fizik 1 fasle 1 - dl.esfand.orgdl.esfand.org/get/sanaye/fizik 1/fizik 1 a.pdf · 1) fx t1cos30...
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1:
1 (: ( :
.(kg)(m)(s).
( : .)
m/s ()kg/m.(
2 (:.
(km/h m/s) ..
(m/s km/h):
.
E1018d10-1
P1015c10-2
T1012m10-3
G109µ10-6
M106n10-9
k103p10-12
h102f10-15
da101a10-18
3 (10:
(10 :10 .0.000,000,000,3
3 10-100.000,000,000,000,0055 10-15.105 10-15
5fm
(:15.6m2%)0.3 (
15.3m15.9m15.6 0.3m . .
15.6.
:1-10
.0.0025604256.0 10-5
2-1200012000.06.3-
.:
36.479´ 2.614.58 = 6.387 = 6.4
4-.17.524+ 2.4 - 3.56= 16.364= 16.4
4 (: .
.
C A2 B2 2 ABcos
.O43.A
•
B•.
OPC•
)C• (A
•B•.
C A B :
)22 BAC += (C•5
.BABA +≠+
••
⇔+=+ BABA••
:.
: .
.
:)1 A B B A
)2 A B C A B C
Qomit.b
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C A2 B2 2 ABcos
.A B A B
:)BA••
−(B•
A•.
:A B B A
.A•)A,(
)2007/10/13 (.
AX AcosAY Asin
A Ax2 Ay2
tan AyAx
. :A
•B•.
Ay AsinBy Bsin
Ax AcosBx Bcos
Rx Ax BxRy Ay By
R Rx2 Ry2
Qomit.b
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ijk
xyz ..
i j k 1
.A Ax i Ay j Az k
A Ax2 Ay2 Az2 . :.
A B Ax i Ay j Azk Bx i Byj Bz kAx Bx, Ay By, Bz Bz
:
.)1 A.B ABcos
)2 A.B Axi Ay j Az k . Bxi Byj BzkAx Bx Ay By Az Bz
Qomit.b
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:
1(B.A A.B
2(A. B C A.B A.C
3(A.B AB A.A A2
4(90A.B 0
:A•
B•
cos A.BAB
cos Ax Bx Ay By Az BzAx2 Ay2 Az2 Bx2 By2 Bz2
:) (A
•B•A B ABsin n
.
.
:A•
B•.
1(A B B A
2 (B A A B
3 (A B C A B B C
4 (A B AyBz AzBy i AzBx AxBz j AxBy AyBx kQom
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:A A 0
i j=k j i=-k i i=0j k=i k j=-i j j=0k i=j i k=-j k k=0
.
A BiAx
jAy
Bx By
kAzBz
Qomit.b
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3:
:. :
.x x2 x1
:
:.v x
t
:-v da
dt
:nmv1a
bv2
:1v
mnv1
bav2
:a v
t
: .va.
t.v v1 v2
2
Qomit.b
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com
ü-tv.
:
x vt x0
v at v0
x v0 v2 t
x x012 v0 v t
x 12 a 2 t 1 v0 n
v22 v12 2 a x
x 12 at2 v0 t x0
:ag
.Qomit.b
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:ü.
t t1 t22
üt1t2tt t1 t2
2üv=0.
:v v0 gt
y v022 g
y y012 v0 v t
t v0g
y y0 v0 t12 gt2
v22 v12 2 g yQomit.b
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4: :
) (.
::
r xi yj zkP1r1P2r2:
r r2 r1 xi yj zk.
v rt
v limt 0rt
d rdt vxi vy j vz k
:vx dx
dt, vydydt, vz
dzdt
:
a drdt axi ayj az k
Qomit.b
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com
:
:v v1, v2, v3r r1, r2, r3v v0 a t
r r012 v0 v1 t
r r0 v0t12 at2
)v.v v2 (:
v2 v02 2a. r r0)x,y (4x4y
.
vx v0x ax t vy v0y ay tx x0
12 v0x vx t y y0
12 v0y vy t
x x0 v0xt 12 ax t y y0 v0yt 1
2 ay t
vx2 v0x2 2ax x x0 vy2 v0y2 2ay y y0
:
.
)v-x=v0x
(.)vy=v0y-gt
.(.
Qomit.b
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:ax 0 , ay g
:1 (:
a)
b)
c)
2 (:d)
e)
f)
3 (:
oscvxt
0
=e:
g)
4 (:vy=0:
h) y e
i) f
:vy=0vx:v v0cos
y tan x g2 v0cos 2 x2
t v0 sing
h v02 sin22g
v0x v0 cosv0y v0 sinvy v0 sin gt
x v0x.t x v0cos .t
y y0 v0y.t12 gt2 y y0 v0 sin
12 gt2
vy2 v0y2 2g y y0 :vy v0sin gtv0y v0 sin
Qomit.b
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T 2 t 2v0 sing
aA g aaB g aaC g2 a2
:
hgsin0v
:
d:
R v0cos 2v0sing R v02 sin2
g :
2sin .cos sin2:
:2
=+
:45.
:
:
A:vA vB vC tA tB tC
:sin =0cos =1.
tan vyvx
Qomit.b
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5:1:
.
:.
F ma
:.:
:
:mMr
F GmMr2
rG
G 6.67 10 11 N.m2kg2
mmgW =
W GmMERE2
g GMERE2
:
) (.
Qomit.b
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1) Fx T1 cos30 T2 cos45 0 T1 cos30 T2 cos45
2) Fx T1 sin30 T2 sin45 W 0 T1 sin30 T2 sin45 W
1T2
T1 cos30cos45 1 22 T12
.
:kg6020. (
F maFx mgsin ma gsin a
9.8 sin20 a 3.3 m s2Fy N mgcos 0
(N mgcos 0 N mgcos 550 N
:ABkgmA4102.1 ×=kgmB
3108×=
.kg5100F22 sm.
(0FF ma
F0 mA mB aF0 1.2 104 0.8 104 2 4 104
(BA
ABBA
.FAB FBA
Qomit.b
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:F0 FAB mA a FAB 1.2 104 2 4 104
fAB 1.6 104:
FBA mB a 0.8 104 2 1.6 104
:.
:mgW =
.
mgW =
)( agmW +=
)( agmW −=
)( agmW −=
)( agmW +=
Qomit.b
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:
.rrva ˆ
2
−=•v
r.:
ntT = :
T2
= rv =
:F ma F m v2
r.
:.
):(cosmgFT R +=
mgRF.mg T FR T FR mg
1180cos −=°:T FR mg
T FR T FR mg
T.
: . .
m2s2.)102 =n ()10=g(
Qomit.b
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.T 2 sr 2 m
2T
v rs ?
fs mg fs s NN FR FR m v2
r m 2 r m 2 r N m 2 rfs mg s N mg s m 2 r mgs
g2 r
1010 2 0.5
:sR fF =.
:.
NsinNcos
m v2R
mg tan v2Rg
:) (
.mM
G.
rGMv =
: ..
Nsin FR FR m v2R
Ncos mg
r Re hF ma GmM
r2 m v2rQom
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m
:
. .
..
:
W FScosFS =
.mnj 11 =
:)F ()F () (.
:.90 W FScos90 F.S. 0 0
:) (.
:ABAB
BA.
FAB FBA WAB WBA
Qomit.b
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kF . .KFS180.°=180
WF FK Scos FK S .0F
.
ABBA .ABA
.
):if(S
:
hyy if −=−g−.Wg mg yf yi mgh
mghWg −=mghWg =.
:kg40m20°= 15
.NT 250=°= 30 .1.0=k
Qomit.b
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: .∑ = 0yF
N mgcos Tsin 397 125 254NNNf 4.25==.cosFSW =:
WT T.s Tscos30 4330jWf f.s fscos180 fs 508jWN N.s 0Wg mg.s mgscos 90 15 2030j
W WT Wf WN Wg 1.79kj
.
: :Fx:
:)sF (:
) (Fs kx
kx.ifixfx
Ws12 k xf2 xi2 Ws
12 Ff xf
12 Fi xi
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) ( kxF +=
:..
Wa bxa
xbFxdxFx
.Wa b Wb a
ixfx:Ws
xi
xf kx dx 12 k xf2 xi2
:Fx∆
W F x ma x:
vf2 vi2 2a x
W 12 mvf2
12 mvi2
K.K 1
2 mv2
:W K
. :
.
Qomit.b
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:.
:P W
tSIsj) (().
:P F.v
. :hp).Whp 7461 =(
:3r•
zyx ,,.dW F.ds
WA BABF.ds
ABFcos ds
:WA B
ABFxdx
ABFydy
ABFzdz
:F.ds
A
Bmg.dsyA
yBmgdy mg yB YA.
:F
0 .FQom
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: .:
Fx F Tsin 0Fy Tcos mg 0
T
)(i F mgtanF .
xFF = .sd•
jdyidxsd•••
+= .dW F.ds Fxdx
)(ii mgtan dxdxdy=tandxdy tan=)(ii
mgdydw = .W
0y0mgdy mgy0
mg L Lcos 0 mgL 1 cos 0L .
)cos1( 00 −= LyQomit.b
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::
.
:.
:.
W U Uf Ui0=U
..
:.
)( ifg yymgW −−=)(21 2
122 xxkW −−=
0=W. :.
: .mghWg −=mghWg += .
0=gW .fdWf −=fdWf −=
fdWf 2−=. :.
WA B WB A 0:.
W1 W2 :
.
Qomit.b
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:.
UW ∆=0=∆K.))ExW ()CW((
.0=+ CEx WWExC WW −=
.Wc U Uf Ui
:.3 : .
) (:
dU dWC FC.dsAB.
UB UA ABFC.ds
: ..
: .
miyfy:Wg mg yf yi
CW)( ifg UUUgW −−=∆−=:Ug mgh
ixfx
Us 12 kx2
:Kf UF Ki Ui
:E
)UKE += (.Ef Ei 0 Ef Ei
Qomit.b
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K 12 mv2 , U mgh
12 mvf2 mghf 1
2 mvi2 mghi
:
E 12 mv2 mgh
.12 mvf2 mghf
12 mvi2 mghi
H
mghU =
KUE +=
.
.12 mvmax2 mgh
: .Ax =
max
2
21 kxE =
.UKE += .0=x2
max21 mvE = .
A−)(
:1 (
) (.
Qomit.b
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2 (iiff UKUK +=+
)0=U (.3 (0=∆+∆ UK
..
:kgm 8.0=mNk 20=
.cm12
( (cm8
( (
: (0=x
12 kA2 1
2 mvmax2 vmax km A 0.6m s
(0 1
2 kA2 12 mv2 1
2 kx2
v k A2 x2m
mA 12.0=mx 08.0−=smv 45.0±= . .
mx 08.0+=
(EUk21
== .
U 12 kx2 1
212 kA2 x A
20.085m
Qomit.b
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T mgcos mv2L
E 12 mv2 mgL 1 cos
(smvv 03.021
max ±==).(222
21
21
21 mvkxkA +=
x kA2 mv2k 0.1m
.
:mL 2=kgm 2= .°= 35smv 2.1= .
: ( (
: . .)y (:
)(i
. . .
y L Lcos) (
)(ii
12 2kg 1.2m s 2 2kg 9.8m s2 2m 1 0.82 8.5j
(0= .)(ii
E 12 mvmax2 0
jE 5.8=smv 9.2±= .)(i
T mgcos mv2L 19.6 8.5 28.1N
Qomit.b
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( 0=v )(ii
E 0 mgL 1 cos max
jE 5.8=783.0cos max = .)0=v
()(i.T mgcos 15.3 N
:)
( ..
- .
W WC WNC KWNC K U
CWNCW.EUK ∆=∆+∆:
E Ef Ei WNC
.
:mk
. .F
.f .-
.
:0=x .0=x
.0=iE
Ef K Ug Us 12 mv2 mgh 1
2 kx2
sinxh =.Ff .
Qomit.b
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WNC Fxcos fx-:
E Ef Ei WNC12 mv2 mgxsin 1
2 kx2 Fxcos fx
:kg2.0mN50
cm20 .cm50
. ( (
:gU)0=x ( ..
E K Ug Us(iKfK.mA 2.0=md 5.0=2002/01/02 .:
Ei12 kA2 , Ef mgdsin
:mgdsin 1
2 kA2 fd
Nf 82.0=. (iEfE0=x
Ef 12 mv2 mgAsin
12 mv2 mgAsin 1
2 kA2 fA
smv 45.2=.
: .
sdFdWdU CC••
.−=−=CF•
sd•2002/01/02dU.
dU FC.ds