ΗΛΙΑΣΚΟΣ ΦΡΟΝΤΙΣΤΗΡΙΑ ΥΠΗΡΕΣΙΕΣ ΠΑΙΔΕΙΑΣ ΥΨΗΛΟΥ ΕΠΙΠΕΔΟΥ Θετικής - Τεχνολογικής Κατεύθυνσης Φυσική Γ Λυκείου Επιμέλεια: ΘΕΟΛΟΓΟΣ ΤΣΙΑΡΔΑΚΛΗΣ e-mail: info@iliaskos.gr www.iliaskos.gr
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f= f= f t+ 0 ) max t+ 0 max - max t+ 0 ) max = - x ± F=-Dx D=m 3
f= K= m U= Dx K+U=E= =U max =K max 4
t) i=- Q t) t) t i=+i. i=± U B = Li U E = U E +U B =E= =U,max =U E,max T= f= = L-C L-C L-C 5
F =-b 0 t= = = = =. 0 x =A t x =A t x=x +x x=at + + x =A tx =A t x=x +x x=a ) ) 1 R 2 f = ( 6
1.1 x x x x x=- x<0 x=0 x>0 x=+ A 7
s f sec H f= t N t f f= T 1 Hz 2 f f= f= s rad/s 8
x=a 0 0 x rad 0 t H rad t rad 0 t 0 9
1.2 1.2.1 x= 0 1.2.2 u=u max 0 u max u=0 =max u=0 u<0 u>0 u<0 u>0 x=- x<0 x=0 x>0 x=+ 0
u=u max u max 2 x=a = = t + 2 - t = 2 rad u= 2 A 2 x 1.2.3 - max 0 max 2 0 - max max x=a
= = t + - t = rad - max - x=a - 2 x a =max =0 a =max >0 <0 x x x=- x<0 x=0 x>0 x=+ 2 max 2 u u 1.2.4 m
- -m x m D -Dx D m - D=k D D=m 2 D=m 2 2 D=m 2 2 m m T D D m - max 0 -m max 0 - max 0
1.2.5-2 A - - 2 A - - -DA - 0 x T -A
u T/2-2 T/2 0-2 T/2 T -DA
1.3 x -Dx - D=k k
1.4 1.4.1 1 2 = mu 2 1 2 max = mu max 2 1 2 1 mu K m u 2 2 2 max t 0 2 2 t mu 2 max t max 1.4.2 0 1 U Dx 2 2 U 1 2 U=U max = DA 2 1 2 0
1 2 1 U Dx U D 2 2 2 U U t max 0 2 2 2 At U DA t 0 1 2 0 max =U max A K max 1 mu 2 2 max 1 m 2 1 2 1 2 2 2 2 2 m DA U max 1.4.3 = DA mu max E K max U max
1.4.4 0 1 DA 2 2 E K=U U TT3T T U= 2 1 Dx 2 K=E-U K=E- 1 Dx 2 2 E K U -A O +A x
1 2 1 E mu 2 U=E- mu 2 2 E K U u -u ma 0 +u max 1.5 du 1. dt du = dt dp 2. dt
dp = dt dp = - dt dp dt dk 3. dt dt dk dw F dk = dt dw F F. = dt dtdx dx = dt dk = dt du 4. dt K+U=E dk+du=0 dk=-du du dk dt dt
1.6 E W W W = 2 1 mu - 2 1 mu W W W = U -U = Dx - Dx 1.7 1. % =. 100% 2. Ti % =. 100% 3. x dp/dt U
p dk/dt du/dt 4. x =-kx l =kl x l xl U= kx U = kl
5. 6. m m k D=km +m D =m D =m D=D +D
1. s rad/s rad/s 2. 3. 4.
5. H 6. 7. 8. x=0
9. 10. 11. 2 max 12. m/s 2-0
13. m/s - 0s ts =- =0 14. - 15. -
16. - 17. 18. 19. s Hz s rad/s 20. 21. mkg - t SI xtsi
s s tsi 22. xm cm s max m/s 0 s max m/s 23. + max s s s s - max
s 24. - 0 N/m N m - x=-m xm 25. rad xm - 0 s -x SI s s s
26. m 27. 28. 2 A 2 x 29. A 3 x= 2
30. t=t 31. m t rad rad t 2. t= 2 t= 32. m/s 0 s - ts
t=8s 33. xt + SI Hz rad/s m/s
=T/4. H D=m. 2 D m D = fhz. = =
iii = =0. + = = ± 1. mkg m fhz t 2 3 max N 11 -t+ 6 2. max m/s max m/s t x m t t -t+
3. H t+ 2 SI ts -m/s 4. t=0 x = 3 m m/s t x m =- t SI -t SI 3 m/s 5. m fhz t x 2 m xm 6. mkg dm ts t N x =-m
Kgm/s t SI -t SIN m/s 37,5 m/s 7. m t x 2 m ts xt+ 4 t+ 4 - t+ 4 8. mkg dm t xm - 3 m/s x t - s 9. m Kg m rad/s t x
t 10. t=0 11. mkg m f z t x x t U=8x K-8x U- t U t 12. mkg N t N t=0 ts
U t ±3m/ =-t 13. s t x x A 3 x=- 2 ts 14. m fhz t x cm t s 15. H mkg max t SI U max t=t 3 m/s A max - 2 m/s = = 80 m/s
16. mkg H =-xsi max m/s t=0 = 2/2 x=t 17. m kn/m t s t t x t=0 m/s t s Kg 3 m/s /s
= =. =. =E 18. 0 km mkg t 2 m/s Sm gm/s 2-2 t t= s 60 =- N 19. mkg N/m 0 m/s
k m K U 20. m mkg 2 m/s gm/s max N U max U max =8
21. mkg k x m dm t=0 t =T gm/s O s W U =9 U 22. mkg d t t=0 m t+ 2 SI 23. mkg kn/m
dm t x - 24. m mkg t=0 k d k N N m E 3 m/s
=E + = + = 25. mkg km x 3 m t m/s x =- xt SI t SI -t SIW
26. m kg m kg hm m m m 1 m 2, =, + = ( + ). + = + =
= =. =. 27. hm m Kg m Kg m m 3/4 m gm/s xm
28. g mg t m/s t s m/s 3 m Kgm/s 29. km mkg u 0 m/s t=0 mu 0 Mk
m/s - 30. km mkg t=0 M P Kgm/s m 1 Ts gm/s kg m/s 2 m 2 t
31. Kg kn/m mkg t 0 gm/s 3 m/s -t 32. Kg kn/cm mkg 0 hm m 0
gm/s 0 13 m/s 33. k=800n/m xm mkg t k. 1 m g m/s m 3 Kgm/s 34. m Kg kn/m hm m m =Kg 0 m/s m t
m t gm/s A- ±20 35. m Kg k m Kg m h Sm h m 1 A m 2 k
h m A /m 36. g hm mkg 0 m/s m k 37. m Kg m Sm m Kg m/s k m 1 S 0 m 2
gm/s dm 38. kn/m m Kg h h 39. Kg k=800n/m xm m=8kg u m/s
t g m/s m/s x 2 t+ 40. m Kg kn/m dm t m Kg / g m/s - m/s 2 m - 2 -/s
41. m Kg N/m 2 1 k d 1 m m d 3 m m g m m 42. m g km m
m 3 m m Kg m/s m 2 1 m 2 m 1 k x/2 x m t p kgm/s - t 3 t 43. g k N/m m x2m m m/s m
t=0 m Kg x2 t SIt s 44. m Kg k N/m m m Kg 3 m/s m ±10N 45. m Kg km
m m g u m/s m 1 u 1 m 2 k A t s xt
46. k x m x 47. Kg kn/m t=0 hm t=t gm/s dm
48. Kg mkg m m t=0 3m/s -
O q V C. q C (1 Farad) V C 1 q 2 C U E 2 1 CV 2 1 U E 2 U 2 E qv V Q=C.V Q=C.E 63
di E L dt L Henry) di s) dt Lenz i - i - V L V L = E 64
1 U Li 2 B 2 LC Thomson T 2 LC 1 1 2 f= T 2 LC 1. LC t qq i t q Qt t=0. t q i t 3 q Qt q Q t 2 65
t qq i t t Q t=0. t q i t i It 3 t 2 - t qq i q Qt q Qt 2 t i I t i q t t 2 2 2 T 4 66
-q=qt Q q t T -Q -i=-it I i t T -I 67
2 1 q U E 2 C 2 1 Q U E,max 2 C 2 1 q 1 U E U E 2 C 2 2 2 Qt 1 Q 2 U E t C 2 C 1 U Li 2 B 2 1 U 2 B max LI 2 1 Li 2 U 2 B U L I t 2 B 1 1 U B LI 2 2 t 2 2 68
U E + U B U E,max =U B,max t q=q i E 2 Q 1 2 C 1 2 LI 2 U E U E =U B U B T/4 T/2 3T/4 T t 1 q, U B E 2 C U E 2 1 q 2 2 C 69
E U B U E q -Q O Q 1 2 E U B Li, U E =E - 2 E 1 Li 2 2 U B U E i -I I 70
dq i dt E di L dt di dt E L di VL dt L (1) V L =V C. (2) q di V q C C di 2 dt L L LC dt 1 2 1 LC LC q q C VC V C q 1 dv d q dv i C 1 C dvc d q C C dt C dt dt C 71
V L =V C. dv i L dvc dvl dvl dvc dt dt dt C du dt du dt E E q Qt It PC VCi i C C QI 2t 2C QI t. t C du B du E U E U B E du E du B 0 du B du E dt dt du B QI 2t dt 2C 72
L-C L-C, L-C f f ff 2 2 2 L-C I i= 2 3 1 2 L-C 73
Q Q Q 3 q= q= q= 2 4 2 Q 2 q= 2 L-C.Q.Q i= i= i=.q. 2 2 2 LC t=0-74
i 0 T T t T 3T t t=t L-C V, V L-C Q q=+q I 3 i=. 2 L-C, A B C A C B =2 C A 75
L A L B = L A. 2 Q Q t q=+q q=qt L-C C A =2C B U E 100 25 B A -Q 0 +Q q 76
q t T B T A C V L 77
q U E U B Q/4 Q/3 4 Q LC L F V C t) (S.I L L H q=10-3 t i=-t) LC L T=2.10-3 st Q=4.10-4 C t 1 78
t 2 = t 1 +T U E U B t 2 t 2 U A) t 1 =0,5.10-3 s ) q=-2 3.10-4 E C ) =3 ) i=+0,2 A U B CF V=400V t s. t s 2 =10. ) U E =0,02J ) dq 8 3.10 dt 3 C / s LC L=1mH CF t -4 C. q=f(t i=f(t). t 1 = 4.10-4 s. 3 t 2 =.10-4 s. 4 A q=2.10-4 4 t (S.I), i=- 4 t (S.I) V c =10 2 V V L 4 t (S.I) LC -3 s 79
q=qt t 1-2 s q 1 =+10-4 C CF. q=+ 3.10-4 C. V. ) i=-0,1500t (S.I) ) i= 5. 10-2 A ) q=+10-4 C LC t 1 i 1 =20mA q 1 C t 2 i 2 =10mA q 2 C. -5 s V -3 Ct L=20mH t=t i=-1a. U E =f(t U B =f(t)) U B =3U E AV=20V U E -2 2 500t, U B -2 2 500t ts, LC QC t 80
ms t U E =U B ) q=+120c, ) i=-240 3 ma, ) - t q=+q i QC CF t =10-4 s t ) =4.10-4 s, L=0,02H ) q=+2,5.10-5 s, i=-0,1253 A LC -4 s i=-t (S.I J t 1 = 6.10-4 s i 1 =+4A - ) dv C 6 ) di / dt =5.10 4 81
CF V L=5mH LC 3.10-4 s -4 s.10-4 s 2 2 ) du B dt=50 3 Js ) (du E max V=40V t=0 U E -2 (1-i 2 ) (SI). t=t s. t=5t s. -3 s U E -2 J, ) V L =-20 3 V LC 3 V f z 82
dv C dt =10 3 Vs r, R, C L=2H 1 2 1 J 1 2 LC f z 1 2 r C L R C=0,5F E=1V i=-t (S.I) U E =q 2 (S.I) V, r R 1 R 2 CF L=10mH 1 2 1 t 83
2 LC. R 1 1 2 r R 2 C L Q q 4 A ) Q=64C, I=0,32A, ) q=645000t (C), i=-0,325000t (SI), ) i= 0,08 15 A L=4mH V r CF R t 84
r C L R L-C t 1 ) =32.10-3 J ) i=45.10 3 t (S.I), q=8.10-4 5.10 3 t (S.I) ) U E =1 U B V, r R L=6,25mH t 85
R 1 2 E,r L C 0 mc. q=f(ti=f(t LC max. C max Fit (SI) V c t (SI), q=10-3 t (SI), C 1 F C 2 F C 1 1 2 C 1 C 2 L t LC 1 86
s t 1-3 s LC 2. LC 2 Q=4.10-5 C U B,max =2.10-4 J B 2 =1,5.10-4 J Q 3.10-5 C 87
F =-b b F= F +F F=-Dx-b F=m -Dx bm 88
0 e -t tt t tt bm b b A0 A1 T... e. A A 1 2 89
R Joule Q =Q 0 e -t tt Q t Q tt R L 2 L R 0 e -t tt
t tt R R L 2 L b R F =-bu b e - t
L-C R e - t 2 0 A t=tt=lntln t=lnt e - t A0 2 /8 e - t t ln 2 2ln 2 3ln 2 3ln 2 t= t= t= t= 3 2
e - t ln 2 t t= /4 /4 - F =-bu b b b k m F k m g
F F = = = / = / e 0 ln 2 t = t A0 A0 e 2 t 1 1 t / 2 e e 2 2 1 / 2 1 t / 2 t 1/ 2 ln 2 94
=. t 2 1 2 2t 2t A e E DA e E E e 1 2 1 E DA E D 0 0 0 2 2 2 e -lnt tt T T s e -t
s e -4t SI m t lns e ln m s mkg e -t SI t J t t =4t t t t m s m k N/m rad/s e -lnt N
m J e -t t=nt =8J t s t t tt - A A N N1 mkg F=-x-u SI x t m N b t x m/s m/s x t t =- -
CF VV LmH i ii 2)/2 mkg k d m i gm/s ii xm sec ln q=±2-4 C B l - m dk/dt s - 98
= = = 99
F=F 0 t F =-Dx F =-b F=F 0 t F m F F' F m Dx bu F t m 0 D=m D=m b max 0 f 0 f f =f max b
L-C f 0 2 R-L-C R-L- C 1 LC
R max 0 f 0 f f =f max R
- -
- kn/m m=4kg s RLC = R - b
RLC R
f f =f - F =. =. =.. =. =... () =
Joule R Joule = =.. = / R A R B,, = LC = LC LC =
mkg N/m m Hz mkg m k N/m f Hz t f Hz Hz m Kg =- J CF L mh L mh R 4
R L 1 C L 2 L -C t ima t - s B t - s Joule Q - C i - t SI q - t SI du/dt=. 10 / BQ - J
x 1 =A 1 t x 2 =A 2 t+ x x x=x 1 +x 2 1 2 1 2 x=at = 2 2 A1 A2 2A1 A2 = 1 2 2 rad x 1 =A 1 t x 2 =A 2 t 1 +A 2 t
rad x 1 =A 1 t x 2 =A 2 t 1 2 xa 1 -A 2 t 2 >A 1 2 -A 1 x 1 =A 1 t 01 x 2 =A 2 t 02 x=a 01 2 2 = A A A A 1 2 2 1 2 02 01 = 1 2 2 02 02 01 01
x 1 =A 1 t x 2 =A 2 t x x x=x 1 +x 2 1 2 t 1 2 t 2 2 1 2 2 A 1 2 t 2
= 1 f f 1 2 2 = 1 2 f = 1 T f f = 2 1 f
m Kg x t SI x t SI x t SI x t SI xt 3 3 3 4 3 3 7
x t SI x 3 t SI t SI t SI t SI x t SI x t SI xtt SI xtt SI xtt SI xtt SI xtt SI s s s s - m Kg x t SI x t SI m f Hz xt SI J
x t SI x t SI x=x + x To m x =ft rad O s x =At SI x =At SI s m O f Hz f Hz m Hz Hz s
x t SI x t SI y =At y =At xtt SI
x t SI x t SI x =4 3 t SI x t+ 2 SI 5 x t+ SI x t+ SI 3 6 7 xt xt+ x 2 t+ 6 12 x tsi x t SI t U 3-3 m/s 3 m/s mkg t SI t SI
J T t x=- 3 m = ft 3 Am 3 t+ SI s m/s m x t SI x 3 t SI x =ft x m Axt+ 3 SI xm x=-m m Kg t SI t SI T t s x=-m N
=ft =ftft t t SI s mg m rad/s rad/s x t x t xtt U max =8 J x =ft x =ft f f f > f t s rad m s x t SI x t SIs
KYMATA -
2, ya ) ya + ) ± ) ya ) ) ( ) 123
r 1 -r 2 N, ±, ±, r 1 -r 2 N+1), ±, ±, ya t y x N,, ±, ±, x N+1),, ±, ±, 124
c,cc, max ) max 2 ) =, = =, = 125
a b =, = n a a n b b crit n b <n a -- Snell 126
127
1 f T x u x t 128
f H y x 129
x t x y=a T x t x y=a T x 0 t x y=a 0 ] T t x t x T T 130
t x u=u max T u max t x - max max 2 T tt 1 y t x x 1 y. T y x y=fxh 131
y 1 +A 0 x 1 t 1 -A xx 1 t x1 t y y. T T y y=f y 1 +A 0 t t 1 1 / -A T 132
tt 1 1 t x 2 1 t 2x 2 T T x=0 2t 1 T t T 1 ut 1 x 2t 1 T 1 ut 0 1 x t x= 1 T x u.t 1 1 x xx 1 133
t x 2t 2 T T x 1 2 1 2x1 T. x1 x1 t u 1 1 2 x 0 t x 1 u 1 A B x x A x x B 134
1 1 t xa t x 2 2 1 T T x A < x B - 1 t xa 2-1 t x x 2 B x A 2 T T. = x y A =y B A B x y A =-y B A =- B x x=x 1 1 2 135
1 t x 1 2 T 1 t2 x 2 2 T 1 1 2 2-1 t2 x1 1 t x1 2-2 2 T T. = t2 1 t T t 1 1 = =. 0 =. ( 0) =. x 1 1 (, ) = 2 = 0 =. =. 136
1 = =. 0 =. ( 0) = x 1 x 1 (, ) = 2 = 0 =. = 137
u u = 2u m 20m y SI u = 4m/s m/s H rad 2xSI xsi 4x SI 138
2xSI s - 0 18 2 2 x M m 0-3 6 9-139
y2 5xSI y 10x SI y2 xsi y xsi y=a x t 1 0 Z M K - 0 1 2 - y=f 140
- 2 SI - 2 SI - 2 SI m m x M m m/s 4 0 2 141
2 2 y2 2xSI m T 1 x m x K m - 1 s 5 t 1 0 m/s s m 2 =2 s rad 142
y + 10xSI N 1 s m m 1 s x M =-m A y SI m/s m =25s =5s y=5cm y/2 xsi yx=29/12 m SI cm cm/s 143
ms y=3cm m/s y=+5cm cm/s x xx =0 y SI m/s =20 s i ii m y- SI vm/s y -s -cm x m/s s =4s m y-m m m/s - 2 -m/s 2 xx m 144
y 1 rad 2 = rad x=70m y SI To xx m/s x=2m x x =5 s A- SI 2 - SI -x y SI m/s 1 s 2 s 3 s y-10x y ( ycm, t s) m/s 1 = rad 145
d 1 = rad y =5cm t x - SI 0,25 0,5 m=10-3 g x 1 m 1 = 2 3 2 max m/s F=- -4 - SI -4 J -x SI =1s 2 m x=10m s s s = 17/4 s 146
xx - 4 x SI A rad s x A =5m =2s x =2s x=16m x=7m rad x=6m x=8m x=10m y-20x ( xm, ycm, t s) rad 1 =5s 2 =8s x=60cm 1 s cmf=5hztsm/sx=3/80 m rad-rad 147
y x SI m=10-3 Kg 1 =2s rad y 1 =+5 3. 10-2 m 2 xx m x =2s 0 2 N 148
=4s x=1m =2s ATs m =1m/s 2-x SI =0 m/s =0 m m m/s x m s y2 (62, 5t 0, 625 x) SI y- 2 SIymv=0 149
1 2 r 1 r 2 2t y=a T t 1 r t r2 y 1 =A y 2 =A T T, y=y 1 +y 2 2 r r2 y 2A 2 t 1 r. 2 T 2 1 r2 150
1 r r 2 2 2 1 r r 2 2 1 r r 2 2 =1 1 r r2 1 2 2 2 1 r r 2 r 1 r 2 N 1, 2,... 2 t=nt 1, 2,... 1, 2,... 1 r r 2 2 =0 1 r r 2 2 =0 1 r r2 0 2 2 2 151
r r 2 2N 1 2 2 1 r 1 r2 (2N 1), 1, 2,... 2 t=(2n+1)t 1, 2,... 1, 2,... = = = = = ( ) 1 2 =, = ( + ) r 1 r 2 =. =. + = + 152
=. +. + + =, =, ±,±, = ( + ), =,±,±, 1 2 1 r 1 2 r 2 (r 2 >r 1 r 2 1 2 yt (SI), t 1 =1s 1 r 1 2 r 2 r 1 >r 2 r 2 153
y= At -25 y= At - y= At - t=0,9s 0 rad rad 1 2 1 r 1 2 r 2 (r 1 >r 2 =90 0 1 2 2 d 1 5 9 10 1 2 H d 1 3 5 7 154
1 2 1 y 1 t 0 2 y 2 =At 0 = rad r 1 r 2 1 r 1 2 r 2 0 0 rad rad m, m 4,25m m 8m B 40m, 155
2 0 1 2 1 2 1 2 1 2 m/s m T=2s r 1 =3m r 2 =2,5m t=4s m=10-3 Kg r 1 =7m r 2 =5m 2 =10) ) t=2,5 s 2 m ) v=-0,1 m/s ) -4 J 1 2 f=5hz mm cm/s
d 1 =31cm d 2 =33cm y=5 2 t- y cm), ts t=0,9s 1 2 cm f=5hz m/s 20cm 1 cm 2 t=0,4s y=2 2 t- 11 ) ( ycm, t s), t 0, 3s, y=-2cm 4 1 2 f=20hz d 1 -d 2 =145cm d 1 -d 2 1 2 157
m/s 1 2 f=10hz m/s 1 2 d A =40m d B =50m 1 2 1 2 m 1 2 d=5m f=100hz m/s 1 2 158
1 2 d m m 7 y (4 t ) (SI 6 1 x 1 =30cm 2 x 2 >x 1 1 2 x 2 1 2 m/s x 2 =40cmf min Hz y 1 =y 2 t (SI m/s d=12m r 1 =5m 1 1 2 2 1 m m y 1 =y 2 =t (SI 8m/s r 1 r 2 r 1 >r 2 159
t-8 SI O y(t) T=0 t=3,5s =4m cm r 1 =20m, r 2 =12m 1 2 m m 1 1 t=2s rad 0 1 xm r 1 =2m r 2 =5/3 m,
2 =10) m m/s ) yt- SI x=0,75m ) m/s 2 r 1 r 2 =, + =, (.) = 4,5 m/s = 2,5 = 0,22. 22 +
x t t y u 2 ya t t x y 1 A T t x y 2 A T 162
2x 2t yy 1 +y 2 y 2A. T H x t 2x 2x 2x 2x 1 2x x, 1, 2,...... 2 x d 2 163
2x 2x 2x x 4 1, 2,...... 2x 2 2 1 d 2 d 4 164
d K d, = 2,, = 3,, = 2, f 1 f 2 f 1 2 2 x 1 x 2 y 1 y 2 1-1 2-2 xox 165
xox max x K x Z - max + max - max L f = ( + 1/2)., = 0,1,2,3,. A K yxt xycmts 166
xcm ts A - K yxt xycmts xcm xcm ts 2 ts - 2 2-24 x x t x xcm yt+x xycmts y6t+ v t+ SI
x y 1 t-2x SI y 2 t+2x SI x x 1 1 3 m 2 yxt SI m max ms max ms 2 x m x yxt SI x 2 3 m 2 y 1 t-x y 2 t+x SI d - m t+ SI -32t+ SI
xx A cm fhz cm cm xx y x y t ( xy, cmt, s) x cm 2 5 4x K cm 5 5yt ( ycm, t s) fhz x ms x t yv yyt ( y cm) xcmxcm x m fhz 169
x x 1 m x 2 m x x 2 m x 3 m ms radf min Hz xx x y t ( x, ycm, t s) 10 x 1-25cm x 2 cm
x x y 1 - y 2 t+ ( x, y cm) m 20 20 cm s fhz +10 y(cm K 0 20 50 x (cm -10 cm i ii
5 6 A y t xy cma 2 cm i m 40 2 70 ii d cm 3 L xl x x t 1 ycm 3cms 4-4 0 0,5 d 1 cm L t 2 s
x cm d 2 cm t 2 s Acm cm Lcm t SI
c 8 m/s u<c E c B E B u E B max max c E B max max u LC 174
t t x T t x T 1 2 3 4 5 6 5 m cm mm 1mm nm nm nm -8 m - m 175
7 - m 14 m f f f 8 m/s f< 8 m/s f f f 8 m/s max max =c LC 176
= nm Rnm 14 t - 6 1 7 xsi c 8 m/s - - - 1 m m LmH pf pf 177
A x 15 t- SI 2 c 8 m/s 7 7 10 10 nm 14 - SI 3 6 f 1 MHz f MHz 10 L-C L 2 C - F f 1 f - F 5 H f 14 Hz 6 V/m B - T 178
i ii c 8 m/s 8 m/s 6 14 t - 5 SI B - 14 t - 5 SI 6 14 t
i ii H 180
a r a r b b n c u n= u c u<c n n A n1 u 2 n u 2 u 1 >u n 1 <n u 1 <u n 1 >n 1 181
Snell) n = n a nb n b a Snell Snell
n2 u 1 n 1 u 2 n2 1 n 1 2 u1 1 u 2 2 c 0 u c n= n= 0 0 u n 183
n a >n b crit ) n > crit r crit =90 0 n 0 n crit 184
Snell n = n n crit =n crit = n n b a crit = n 1 n <n crit = = =.. 185
n A n B Emax Emax B max Bmax 4 8 0 0 0 d n 1 n n 1 n 2 =.( ) =. ( ) t=0 n 1 =2 n 0 186
n B 1) 0 2 3 ) ) 3 ) 3 2) n 60 0 45 0 30 0 d 187
() = 5/8 () = 8/9. () = 5/9 () > = / () = 5/7 () = 5/7 ) t A /t B =64/65 ) t A /t B =8/9 ) t A /t B =9/8 - - 188
A - c 8 m/s = 3 3 n= 3 3 8 m/s =35 0 =600nm = 3 0 n c 8 m/s 0 0 cm 189
0 n=2 45 0 0 0 0 - nm c 8 m/s n 15 7 8 m/s 190
f 14 Hz - c 8 m/s 3 nm 3 m n= 2-11 c 8 m/s 2 m 2 10 8 m/s =6 2 10-3 V/m n= 3 t- SI m 191
t 1 1 V/m 6m n i ii c 8 m/s m -10 8 t- -10 i -8 s ii 36 c 8 m/s n= 3 2 6 108 m/s n 1 n 1 =300nm 30 V/m
c 8 m/s 3 1, 732 =10-10 Tn = 3 2 nm f 10 Hz d=303 cm n=2 0 c=3 8 m/s 0 n= 3 2 45 0 2 193
n= 0 194
-
x x dt dx. : = S.I m/s. dt d = S.I m/s 2. =, =. 202
= +, =. +. =, =.. R dt ds. H R = / K 203
. = =. = 204
= + d dt = d ds S.Irad/s. d rad R ds 205
=. R dt ds d =. = =. =. =. d dt = 206
S.Irad/s 2. = (. ) = =. =. 207
=, =. =, =. = ±., = ±., =. ±.. =. ±.. OIKIN 208
: R =., =., =. 209
= =. =0. =, =, = H = =. =. = +. = +.( ) = 0 = +. () = 0 & = 0 =. 0
= =. + = 0 =. + () = 0 & = 0 = 0 0 < =., =.
F. =. = o.
cm =.. h cm. rr rr R
=. +. u cm R cm ds d ds dx = (1) = =. (2) dsdx =. =. =. cm R
. H = (. ) = =. =. ds d : =. cm : =. cm =.. u cm u cm u u A u cm u
cm R R u u cm u u A cm u A R R u A R = cm. B u B cm - u B R - R = cm = 2 = = (2 ) = 2 =
t : 0 t t 0 R /R 2 2 2 2
R /R 2 2 N /N 2 2/5 5/2 - rad/s 20 ts 0 s t s t s
- 0 t 2t 4t t t 2t t t t t 0 0 t 0 t 2t 5t
R. t t 2 t R R R R R m R 2 m. Km/h ts rad/s rad/s rad/s 4 rad/s cm S 220
R r A S R.S/r r.s/r 2S cm cm cm.r/r cm RrR - Rm xm ts rad/s. R 2 m/s. R m rad/s 2 t t s rad/s. t 2 s m/s. t 3 s m/s.
t 4 s s m. um/s R R 2 u m/s. T m/s. R u cm. u cm x 222
A 1 i ii r r r t = =, =. t rad/s 2 m -4 Kg d 223
m/s 2 t s t t. 20 rad/s -3 0 rad/s t rad/s 2 0. t 0. t t. t -5t S.Is rad rad/s 2 rad/s 2 m/s R 224
M cm 103m/s cm =, =., cm = ±., =. ±. =, =. 225
= ±, =. ± =., =., =. O = S = m/s Rm. ts : cm Rm Sm cm m/s. 226
: cm m/s 2 rad/s 2 tsrad/s Rm t t s hm : t : 2 Rm cm m/s t : 2 cm Rm cm m/s 2 t rad/s t t 227
t s d R : 2m/s r R =. =.. rm Rm m/s S cm cm = = =, =, =, =, 228
=. =.. =. = = =. =.. =. = = =. =.. =. = = R m R 2 m t t s Sm : 2 t t t. 2-2 2 229
, 0 t 0 t+ t 2 r r 2 r + r cm R cm R SR 4 S r cm cm S 197
cm cm R cm F l d Fd F F x F y 1 r 2 1 +m 2 r 2 2 +. cm +Md 2 Steiner 198
L L 1 +L 2 + 199
L 1 1 2 2 2 cm 2 cm 2 ± ± = t 200
22-12 W =. =. = + =. +. 201
SIm l =. l =. 230
=. d F Fd
1. A 1. m F 1 45 0 F K 2 F 3 F 2 N F 2 N F 3 N 232
= ( ) = = ( ) = - - - - 233
E 1. 2. Fmg R /R 2 (R >R 2 4 F 2mg 3mg 3. AB w F 234
F A H F Fw Fw/2 4. 5.
A 1. wn lm m 60 0 w 1 60 w N 400 F x 400 NF yn 2. m m kn/m 3. wn w 3 m 236
30 0 30 0 3 m 3 N 28 4. wn 0 F 237
5. Lm wn K d 1 w N d m 2 Kg m N -x (SI m 6. Lm wn w N w 2 N d m d 2 m w 1 w 2
m w 3 N m m, =, = =. 7. wn 8. Lm wn 239
0 mkg gm/s 2 3 39 m 9. 0 10. Lm wn 2 d m d 2 m w N 240
L d 2 d 1 A 1 2 B 2 x f(x N 2 f(x 2-40x N 2 x m 11. m Kg m/s m 2 g MKg k N/m m 1 m 2 u A k
Lm m 2 t 2 m ts dp/dt-n dk/dt m m 2 m n =. +. + m r =. Kgm 2 H 242
=. R R m R 2 m 2 R 2 m 2 2 =. R 243
Steiner. cm d = +. cm d To Steiner cm E 1. 2. R mm d R 2 244
d R R/2 R/4 A 2 = + + 1. g R dm yy kgm 2 R mg - yy m = 1 2. Rm rm
2. d d 2 d d 2 L L L = 1 12.. 3. R MM RR zz = 1 2. z A = 13 32. 246
t =. i ii iii 247
E 1. 2. R mm R 2 g 4/3 Mg Mg 7/6 g m 3.
rads ts -20 Kgm 2-4 Nm -Nm Nm Nm 4. cm R 2 cm R 2 5. 6. R F 249
R 2 T T F F F F - 7. R 2
g 1 i =. ii = +. =. +.. =. 1. g Rm t F F 2 F m rad/s 2
F F 2 t s rad/s N 2. kg Rm yy t i. F yy ii. m yy F t s F t 2 s F
yy 2 rad/s 2 Nm =. 3. m Lm MKg mkg O - 30 0 m 2 gm/s 2 2 2 2
2 i =. = +. =. +.. ii =. = +. =. +.. 4. Kg Rm m Kg m 2 Kg t MR m m 2
t s hm 2 gm/s 2 2 2 5. Mkg Rm m F mkg - t m FN m t rad/s t m/s
R 2 gm/s 2 Arad/s 2 m 6. mkg Rm m O m- t t m/s rad gm/s 2 rad/s 2 m 2
i,, ii,, =., =., =. 7. R m R 2 m 2 Kg m 1 m Kg m 2 Kg m 2 t m t t Lm t m 2 u 2 m/s 2 gm/s 2
2 2 2 3 i =. = ±. =. ±. ii =. = ±. =. ±. iii =., =., =. 8. t h
R 2 R 2 R 2 9. Rm t 2 gm/s 2 m/s 2 rad/s 2 23/21 rad/s 2 10. kg Rm F K t FN
hm F 2 gm/s 2 2 2 20/3 11. g F Rm F o rad/s 2 F F 2 g m/s 2 FN NN 12. Kg Rm 0 rad/s t F t s 260
F 2 Am/s 2 13. Kg Rm u 0 m/s F t FN F N N t s N F g m/s 2 2 2
14. g Rm t FN T 2 g m/s 2 rad/s 2 Nm N 15. mkg rm F MKg Rm t F t s rad/s F 262
2 Kgm 2 Nm B- 16. kg Rm t T lm 2 gm/s 2 20/3 m/s 2 rad/s 2 17. R R t 200/3 rad/s 2 m 263
i N R ii t t s R 2 gm/s 2 2 18. T 1 kg Rm t T N m t s m m 264
h m t t 2 2 rad/s 2 gm/s 2 2 2
m r z z z z =.. SIKgm 2 /s z L r u p z r =. 266
L = + + = + + = =. = + + = = + ( ) 267
= = dl/dt: + = dl /dt = 268
1. u=5m/s m=4kg Rm ) 2 /s ) 2 /s 2 /s 2 /s 2. 2 L (Kg.m 2 /s) (rad/s) ) 40 Kgm 2 ) 20 Kgm 2 ) 5 Kgm 2 ) Kgm 2-3. 269
L (Kg.m 2 /s) 20 t(s) 0 5 t m 4. 0 t t t 270
5. Kgm 2 t m rad/s 2 Kgm 2 /s 2 t =2s Kgm 2 /s 6. Kgm 2 L(Kg.m 2 /s) 0 5 t(s) - Kgm 2 /s 2 t=5s m t=8s 3rad/s 7. R 2 MR 2 R
8. Kg Rm =20rad/s mkg u =25m/s rm R 2 9. t=0 F t 272
A 1 1. l=2m kg m mkg i ii. iii. =5rad/s 2 m - m/s cm = 2 gm/s 2 2 2 2 /s 273
2. Kg 0 Rm t=0 mkg rm t - 0 rad/s t F t =2s ) i) - t=0 ii) - iii) F - t 2 2 2 /s 2 3. Kg Rm 0 =20rad/s T t t =5s Kgm 2 /s 274
t t 2 2 2 20/3s 4. H d Kgm 2 f 0 = z (t t =5s u=4m/s t 2 /s 2 2 /s 2 5. Kg Rm m t i) ii) iii) 2 g m/s 2 275
2 /s 6. t 0 t =6s h =24Kgm 2 /s Kgm 2 u=0 u 1 Z =30 0 t h 2 g m/s 2 2 2 /s 2 7. grm 0 =20rad/s A) ts 276
0 =20rad/s 0 s 0 /dt=- A) =. =. B) 277
i) ii) iii) 1. 2. 0 0 278
0 0 /4 0 /5 0 /3 0 3. R F F 4. 5. 6. 279
7. f I cm =mr 2 V=R 3 8. 9. 280
10. A 1 1. m=5kg d =20cm -- rad/s =4kgm 2 -
d 2 m s - 2 /s 2. m=2kg r m = Hz F max m 2 /s 282
2 3. m =5Kgm 2 =2Kg R m R 2 m O rad/s 2 =56rad/s 1 2 s mr 2 2 2 /s - 2 2 /s 283
4. m =4Kg m 2 Kg 1 R m R 2 m Kgm 2 /s 2 t F 2 /dt m i) F ii) t =2 s iii) mr 2 2 3 284
5. Kg Rm mkg d m d s m d =508m/s 2 Kgm 2 /s m d 1 d 6. kg O l=2m d 1 mg m/s m 0 A d m m/s 285
s 2 gm/s 2 2 /s 4 7. M g Rm m=60kg m =4Kg 0 =20m/s 2 2 286
m = = = 1 2 = = = = + 287
d =. =. - t =. W t t = 288
- = = + + = + = ± 289
h - h = h 290
=. =. =. +. m R cm =mr 2 u cm 291
2 mu cm 2 mu cm mu cm 2 mu cm 2 r max r min r max =4 r min M m R cm =mr 2 1 R R 2 l cm =Ml 2 H 2/ 6/ 9/ 292
m cm = 2 u mu 2 mu 2 mu 2 mu 2 1 2 I 1 I 2 1 2 2 4 rads 2 Kgm 2 4 J 2 J 8 J J
1 =10 rads Kgm 2 t rads -100 J J -200 J l l 2 2gl 3gl 5gl 6gl I cm =mr 2 I cm =mr 2-294
0 0 0 0 0 cm =R 2 R I cm =mr 2
120J 60J 40J A kg Rm t F F i t 1 s iii F t 1 t 1 F 1 t 2 =9s i F 1 296
ii F 1 t 1 t 2 2 g=10ms 2 2 2 - =2m MKg 0 =10rads O A S=18 m u A =18 ms 2-72 J 297
m M=4Kg m=2kg m A L - 2 g=10 ms 2 2 2 298
g, R=0,2m m 1 Kg m 2 =2 Kg m 1 m 2 t h=0,4 m 2 g=10ms 2 2 2 2 2 2 299
M=2Kg Rm t=0 F t 1 =4s dk dt=16js F t 1 F t t 1 F t 1 2 kg Rm t t 1 1 =J tt 1
t 1 2 g=10ms 2 2 2 1 2 R 1 =0,2m R 2 =0,4m M 1,R 1 M 2,R 2 t F 1 =F 2 =10 t 1 =2s t t 1 t 1 2 2 2 2 2
m=0,7kg m,r r N hr h=2,7m K R r R R r=0,7m R 1m 2 g=10ms 2 5 R=1,2m mkg =1,2m
g RO m L K cm = 2, g=10 ms 2, 24=4,9 2 2 Kg =4m m hm
m Kg A I cm = 2 Kgm 2 rads 2 60 /7 ms60/7 ms 60/7 m 1 =1Kg m 2 =4Kg M=2Kg R=m m 1 t m 1
t 1 1 =8J m 1 M,R m 2 - t 1 m 1 t t 1 t 1 m 2 t t 2 - J 2 g=10 ms 2 J m Js J Rm 0 0 =80rads I cm R 2 g=10ms 2 2 s
m=1 Kg R=0,1m 0 hm g=10 ms 2 I cm =2mR 2 23/21 t=1,4s =0,2 Kgms Kg R km I cm R 2 T=0,2 s
F g R=0,1m F F F rads I cm R 2 g=10ms 2 J
-
1 1 2 2 = + + + = + + + m 1 m 2 = + m 1 m 2 = + m 2 m 1 1 1 =- 1 2 =0 m 1 m 2 m 2 310
p =p =Q= - DOPPLER S () =340m/s f A S f S S S () = f A =f S 311
S () = ± f A = ± f S S ± S T ) = f A = f S ± f A = ± f S ± - S - S 312
F,, =, + = + + = = = 313
= () = + () = + () =, =, + = + + = ( ) = =, >, =,, 314
m 1 m 2 m 1 m 2 1 2 1 2. +. =. +. () + = + () + = + 1 = ( ) ( + ) + ( + ) () = ( + ) + ( ) ( + ) () 315
= = = ( ) ( + ) = ( + ) 1 = = 316
1 1 = - 1 = = 1 F 1, =,, =, 317
m 1 u 1 m A /4 / 5 1 7 3 7 3 5 m 1 m =3m 1 2m u 2u m O 318
m 1 m >m 1 m m 1 u 1 m 2 m2 2 m1 1 m m =3 2 >>1 m m1-319
m 1 m u 1 u u 1 u m 1 = m 2 u u ' 2 ' 1 1 m 1 m 1 m 1 u m 1
m 1 4 2 1 m 1 u m m 1 m 1 m - m 1 m A m1 m 2 (u m 1 =m m =4m
m m m 1 =m 1 m =4m m 1 1 p 1 m =4m 1 m 1 u 1 m 2 p 1 1 1 m 1 p 1 m m 1 m m 1 m 1 m 1 =4m
- 1-1 - 1 m - - - m m m 1 1 J m =3m 1 H 10J 15J m 1 Kg m =3 Kg 1 =10 ms =5 ms 75J -75J -150J
3m u 3u m m 1 =m 1 1 1 m 1 m =3m 1 2 m 1 m 2 1 1 1 1 m 3 2 1 1 1 1 1 1 6 6
- u 1 u u K u 1 u u K = u 1 u m m 1 =- m
m 1 u m m 1 m A 1 + = +
= p t % =. % =. % % =. % =. % m 1 g m g 1 =4ms ms m 1 1 2 m 2
s 1-5ms ms 1 =-9kgms kgms F 1 =F =900N 1 - m g m 1 g 1 J m 1 m 2 1 m 1 m 1 ms 6ms m 1 m (m >m 1 1
m 1 m m1 m = 1 3 2 m A =m m B m m m Karx 81 K tel m 1 g 1 =18ms m g kgms m 1 m 2 1 2
m m ms J 1-10ms ms J m 1 =3Kg m =1Kg u 1 =6ms u m 1 m u m m 1 - m 1 =10Kg m u 1 =6ms u m u ms m u - m 1 Kg p 1 Kgms 330
m =m 1 p 1 Kgms Kgms 2 1 2 % =. %, = + = =. =. 331
m 1 Kg m =6Kg u 1 ms u =4ms m m 1 u 1 ms ms Kgms m 1 =3 Kg u 1 m p =48Kgms =144J u 1 m 1 =7Kg m =3Kg u 1 u m 1 u 1 ms m u 1
m - m 1 =3 Kg m =4 Kg 0 =7 ms A =10-3 s B 1 =- 3 N 3 333
= = l h w. T w O 334
, =. +. =. =. ( ).. m g Lm m 1 g 1 m L m 1 1 m 2 i 1 335
ii 1 m 1 1 = 2, 25 10 m Lm =8ms m m 1 m 1 m 1 m 1 =3m O L m 2 m 1 1 m m m =1Kg g=10ms 1 =-10ms ms 336
m L m 0 =..() m 1 =4Kg m =8Kg Rm H m 1-96Kgms R m 2 m 1 u 1 m 337
m m 1 m 1 m g=10 ms - - 4 0 k m =4Kg m 1 Kg 1 =11ms =0 m m x (SI 1 m 1 m 2 k 338
m m sm m =4Kg k m 1 Kg u 1 =6ms m m J s u 1 m 1 m 2 k m m p m 1 =4Kg m rads x 1 339
m Kg u = m 1 3 ms u 2 u 1 k m 2 m 1 A/2 m 1 m 1 3 ms x F=- m 1 u 1 ms m =4Kg k=100nm = 0,4 u 1 k m 2 m 1 l max 340
m m 1 m m 1 m 1 - m 1 k=400nm 1 m= xx 1 u=u 1 m =4Kg u m 1 u SI +x 1 m 1 u 1 m 2 u 2 m m 1 341
m 1 ms J m 1 Kg k=800nm x m m =6Kg k u 1 m 1 m 2 x m 1 =-80 knm
m Kg m 1 =1Kg hm m m 1 g=10ms m m m 1 g k hm m 1 =m m 1 m m m 1 m 1 m 1 g=10ms =10 1 1 m h m 2 m 1 343
m 1 g =5ms xm m =3kg m km k m 2 x 0 m 1 m m 1 g=10ms x max m 13 ms 344
DOPPLER Doppler Doppler : f S : f A : S : A : S : : f A f S Doppler f A >f S f A <f S Doppler f A =f S Doppler 345
f S S S f S f S S A A S = A f A f A = / A f A Rf S Doppler s =0 =0 S A = 346
() = + s =0 S A = + () = s =0 S A = 347
=. s =0 S A = = +. s =0 S A = + = ± - 348
- s S A = m m H m f S m 349
A m 2 u 1 m 1 m m / f S f S f S f S f S t d=544 m f S =340 m/s f S 350
f f 1 f f f f f f f f f f f S 1 10 f A 1 10 f A = f S f A f S f A = f S 10 11 10 1
1 10 9 19 10 9 10 10 u S =34 m/s f S =850 Hz u=340 m/s f S f S f S u m/s f S u=340 m/s f A Hz
s Hz f S f = f S f = f S f = f S R f S S f f S H I=R 11 = S 6 5 = S 6 7 = S 6 5 216 9 256 1 72 353
- S f S S S S S S f S f S 354
1 = +, () = +, = =, () =, = =, () =, =. 355
= +, () =, = +. = +, () = +, =. = +, () =, = +. = + +, () = +, = +. =, () =, =. () =. =. 356
m/s 3 m/s O f =480Hz 1 2 3 1 A 2 3 f A =495Hz f =450Hz 2 = 34m/s f s 357
2 1 2 1 =340 m/s 3 S f S t S = =. O f A t A = =. =. =. 358
f S =680Hz t S s f =600Hz =340 m/s m/s s 4 Doppler 0 = = f f m/s f S Hz 359
s =340 m/s 5 A = ± = ±. =. ( + ) g f= z m f S =676 Hz mkg 3 m/s 360
M m - t m/s A m/s =-m/s xt SI f Amax =680Hz F=60N kn/m mkg - m f S =Hz
A S =340 m/s Hz ft SI B = ± = ±. =. ( + )
m t m/s f S =400Hz m =340 m/s mkg kn/m f S Hz m m =340 m/s f max =3060Hzf min Hz xm 363