fizika - old.eqe.geold.eqe.ge/.../fizika/diogene/fizika9.pdf · modeli (sur.1) seqmna: man samyaros...
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fizika
9moswavlis wigni
saxelmZRvanelo grifirebulia ganaTlebis xarisxis
ganviTarebis erovnuli centris mier
(brZ. N375, 18.05.2012 weli)
qeTevan tatiSvili
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Sinaarsi
Tema I. meqanikuri moZraoba ...................................................................................... 7 1.1. meqanikuri moZraoba .................................................................................... 8 1.2. gadaadgileba ............................................................................................. 12 1.3. moqmedebebi veqtorul sidideebze ......................................................... 14 1.4. sxeulis koordinatebis povna ................................................................. 17 1.5. wrfivi Tanabari moZraoba ........................................................................ 20 1.6. wrfivi Tanabari moZraobis warmodgena grafikulad .......................... 23 1.7. moZraobis fardobiToba. siCqareTa Sekreba .......................................... 27 1.8. araTanabari moZraoba. saSualo siCqare ................................................. 32 1.9. fizika amocanebSi: araTanabari moZraoba. saSualo siCqare ................ 36 1.10. wrfivi TanabaraCqarebuli moZraoba .................................................... 38 1.11. siCqarisa da aCqarebis grafikebi ......................................................... 40 1.12. gadaadgileba wrfivi TanabaraCqarebuli moZraobis dros ................ 42proeqti: TanabaraCqarebuli moZraobis Seswavla ........................................................ 46 1.13. Tavisufali vardna .................................................................................. 47 1.14. moZraoba wrewirze .................................................................................. 50 1.15. centriskenuli aCqareba ......................................................................... 54 1.16. wrewirze moZraobis periodi da sixSire .............................................. 57 Seamowme Seni codna ................................................................................ 59
Tema II. niutonis kanonebi. impulsi ......................................................................... 61 2.1. niutonis I kanoni ....................................................................................... 62 2.2. masa _ inertulobis zoma ......................................................................... 65 2.3. niutonis II kanoni ...................................................................................... 68 2.4. niutonis II kanonis Sedegebi .................................................................... 70 2.5. niutonis III kanoni ..................................................................................... 73 2.6. impulsi ..................................................................................................... 76 2.7. impulsis mudmivobis kanoni ..................................................................... 79 2.8. reaqtiuli moZraoba ................................................................................. 82 2.9. aTvlis inerciuli da arainerciuli sistemebi ..................................... 85 Seamowme Seni codna .................................................................................. 89
Tema III. Zalebi .............................................................................................................. 91 3.1. msoflio mizidulobis kanoni ................................................................. 92 3.2. fizika amocanebSi: msoflio mizidulobis kanoni ................................ 96 3.3. simZimis Zala .............................................................................................102 3.4. drekadobis Zala ......................................................................................104 3.5. myari sxeulis deformaciis saxeebi .......................................................107 3.6. myari sxeulis meqanikuri Tvisebebi .......................................................109 3.7. xaxunis Zala ..............................................................................................112 3.8. wona ............................................................................................................116 3.9. uwonoba. gadatvirTva .............................................................................113 Seamowme Seni codna .................................................................................122
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Tema IV. sxeulTa moZraobis aRwera dinamikis kanonebis gamoyenebiT ............123 4.1. fizika amocanebSi: moZraoba simZimis Zalis gavleniT ..........................125 4.2. fizika amocanebSi: moZraoba daxril sibrtyeze .................................130 4.3. fizika amocanebSi: gadabmuli sxeulebis moZraoba .............................135 4.4. fizika amocanebSi: mosaxvevSi moZraoba .................................................139 Seamowme Seni codna .................................................................................142
Tema V. muSaoba. energia ...............................................................................................143 5.1. meqanikuri muSaoba ...................................................................................146 5.2. Teorema kinetikuri energiis Sesaxeb ....................................................149 5.3. simZimis Zalis muSaoba .............................................................................151 5.4. drekadobis Zalis muSaoba ......................................................................154 5.5. energiis mudmivobis kanoni .....................................................................156 Seamowme Seni codna .................................................................................159
Tema VI. sinaTlis movlenebi ........................................................................................161 6.1. sinaTlis wrfivi gavrceleba .................................................................162proeqti: ratom xdeba mzisa da mTvaris dabneleba .....................................................166 6.2. sinaTlis siCqare ......................................................................................168 6.3. sinaTlis arekvla ....................................................................................172proeqti: kamera _ obskura ..............................................................................................176 6.4. sinaTlis gardatexa .................................................................................177 6.5. sruli arekvla .........................................................................................182proeqti: miraJi ................................................................................................................184 6.6. linzebi ......................................................................................................185proeqti: linzebi _ xidi Seucnobelisken .....................................................................189 6.7. gamosaxulebis ageba linzaSi ..................................................................191 6.8. Txeli linzis formula ..........................................................................194proeqti: hukis mikroskopi .............................................................................................196 6.9. Tvali - cocxali optikuri sistema ......................................................197 Seamowme Seni codna .................................................................................202 maTematika, romelic fizikis Seswavlisas dagexmareba .......................204 damatebiTi kiTxvebi, amocanebi ..............................................................205 testebis pasuxebi .....................................................................................219
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Zv. w. II saukuneSi aleqsandrielma swavlulma klavdios ptolemeosma samyaros geocentruli modeli (sur.1) Seqmna: man samyaros centrad dedamiwa miiCnia da planetebis moZraoba mis mimarT aRwera. aRmoCnda, rom calkeuli pla-neta ormocamde erTmaneTisagan damoukidebel wriul moZraobas asrulebda. planetebis moZ-raoba imdenad rTuli da qaosuri iyo, rom kas-tiliis mefe alfons X-s (me-13 saukune) gao-cebuls aRmoxda: `me rom RmerTi vyofiliyavi, samyaros ufro mowesrigebuls Sevqmnidio.~
me-16 saukuneSi kopernikma samyaros centrad mze miiCnia da planetebis moZraoba mzis mimarT ganixila (samyaros aseT models heliocentruli modeli (sur.2) hqvia): planetebi mzis irgv-liv martiv, wriul orbitebze ganlagdnen!
ra mizeziT Seicvala planetebis moZraobis xasiaTi kopernikis mier aRweril sistemaSi? sinamdvileSi xom planetebi isev winandeburad moZraobdnen? am kiTxvaze pasuxis gasacemad Ca-vataroT cda
1.7 moZraobis fardobiToba.
siCqareTa Sekreba
diax, Sen ici, rom moZraoba da uZraoba fardobiTia: sxeulis moZraobis ganx-ilvisas aucilebelia aTvlis sxeulis (aTvlis sistemis) miTiTeba, radgan ar arsebobs absoluturad uZravi sxeuli: mocemuli sxeuli erTsa da imave dros SeiZleba erTi aTvlis sxeulis (sistemis) mimarT moZraobdes, xolo meoris mimarT uZravi iyos.
aseve, fardobiTia moZraobis traeqtoriac: traeqtoria damokidebulia aTv-lis sistemis arCevaze. cxadia, swored am mizeziTaa planetebis moZraobis trae-qtoria gansxvavebuli dedamiwasTan da mzesTan dakavSirebul aTvlis sistemaSi.
sur. 1
sur. 2
cda I
magidaze dade qaRaldis furceli da centrSi WikartiT daamagre.
sTxove megobars, furceli damagrebuli centris garSemo atrialos.
amave dros Seecade, furclis centridan magidis kidisken fan-qriT swori xazi gaavlo (anu magidasTan dakavSirebul aTvlis sistemaSi fanqris wveris traeqtoria wrfivia). es Zalian nela da auCqareblad unda gaakeTo.
aRwere, rogoria fanqris wveris traeqtoria furcelTan da-kavSirebul aTvlis sistemaSi? erTnairia Tu ara fanqris wveris traeqtoria magidis zedapirTan da furcelTan dakavSirebul aT-vlis sitemebSi? fanqris wveris mier gavlili manZili?
gaakeTe daskvna: aris Tu ara damokidebuli moZraobis traeq-toria aTvlis sistemis arCevaze? gavlili manZili?
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1.7 moZraobis fardobiToba. siCqareTa Sekreba
dafiqrdi:
daakvirdi sur.4-s: moZravi matareblis vagonSi mgzavri imy-ofeba. erTnairia Tu ara aTv-lis sxvadasxva sistemis mimarT (romelTagan erTi dakavSirebulia moZrav vagonTan (X’O’Y’), xolo meore dedamiwis zedapirTan (XOY)) mgzavris koordinatebi?
gaakeTe daskvna: aris Tu ara da mokidebuli aTvlis sistemis arCevaze, sxeulis mdebareoba, anu koordinatebi?
TviTmfrinavebi ise moZraoben, rom maT
So ris manZili ar icvleba (sur. 5). Seadare: erTnairia Tu ara dedamiwasTan da 1-l TviT-mfrinavTan dakavSirebul aTvlis sistemaSi TviTmfrinavebis
a) traeqtoria; b) gavlili manZili;g) koordinatebi; d) gadaadgileba;
maS ase, aTvlis sistemis arCevazea damokidebuli, anu fardobiTia meqani-kuri moZraobis maxasiaTeblebi: moZraobis traeqtoria, gavlili manZili, gadaadgileba.(swored gavlili manZilis fardobiTobaSia is saidumlo, romelic zenonis paradoqsis amoxsnaSi dagexmareba. scade!)
cda II saWiro xelsawyoebi: saxazavi, fan-
qari, rveulis furceli. samuSaos msvleloba:
dade magidaze rveulis furceli.
furclis zeda mxares dade saxazavi da Seecade, fanqari saxazavs hori-zontaluri mimarTulebiT gaayolo da imavdroulad saxazavi furcel-ze qveviT Caasrialo (sur. 3).
miuTiTe fanqris wveris gadaadgileba: a) furclis mimarT; b) saxazavis mimarT.
imsjele cdis Sedegze. gaakeTe daskvna: aris Tu ara damokidebuli gadaadgileba aTvlis
sistemis arCevaze?
sur. 3
X’O’
Y’
O X
Y
sur. 4
sur. 5.
1
XO
Y
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moZraobis fardobiToba. siCqareTa Sekreba 1.7
siCqareTa Sekreba
aris Tu ara siCqare fardobiTi? pasuxi am kiTxvaze yvela zemoT ganxiluli magaliTidanac Cans, Tumca siCqaris fardobiTobis ukeT gasagebad ganvixiloT martivi amocanebi, davakvirdeT erTi da imave sxeulis moZraobas aTvlis ori sxvadasxva sistemis mimarT, romlebic erTmaneTis mimarTac moZraoben.
ori avtomobili, romelTa siCqareebi dedamiwis mimarT 80 da 50 m/wmia, Semxvedri mimarTulebiT wrfivad da Tanabrad moZraobs gzatkecilze (sur. 6).vTqvaT, avtomobilebis moZraobas ori damkvirvebeli akvirdeba:erTi _ dedamiwaze O wertilSi uZravad mdgomi, xolo meore A avtomo-bilSi mjdomi. ganvixiloT B avtomobilis siCqare A-sTan dakavSirebul aTvlis sistemaSi(X’O’Y’). gansazRvreT dakvirvebis dawyebis momentSi dedamiwasTan dakavSirebul aTvlis sistemaSi (sur 6. ): a) avtomobilebis koordinatebi; b) avtomobilebs Soris manZili.
amocana 1
gaaanalizeT, ras gviCvenebs siCqaris ricxviTi mniSvneloba, anu ris tolia TiToeuli avtomobilis gadaadgileba 1 wm-Si. gansazRvreT 1 wmis Semdeg dedamiwasTan dakavSirebul aTvlis sistemaSi (sur 7):
a) avtomobilebis koordinatebi;b) avtomobilebs Soris manZili.
sur. 6. avtomobilebis mdebareoba dakvirvebis dawyebis momentSi.10 x, m
80 m/wm
B50 m/wm
AX’O’
Y’
O
Y
sur. 7. avtomobilebis mdebareoba 1 wm-is Semdeg.
10 x, m
80 m/wm
B50 m/wm
AX’O’
Y’
O
Y
daakvirdiT sur. 6-7-s da dafiqrdiT:
ra manZiliT uaxlovdebian avtomobilebi erTmaneTs 1wm-Si?
ris tolia siCqaris moduli, romliTac avtomobilebi erTmaneTs uaxlovdebian, anu B avtomobilis siCqaris moduli A-sTan dakavSirebul aTvlis sistemaSi (an piriqiT)? SeadareT im siCqares, romelic B avtomo-bils dedamiwis mimarT aqvs.
gaakeTeT daskvna: damokidebulia Tu ara siCqare aTvlis sistemis arCevaze?
dafiqrdiT, rogor gamoiTvleba B avtomobilis siCqaris moduli A -sTan dakavSirebul aTvlis sistemaSi anu avtomobilebis fardobiTi siCqare (siCqare, ra siCqariTac eCveneba moZravi B avtomobili A avtomo-
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1.7 moZraobis fardobiToba. siCqareTa Sekreba
+
erTi sxeulis fardobiTi siCqaris moduli meoris mimarT, roca isini erTi wrfis gaswvriv erTmaneTis Sesaxvedrad moZraoben, tolia dedamiwis mimarT maTi siCqareTa modulebis jamisa.
bilSi mjdom damkvirvebels, anu siCqare, ra siCqariTac avtomobilebi uaxlovdebian erTmaneTs)?
maS ase, siCqare fardobiTia: is damokidebulia aTvlis sistemis arCevaze.
ori avtomobili, romelTa siCqareebi dedamiwis mimarT 40 da 30 m/wmia, erTi mimarTulebiT wrfivad da Tanabrad moZraobs gzatkecilze.
(sur. 8).vTqvaT, maT moZraobas ori damkvirvebeli akvirdeba:erTi _ dedamiwaze O wertilSi uZravad mdgomi, xolo meore A av-
tomobilSi mjdomi.
gansazRvreT avtomobilebs Soris manZilis sawyisi mniSvneloba (sur. 8).
amocana 2
sur. 9. avtomobilebis mdebareoba 1 wmis Semdeg.
sur. 8. avtomobilebis mdebareoba dak-virvebis dawyebis momentSi.
O 10 x, m
40 m/wm
B30 m/wm
AX’O’
Y’Y
O 10 x, m
40 m/wm
B30 m/wm
AX’O’
Y’Y
gansazRvreT:
ra manZiliT Sordeba dedamiwaze myof damkvirvebels B avtomobili 1wm-Si?
ra manZiliT Sordeba imave damkvirvebels A avtomobili 1wm-Si?
avtomobilebis koordinatebi 1 wm-is Semdeg (sur. 9);
avtomobilebs Soris manZili 1 wm-is Semdeg. dafiqrdiT, ra sididiT mcirdeba 1wm-Si avtomobilebs Soris manZili?
ras SeamCnevs A avtomobilSi myofi damkvirvebeli: ra siCqariT uax-lovdeba mas B avtomobili, anu ris tolia avtomobilebis fardo-biTi siCqare? daakvirdiT, rogor gamoiTvleba is?
maS ase,
erTi sxeulis fardobiTi siCqaris moduli meoris mimarT, roca isini erTi wrfis gaswvriv erTi mimarTulebiT moZraoben, tolia dedamiwis mimarT maTi siCqareTa modulebis sxvaobis modulisa.
-
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moZraobis fardobiToba. siCqareTa Sekreba 1.7
axla ufro zogadi SemTxveva ganvixiloT.
daakvirdi sur.10-s: tivze myofi adamiani A wertilidan B wertilisken miemarTeba. vTqvaT, adamianis moZraobas akvirdeba ori damkvirvebeli: erTi, romelic napirze imy-ofeba O wertilSi da meore, romelic tivzea A wertilSi.
dafiqrdi romeli veqtori gamosaxavs:
amocana 3
Oa a
bb
sur. 10
adamianis gadaadgilebas tivze myofi damkvirveblisadmi (anu moZ-ravi aTvlis sistemis mimarT)?
adamianis gadaadgilebas napirze myofi damkvirveblisadmi (anu uZ-ravi aTvlis sistemis mimarT)?
tivis gadaadgilebas napirze myofi damkvirveblisadmi (anu moZravi aTvlis sistemis gadaadgilebas uZravis mimarT)?
klasikur meqanikaSi, romelic galileisa da niutonis Sromebs efuZneba da romlis safuZvlebsac Cvens axla vswavlobT, dro ar aris damokidebuli aTvlis sistemis arCevaze (ainStainis fardobiTobis Teoriis Tanaxmad ki dro fardo-biTia). amitom Tu (1)-li tolobis orive mxares t -ze gavyofT, miviRebT, rom
maS ase,
sxeulis (adamianis) gadaadgileba uZravi aTvlis sistemis (dedamiwis) mimarT tolia S1 da S2 gadaadgilebebis jamisa, sadac S1 sxeulis (adamianis) gadaadgilebaa moZravi aTvlis sistemis (tivis) mimarT, xolo S2 moZravi aTvlis sistemis (tivis) gadaadgilebaa uZravis (dedamiwis) mimarT.
S = S1 + S2 (1)
me-(2)-s siCqareTa Sekrebis formula ewodeba. maS ase, meqanikuri moZraobis damaxasiaTebeli kidev erTi sidide _ sxeulis
siCqare fardobiTi sididea. igi damokidebulia aTvlis sistemis arCevaze.
sxeulis v siCqare uZravi aTvlis sistemis mimarT ase gamoiTvleba
v = v1 + v2 (2)
sadac v1 sxeulis siCqarea moZravi aTvlis sistemis mimarT, xolo v2 moZravi aTvlis sistemis siCqarea uZravi aTvlis sistemis mimarT.