leqcia 3 - uCoz · ( man icis rom maimuni Camoxteba gasrolisTanave !) Physics 211: Lecture 1, Pg 38 zgravitacia rom ar arsebobdes cxadia, rom pirdapir unda daumiznos. zgravitaciis

leqcia 3

Tavisufali vardna

veqtorebi

2-ganzomilebiani moZraoba

Physics 211: Lecture 1, Pg 2

mudmivi aCqarebis SemTxvevaSi Cven vnaxeT:

atvv 0 +=

200 at

21tvxx ++=

consta =

x

a

v t

t

t

v)(v21v

)x2a(xvv

0av

020

2

+=

−=−

sasargeblo formulebi:

TanabaraCqarebuli moZraobis modelireba


TavisufaliTavisufali vardnavardna

y

ay = − g

y 0yv = v - g t2

y00 tg21tvyy −+=

y

a

v

t

t

t

gay −=


Galileo Galilei (1564-1642)


g ar aris damokidebuli sxeulis masaze !

Galileo Galilei (1564-1642)

g = 9.81 m/s2

ekvatorze g = 9.78 m/s2

CrdiloeT polusze g = 9.83 m/s2

Tavisufali vardnis aCqarebis gazomvebi

gamoiyeneba geologiasa da geografiaSi

g -s ganawilebis ruqa aSS-s teritoriaze

videofilmi Tavisufal vardnaze


vardnis dro da saboloo

siCqare ?

1000 m


avirCioT koordinatTa

sistema.aTvlis wertili damimarTuleba.

v0y = 0.

20y0 gt

21tvyy +=

20 gt

21yy −=

1000 m

y = 0

y


y = 0 da y0 = 1000 m.

gavixsenoT:y0 = 1000 m

y

2.14gy2t 0 ==

20 gt

21yy -=

y = 0

)( 02

y02y yya2vv -- =

140gy2v 0y −=±= m/wm

wm


ormoSi vagdebT qvas da vzomavT drosromelic dasWirdeba qvas ormos fskerismisaRwevad.

Tu y RerZs mivmarTavT qveviT:

y0=0 ; v0y = 0.

20y0 gt

21tvyy ++=

2gt21y =

amocana: rogor ganvsazRvroT ormos siRrme

vTqvaT t=3 wm.maSin y≈45 m.


oriori adamianiadamiani dgasdgas simaRlezesimaRleze HH. . oriveorive isvrisisvris

burTsburTs sawyisisawyisi siCqariTsiCqariT vv00, , pirvelipirveli isvrisisvris qveviTqveviT

dada meoremeore isvrisisvris zeviTzeviT. . burTebisburTebis siCqaresiCqare miwazemiwaze

davardnisasdavardnisas arisaris vvAA dada vvBB .. romeliromeli pasuxiapasuxia

sworiswori: :

(a)(a) vvAA < < vvBB (b) (b) vvAA = = vvBB (c) (c) vvAA > > vvBB

vv00

vv00

2211

HHvvAA vvBB


radgan moZraoba zeviT da qveviT simetriulia,

intuicia gckarnaxobs rom v = v0

marTlac, SegviZlia vnaxoT:

vv002 2

HH

vv = v= v00

( ) 0HHg2vv 20

2 =−−=− )(

y = 0y = 0


SegviZliaSegviZlia pirdapirpirdapir gamoviyenoTgamoviyenoT formulaformula::

( )H0g2vv 20

2 −−=− )(1:1:

vv00

vv00

11 22

y = 0y = 0

( )H0g2vv 20

2 −−=− )(2:2:erTmaneTiserTmaneTis toliatolia !!!!

moZraobis aRweramoZraobis aRwera

erTganzomilebiani

moZraoba

organzomilebiani

moZraoba

saWiroa

SemovitanoT


veqtorebiveqtorebi ((mimoxilvamimoxilva))::1 ganzomilebaSi mimarTulebas avRniSnavdiT + an –niSniT.

2 an 3 ganzomilebaSi ar aris sakmarisi niSnismiTiTeba:

magaliTisaTvis ganvixiloT mdebareobis veqtori rr2 ganzomilebaSi.

kiTxvakiTxva: sad aris rusTavi?avirCioT aTvlis wertili

TbilisSi

unda mivuTiToT aramarto manZili aramed

mimarTulebac.

Tbilisi

rusTavi

r r


skalarebs aqvT mxolod sidide.

skalarebia: masa, moculoba, temperatura.

veqtorebs gaaCniaT sidide da mimarTuleba.

veqtorebia: siCqare, aCqareba, Zala.

veqtorebi da skalarebi


veqtorebiveqtorebi......

veqtorebis ori aRniSvna:

A A anan

A A =rA

rA

SeiZleba gadavaadgiloT veqtorebi rogorcgvinda, magram unda SevinarCunoT sigrZe da

mimarTuleba !!

veqtorebis paraleluri gadatana

Sekrebis Tanmimdevrobas mniSvneloba ara aqvs

veqtorebis grafikuli Sekreba

ganvixiloT ori veqtori AA and BB. movnaxoT maTi jami AA + BB.

veqtorebis Sekrebis ilustracia


1 2 3A A A+ +r r r

movZebnoT veqtorebis

jami

1 2 3 4 5

1Ar

2Ar

3Ar


1 2 3A A A+ +r r r

1 2 3

t2

Slide 24

t2 11128teacher; 25.08.2002


veqtorebisveqtorebis gamravleba/gayofagamravleba/gayofa skalarzeskalarze


kerZokerZo SemTxvevaSemTxveva, , gamravlebagamravleba --11--zeze


magaliTebimagaliTebi: : veqtorebisveqtorebis skalarebzeskalarebze

gamravlebagamravleba


2 A B−r r

1 2 3 4 5

airCieT swori pasuxi

Aur

Bur


swori pasuxia (1)

1 2 3


veqtorisveqtoris komponentebikomponentebi

veqtorisveqtoris komponentebikomponentebi arisaris veqtorisveqtoris

proeqciaproeqcia koordinatTakoordinatTa RerZebzeRerZebze

{xa

aya

y

xxauur

yauur

y

x

a

x ya a= +uur uur

a


veqtorisveqtoris komponentebikomponentebi SeiZlebaSeiZleba iyosiyos

dadebiTidadebiTi an an uaryofiTiuaryofiTi..

b

y

x

by > 0

bx < 0

{}

y

xxbuur

ybuurb

b x yb b= +uur uur


veqtoris sigrZe ar aris damokidebulimimarTulebaze

2 2x ya a a a= = +

rar

ya

xa x

y

absoluturi mniSvneloba (sigrZe) rr veqtorisamovnaxoT piTagoras Teoremis gamoyenebiT:


trigonometriistrigonometriis meSveobiTmeSveobiT veqtorisveqtoris

komponentebiskomponentebis monaxvamonaxva

θ

ar

ya

xa x

y

cossin

x

y

a aa a

θθ

==

ay = ax tan θ

tan θ = ay/ax


33--ganzomilebiani ganzomilebiani kinematikakinematika

sxeulis mdebareoba, siCqare da aCqareba

3 ganzomilebaSi:

rr = x + y + zvv = vx + vy + vz

aa = ax + ay + az

mudmivi aCqarebis SemTxvevaSi:

aa = constvv = vv0 + a a trr = rr0 + vv0 t + 1/2 aa t2

(sadac aa, vv, vv0, rr, rr0, veqtorebia)


romeli burTi davardeba miwaze ufro adre ?

a) pirveli

b) meorec) erTdroulad

1 2

h h

y=y0+v0yt-gt2/2v0y=0 da y=0t=(2y0/g)1/2

dro ar aris damokidebuli v0x-ze

moZraoba x da y RerZebis gaswvriv

SegviZlia ganvixiloT

erTmaneTisagan damoukideblad !

22--ganzomilebiani ganzomilebiani moZraobamoZraoba


sad unda daumiznos zooparkis

TanamSromelma rom moartyas maimuns ?

( man icis rom maimuni Camoxteba gasrolisTanave ! )


gravitacia rom ar arsebobdes cxadia, rom

pirdapir unda daumiznos.

gravitaciis SemTxvevaSi mainc pirdapir

unda daumiznos. r = r0

r =v0t


rr = vv0 t - 1/2 gg t2

rr = r0 - 1/2 gg t2

bravo !


x x = = xx00

yy = -1/2 gg t2

igive situacia sxva perspeqtividan.

xx = = vv0 0 ttyy = -1/2 gg t2

Documents

leqcia 3 - uCoz · ( man icis rom maimuni Camoxteba gasrolisTanave !) Physics 211: Lecture 1, Pg 38 zgravitacia rom ar arsebobdes cxadia, rom pirdapir unda daumiznos. zgravitaciis