leqcia 3 - uCoz · ( man icis rom maimuni Camoxteba gasrolisTanave !) Physics 211: Lecture 1, Pg 38...
Transcript of leqcia 3 - uCoz · ( man icis rom maimuni Camoxteba gasrolisTanave !) Physics 211: Lecture 1, Pg 38...
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leqcia 3
Tavisufali vardna
veqtorebi
2-ganzomilebiani moZraoba
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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:
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TanabaraCqarebuli moZraobis modelireba
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Physics 211: Lecture 1, Pg 4
TavisufaliTavisufali vardnavardna
y
ay = − g
y 0yv = v - g t2
y00 tg21tvyy −+=
y
a
v
t
t
t
gay −=
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Physics 211: Lecture 1, Pg 5
Galileo Galilei (1564-1642)
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Physics 211: Lecture 1, Pg 6
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
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Tavisufali vardnis aCqarebis gazomvebi
gamoiyeneba geologiasa da geografiaSi
g -s ganawilebis ruqa aSS-s teritoriaze
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videofilmi Tavisufal vardnaze
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Physics 211: Lecture 1, Pg 9
vardnis dro da saboloo
siCqare ?
1000 m
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Physics 211: Lecture 1, Pg 10
avirCioT koordinatTa
sistema.aTvlis wertili damimarTuleba.
v0y = 0.
20y0 gt
21tvyy +=
20 gt
21yy −=
1000 m
y = 0
y
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Physics 211: Lecture 1, Pg 11
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
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Physics 211: Lecture 1, Pg 12
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.
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Physics 211: Lecture 1, Pg 13
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
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Physics 211: Lecture 1, Pg 14
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
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Physics 211: Lecture 1, Pg 15
SegviZliaSegviZlia pirdapirpirdapir gamoviyenoTgamoviyenoT formulaformula::
( )H0g2vv 20
2 −−=− )(1:1:
vv00
vv00
11 22
y = 0y = 0
( )H0g2vv 20
2 −−=− )(2:2:erTmaneTiserTmaneTis toliatolia !!!!
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moZraobis aRweramoZraobis aRwera
erTganzomilebiani
moZraoba
organzomilebiani
moZraoba
saWiroa
SemovitanoT
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Physics 211: Lecture 1, Pg 17
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
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Physics 211: Lecture 1, Pg 18
skalarebs aqvT mxolod sidide.
skalarebia: masa, moculoba, temperatura.
veqtorebs gaaCniaT sidide da mimarTuleba.
veqtorebia: siCqare, aCqareba, Zala.
veqtorebi da skalarebi
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Physics 211: Lecture 1, Pg 19
veqtorebiveqtorebi......
veqtorebis ori aRniSvna:
A A anan
A A =rA
rA
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SeiZleba gadavaadgiloT veqtorebi rogorcgvinda, magram unda SevinarCunoT sigrZe da
mimarTuleba !!
veqtorebis paraleluri gadatana
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Sekrebis Tanmimdevrobas mniSvneloba ara aqvs
veqtorebis grafikuli Sekreba
ganvixiloT ori veqtori AA and BB. movnaxoT maTi jami AA + BB.
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veqtorebis Sekrebis ilustracia
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Physics 2211: Lecture 5, Pg 23
1 2 3A A A+ +r r r
movZebnoT veqtorebis
jami
1 2 3 4 5
1Ar
2Ar
3Ar
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Physics 2211: Lecture 5, Pg 24
1 2 3A A A+ +r r r
1 2 3
t2
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Slide 24
t2 11128teacher; 25.08.2002
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Physics 2211: Lecture 5, Pg 25
veqtorebisveqtorebis gamravleba/gayofagamravleba/gayofa skalarzeskalarze
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Physics 2211: Lecture 5, Pg 26
kerZokerZo SemTxvevaSemTxveva, , gamravlebagamravleba --11--zeze
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Physics 2211: Lecture 5, Pg 27
magaliTebimagaliTebi: : veqtorebisveqtorebis skalarebzeskalarebze
gamravlebagamravleba
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Physics 2211: Lecture 5, Pg 28
2 A B−r r
1 2 3 4 5
airCieT swori pasuxi
Aur
Bur
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Physics 2211: Lecture 5, Pg 29
swori pasuxia (1)
1 2 3
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Physics 2211: Lecture 5, Pg 30
veqtorisveqtoris komponentebikomponentebi
veqtorisveqtoris komponentebikomponentebi arisaris veqtorisveqtoris
proeqciaproeqcia koordinatTakoordinatTa RerZebzeRerZebze
{xa
aya
y
xxauur
yauur
y
x
a
x ya a= +uur uur
a
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Physics 2211: Lecture 5, Pg 31
veqtorisveqtoris komponentebikomponentebi SeiZlebaSeiZleba iyosiyos
dadebiTidadebiTi an an uaryofiTiuaryofiTi..
b
y
x
by > 0
bx < 0
{}
y
xxbuur
ybuurb
b x yb b= +uur uur
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Physics 2211: Lecture 5, Pg 32
veqtoris sigrZe ar aris damokidebulimimarTulebaze
2 2x ya a a a= = +
rar
ya
xa x
y
absoluturi mniSvneloba (sigrZe) rr veqtorisamovnaxoT piTagoras Teoremis gamoyenebiT:
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Physics 2211: Lecture 5, Pg 33
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
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Physics 211: Lecture 1, Pg 34
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)
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Physics 211: Lecture 1, Pg 35
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
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Physics 211: Lecture 1, Pg 37
sad unda daumiznos zooparkis
TanamSromelma rom moartyas maimuns ?
( man icis rom maimuni Camoxteba gasrolisTanave ! )
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Physics 211: Lecture 1, Pg 38
gravitacia rom ar arsebobdes cxadia, rom
pirdapir unda daumiznos.
gravitaciis SemTxvevaSi mainc pirdapir
unda daumiznos. r = r0
r =v0t
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Physics 211: Lecture 1, Pg 39
rr = vv0 t - 1/2 gg t2
rr = r0 - 1/2 gg t2
bravo !
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Physics 211: Lecture 1, Pg 40
x x = = xx00
yy = -1/2 gg t2
igive situacia sxva perspeqtividan.
xx = = vv0 0 ttyy = -1/2 gg t2