ aRniSnulia molekulebSorisi moqmedebis radiusi _ es aris<br />
manZili molekulebs Soris wonasworuli mdgomareobisas, rodesac<br />
siTburi moZraoba ar warmoebs.<br />
eTanadeba molekulebis wonasworul mdgomareobas, rasac<br />
ewinaaRmdegeba molekulebis siTburi moZraoba.<br />
nax. 46<br />
nivTierebebis sxvadasxva agregatuli mdgomareobis kriteriums<br />
warmoadgens Tanafardoba molekulebis urTierTqmedebis minimalur<br />
potencialur da sidides Soris. gansazRvravs mizidvis<br />
Zalebis sawinaaRmdego muSaobas, raTa daaSoron molekulebi<br />
wonasworul mdgomareobas ( ), xolo sidide gansazRvravs<br />
molekulebis siTburi moZraobis intensivobis xarisxs.<br />
Tu , nivTiereba imyofeba airovan mdgomareobaSi, radgan<br />
molekulebis intensiuri siTburi moZraoba ewinaaRmdegeba maT SeerTebas.<br />
Tu , nivTiereba imyofeba myar mdgomareobaSi. am dros<br />
molekulebs Soris mizidvis Zalebs gaaCniaT didi mniSvnelobebi da<br />
isini asruleben mxolod rxeviT moZraobas wonasworuli mdgomareobis<br />
91
maxloblobaSi. Tu nivTiereba imyofeba Txevad mdgomareobaSi.<br />
siTburi moZraobis Sedegad molekulebi gadaadgildebian siTxis mTel<br />
moculobaSi, magram ar scildebian erTmaneTs -ze met manZilze.<br />
amgvarad, nebismieri nivTierebis agregatuli mniSvneloba<br />
ganisazRvreba -sididiT. magaliTad, inertuli airebis mcire<br />
sidideebia, xolo liTonebis didi, amitomac Cveulebriv (oTaxis)<br />
temperaturaze isini Sesabamisad imyofebian airovan da myar<br />
mdgomareobebSi.<br />
7.2. van der vaalsis gantoleba<br />
realuri airis gantolebis misaRebad holandielma mecnierma<br />
idealuri airis gantolebaSi ori Sesworeba Seitana: 1. Sesworeba<br />
molekulebis sakuTar moculobaze, 2. Sesworeba molekulebis<br />
urTierTmizidvaze.<br />
1. imis gamo, rom realuri airis molekulebs sakuTari moculoba<br />
gaaCniaT, maT SeuZliaT moZraoba ara mTel moculobaSi, aramed<br />
moculobis im nawilebSi, romelic Tavisufalia. Tu -Ti aRvniSnavT<br />
moculobis im nawils, romelic molekulebisTvis SeuRwevadia, maSin<br />
molekulebis moZraobis Tavisufali moculoba iqneba ara , aramed<br />
. warmoadgens Sesworebas molekulebis sakuTari moculobis<br />
gaTvaliswinebiT, da is tolia erT mol gazSi arsebuli molekulebis<br />
gaoTxkecebuli moculobis:<br />
sadac _ avogadros ricxvia, _ molekulis diametri.<br />
2. airSi molekulebis urTierTmizidvis gaTvaliswineba iwvevs<br />
damatebiTi wnevis warmoqmnas, romelsac Sinagani wneva ewodeba. van der<br />
vaalsis gamoTvlebiT Sinagani wneva tolia<br />
sadac _ mudmivaa, damokidebulia airis gvarobaze, _ molaruli<br />
moculobaa.<br />
92
Sesworebebis gaTvaliswinebiT realuri airis mdgomareobis<br />
gantoleba _ van der vaalsis gantoleba _ erTi moli airisTvis, iqneba<br />
saxisaa<br />
nebismieri masisaTvis realuri airis mdgomareobis gatoleba Semdegi<br />
sadac airis moculobaa.<br />
Tu da , van der vaalsis gantoleba gadadis<br />
klapeironis gantolebaSi.<br />
7.3. realuri airis izoTermebi<br />
realuri airis izoTerma warmoadgens airis molaruli moculobis<br />
damokidebulebas wnevaze mudmivi temperaturis pirobebSi. kritikul<br />
mdgomareobamde ( -mde), mrudebi warmoadgenen nivTierebis uwyvet<br />
gadasvlas airovani mdgomareobidan siTxeSi (nax. 11).<br />
monakveTi Seesabameba nivTierebis airovan mdgomareobas, _<br />
airovani mdgomareobis gadasvlas siTxur mdgomareobaSi, _ siTxes.<br />
wertili Seesabameba mduRare siTxes, _ mSral najer orTqls (nax.<br />
11).<br />
nax. 47<br />
93
temperaturis gadidebiT grafiki iwevs zeviT da orTqlis<br />
kondensaciis dasawyisis da damTavrebis wertilebi erTmaneTs<br />
uaxlovdeba. rac metia temperatura, miT naklebi moculobis dros iwyeba<br />
da miT meti moculobis dros mTavrdeba orTqlis siTxed qceva. Tu<br />
avagebT izoTermebs TandaTan ufro maRal temperaturaze, miviRebT, rom<br />
erT garkveul temperaturaze, romelsac kritikuli ewodeba, grafikis<br />
nawili moispoba da am ubnis nacvlad miviRebT gadaRunvis<br />
wertils. -s Sesabamiss mdgomareobas kritikuli ewodeba, xolo mis<br />
Sesabamis parametrebs _ kritikuli wneva , kritikuli moculoba da<br />
kritikuli temperatura .<br />
kritikul temperaturaze ispoba gansxvaveba airsa da siTxes Soris.<br />
Tu izoTermas avagebT temperaturaze, vnaxavT, rom realuri airis<br />
izoTerma emTxveva idealuri airis izoTermas, e.i. aq nivTiereba SeiZleba<br />
imyofebodes mxolod airis mdgomareobaSi, anu -s zeviT SeuZlebelia<br />
airis (orTqlis) gaTxevadeba.<br />
van der vaalsis gantolebidan kritikuli mdgomareobisaTvis,<br />
SesaZlebelia kritikuli parametrebis gamoTvla.<br />
94
damateba<br />
cdomilebaTa Teoriis ZiriTadi debulebebi<br />
fizikuri sididis gazomva niSnavs mis Sedarebas imave gvaris<br />
fizikur sididesTan, specialuri gamzomi saSualebebis (xelsawyoebis)<br />
gamoyenebiT.<br />
gazomvas, romlis drosac fizikuri sididis mniSvnelobas uSualod<br />
vsazRvravT cdiT, pirdapiri gazomva ewodeba. aseTi gazomvis magaliTia<br />
temperaturis gazomva TermometriT, denis Zalis – ampermetriT da sxva.<br />
pirdapiri gazomvisas sidideebis mniSvnelobebi uSualod aiTvlebian<br />
xelsawyoebze.<br />
arapirdapiri gazomvebis SemTxvevaSi, saZiebeli sidideebis<br />
gansazRvrisas, eyrdnobian sxva fizikuri sidideebis pirdapiri gazomvis<br />
Sedegs, romlebTanac saZiebeli sidide funqcionalur kavSirSia.<br />
uxeSi.<br />
gazomvis cdomilebebi SeiZleba iyos sistematuri, SemTxveviTi da<br />
uxeSi cdomilebebi dakavSirebulia gamzomi xelsawyoebis<br />
dazianebasTan, eqsperimentatoris SecdomebTan anaTvlis aRebisas an<br />
gazomvis pirobebis mkveTr cvlilebasTan.<br />
sistemuri cdomileba ori saxisaa: meToduri da instrumentaluri.<br />
meToduri cdomileba gamowveulia movlenis fizikuri Teoriis,<br />
gazomvis meTodis da saZiebeli sididis saangariSo formulis<br />
naklovanebebiT.<br />
instrumentaluri cdomileba gamowveulia danadgaris konstruqciis<br />
da gamzomi xelsawyobis arasrulfasovnebiT.<br />
gazomvis SemxveviTi cdomilebebi iseTi cdomilebebia, romelTa<br />
absoluturi sidideebi da niSani icvlebian erTi da igive fizikuri<br />
sididis mravaljeradi gazomvebisas. maTi gamomwvevi faqtorebi mravalia<br />
da ar eqvemdebarebian aRricxvas. SemTxveviT cdomilebebi Tan sdevs<br />
nebismier gazomvas, maTi Tavidan acileba SeuZlebelia.<br />
cdomilebaTa Teoriis saSualebiT SeiZleba gamoviTval-<br />
oTYmosalodneli cdomileba da davadginoT sazRvrebi, romelTa Sorisac<br />
unda iyos moTavsebuli gasazomi sididis WeSmariti mniSvneloba.<br />
95
cdomilebaTa sruli Teoriis ganxilva warmoadgens sakmarisad rTul<br />
amocanas. Cven gavecnobiT damuSavebis ZiriTad da gavrcelebul meTodebs.<br />
cdomilebis Semcirebis mizniT mizanSewonilia saZiebeli sididis<br />
mravaljeradi gazomva. mravali gazomvis saSualo ariTmetikuli, cxadia<br />
yvelaze axlos iqneba gasazomi sididis WeSmarit mniSvnelobasTan.<br />
davuSvaT Catarda fizikuri sididis -jer gazomva da gazomvis<br />
Semdegad miRebuli iqna mniSvnelobebi. gasazomi fizikuri<br />
sididis saSualo mniSvneloba iqneba<br />
calkeuli gazomvebis absoluturi cdomilebebi<br />
sididis saSualo absoluturi cdomileba iqneba:<br />
gasazomi sididis WeSmariti mniSvneloba moTavsebuli iqneba<br />
da sidideebs Soris, cdis pasuxi Caiwereba:<br />
romelsac xSirad ase warmoadgenen:<br />
mxolod absoluturi cdomileba ver gansazRvravs gazomvis<br />
sizustes. erTi da igive absoluturi cdomileba SeiZleba mcired<br />
CaiTvalos erT SemTxvevaSi da piriqiT, Zalian uxeSad sxva<br />
SemTxvevisaTvis, es damokidebulia gasazomi fizikuri sididis<br />
mniSvnelobaze. gazomvis sizustis Sesafaseblad saWiroa ganisazRvros<br />
fardobiTi cdomileba. fardobiTi cdomileba aris absoluturi<br />
cdomilebis Sefardeba gasazomi fizikuri sididis WeSmarit<br />
mniSvnelobasTan, is gviCvenebs gasazomi sididis ra nawils Seadgens<br />
absoluturi cdomileba. Cveulebriv fardobiT cdomilebas procentebSi<br />
gamosaxaven. cdis sizuste ganisazRvreba saSualo fardobiTi<br />
cdomilebiT .<br />
96
Tu calkeul gazomvaTa SemTxvevaSi cdomilebebi ar aRemateba im<br />
Secdomas, rasac xelsawyo iZleva, sakmarisia Catardes erTjeradi<br />
gazomva. (magaliTad: temperaturis gazomva TermometriT). im SemTxvevaSi<br />
rodesac SeiZleba SemovifargloT erTi gazomviT, absoluturi<br />
cdomileba xelsawyos umciresi danayofis naxevris toli iqneba.<br />
magaliTad, Tu Termometris umciresi danayofi -ia, maSin absoluturi<br />
cdomileba aiReba .<br />
arapirdapiri gazomvebis SemTxveviTi cdomilebebis gamoTvla.<br />
sidideebis arapirdapiri gamoTvlebisas fizikuri sidide<br />
gamoiTvleba formuliT<br />
sadac fizikuri sididis pirdapiri<br />
gazomvis Sedegebia. arapirdapiri gazomvis absoluturi cdomileba<br />
gamoiTvleba formuliT , (1)<br />
sadac , funqciis kerZo warmoebulia -iT; absoluturi<br />
cdomilebaa sididis gazomvisas.<br />
arapirdapiri, (iribi) gazomvis Sedegs warmoadgenen:<br />
sadac - sadac funqcia -is<br />
mniSvneloba Seesabameba -bis saSualo mniSvnelobas. fardobiTi<br />
cdomilebebisTvis gveqneba<br />
sadac<br />
gamoviTvaloT cdomileba cilindruli formis sxeulis simkvrivis<br />
gansazRvrisas:<br />
sadac - sxeulis simkvrivea, - misi masa, - cilindris diamteria,<br />
- misi simaRlea.<br />
(1) formuliT gamoviTvaloT absoluturi cdomileba:<br />
;<br />
97
sadac , , - pirdapiri gazomvebis absoluturi cdomilebebia –<br />
masis, diametris da simaRlis.<br />
gamoTvlebis pasuxia<br />
cdomilebebis gamoTvla (2) formuliT<br />
gavalogariTmoT -s formula:<br />
gansazRvroT warmoebulebi :<br />
fardobiTi cdomileba:<br />
.<br />
sadac -sidideebis saSualo mniSvne-<br />
lobebia, -pirdapiri gazomvebis cdomilebebia, _<br />
absoluturi cdomilebaa.<br />
gamoTvlebis pasuxia<br />
absolutur cdomilebas da saSualo Sedegs amrgvaleben<br />
Semdegnairad:<br />
• Tu pirveli ukusagdebi cifri metia 4-ze, maSin mis Semdeg cifrs<br />
emateba erTi. magaliTad, 18,6782 damrgvalebisas measedamde gveqneba 18,68.<br />
• Tu pirveli ukusagdebi cifri naklebia an tolia 4, maSin bolo<br />
cifri ar icvleba. magaliTad, Tu vamrgvalebT measemde 29,3531, gveqneba<br />
29,35.<br />
• Tu dasamrgvalebeli nawilis bolo ricxvSia 5, maSin mas<br />
amrgvaleben ise, rom bolo ricxvi darCes luwi. magaliTad meaTemde<br />
damrgvalebisas 25,65 Caiwereba 25,6, xolo 27,75 iqneba 27,8.<br />
saSualo ariTmetikuli meTodiT cdomilebaTa gamoTvlis wesi:<br />
1) erTi da igive ucvleli sididis gazomva xdeba mravaljeradad<br />
erTnair pirobebSi.<br />
2) yvela gazomva warmoebs erTnairi aTvlis cdomilebiT<br />
3) am meTods iyeneben im SemTxvevaSi, rodesac gansxvaveba calkeul<br />
gazomvebs Soris aRemateba TiToeuli gazomvis an dasaSveb<br />
instrumentalur cdomilebas.<br />
4) Tu saZiebeli sidide mniSvnelovania (didia) da damokidebulia<br />
gazomvebis mravaljeradobaze, maSin praqtikulad savsebiT sakmarisia<br />
98
gazomvebis imdenjer gameoreba, rom saSualo ariTmetikuli cdomileba<br />
miuaxlovdes dasaSveb instrumentalurs, an dayvanil iqnas aTvlis<br />
calkeuli gazomvis cdomilebaze.<br />
5) Tu ganmeorebiTi gazomvisas miiReba erTi da igive Sedegebi, maSin<br />
gazomvis cdomilebad miiReben gamzom xelsawyos, an instrumentalur<br />
cdomilebas.<br />
SeniSvnis saxiT aRvniSnavT, rom saSualo ariTmetikuli cdomileba<br />
dakavSirebulia saSualo kvadratul cdomilebasTan formuliT<br />
sadac<br />
Tu miviCnevT, rom maSin wina formula SeiZleba<br />
CavweroT gamoTvlebisaTvis iol formaSi .<br />
qvemoT cxrilis saxiT mogvyavs absoluturi da fardobiTi<br />
cdomilebebis formulebi. da miaxloebiTi ricxvebia, -Sesabamisi<br />
absoluturi cdomilebebis sazRvrebi, .<br />
N<br />
1<br />
2<br />
3<br />
4<br />
5<br />
6<br />
7<br />
8<br />
algebruli<br />
maqsimaluri cdomileba<br />
gamosaxuleba absoluturi fardobiTi<br />
rogorc formulebi aCveneben, absoluturi cdo-milebis moZebnis<br />
wesebi emTxveva gadiferencialebis wesebs, im gansxvavebiT rom<br />
absolutur cdomilebaTa formulebSi damoukidebeli cvladebis<br />
99
diferencialebi Secvlilia fizikur sidideTa gazomvis absoluturi<br />
cdomilebebiT da kerZo warmoebulebi aRebulia dadebiTi niSnebiT.<br />
fardobiTi cdomilebis wesebi ki emTxveva logariTmul gadife-<br />
rencialebis Sesabamis wesebs.<br />
100
ibeWdeba avtoris mier warmodgenili saxiT<br />
gadaeca warmoebas 03.07.2009. xelmowerilia dasabeWdad<br />
10.07.2009. qaRaldis zoma 60X84 1/16. pirobiTi nabeWdi Tabaxi 6.<br />
tiraJi 100 egz.<br />
sagamomcemlo saxli `teqnikuri universiteti~, Tbilisi,<br />
kostavas 77