. (, , ) .Copyright 2009 Mavromatis Books & Stationery LtdISBN 978-9963-9609-0-3 : 121, 2064 .. 25042, 1306 , : 00357 77777650, : +357 22873037E-mail: mavromatisbookshops@cytanet.com.cy2 . 3 , , , , .3 . , . . , - . . : , . - . . Matlab LaTEX. . . , . - . . ,, Email: Thpapagiannis@Hotmail.com: 994583624 . 1 1.1 1. - 1 109: : - : . m - v :

P = mv . , - . , - . :

P = m1v + m2v + ... + mv

P = (m1 + m2 + ... + m) v2. - 2 109: ;5 1. : :F =Pt , , . .3. - 3 109: ;: - .F =Pt , - . , , .4. - 4 109: ;: , - . .6 . 1.1. 75. - 5 109: , ;: !!!6. - 6 109: - , ;: , -. !7. - 7 109: ; -.: , . . . : , . ( ) .8. - 8 109: .: - :E=12 m v2(1.1)P = m v (1.2)7 . 1. 1.2 :P2= m2 v2(1.3) 1.1 m:E m =12 m2 v2(1.4) 1.3 1.4 :E m =12 P2E=P22m9. - 10 109: m1, m2 . m2< m1 ;:8 :E=P22mE1= E2P212m1=P222m2P21P22=m1m2P21P22> 1 |P1| > |P2| .10. - 11 109: m1, m2 . E1E2 .:8 :E=P22mP1= P2E1 2m1= E2 2m2 8 . 1.1. 9E1E2=m2m111. - 12 109: ;: .12. - 13 109: P= f(v) E= f(P): , :P= mv E=P22m. - . 1.1 10 5 .0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 505101520253035404550v (m/s)P (kg m/s)P=f(v) m1=10 kgm2=5 kg0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5020406080100120140v (m/s)E (J)E=f(v) m1=10kgm2=5kg 1.1: P= f(v), E= f(p)9 . 1. 13. - 14 109: F t;: t . . , . = F t = P.14. - 17 109: :() ;() ;() ;: .() , , -. , .() .() - .10 . 1.2. 111.2 1. - 11 7: 1, 2 m/s. (). 50 g .: F =Pt . . - ( ) . v= 1.2 m/s v= 0 m/s . :F =Pt=m (vv)tF =0.05 (0 1.2)1= 0.06 N .2. - 12 7: , 5 Kg. F . v 1.2.() F= f(t), F= f(x) x .() P E ; - 0 20s 20 30s.() P= f(t) E= f(t)11 . 1. 0 5 10 15 20 25 30 35051015202530354045t (s)v (m/s) 1.2: v= f(t): -. : 2 , 0 20s 20 30s . . :a =vt=40 020 0= 2 m/s :F= m a = 5 2 = 10 N12 . 1.2. 13 :a =vt=0 4030 20= 4 m/s :F= m a = 5 (4) = 20 N- . :x =12 a t2=12 2 202= 400 m 40m/s. - :x30s= x20s + v20s t 12 a t2= 400 + 40 10 200x30s= 600 m 1.3. P E .P = m vE=12 m v2 v=f(t) 0 30s. - t 20sP = 5 40 = 200 m/sE=12 5 402= 4000 J P= f(t) E= f(t) 1.4.13 . 1. 0 5 10 15 20 25 30 35252015105051015t (s)F (N)0 100 200 300 400 500 600252015105051015x (m)F (N) 1.3: F= f(t) F= f(x)3. - 14 8: 0, 2 kg 3.2 m . 103s .: . - . 14 . 1.2. 150 5 10 15 20 25 30 35020406080100120140160180200220t (s)P (kg.m.s1)0 5 10 15 20 25 30 35050010001500200025003000350040004500t (s)Ek (J) 1.4: P= f(t) E= f(t) .h =12 g t2t =2 hg= 0, 8 sv = g t = 8 m/s F=Pt=m (vv)tF=0.2 (8 (8))103= 3200 N15 . 1. :F=Pt+ m g= 3202 N4. - 15 8: v=20 m/s, - . 75 kg , 0, 2 s. .: ,v=20 m/s, v=0 m/s. :F =Pt=m (vv)tF =75 (0 20)0.2= 7500 N - :E = EE=12 m v212 m v2 E = 15000 J5. - 18 9: 20 g 30 g - 30m/s 10m/s ( 1.5). . ) 16 . 1.2. 17 1.5: ) .: - . . .P= P m1 v1+ m2 v2= mo vk vk=m1 v1 + m2 v2movk=0.02 30 + 0.03 (10)0.05vk= 6 m/s :E = EE==12 mo vk212 m1 v12+12 m2 v22=17 . 1. =12 0.05 6212 0.02 302+12 0.03 102=E = 9.6 J6. - 19 9: M1 M2 2 kg 3 kg 6m/s 2m/s ( 1.6) -. 0.02 s.() () P1 P2 Po ( ).() F1=f(t) F2=f(t) F1 F2 ( ) M1 M2 . 1.6: : - - .P= P 18 . 1.2. 19m1 v1 + m2 v2= m1 v

1 + m2 v

2 m1 v1m1 v

1= m2 v

2m2 v2 m1 (v1v

1) = m2 (v

2v2) (1.5) (- ) :E= E 12 m1 v12+12 m2 v22=12 m1 v

12+12 m2 v

22m1 (v12v

12) = m2 (v22v

22) m1 (v1v

1) (v1 + v

1) = m2 (v2v

2) (v2 + v

2) (1.6) 1.5 1.6 1.7 :v1 + v

1= v2 + v

2(1.7) 1.5 1.7. , - . . - !m1 (v1v

1) = m2 (v

2v2) 12 2 v

1= 3 v

2 + 6 v

2=6 2 v

13(1.8)19 . 1. v1 + v

1= v2 + v

2 6 + v

1= 2 + v

2 v

2= 8 + v

1(1.9) 1.8 1.9:6 2 v

13= 8 + v

1 24 + 3 v

1= 6 2 v

1 v

1= 3.6 m/s 1.9:v

2= 8 + v

1 v

2= 4.4 m/s P1 P2 Po.P1= m1 v1= 12m/sP1= m1 v1

= 7.2m/sP2= m2 v2= 6m/sP2= m2 v2

= 13.2m/sF1=Pt= 7.2 120.02= 960NF2=Pt=13.2 + 60.02= 960N 1.8 :20 . 1.2. 210 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04105051015t (s)P (kg.m.s1) P1P2Ptotal 1.7: 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04100080060040020002004006008001000t (s)F (N) 1.8: 7. - 20 10: P1 1 kg, - m 1.9.21 . 1. m.0 10 20 30 40 50 60 70 80 90 10005101520253035t (s)P (kg.m.s1) 1.9: : . 1 P=30 kg m s1. - P=10 kg m s1. 1 :P= 10 kg m s1m1 v1= 10 kg m s1v1= 10 m/s , . - m2 .P= P 22 . 1.3. 2330 = (m1 + m2) vo 3010= 1 + m2 m2= 2 kg1.3 1. - 26 12: M1 4kg 10 m/s M2 16 kg 4 m/s. 0.02 s. .() , . .() P1 P2 Po .() F1=f(t) F2=f(t), F1 F2 ( ) M1 M2 .: . :P= P m1 v1 + m2 v2= (m1 + m2) vo vo=m1 v1 + m2 v2m1 + m223 . 1. vo=4 10 + 16 44 + 16vo= 5.2 m/s 1 2 P1= f(t), P2= f(t) Po= f(t).P1= m1 v1= 4 10 P1= 40 kg m s1P1= m1 vo= 4 5.2 P1= 20.8 kg m s1P2= m2 v2= 16 4 P2= 64 kg m s1P2= m2 vo= 16 5.2 P2= 83.2 kg m s1Po= P1+ P2 Po= 104 kg m s1Po= P1 + P2 Po= 104 kg m s1-. - - .F1=Pt=20.8 400.02F1= 960 N24 . 1.3. 25F2=Pt=83.2 640.02F2= 960 N 1.100102030405060708090100110t (s)P (kg.m.s1) P1P2Ptotal100080060040020002004006008001000t (s)F (N) F1F2 1.10: P= f(t) E= f(t)25 . 1. .P= P m1 v1 + m2 v2= (m1 + m2) vo vo=m1 v1m2 v2m1 + m2vo=4 10 16 44 + 16vo= 1.2 m/s 1 2 P1= f(t), P2= f(t) Po= f(t).P1= m1 v1= 4 10 P1= 40 kg m s1P1= m1 vo= 4 (1.2) P1= 4.8 kg m s1P2= m2 v2= 16 (4) P2= 64 kg m s1P2= m2 vo= 16 (1.2) P2= 19.2 kg m s1Po= P1+ P2 Po= 24 kg m s1Po= P1 + P2 Po= 24 kg m s1- . -26 . 1.3. 27 - .F1=Pt= 4.8 400.02F1= 2240 NF2=Pt= 19.2 (64)0.02F2= 2240 N 1.118060402002040t (s)P (kg.m.s1) PtotalP1P2250020001500100050005001000150020002500t (s)F (N) F1F2 1.11: P= f(t) E= f(t)27 . 1. 2. - 28 13: m=3 kg . h1=40 m . mA=m3mB=2m3 . h2= 20 m ( 1.12). :() .() .() .() ; 102s. 1.12: 28 . 1.3. 29: , 20 m. - :vA= g t (1.10)h = vA t 12 g t2(1.11)(1.12) 1.10 t 1.11 :t =vAgh =vA2g12 vA2gh =12 vA2gvA=_2 g h = 20 m/s h1=40 m - :E=12 m v2= 0 v2= 0 v = 0 - :P= P 0 = mA vA + mB vB 0 =m3 20 +2m3 vB vB= 10m/s29 . 1. - :E=12 mA vA2+12 mB vB2E=12 1 202+12 2 102E= 300 J . . . . .EB0m= EB40m 12 mB vB

2= mB g h1 +12 mB vB2vB

2= 2 g h1 + vB2vB

= 30 m/s . : !F =Pt+ m g F =mB (vB

vB)t+ mB g 30 . 1.3. 31F =2 (30 (30))102+ 2 10 F = 12020 N31 . 1. 32 . 2 2.1 1. - 10 28: 2,4 . , 6/10 . ;:- :L= L I = I I =610 I 2f=106 2 2, 4 f= 4 /s2.2 1. - 11 28:-1 Hz 33 2. . 8 g 0.5 m . 0.8 Hz.() () . . 2.1: : -:I =n

i=1mi ri2(2.1)L= L(2.2)E=12 I 2(2.3) = 2 (2.4) 2.2 ( 2.1), :34 . 2.2. 35L= L I = I I = (I + m r2) I I = m r2 I=m r2 I=0.008 0.52 5.0246.28 5.024= 8 103kg m2 . :I= I + m r2= 0.01 kg m2 2.3:E=12 8 103 6.282= 0.1578 JE=12 0.01 5.0242= 0.1262 J: . - . , , - !2. - 12 28: - 35 . 2. . 2 kg m2. 1.5 rad/s. 1.2 kg m2() () -. ; 1.8 kg m2. , .: ( - ), :L= L I = I =I I= 2.5 rad/s - 2.3:E=12 1.2 1.52= 2.25 JE=12 1.2 2.52= 3.75 JE = EE= 1.5 J 1.8 kg m2. - , - :36 . 2.2. 37

=I

I

=1.2 2.51.8= 1.67 rad/sE

=12 1.8 1.672= 2.5 J3. - 13 28: 120 kg 1 m, - . 60kg - 10 m/s. - , - ;(: - . : I=12 m r2): - - : =vr=101= 10 rad/s 2.1 - :I= I + m r2I=12 m r2+ m r2I=12 120 1 + 60 12= 120 kg m237 . 2. :I

= I + m r

2I

=12 m r2+ m r

2I

=12 120 1 + 60 02= 60 kg m2 - . :L= L I = I

=I I

=120 1060= 20 rad/s = = 10 rad/sE=12 120 102= 6000 JE=12 60 202= 12000 JE = EE= 6000 J4. 14 29: , 60 kg, -2 m. 360 kg m2. 1.5 m/s .38 . 2.2. 39() ;() . ;: . - , - - . :L= L 0 = I I I = I =I I=m r2 I=60 22 0.75360= 0.5 rad/s :=vr=1.52= 0.75 rad/s -. . .L= L 0 = I I =I I=0 0360= 0 rad/s39 . 2. 2.3 1. 15 29: I1 0 . - , I2 , .() I1, I2 0.() .() 0 ;: , . , , . :L= L I1 0= (I1 + I2) =I1 0I1 + I2 . :E=12 I 240 . 2.3. 41 :EE=12 (I1 + I2) (I10I1+I2)212 I1 02EE=I1I1 + I22. - 1 135: l = 0.4 m . IK=ml212. :() .() . 2.2: .: . . :41 . 2. Steiner . 2.5. IK , IA , m x .IA= IK + m x2(2.5) , 2.2 :I0= IK + m x2=m l212+ m x2I0=m 0.4212+ m 0.22I0= 0.0533 m - . , 120. :I0=m l23= 0.0533 m . . !!!Eo= E 42 . 2.3. 43m g l = m g l2+12 IO 2m 10 0.4 = m 10 0.42+12 0.0533 m 24 = 2 + 0.0266 2 =4 20.0266= 8.67 rad/s :v = r r . :vK= r = 8.67 0.2 = 1.734 m/sv= r = 8.67 0.4 = 3.468 m/s3. - 2 135: 0.2 kg R=0.1 m IK=25 m R2 - 1.75 m , 30o 2.3. :() () () -.: - , . .43 . 2. 2.3: . , . . - , , 2.3 , ! . - : , .I0= IK + m x2=25 m R2+ m x2I0=2 0.2 0.125+ 0.2 0.12I0= 2.8 103kg m2EA= E 44 . 2.3. 45m g h =12 I0 2 =2 m g hI0= 50 rad/s , , :vK= R = 5 m/s :E=12 m vK2= 2.5 JE=12 I0 2= 3.5 J4. - 4 135: - . 2.5 kg m2. = 2 rad/s. , 0.5 kg m2. :() () .: , , :45 . 2. L= L I = I

=I I

=2.5 20.5= 10 rad/s - :E=12 I 2= 5 JE=12 I

2= 25 J2.4 1. - 2007-2008: m1 m2 I. - 2.4. , - h :v=_2 (m2m1) g hm1 + m2 +IR2: . 1 2. 2 h 46 . 2.4. 47 2.4: . 1, 2 .E= E m2 g h = m1 g h +12 m1 v2+12 m2 v2+12 I 2m2 g h = m1 g h + v2 (12 m1 +12 m2 +12 I1R2) v2=2 (m2 g h m1 g h)m1 + m2 +IR2v =_2 (m2 g h m1 g h)m1 + m2 +IR22. - 1986: 1. 47 . 2. 2, .: . , , . :I=2

i=1mi ri2= m1 r2+ m2 r2I=2

i=1mi ri2= m1 (r2)2+ m2 (r2)2I= 4 I :L= L I 1= I 2 I 1=14 I 2 2= 4 13. - 1993: m1 r2 r. m=2 m1 1. - . 2=10 Hz. . 1 . I=12 m r248 . 2.4. 49 2.5: - .: -, 2.5 .I= m1 (r2)2+ I= m1 r2+12 m r2I=54 m1 r2I= m1 r2+ I= m1 r2+12 m r2I= 2 m1 r2 :L= L I 1= I 2 54m1r2 21= 2m1r2 22 1=85 2= 16 Hz49 . 2. 4. - 1996: R=20 cm M=0.5 kg - 1=120cyclesmin . m=100 g r = 10 cm -. , .: :I= moo r2+ I= moo r2+12 m R2I= 103+ 0.01 = 0.011I= I= 0.01 :L= L I 1= I 2 0.011 21= 0.01 22 2=0.0110.01 1 2= 132cyclesmin= 132cycles60 s 2= 2.2 Hz5. - 1997: m Mr. 1 K. v2. 2. :50 . 2.4. 51() - () :M=2kg, r =1m, 1=10rad/s, 2=15rad/s, m=0.1kg, to= 0.1s, I=12 m r2i. v2ii. iii. t=0s t=0.5s, t = 0.2s 2.6: - , ) ) .: . :I= m r2+ I= m r2+12 M r2L= I 1 L= (m r2+12 M r2) 1 . :51 . 2. . . ( v= r).L= I 2Iv2rL=12 M r2 2m r2v2rL=12 M r2 2m r2v2rL=12 M r2 2m v2 r . - . v2 :L= L (m r2+12 M r2) 1=12 M r2 2m v2 r v2=12 M r2 2(m r2+12 M r2) 1m rv2=0.5 2 12 15 (0.1 12+ 0.5 2 12) 100.1 1v2= 40 m/s . . :E=12 I 12=12 (m r2+12 M r2) 1252 . 2.4. 53E= 0.5 (0.1 12+ 0.5 2 12) 102E= 55 JE=12 I 22+12 m v22E=12 (12 M r2) 22+12 m v22E= 0.5 (0.5 2 12) 152+ 0.5 0.1 402E= 192.5 JE = EE= 192.5 55 E = 137.5 J - . :L= I 1= 10 kg m2 rad/sL= I 1= 1 kg m2 rad/s -:L= I 2= 15 kg m2 rad/sL= Iv2r= 4 kg m2 rad/s53 . 2. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5420246810121416t (s)L (kg.m2.rad/s) LdiscLparticle 2.7: () (): - . 2.7 . .M = I a = I t==I ()t=LLtM =Lt54 . 2.4. 55 , .55 . 2. 56 . 33.1 1. - 3 41: . a = f(t) - 3.1. t = 0.5 s 2= 10.0 1 2 3 4 5 6 7 81086420246810t (s)a (cm/s2) 3.1: ..57 3. : t =5s. : ( ) T= 4s a = 10cm/s2 y0. =2T=2 104= 1.58a0= 2 y0 y0=a02=10(24)2 y0= 4 cm :y = y0 sin(t + ) :y = y0 sin(t + ) (3.1)dydt= v = v0 cos(t + ) (3.2)dvdt= a = y0 2 sin(t + ) (3.3) .58 . 3.1. 59 t=1s a=10cms2 . 3.3 :a = y0 2 sin(t + ) 10 = 4 (24)2 sin(24 1 + ) 1 = sin(2+ ) = 3.1 :y = y0 sin(t + ) y = 4 sin(24 0.5 + ) = 4 (22)y = 222. - 4 41:3.2 y t ... :() t = 4s() t = 2s() t = 8s() t = 8s() t = 4s: - .() t =4s. . .59 . 3. 0 1 2 3 4 5 6 7 8 9 101086420246810t (s)y (m) 3.2: ..() t = 2s y= 0. .() t =8s .() t=8s . 3.1 3.3y = y0 sin(t + )a = y0 2 sin(t + )a = 2 y() t=4s . . y ymax :E=12 k y260 . 3.1. 613. - 5 42: l0 m 3.3.() - ; .() .15 16 17 18 19 20 21 22 23 24 2502468101214 3.3: : 3.3 ( MatLab) l0= 20cm x0= 5cm. . - - (x=15 x=25). - 61 . 3. . . - . -, , . 3.4 .15 16 17 18 19 20 21 22 23 24 2502468101214 3.4: , 4. - 6 42:() . , ;() 30o. ;() - - .62 . 3.1. 63: 3.5. 3.5: . 3.5, . : W S , .Sx= S sinSy= S cos , 6o sin =tan = rad . 63 . 3. l. y y:Sy= W Sy= m g S cos = m g S =m gcos x :___Sx= S sinS =mgcos___ Sx= m g tan , , lyl. :tan =xly=xlSx= m g xl(3.4) , 3.4. . - , 3.4 ._Sx= m g xlF = k x_k =mgl64 . 3.1. 65k = m 2k =mglm 2=mgl =_gl 2T=_gl T = 2 lg: - l, . - g, .() . . . : , . - !!!() : 6o sin=tan= rad. .() . . l ly= cos l.65 . 3. 5. - 9 43: - -x0. :() () , () : . :E =12 k x02=12 m v02 :E=12 m v02E=12 2m v02= m v02 . . . k :k= m 2k= 2m 2 .66 . 3.2. 676. - 10 43: , ;: : - . - ( ) l =g2, . , , .3.2 1. - 12 43: ... ( ) -52cm.s2. 4cm , 3cm/s. , .:, :() ...:x = x0 sin(t + )v= v0 cos(t + )a = a0 sin(t + )67 . 3. () a0= 52cm.s2() x = 4cm v= 3cm/s :4 = x0 sin(t + )3= x0 cos(t + ) sin cos. - , , - :4 = x0 sin(t + )3 = x0 cos(t + )162= 2 x02 sin2(t + )92= 2 x02 cos2(t + )162+ 92= 2 x02 [sin2(t + ) + cos2(t + )] 162+ 92= 2 x02 :2 x0= 52 , - :(x0216)2= 922 x0= 52(x0216)52x0= 92x0216 =95x068 . 3.2. 69 - :x0295x016 = 0x01,2=95 _(95)2+ 4 1 162 1 :x01= 5cm x02= 3.2cm. . :2 x0= 522= 2 = T =2=2= 2s :v0= x0= 5cm/s2. - 13 44: 3.6 , ... ..: - ... :69 . 3. 6 4 2 0 2 4 615105051015X: 6Y: 12x (m)a (m/s2)X: 3Y: 6X: 3Y: 6X: 6Y: 12 3.6: ...x = x0 sin(t + )a = x0 2 sin(t + )a = 2 x (3.5) y=x + = 2 =0. 2. ... , . =12 06 0= 22= 2 =2 2T=2 T=2270 . 3.2. 71T = 4.44s3. - 14 44: 2kg ... 0.5m. D = 200N/m. t1 - v1= 2.5m/s. : t1 : m = 2kg D = 200N/m t1 v1= 2.5m/s D = m2=Dm =2002= 10rad/s t1. (x0, D ) - (v1, m ). 1 x1:Eo=12 D x02= 25J71 . 3. E=12 m v12= 6.25JE1=12 D x12= 25 6.25 x1=2 18.75200= 0.433m :a1= 2 x1= 100 0.433 a1= 43.3m/s24. - 15 44: 0.05kg x=5sin(40t +2) x cm, t s. 2= 10. :() () () - t = 0.5s() t =0s t = 0.5s() , - : ... :x = x0 sin(t + )x = 5 sin(40t +2) :72 . 3.2. 73 x0= 5cm = 40 T= 0.05s :v0= x0 = 0.05 40= 210Emax=12 m v20=12 0.05 (210)2= 1J t=0.5s ...:_F = m aa = 2 x0 sin(40t +2)_F= m 2 x0 sin(40t +2) F= 0.05 (40)2 0.05 1 = 40N t = 0s t =0.5s ( ). T=0.05s. , , t = 0 x0= 0.05m. :C=tT=0.50.05= 10 4 , d1o= 4 0.05m = 0.2m :Soo= C d1o= 2m73 . 3. 5. - 17 45:m h . - y. k . kg; 3.7: h: h . y. 1 , .m g (h + y) =12 k y2m =k y22g (h + y)1 + y74 . 3.2. 756. - 18 45: 3.8 .. T= 2s , ,x0 20cm. . 3.8: : . . 3.9. - . F . , . : 3.9: 75 . 3. T = N= m gFmax= m a0= m 2 x0T = Fmax m g = m 2 x0 =2 x0g=42 x0T2 g = 0.27. - 19 45: 3.10 . K1=120N/m K2=80N/m. 2kg . , ... . 3.10: : ... , . x , 1 K1 2 K2 , 3.11. 76 . 3.2. 77 1 2 2. 3.11: (Hooke) :F1= k1 xF2= k2 x :F = F1F2 F = k1 x k2 x F = (k1k2) x (3.6) 3.6 - ... k1k2:2 1 . 2 77 . 3. k1k2= m 242T2=k1k2mT =m 42k1k2=2 42120 80 T = 0.28. - 20 46: (Body Measuring Device - BMMD), - . . -. K=600N/m. 0.9s 2.1s . 2= 10.: - , k . k :k = m 2 - 0.9s 2.1s.k = m 2 78 . 3.2. 79m=k2=600420.92= 12.15kgk = mo 2o= (m + m) 2om 2= (m + m) 2o m=m 22om m=12.15 42T242T2o12.15 =12.15 T2oT212.15 m= 54kg9. - 25 48: 1 m1= 1kg k= 400N/m x0= 0.1m .1- 2 m2=3kg. . :() () : 1 2. 1 . : x0= 0.1m k = 400N/m m1= 100kg79 . 3. 3.12: - m2= 3kg :k = m1 2= 400 2=km1=4001 =400 = 20rad/s v0= x0= 20 0.1 v0= 2m/s . :E= E 80 . 3.2. 8112 m1 v21=12 m1 v1

2+12 m2 v22 12 1 22=12 1 v1

2+12 3 v22 3 v22 + v1

2= 4 (3.7)P= P m1 v1= m1 v1

+ m2 v2 1 2 = 1 v1

+ 3 v2 v1

= 2 3 v2(3.8)3.7 3.8 :3 v22 + v1

2= 42 3 v2= v1

3 v22 + (2 3 v2)2= 4 3 v22 + 4 12 v2 + 9 v22= 4 12 v22= 12 v2 v2= 1m/s :v1

= 1m/s 1 v1

= 1m/s. :x0=v1

= 0.05m , . :81 . 3. P= P m1 v1= (m1 + m2) V V =m1 v1m1 + m2=1 21 + 3 V = 0.5m/s .k = (m1 + m2) 2=4004 = 10rad/s :x0=V=0.510= 0.05m/s3.3 1. - 27 48: , , 6 , 12 6 . 0oC , 10oC - 0oC . - ... :() . 6:00 . t = 0s.() 9 .82 . 3.3. 83() - 5oC, ;: ... . .. :T4= 6h t = 0s = 0oC 6h 0= 10oC . .. : = 0 sin(t + ) : = 10 sin(24 6t + )t = 0s = 0oC0 = 10 sin( 12 0 + ) sin = 0 = 0 : = 10 sin( 12t) 3.1383 . 3. 0 2 4 6 8 10 12012345678910t (hours)o C 3.13: , 9.. . t = 0s 6 .. 9 6 = 3. = 10 sin( 12t), t = 3 = 10 sin( 12 3) = 10 sin4 = 7oC 5oC. : = 10 sin( 12t), 5oC84 . 3.3. 855 = 10 sin( 12t) 0.5 = sin( 12t) 12t =6 12t =56t = 2h t = 10h8:00. 16:00, 8 !!!2. - 29 49:M=2kg ..., x0=10cm T, K=800N/m, 3.14. m=500g M v=4m/s M . . :() T () T

() () 3.14: 85 . 3. : T :k = M 2=kM T= 2 MkT = 2 2800= 0.314s . , mo= 2.5kgT

= 2 _mok= 2 2.5800 T

= 0.351s : M ( ) v2= x0=2T x0=20.314 0.1 v2= 2m/sP= P m v1 + M v2= (m + M) V V =m v1 + M v2m + MV =0.5 4 + 2 22.5= 2.4m/s86 . 3.3. 87 . ( - ):V = x0

x0

=V=V2T

x0

= 0.134m3. - 30 49: M= 1kg - k =200N/m . m=0.2kg - v= 2m/s. :() () () : . - , . 0 ( ), :P= P 0 = m v + M v 0 = 0.2 2 + 1 v v= 0.4 0.4m/s. 87 . 3. . , , Hooke:F = k x x =Fk=m gk=0.2 10200x = 0.01m :Eo= E + E Eo=12 M v2+12 k x2=12 1 0.42+12 200 0.012Eo= 0.09JEo=12 m x20 x0=2 Eok=2 0.09200x0= 0.03m4. - 32 50: k=100N/m l0= lm . m=1kg .88 . 3.3. 89() ... t =0s .() () () , .() . ; ; 3.15: ) ) ) 89 . 3. : ... . 0.F = 0 F.B = 0 F.= B F.= m g 3.15. x :F = B F

F

= k (x + x) = F. + k x (3.9)F.= B= m g (3.10) 3.9, 3.10:F

= k x ... . :y = y0 sin(t + )k = m 290 . 3.3. 91 =km= 10rad/sT = 2 _mk= 0.628sF = k y0 y0=m gk= 0.1m t = 0s x0 :0.1 = 0.1 sin(10t + ) 1 = sin() =32 :E=12 k (2 y0)2= 2J , :E=12 k y20= 0.5JE= m g h = m g y0= 1JE=12 m v20=12 m ( y0)2= 0.5J . .91 . 3. 3.4 1. 2003: l0= 10cm k = 100N/cm. . () 10cm 15cm() 15cm 20cm: S.I.. k =104N/m, l0=0.1m. - :E0.15=12 k x2=12 104 0.052= 12.5J - 0.15m 0.2m, - 0.2m 0.15m:E0.2=12 k x2=12 104 0.12= 50JE = E0.2E0.15= 50 12.5 E = 37.5J2. 2000: x .92 . 3.4. 93: ..:x = x0 sin(t + )a =d2xdt2= 2x0 sin(t + ) a = 2 x 2 .xa 3.16: a = f(x)93 . 3. 3. 1999:.. 3.17. , .0 0.5 1 1.5 2 2.5 3 3.5 454321012345t (s)x (cm) 3.17: x = f(t): : x0= 5cm T= 2s f=1T= 0.5Hz =2T= - , (t =0, x = x0= 5cm) :94 . 3.4. 95x = x0 sin(t + )5 = 5 sin( 0 + ) sin = 1 =2 :x = 5 sin(t +2)4. 1999: x =x04 , x0 .: . , Emax=12 k x20. x04 :E= EoE E=12 k x2012 k (x04)2E=12 k (x20x2016) = k (15x2032)EE=15x2032x2032= 1595 . 3. 5. 2001: 3.18 v x ... .0.2 0.15 0.1 0.05 0 0.05 0.1 0.15 0.23210123X: 0Y: 3.142X: 0.2Y: 0 3.18: v= f(x): . - , .x = x0 sin(t + ) (3.11)v = x0 cos(t + ) (3.12) 3.40 , :96 . 3.4. 972 x2+ v2= 2 x20 sin2(t + ) + 2 x20 cos2(t + )2 x2+ v2= 2 x20 (sin2(t + ) + cos2(t + )) 2 x2+ v2= 2 x20 x2x20+v22 x20= 1 (3.13) 3.42 x0=0.2m v0= x0= . : x0= 2T 0.2 = T =0.2 2= 2.5s6. 2000: ... x0T. - - ( 3.19). 3.19: - ..: - 97 . 3. . . :x = x0 sin( tOB) 0.5 x0= x0 sin( tOB) tOB=6 tOB=6=T 12=T12 . , , :x = x0 sin( tOA) 0.707 x0= x0 sin( tOA) tOA=4 tOA=4=T 8=T8tAB= tOB + tOA=T8+T12 tAB=524 T7. 2003: , y0 2y0. :() () () 98 . 3.4. 99: :T1= 2 _mkT2= 2 _mkT1T2= 1 k . :E1=12 k x20E2=12 k (2x0)2E1E2=12 k x2012 k 4x20=14 :a1= 2x0a2= 2 2x0a1a2=2x02 2x0=128. 2002: - .. 3.20. - .99 . 3. 5 4 3 2 1 0 1 2 3 4 50.50.40.30.20.100.10.20.30.40.5X: 5Y: 0.4935x (cm)a (m/s2)X: 5Y: 0.4935 3.20: a = f(x): - : a0= 0.493m/s2 x0= 5cm. :a0= 2 x0 =a0x0 =0.4930.05= 100 . 3.4. 101T =2= 2s - 3.210 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 254321012345t (s)x (cm) 3.21: x = f(t)9. 2000: (x) (x0) .: : x =x02 () , 101 . 3. E= EoE E=12 k x2012 k x0222E=12 k (x20 +x204) E=12 k 34 x20EE=12 k 34 x2012 k x0222= 310. 2001: . 3.23. :() (t>0) :i. ii. () a0Aa0B, a0A, a0B .: : : TA= 2s y0A= 10cm : TB= 4s y0B= 5cm .. . T4=0.5s T4=1s. 102 . 3.4. 103 3.22: x = f(t) . T2= 1s T2= 2s. :a0Aa0B=y0A 2Ay0B 2B=0.1 (22)20.05 (24)2= 811. 2001: m = 0.5kg . - F x.() - k() m .i. ;ii. ;iii. ;() 1.3J- .103 . 3. 0 2 4 6 8 10 12 14 16 18 2000.511.522.533.544.55x (mm)F (N) 3.23: F= f(x): . Hooke F= k x F= f(x) . :k =FFxxk =5 00.02 0= 250 N/m . , . 104 . 3.4. 105 - . E=1.3J. . :E=12 k x20= 1.3 J x0=2 1.3250= 0.1 m12. 2002: -. m, t, - . : g 0 10 20 30 40 50 s 4 5,6 6,9 8 8,9 9,8() - .() . ;() ;: . k- :105 . 3. k = m 2 :k = m 2 =km 2T=kmT = 2 _mkT2=42k m -T2=f(m) 42k. , k : 20 . - 20 - . T2= f(m) 42k k. 3.24 :42k=yyxx42k=0.2401 0.040.050 0= 4 k =424= 9.87 N/m106 . 3.4. 107 g s T T20 4 0,2 0,0410 5,6 0,28 0,078420 6,9 0,345 0,11902530 8 0,4 0,1640 8,9 0,445 0,19802550 9,8 0,49 0,24010 5 10 15 20 25 30 35 40 45 5000.050.10.150.20.25m (g)T2 3.24: T2= f(m) k :k = m 2m=k2=k T242=4 0.0442m= 4 103kg= 4 g107 . 3. . . - , . 20 -. . .13. 2003: :() () , k, - . m, - l0 0. .i. .ii. .:() - . -: F= k : .108 . 3.4. 109 : , . 3.25: ) ) ) () ... - . 0.F = 0 F.B = 0 F.= B F.= m g 3.25. x :109 . 3. F = B F

(3.14)F

= k (l0 + x) = F. + k x (3.15)F.= B= m g (3.16) 3.14, 3.15 3.16:F = k x ... . : =2T(3.17)k = m 2(3.18) 3.17, 3.22 :k = m 2= m (2T)22T=km T = 2_mk .14. 2002: :() - . .110 . 3.4. 111() - . - 60kg f=3.2Hz. - f

= 2.2Hz. - .() . f

=2.2Hz. () , .:() . .() - . k = m 2(3.19) . : = 2f (3.20) 3.22, 3.20 :k = m (2f)2(3.21) k () 111 . 3. ! -. mchair - , mtot=mchair+ mastr. :(mchair + mastr) (2f

)2= mchair (2f)2(mchair + mastr) f

2= mchair f2mastr f

2= mchair f2mchair f

2mastr= mchair(f2f

2)f

2mastr= 60 3.222.222.22mastr= 66.94kg() . - f

f

.mastr= mchair(f2f

2)f

2mastr= 64.67kg 2.27kg !!!() . . ,112 . 3.4. 113 - , .15. 1998: , m, l, g. , .() .() .() - . 3.26: : . : .113 . 3. .. - . 6 . 3.33 . 3.27: , , l . 3.33 . - 0.Fy= 0 SyB= 0 Sy= B Sy= mg (3.22) S :Sy= S cos (3.23)Sx= S sin (3.24)114 . 3.4. 115 3.32 3.33 S cos = mg (3.25)S=mgcos(3.26) 3.36 3.34 :Sx= mgcos sin (3.27) 3.33 l :sincos= tan =xl(3.28) 3.38 3.37 :Sx= mgl x (3.29) Sx, . .- . - D ( - ). -D=m2. : D =mgl D = m2 =2T115 . 3. m2=mgl2=gl :(2T)2=gl2T=_gl T= 2 lg - l g. . g. : 20 ( n) 3 . - 20 20 . T2= f(l) (T2=42g l)3 20 n . 20 .116 . 3.4. 117 , , =42gg=4216. 1999: ; :() ;() ;() ;: . - .T = 2 lg(3.30) 3.30. . :T= 2 lgT

= 2 _l4g= 2 l4 g=12 (2 lg) T

=12 T . (g=g6 ), :117 . 3. T= 2 lgT

= 2 _lg6= 2 6 lg=6 (2 lg) T

=6 T17. 1999: T m - k. - . / X0 kg kN/m Ts1 0,10 0,2 20 0,632 0,10 0,3 20 0,773 0,10 0,2 30 0,514 0,15 0,2 20 0,635 0,10 0,4 20 0,896 0,10 0,2 40 0,447 0,20 0,2 20 0,63 3.1: m, x0, k :() .() T :i. X0ii. miii. k() - T= f(X0), T= f(m), T= f(k). ;118 . 3.4. 119() - T .: . : n ( -) n . ( ) . - . y=f(x1, x2, ..., xn) n. y x1 , x2... ... x1 x1. , y, , . :i X0 ; -, m k X0. :119 . 3. / X0 kg kN/m Ts1 0,10 0,2 20 0,634 0,15 0,2 20 0,637 0,20 0,2 20 0,63 3.2: X0. m, k . .ii m ; , X0 k m. : / X0 kg kN/m Ts1 0,10 0,2 20 0,632 0,10 0,3 20 0,775 0,10 0,4 20 0,89 3.3: m. X0, k .iii k ; k , X0 m - k. : / X0 kg kN/m Ts1 0,10 0,2 20 0,633 0,10 0,2 30 0,516 0,10 0,2 40 0,44 3.4: k. m, X0 k, .120 . 3.4. 121 .0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20.500.511.520(m)T (s) 3.28: . 3.28 .0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.40.650.70.750.80.850.90.95m (kg)T (s) 3.29: 3.29 . 3.30 - .121 . 3. 20 22 24 26 28 30 32 34 36 38 400.40.450.50.550.60.65k (N/m)T (s) 3.30: 18. 2004: : / l(m) 10T(s) T 1 0,6 152 0,8 183 1,0 204 1,2 225 1,4 24 3.5: g() .() ;: 3.5 -: - , TT2. 10 , 10 - . 3.6122 . 3.4. 123 T2= f(l) (T2=42g l) , , =42gg=42 / l(m) 10T(s) T T21 0,6 15 1,5 2,252 0,8 18 1,8 3,243 1 20 2 44 1,2 22 2,2 4,845 1,4 24 2,4 5,76 3.6: g 3.31:0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.422.533.544.555.56l (m)T2 (s2) y = 4.3*x 0.29data 1 linear 3.31: g 3.6 , . .123 . 3. - 3.31 ( , x), =4.3 g. =42gg=42g=424.3 g= 9.18ms2 , - -. , l. .19. 2002: - 3.7.() - ;() (); ;() .() T .124 . 3.4. 125 / 100T(s) l(m) m(kg) X0(cm) gms21 199 1 0,05 5 10.02 199 1 0,05 10 10.03 199 1 0,02 5 10.04 162 1 0,05 5 15.05 140 1 0,05 5 20.06 126 1 0,05 5 25.07 115 1 0,05 5 30.08 140 0,5 0,05 5 10.0 3.7: g: . - 17 . ( ) , .i ; 3.7 . 3.8. / 100T(s) l(m) m(kg) X0(cm) gms21 199 1 0,05 5 10.03 199 1 0,02 5 10.0 3.8: ( ) . .ii ; . 3.9.125 . 3. / 100T(s) l(m) m(kg) X0(cm) gms21 199 1 0,05 5 10.02 199 1 0,05 10 10.0 3.9: 3.9 . . . - 3.10. / 100T(s) l(m) m(kg) X0(cm) gms21 199 1 0,05 5 10.08 140 0,5 0,05 5 10.0 3.10: . . (T=2 _lg ) . -. 3.32 . a . - a .F= m a S B= m a S= m a + m g 126 . 3.4. 127S= m (a + g) (3.31) 3.32: 3.31 () g a . 15 .20. 2004: l m. .() .() .() .127 . 3. () , , (E=f(x2),E=f(x2) E=f(x2)).: . : . .. - . 6 . 3.33 . 3.33: , , l . 3.33 . - 0.128 . 3.4. 129Fy= 0 SyB= 0 Sy= B Sy= mg (3.32) S :Sy= S cos (3.33)Sx= S sin (3.34) 3.32 3.33 S cos = mg (3.35)S=mgcos(3.36) 3.36 3.34 :Sx= mgcos sin (3.37) 3.33 l :sincos= tan =xl(3.38) 3.38 3.37 :Sx= mgl x (3.39) Sx, . .129 . 3. . 1s. .T= 2 lgT242=lg l = g T242 l = 10 1242= 0.253 m 0.253 m. - . , .x = x0 sin(t + ) (3.40)v = x0 cos(t + ) (3.41) 3.40 , :2 x2+ v2= 2 x20 sin2(t + ) + 2 x20 cos2(t + )2 x2+ v2= 2 x20 (sin2(t + ) + cos2(t + )) 2 x2+ v2= 2 x20 x2x20+v22 x20= 1 (3.42)130 . 3.4. 131x2E EdynEmechEkin 3.34: - - x2 E=f(x2), E= f(x2) E= f(x2).21. 2001: m=0, 25kg -k=50Nm. m=0, 25kg 3.35. 20cm t = 0.() () .() , .() , . :i. ii. :131 . 3. 3.35: , . : F= k 0.F = 0 F.(B + B) = 0 F.= B + B F.= (m + m) g 3.25. x :132 . 3.4. 1333.36: ) ) ) F = B + BF

(3.43)F

= k (l0 + x) = F. + k x (3.44)F.= B + B= (m + m) g (3.45) 3.43, 3.44 3.45:F = k x - ...133 . 3. . - : 0 :k = m 2=km =500.5= 10rads - 20cm . t = 0 s 20cm:x = x0 sin(t + 0) 0.2 = 0.2 sin(10 0 + 0) sin(0) = 1 0= 2 :x = 0.2 sin(10t 2) .134 . 3.4. 135 . . :dxdt= v= 0.2 10 cos(10t 2) v= 2 cos(10t 2)dvdt= a = 2 10 sin(10t 2) a = 20 sin(10t 2) 3.37 3.38 - .0 0.1 0.2 0.3 0.4 0.5 0.6 0.721.510.500.511.52t (s)v (m/s)v=f(t) 3.37: . 3.39 m=0.25kg , : , N=0. 135 . 3. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7201510505101520t (s)a (m/s2)a=f(t) 3.38: 3.39: . ... , :F= N BN B= k xN= 0 :136 . 3.4. 137B= k x m g= kx x =m gk=0.25 1050x = 0.05m 20cm 5cm. 5cm :x = x0 sin(10t 2) 0.05 = 0.2sin(10t 2) sin(10t 2) = 0.25 10t 2= sin1(0.25) t =sin1(0.25) +210= 0.182s t = 0.182s22. 1999: 1 2 m1=150g m2=50g , k 3.40.() 20cm :i. kii. - g= 10ms2.137 . 3. () 1 2 2 1 . :i. x0 ii. .() 1 t0, .() - 1 f, 1; 1 ; 3.40: .: . 0.2m. Hooke - . Hooke :F = k x k =Fx(3.46)138 . 3.4. 139: F . 1 2. k x 3.46 - :k =Fx=B1 + B2xk =m1 g + m2 gxk =0.15 10 + 0.05 100.2= 10Nm - , :k = m2k = m (2T)2km= (2T)22T=km T= 2 _mk(3.47) 3.47 - :T = 2 m1 + m2kT = 2 0.210= 0.89s139 . 3. , m2= 0.05kg 1 . , X0 . ( -) 2 - 1. Hooke .F = k x x =Fk=B1kx =m2 gkx =0.05 1010= 0.05m 1 3.47 1.T = 2 _m1kT = 2 0.0510= 0.44s 1 3.48:x = x0 sin(t + 0) (3.48)140 . 3.4. 141 x0= 0.05m =_km1=_100.15= 8.16rads 0: 3.48 t = 0s0.05 = 0.05 sin(8.16 0 + 0) sin(0) = 1 0=2 : x = 0.05 sin(8.16t +2) -f 1, . f , f0. := 2f0 f0=2 f0= 1.298Hz23. 1998: m=0.5kg . v=20 sin(5t +23), v cms ,t s cm.() y= f(t) .() - 3.41, - .() .141 . 3. 3.41: - : y= f(t) . :v= 20 sin(5t +23) :v= y0 cos(t + 0) :v= 20 sin(5t +23) v= 20 sin(5t +232+2) v= 20 sin(5t +4636+2) v= 20 sin(5t +6+2) v= 20 cos(5t +6) 142 . 3.4. 143 :sin( +2) = cos() : : , = 5rads 0: 0=6 y0:y0 = 20 y0=20=205 y0= 4cm (y cm) :y= 4 sin(5t +6) . t =0s. 0 :y= 4 sin(5 0 +6) y= 4 sin(6) y= 4 0.5 y= 2cm143 . 3. 3.42: , . y=2cm y=4cm. t=0s , y= 4cm:y= 4 sin(5tA +6) 4 = 4 sin(5tA +6) sin(5tA +6) = 1 5tA +6=2 5tA=2 6 tA=35 tA= 0.209s24. 2000: m = 150g , 3.43 , f=10 Hz. - F= 12N. :() 144 . 3.4. 145() () () , :i. x0ii. 3.43: .: :k = m2k = 0.15 (2 f)2 k = 0.15 (2 10)2 k = 60Nm . Hooke k :145 . 3. F= k x x =Fk=1260 x = 0.2m :EA=12 k x2 EA=12 60 0.22 EA= 1.2J . - -, . - (x0), .Eo= Emax EA + EA=12 k x20 EA + 3 EA=12 k x20 1.2 + 3 1.2 =12 k x20 1.2 + 3 1.2 =12 60 x20 146 . 3.4. 147 x20=2 (1.2 + 3 1.2)60 x0=2 (1.2 + 3 1.2)60 x0= 0.4m , EA=3.6J:EA=12 m v212 m v2= 3.6 v=2 3.6m=2 3.60.15 v= 6.928ms25. 2004: M T =2s. 3.44 E x . - :() () k() () M() 147 . 3. 0.05 0.04 0.03 0.02 0.01 0 0.01 0.02 0.03 0.04 0.0500.511.522.5x 103X: 0Y: 0.002406x (m)E (J)Ekin=f(x) 3.44: M .() E x : 3.44 : 2.4 103J. M x0= 0.05m. T =2s -. k. - . :Emax= Emax 12 k x20= 2.4 103 k =2 (2.4 103)x20=2 (2.4 103)0.052148 . 3.4. 149 k = 1.92Nm :f=1T=12 f= 0.5Hz :k = M 2 M=k2=k(2T)2 M=1.92(22)2= 0.195 kg - :12 M v20= Emax 12 0.195 v20= 2.4 103 v20=2 (2.4 103)0.195 v0=2 (2.4 103)0.195= 0.157ms . 3.45 :149 . 3. E=12 k x2E=12 k (x0 sin(t))20.05 0.04 0.03 0.02 0.01 0 0.01 0.02 0.03 0.04 0.0500.511.522.5 x 103x (m)E (J)E=f(x) 3.45: M .26. 1999: - 3.46. , m=50g, . f0= 10Hz.f (Hz) 2 4 6 8 9 10 11 12 14 16 18f (Hz) 2,1 3,9 6 8,1 8,9 10 11,1 11,9 14,1 16 17,9 a (cm) 0,7 0,9 1,3 2,2 3,2 4 3,1 2,3 1,2 0,8 0,6 3.11: () - () :i. f= f(f)ii. a = f(f)150 . 3.4. 151 3.46: . m=50g, m

= 200g - (ii);151 . 3. : 3.46, . . . 3.11. f= f(f) 3.47 a = f(f) 3.48.2 4 6 8 10 12 14 16 1824681012141618f (Hz)f (Hz)f = f(f) data 1 linear 3.47: a. : . 3.47. . , 152 . 3.4. 1532 4 6 8 10 12 14 16 180.511.522.533.544.5f (Hz)a (cm)a=f( f ) data 1 spline 3.48: a. . - . (f0=10Hz), . 3.48. m = 50g, m

=200g , - . k - :k = m 2= m (2f)2 k = 197.39Nmk = m

2= m

(2f

)2 2f

=km

f

=12 km

f

= 5 Hz153 . 3. 0 5Hz . f=5Hz . .27. 2004: 3.49, k = 4Nm m=0.15kg. . =4rads x0. 0.20kg, 0.25kg, 0.30kg, 0.35kg 0.40kg.() () x0, m x0=f(m) m 3.49: .154 . 3.4. 155: -. 3.49 = 4rads , . (), . -. - f=12_km k = m(2f)2. . . :f=12 km : mf= 2 _km0,15 0,8220,2 0,7120,25 0,6370,3 0,5810,35 0,5380,4 0,503 3.12: . := 2f f=2= 0.637Hz155 . 3. -. . x0= f(m), 3.50.0.15 0.2 0.25 0.3 0.35 0.4mx0x0=(m) 3.50: .28. 2005: ( ) 12cm Hooke . 4cm F= 0.2N. 14cm 16cm.: 14cm 16cm : 14cm 16cm - 16cm 156 . 3.4. 15714cm. k :F= k x k =Fx k =0.20.04= 5NmE1216cm=12 k x2 E1216cm=12 5 0.042 E1216cm= 4 103JE1214cm=12 k x2 E1214cm=12 5 0.022 E1214cm= 1 103JE1416cm= E1216cmE1214cm E1416cm= 4 1031 103 E1416cm= 3 103J29. 2005: k=20Nm 0, 1J - x. 3x.: - . .157 . 3. E=12 k x2= 0.1JE

=12 k (3x)2 E

=12 k 9 (x)2 E

= 9 12 k (x)2 E

= 9 E= 0.9J30. 2005: l . . =l4, l g. 3.51. 3.51: .: l, , 3l4, , , - l. 158 . 3.4. 159 - l 3l4.T=T12+T22 T=2 _lg2+2 _3l4g2 T= lg+ 3l4g T= lg+32 lg T= (1 +32) lg T= 5.86 lg159 . 3. 160 . 44.1 1. - 1 244: . - ;: . - . , - ( ) .2. - 2 244: ; ;: . :f y0 161 4. v 3. - 3 244: .: :() : . .() : . .4. - 4 244: () ;() ;: () . , :x = = 1, 2, ...() 162 . 4.1. 163 yA= yB ,vA= vB . - , :x = 2 = 1, 2, ...5. - 8 244: ;: (), .6. - 9 244: - ;: - . 4.1 = 2 ( tT x) (4.1) , :A= 2 ( tT xA) B= 2 ( tT xB)163 . 4. = AB = 2 ( tT xA) 2 ( tT xB) = 2 tT 2 xA2 tT+ 2 xB = 2 xB2 xA = 2 xBxA = 2 x .7. - 10 244: 74 ;: - . : = 2 x = 2 74= 2 74 = 7 28. - 11 244: ;164 . 4.1. 165: . .9. - 12 15 244: ; ;: - . , - . . .: . . x t =xv. t =xv. :y1= y0 sin_2( tT x)_y2= y0 sin_2( tT+x)_ : = y1 + y2=165 . 4. = y0 sin_2( tT x)_+ y0 sin_2( tT+x)_== y0_sin_2( tT x)_+ sin_2( tT+x)__ 4.7 .sinA + sinB= 2 cos(A B2) sin(A + B2) (4.2) = y0_sin_2( tT x)_+ sin_2( tT+x)__== 2y0_cos(2 tT x tT x2) sin(2 tT x+tT+x2)_== 2y0_cos(2 2x2) sin(2 2tT2 )_ = 2y0 cos(2 x) sin(2 tT )cos(x) =cos(x) : = 2y0 cos(2 x) sin(2 tT ) (4.3) 4.3 .: 2y0cos(2x) . - . sin(2 tT ), .166 . 4.1. 167 , , , .: cos(2 x) , :cos(2 x) = 1 2 x= x = 2 = 0, 1, 2, ... (4.4) 4.4 - . , . cos(2 x) 0.cos(2 x) = 0 2 x= (2 + 1) 2 x = (2 + 1) 4 = 0, 1, 2, ... (4.5) 4.5 - . 15 . 12 . .167 . 4. x1o= (2 + 1) 4, x1o= 2 = 0x =2 4 x =410. - 13 244: y= y0 sin_2 (tT x)_. x =54 ;: , . 0. , = 2 (tT x). x =54 . = 0 0 = 2 ( tT 54 ) tT=54 t =54 T11. - 14 244: 6 3 .() ;() ;: . 168 . 4.1. 169: 2y0 cos(2 x) . . : - - 2y0 cos(2 x) . :cos(2 xA) = cos(2 6) = cos(26) = 0.5 :cos(2 xB) = cos(2 3) = cos(23) = 0.5 . : :A= 2y0 0.5 A= y0 :B= 2y0 (0.5) B= y0 .169 . 4. 4.2 1. - 1 247: . - . y0= 0.2m. 0.5m. 5 5sec. t = 0 x=0 x, , .: , : y0 :y= y0 sin_2(t f x)_ 0.2m y0= 0.2m 0.5m. . 5 t = 5sec.f=cyclest=55= 1Hz , ().170 . 4.2. 171 :y = y0 sin_2(t f x)_== 0.2 sin_2(t 1 x0.5)_y = 0.2 sin[2(t 2x)]2. - 2 248: y= 2sin_(8t x16)_.( cm s).() , , - .() , 60cm .() ,13cm .: . - :y= y0 sin_2( tT x)_(4.6) 2:y= 2sin_22 (8t x16)_= 2sin_2(82 t x2 16)_= 2sin_2(4 t x32)_171 . 4. - 4.6 : y0= 2cm 4t =tT T=t4t T= 0.25sx=x32 =32xx = 32cm v= 1T=320.25 v= 128cms - . :t =xv=60128 t = 0.47s t =0s t =0.47s . t = 0.47s yM= 2sin_2(4 t x32)_0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 121.510.500.511.52t (s)yM (cm)y=y0 sin[(8tx/16)] 4.1: . t=13s. .172 . 4.2. 173x = v t = 128 13 = 1664cm t=13s x 0 1664cm. - 1600cm 1664cm.1600 1610 1620 1630 1640 1650 1660 167021.510.500.511.52x (cm)y (cm) 4.2: t = 13s.3. - 3 248: O1 O2 v=3ms . M d1=5m d2=7m . f =2Hz y0= 2cm. M t1= 25s t2= 3.125s.173 . 4. 4.3: M.: - . - M - M . . :y1= y0 sin_2( tT x1 )_y2= y0 sin_2( tT x2 )_ . x1 x2 - .- : = y1 + y2== y0 sin_2( tT x1 )_+ y0 sin_2( tT x2 )_174 . 4.2. 175= y0_sin_2( tT x1 )_+ sin_2( tT x2 )__ 4.7 .sinA + sinB= 2 cos(A B2) sin(A + B2) (4.7) = y0_sin_2( tT x1 )_+ sin_2( tT x2 )__= 2y0_cos_2(tT x1 ) 2(tT x2 )2_ sin_2(tT x1 ) + 2(tT x2 )2__== 2y0_cos_2tT2x12tT+2x22_ sin_2tT2x1+2tT2x22__== 2y0__cos(2 (x2x1)2) sin(4tT2(x2+x1)2)__ = 2y0 cos_2 (x2x12)_ sin_2 ( tT x1 + x22)_(4.8) 4.8 , x1 x2 . , - 4.8 M. x1 x2 . ( ). , - . :v= f =vf = 1.5m175 . 4. :T=1f T=12 T= 0.5sM= 2y0 cos_2 (x2x12)_ sin_2 ( tT x1 + x22)_M= 2 0.02 cos_2 ( 7 52 1.5)_ sin_2 (t0.5 5 + 72 1.5)_M= 0.04 cos(4.189) sin[2 (2t 4)] (4.9) : t1= 25sM= 0.04 cos(4.189) sin[2 (2 25 4)] = 0m t1= 3.125sM= 0.04 cos(4.189) sin[2 (2 3.125 4)] = 0.02m M .4. - 5 248: y= 16 cos(x30) sin(80t) x, y cm t s. :() () 67.5cm() - 8cm.176 . 4.2. 177: 9 153, : = 2y0 cos(2 x) sin(2 tT ) - : 2 y0= 16 y0= 8cmx30= 2x =2x30x = 60cm 2tT= 80t T=2t80t T= 0.025s . , 9 153.x = (2 + 1) 4 = 0, 1, 2, ... = 0 = 1: :x = (2 + 1) 4 x = (2 0 + 1) 604= 15cm :x = (2 + 1) 4 x = (2 1 + 1) 604= 45cm177 . 4. x = 67.5cm. 2y0 cos(2 x), :0(67.5)= 2y0 cos(2 x) 0(67.5)= 16 cos(2 67.560) 0(67.5)= 11.31cm y= 8cm. 2y0 cos(2 x). :2y0 cos(2 x) = 8 16 cos(2 x60) = 8 16 cos(2 x60) = 8 cos(2 x60) =12 cos(2 x60) =12 2 x60=3 x =603 2= 10cm5. - 6 248: y=4 sin(15.7t), (y cm, t s). M1 x1= 2m , t = 3s. M2 x2= 5m t1= 10.25s t2= 12.5s.: M2 :178 . 4.2. 179 M2 - , , . :y= y0 sin(2Tt) :y= 4 sin(15.7 t) : y0= 4cm2T= 15.7 T=215.7= 0.4s t = 3s M1 x1=2m :v=x1t= 0.67msv= 1T = v T = 0.267m179 . 4. :y= y0 sin_2( tT x)_y= 4 sin_2(t0.4 x0.267)_y= 4 sin[2(2.5 t 3.745 x)] M2 - x x2 , t1 t2. t1= 10.25syM2= 4 sin[2(2.5 t 3.745 x2)]yM2= 4 sin[2(2.5 10.25 3.745 5)]yM2= 2.35cm t1= 12.5syM2= 4 sin[2(2.5 t 3.745 x2)]yM2= 4 sin[2(2.5 12.5 3.745 5)]yM2= 0.625cm6. - 7 249: , 1cm, 21.6cm t = 1.2s. :() () 8cm 12.180 . 4.2. 181: - , 12. , = 1cm. :v=xt=21.61.2v= 18cms :v= f f=v f= 18Hz 12 - t. . :B= 2(t f xB) B2= t f xB t =B2+xBf=122+8118 t = 0.778s t

=1.2s . .: , 181 . 4. :A= 2(t f xA)7. - 8 249: y= y0sin[2(2 t 0.01 x)]. x, y cm t s. :() , , () - : :y= y0 sin_2( tT x)_ y0= 10cm = 0.1mtT= 2t T= 0.5s x= 0.01 x = 100cm v= 1T= 10010.5 v= 200cms= 2ms . , , . - . =dydt=ddt_y0 sin_2( tT x)__ =2Ty0 cos_2( tT x)_(4.10)0=2Ty0182 . 4.2. 183a =ddt=ddt_2Ty0 cos_2( tT x)__ a = (2T)2y0 sin_2( tT x)_(4.11)a0= (2T)2y0 0=2Ty0 0= 0.4ms a0= (2T)2y0 a0= 1.6 2 ms2:4.104.11- , .8. - 9 249: y0= 10m, f= 10Hz v= 1ms .: :y= y0 sin_2(f t x)_ . y0= 10m f= 10Hz v= f =vf=110 = 0.1m :y= 10 sin_2(10 t x0.1)_183 . 4. 4.3 -1. - 1 272: l = 1m, m = 5g . f= 130.5Hz. ;: , . . , . , -. 2. :v=F(4.12)v= f (4.13) 4.12, F =ml . . : :l =2. 4.12,4.13 . F : f=F ( f)2=F F= ( f)2 l =2 = 2 l184 . 4.3. 185F= (2 l f)2=ml (2 l f)2 F=0.0051 (2 1 130.5)2 F= 340.6N2. - 2 272: l1=33cm f1=440Hz. f2 f2f1=32; f2;: f1=440Hz. l, 2. - :l =12 1= 2 l = 66cm f2 f2f1=32:f2f1=32v= 1 f1= 2 f2 :185 . 4. f2f1=12f2f1=322=23 1= 44cm - f2. , f2 l

:l

=22 l

=442= 22cm l

=22cm. 11cm . f2:f2f1=32f2=32 f1=32 440Hz f2= 660Hz3. - 3 272: 68cm. v= 340ms .() ;() f2 f2f1=32;186 . 4.3. 187: , , . . - ,4= l, l .( 4.4). 4.4: . v = f :4= l = 4 l = 4 0.68 = 2.72m :187 . 4. v= f f=v f=3402.72= 125Hz : f2 f1f2=32 v=

f2

=vf , l

=

4 f2:f1f2=32 f2=23 f1=23 125 f2= 83.33Hz :v=

f2

=vf

=34083.33

= 4.08m :l

=

4 l

=4.084 l

= 1.02m188 . 4.3. 1894. - 7 273: l =0.75m . v =1500ms . :() () 4 .: 4 . 4.5. 4.5: , 4 . l =3 2. 2.l = 3 2 =2 l3 =2 0.753 = 0.5m . :189 . 4. v= f f=v f=15000.5= 3000Hz5. - 8 273: y= 10 cos( x6) sin(50t) x, y cm t s. :() 1,2 () : . , ( ). - .y= 2y0 cos(2 x) sin(2f t) y0: 2y0= 10 y0= 5cm f: 2f= 50 f=502= 25Hz :2x=x6 = 12cm - 2. x. :x.=2=122 x.= 6cm190 . 4.4. YOUNG 1914.4 Young4.4.1 1. ; ;: - . Huygens : . 4.6: ) ) - .191 . 4. 2. - 1 283: ;: . , 4.6.3. - 2 283: ;: - ,. - - .4. - 3 283: ;: .5. - 4 283: Young - . .: Young 4.7. 1 2. 1 2 - 2 . 192 . 4.4. YOUNG 193 4.7: Young , - . -. . - , , . x = k (4.14) x = (2k + 1) 2(4.15)193 . 4. x , k . 2, x=O2. 4.7 2. 2 - - 1 :sin =O2aO2 = sin a D :sin tan :tan =ykD :x =ykD a (4.16) : 4.14 4.16x =ykD ax = k ykD a = k (4.17)194 . 4.4. YOUNG 195 4.15 4.16x =ykD ax = (2k + 1) 2ykD a = (2k + 1) 2(4.18)- .6. - 5 285: - () ;() ;: 5, . 4.14 yk:ykD a = k yk=D k a(4.19) : - 4.19 . k .195 . 4. : . , a - a 4.19 yk . (k ) .: .4.4.2 1. - 1 285: Young -. a = 0.5 103m D = 2m x = 10 103m() - () ;: -. , :yk=D k a . 196 . 4.4. YOUNG 197 x 5 . k = 5.yk=D k a =yk aD k =10 103 0.5 1032 5 = 5 107m . a

= 2a yk=Dka.2. - 2 285: Young =5.89 107m 2m. 1.178cm.() ;() (=4.5 107m), ;() () .: a. D = 2m y10= 1.178cm k = 10 = 5.89 107m197 . 4. yk=Dka a :yk=D k a a =D k yk=2 10 5.89 1070.01178 a = 1 103m = 1mm - , =4.5 107m. - yk yk+1. o= yk+1yk:o= yk+1yk==D (k + 1) aD k a==D k a+D 1 aD k ao=D a :o=D a=2 4.5 1071 103o= 9 104m = 0.9mm :y5=D 5 a=2 5 4.5 1071 103y5= 4.5 103m = 4.5mm198 . 4.5. 1994.5 -1. 2005: 4.8 4.9 .0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.0810.80.60.40.200.20.40.60.81x (m)y(m) 4.8: .0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.610.80.60.40.200.20.40.60.81t (s)y(m) 4.9: . :() 199 . 4. () () : 4.8 . - 2 . = 0.04m 4.9, , . . . :T= 0.8s v=T:v=T=0.040.8 v= 0.05ms2. 1993: 4.10 y=f(x) t=t0. 50Hz 0 . :() t0200 . 4.5. 201() () () , dAB= 0.3m, t = t +0.01s. xA= 0.9m xB= 1.2m() , = f(x), t = t0.0 0,3 0,6 0,9 1,20.40.30.20.100.10.20.30.4x (m)y (m) 4.10: .: - 4.10. . : = 0.6m f= 50Hz, - :v= f= 0.6 50 v= 30ms201 . 4. 4.10 0.9m t0 . v=xt t0:v=xt t0=xv=0.930 t0= 0.03s :y= y0 sin_2(t f x)_y0 y0=0.4m. - :y= y0 sin_2(t f x)_ y= 0.4 sin_2(50t x0.6)_ t =t+0.01s. : yB x t = t + 0.01s = 0.04syB= 0.4 sin_2(50t xB0.6)_ yB= 0.4 sin_2(50 0.04 1.20.6)_ yB= 0m202 . 4.5. 203 () t=t +0.01s=0.04s :B=ddt_0.4 sin_2(50t xB0.6)__ B= 2 50 0.4 cos_2(50t xB0.6)_ B= 2 50 0.4 cos_2(50 0.04 1.20.6)_ B= 40ms =(x) t =t0. t0 : = 2(t0 f x) = 2(50 0.03 x0.6) t0= 0.03s x = 0.9m:0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9012345678910x (m) (rad) 4.11: t = t0.203 . 4. 3. 1992: x - y= 0.02sin(20t 0.5x). . . :() () t = 0.2s .() x, t = 0.3s, .() y= 0.015m .() , .: . - .y= y0 sin_2( tT x)_ y= y0 sin(2T t 2v T x) . :y= 0.02sin(20t 0.5x)y= y0 sin(2T t 2v T x)204 . 4.5. 205 y0= 0.02m2T= 20 T= 0.1s 2v T= 0.5 v=20.5 T v= 40ms t = 0.2s . v=40ms : x = v t = 40 0.2 = 8m0 1 2 3 4 5 6 7 80.020.0150.010.00500.0050.010.0150.02x (m)y (m) 4.12: t = 0.2s. t =0.3s. =20t 0.5x t =0.3 .x = v t = 40 0.3 = 12m - y=0.015m - .205 . 4. 0 2 4 6 8 10 1202468101214161820x (m) (rad) 4.13: t = 0.3s.y= 0.02sin(20t 0.5x)v=dydt= 20 0.02cos(20t 0.5x)a =d2ydt2=dvdt= (20)2 0.02sin(20t 0.5x) sin(20t0.5x) . . :y= 0.02sin(20t 0.5x)0.015 = 0.02sin(20t 0.5x) sin(20t 0.5x) =34sin2+cos2 =1 :sin2(20t 0.5x) + cos2(20t 0.5x) = 1 206 . 4.5. 207 cos2(20t 0.5x) = 1 sin2(20t 0.5x) cos2(20t 0.5x) = 1 (34)2 cos(20t 0.5x) =1 (34)2 cos(20t 0.5x) = 0.6614cos(20t 0.5x) =0.6614 sin(20t 0.5x) =0.75. - - :v= 20 0.02cos(20t 0.5x) v= 20 0.02 0.6614 = 0.83msa = (20)2 0.02sin(20t 0.5x) a = (20)2 0.02 0.75 = 59.2ms2 , . y0=0.01m,f =20Hz + .: . v= f =vf=4020= 2my= 0.01sin_2(f t +x)_y= 0.01sin_2(20 t +x2)_207 . 4. 4. 2003: 4.14 t0, f =0.25Hz. :() xA= 0.5cm xB= 2cm() t = t0 + 1s0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 53210123x (cm)y (cm) 4.14: t = t0.: . = 2 (tT x) + 0. . t0. = 2cm, 4.14 v= f= 2 0.25 = 0.5cms t0 4cm v= 0.5cms .v=xt0t0=xv=40.5 t0= 8s208 . 4.5. 209 : = AB== 2 ( tT xA) + 02 ( tT xB) 0== 2 (84 0.52) 2 (84 22) == 2 1.75 2 1 = 1.5 -t =t0+1s. 1s T4T =4s. t =t0=8s. 1s 0. - - t=9s ,xA=0.5cm.y= 2sin_2(f t +x)_ y= 2sin_2(0.25 9 +0.52)_ y= 05. 1991: Young = 6 107m. S1=1mm. D=2m, S2= 3mm. .209 . 4. : :o= yk+1yk==D (k + 1) aD k a==D k a+D 1 aD k ao=D a . D - D

= D + D .o=D a(4.20)

o=D

a

o=(D + D) a (4.21) a - 4.20 D 4.21.D =a o

o=(ao+ D) a(4.22) 4.22 a - . :210 . 4.5. 211 = 6 107m S1= o= 1mm S2=

o= 3mm D = 2m

o=(ao+ D) a a

o= a o + D a (

oo) = D a =D

oo=2 6 1070.003 0.001 a = 6 104m6. 2005: -f=2Hz, y0=0.01m v=0.1ms . . t0=0s . x1=0.4m 1 x2=0.6m 1=2. :() 1 1 t0= 0s .() .() , , 0 t 8s.211 . 4. 4.15: .: 1 , : y0= 0.01m f= 2Hz v= 0.1ms =vf=0.12= 0.05m :y= y0sin_2(f t x)_ :212 . 4.5. 213y= y0sin_2(f t x)_ y= 0.01sin_2(2t x0.05)_ , . . 3 161 : = 2y0 cos_2 (x2x12)_ sin_2 ( tT x1 + x22)_ () -1 1 0 -. :cos_2 (x2x12)_= cos_2 (0.6 0.42 0.05)_= cos_2 (0.20.1)_= cos(4) = 1 - , ., 0 t 8s. .: , , - . .213 . 4. - . - . 1 :v=x1t1t1=x1v=0.40.1 t1= 4s, 2 :v=x2t2t2=x2v=0.60.1 t = 6s : 0 t 4s 4 t 6s 1 y= 0.01sin_2(2t x0.05)_ 6 t 8s = 2y0 cos_2 (x2x12)_ sin_2 ( tT x1 + x22)_ 4.16.214 . 4.5. 2150 1 2 3 4 5 6 7 80.020.0150.010.00500.0050.010.0150.02 t (s)yo ( m )4.16: t.215 . 4. 216 . 5 5.1 1. II- 1 24: , , 5.1. .t1 t2 t3Iot II=f(t) 5.1: t.: 217 5. . 5.1E= LdIdt(5.1) 5.1 - . . 5.1 () : 0 I0 0 t1. :E= LdIdt= LIt E= L(I00)(t10) E= LI0t1() : I=I0 t1t2. :E= LdIdt= LIt E= L(I0I0)(t2t1) E= 0() : I0 0 t2 t3. - :218 . 5.1. 219E= LdIdt= LIt E= L(0 I0)(t3t2) E= LI0t3t2 5.2.t1 t2 t3L*I_0\t105L*I_0\(t3t2)tE 5.2: t.2. II- 6 26: 5.3 - . .: - Faraday : :219 . 5. 0 0.5 1 1.5 2 2.5 3 3.5 4201510505101520t (s) (Wb)=f(t) 5.3: t.E= t(5.2) - =1. (), 5.3 ( ) . 5.2.() : =0 =20Wb t =0 t =2s. :E= t= 20 02 0E= 202= 10 V() : = 20 =20Wb t = 2 t = 4s. :220 . 5.1. 221E= t= 20 (20)4 2E= 402= 20 V t 5.4.0 0.5 1 1.5 2 2.5 3 3.5 4252015105051015t (s)V (v)V=f(t) 5.4: t.3. II- 1 27: 5.5 . SA, SB=2 SA S= 3 SA . :() ;() ; .: . - Weber Wb. :221 . 5. 5.5: . = B S = BScos (5.3) B S 1S B. 5.6 . 5.3 5.6 :() :A= B SA= BSAcos A= BSAcos900= 0 Wb() :B= B SB= BSBcos B= BSBcos00= 2BSAWb1 , .222 . 5.1. 223 5.6: .() := B S= BScos = 3BSAcos600= 1.5BSAWb- .4. II- 2 27:1 T, 15 , -, 20cm. . , , 0.1s.: d=20cm. :S= r2= (d2)2= (0.22)2 S= 0.0314m2 . 223 . 5. = 00 . , B=B2 Faraday :E= t E= BScos BScost= 150.5 0.0314 1 1 0.0314 10.1 E= 2.353 V5. II- 3 27: , , v= 360km/h. l = 30m. B= 0.3 104T.: , . - . Faraday. S.I :v= 360kmh= 3601000m3600s= 100ms . . Faraday :224 . 5.1. 225E= t= t(BS) E= B t(l x) = B lxt E= B l v= 0.3 104 30 100 E= 0.09 V6. II- 4 27: 0.2m - - . 0.1m2s , 18mV . ;: . - - , . St=0.1m2s . , - . :E= t= t(BS) E= B St B= E 1St= 18 10310.1 225 . 5. B= 18 102T7. II- 5 28: , a=0.4m, . Bz - 5.7. E= f(t) , .0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160.0500.050.10.150.20.250.30.350.40.45t(ms)Bz (T)Bz=f(t) 5.7: Bz t.: Fara-day. . B, Bz. :E= t= t(BS) E= S Bzt(5.4)226 . 5.1. 227 5.4 5.7 7 .: 5.7 Bzt . S= a a = 0.16m2 1:E= S Bzt= 0.160.4 0(3 0) 103 E= 21.33 V 2:E= S Bzt= 0.160.4 0.4(5 3) 103 E= 0 V 3:E= S Bzt= 0.160 0.4(7 5) 103 E= 32 V 4:E= S Bzt= 0.40 0(9 7) 103 E= 0 V 5:E= S Bzt= 0.40.4 0(12 9) 103 E= 21.33 V227 . 5. 6:E= S Bzt= 0.160.4 0.4(14 12) 103 E= 0 V 7:E= S Bzt= 0.160 0.4(16 14) 103 E= 32 V 5.80 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16302010010203040t ( ms )E ( v )E=f( t ) 5.8: E t.8. II- 6 28: 5.9 , l =1m =20rads , B= 0.5T. 228 . 5.1. 229 5.9: . . .: . - , . - , : - , , . Faraday . :=2TT=2=220 T=10s r = l = 1m :S= r2= 12229 . 5. S= m2 :St=STT=10St= 10m2s Faraday .: . 1800 B 5.10.: :E= t(B S) = BSt 5.10: S B.E= t= t(B S) 230 . 5.1. 231 E= BSt cos = 0.5 10 cos1800= 0.5 10 (1) E= 5 V9. II- 7 28: B=0.2T - 5.11. v= 15ms t = 0 . xA= 0.5m. :() , () ; 5.11: .: 5.11 v= 15ms . . 5.12 . :231 . 5. 5.12: .t= B St t= B (l x)t l = .t= B lxt= B l v t= 0.2 0.5 15 = 1.5 Wb - . Faraday = 1 :E= t= 1.5 V10. II- 8 28: 1m, 103 30cm2 . . , 232 . 5.1. 233 = 1950;: 5.5:E= L It(5.5) . 5.5 Faraday. Faraday .: , . B=0 N Il(5.6)E= ddt= ddt(B S) E= dBdt S dSdt B dSdt= 0 E= d(0NIl)dt S E= 0 Nl S dIdt 5.5, :L =0 N Sl233 . 5. 0= 4 107 N= 103 l = 1m S= 30 104m2L =4 107 103 30 104 1031 L = 3.77 mH . 5.5 = 1950 :L = 0 N Sl L = 1950 3.77 L = 7.35 H11. - - 23: A1y1 A2y2 1m . A1 A2 , , - ..E=20V r =2. , l= 1m, m = 0.3kg 8, , A1y1 A2y2 . B= 1T, A1y1 A2y2. . t = 0s . :() .234 . 5.1. 235() -() - vo , v= vo.() I v , I =f(v) .() v= vo, :i. ii. iii. . 5.13: .235 . 5. : . , - Faraday .. .() - . r =2 RK=8. , , :Ro= r + RK= 2 + 8 Ro= 10 - Ohm :I=VRo=2010 I= 2 A() . F =m a . : B= mg= 0.3 10 = 3 N Laplace FL= B I L = 1 2 1 = 2 NF= m a a =Fm=B FLm a =3 20.3= 3.33ms2236 . 5.1. 237 5.14: .() . , Faraday ... ... I=ERo LaplaceFL=B I L. FL a = 0ms2 . - F= 0 .. Faraday.F= 0 FLB= 0 FL= B B Io L = mg Io=mgBL= 3 A . Faraday . 237 . 5. I=ER=2010= 2 A .. ..:I= IoI= 3 2 = 1 AE= I Ro= 1 10 = 10V Faraday :E= t= B St E= B (l y)t l = . lt= 0 E= B lyt= B l vo vo= EB l= 101 1 vo= 10ms vo=10ms() . :I= I+ I I=ERo+tRo I= 2 +B v lRo I= 2 +v10238 . 5.1. 239 5.15.0 2 4 6 8 10 12 14 16 18 2000.511.522.533.54I=f(v)v (m/s)I (A) 5.15: , I, v.() :i. :P= I V= 3 20 P= 60 Wii. :P= I Vo= 3 30 P= 90 Wiii. :P= I Vo= PP= 90 60 P= 30 W12. 2004: OX1 OX2-, O, 239 . 5. X1OX2, . yy

v X1OX2 . . B, 5.16. t0= 0s yy

O t(t>0s) OX1 OX2 . : 5.16: .() Faraday() t.() t, ... E= (2Bv2tan)t() -OX1 OX2 yy

r.() .() -, 240 . 5.1. 241 . .:() Faraday : -() . 5.16 2 . x v t v=xt .tan =KMx(5.7)x = v t (5.8) 5.7, 5.8 K = 2KM :KMtan= v t KM= tan v tK = 2KM= 2 tan v t , E=o2, 5.16 - :S=K x2241 . 5. S=(2 tan v t) (v t)2 S= tan v2 t2() Faraday :E= ddt= ddt(B S) E= BdSdt E= Bd(tan v2 t2)dt E= 2Btan v2 t() :RK= r K RK= 2r tan v t() . .. , Ohm, :I=ERo I= 2Btan v2 t2r tan v t I= B vr242 . 5.1. 243() - Laplace FL. 0 ( ), vo. :F= FL F= B I L F= B (B vr) (2 tan v t) F=B2 v2r 2tan t13. : - . 5.17: Biot-Savart.: Biot-Savart 5.9:243 . 5. d B= 0I ds sin4R2(5.9) I ds Biot-Savart = 0 = 2. : =2.ds ds = Rd :d B= 0I ds sin4R2 B=_200I ds sin4R2 B=_200I R d sin(2)4R2 B=0I4R_20d =0I4R []20 B=0I2R244 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 51.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 . . . . . . . . . . . . . . . . . . . . . 111.3 . . . . . . . . . . . . . . . . . . . . . . 232 332.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.4 . . . . . 463 573.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 823.4 . . . . 924 1614.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1614.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1704.3 . . . . . . . . . . 1844.4 Young . . . . . . . . . . . . . . . . . . . . . . . . . . 1914.4.1 . . . . . . . . . . . . . . . . . . . . . . . . . 1914.4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . 1964.5 . . . . . . . . 1995 2175.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217245246 . 1.1 P= f(v), E= f(p) . . . . . . . . . . . . . . . . 91.2 v= f(t) . . . . . . . . . . . . . . . . . . . . . . . 121.3 F= f(t) F= f(x) . . . . . . . . . . . . . . . 141.4 P= f(t) E= f(t) . . . . . . . . . . . . . 151.5 . . . . . . . . . . . . . . . . . . . . . . . . . 171.6 . . . . . . . . . . . . . . . . . . . . . . . . . 181.7 . . . . . . . . . . . . 211.8 . . . . . . . . . . . . 211.9 . . . . . . . . . . . . 221.10 P= f(t) E= f(t) . . . . . . . . . . . . . 251.11 P= f(t) E= f(t) . . . . . . . . . . . . . 271.12 . . . . . . . . . . . . . . . . . . . . . . . . 282.1 . . . . . . . . . . . . 342.2 . . . . . . . . . . . . 412.3 . . . . . . . . . . . . . . 442.4 . . . . . . . . . . . 472.5 - . . . . . . . . . . . . . . . . . . . . 492.6 - , ) ) . . . . . . . . . . . 512.7 () () . . . . . . . . 543.1 .. . . . . . . . . 573.2 ... . . . . . . 603.3 . . . . . 613.4 , . . . . . . . 623.5 . . . . . . . . . . . . . . . . . . . . . . . . 633.6 ... . . . . . . . . 703.7 h . . . . . . . . . . . . . . . . . 743.8 . . . . . . . . . . . . . . . . . . . . . 753.9 . . . . . . . 753.10 . . . . . . . . . . . . . . . . . . . 76247 3.11 . . . 773.12 - . . . . . . . . . . . . . . . . . . 803.13 . . . . . . . . . . . . . . . . . . . . 843.14 . . . . . . . . . . . . . . . . 853.15) ) ) . . . 893.16 a = f(x) . . . . . . . . . . . . . . . . . . 933.17 x = f(t) . . . . . . . . . . . . . . . . . . 943.18 v= f(x) . . . . . . . . . . . . . . . . . . 963.19 - ... . . . . . . . . . . 973.20 a = f(x) . . . . . . . . . . . . . . . . . . 1003.21 x = f(t) . . . . . . . . . . . . . . . . . . 1013.22 x = f(t) . . . . . . . . . . . . . . . . . . 1033.23 F= f(x) . . . . . . . 1043.24 T2= f(m) . . . . . . . . . . . . . . . . . 1073.25) ) ) . . . 1093.26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1133.27 . . . . . . . . . . . . . 1143.28 . . . . . . . . . . . . . . 1213.29 . . . . . . . . . . . . . . . 1213.30 . . . . . . . . . . . . . . . 1223.31 g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1233.32 . . . . . . . . . . . . . 1273.33 . . . . . . . . . . . . . 1283.34 - - x2. 1313.35 . . . . . . . . . . . . . . . . . . . . 1323.36) ) ) - . . . . . . . . . . . . . . . . . . . . . . . . 1333.37 . . . . . . . . . . . . . . . . 1353.38 . . . . . . . . . . . . . . . 1363.39 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1363.40 . . . . . . . . . . . . . . . . . 1383.41 - . . . . . . . . . 1423.42 . . . . . . . . . . . . . . . . . . . . . . 1443.43 . . . . . . . . . . . . . 1453.44 M . . 1483.45 M . 1503.46 . . . . . . . 1513.47 a. . . . . . . . . 1523.48 a. . . . . . . . . . 153248 . 2493.49 . . . . . . . . . . . . . . . . . . . . 1543.50 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1563.51 . . . . . . . . . . . . . . . . . . . . 1584.1 . . . . . . . . . . . . . . . . . . . . . . . . 1724.2 t = 13s. . . . . . . . . . . . 1734.3 M. . . . . . . . . . . . . . . . . . . 1744.4 . . . . . . . . 1874.5 , 4 . . . . . . . . . . . . . . 1894.6 ) ) - . . . . . . . . . . . . . . . . . . . . . 1914.7 Young . . . . . . . . . . . . . . . . . . 1934.8 . . . . . . . . . . . . . . . . . . . . . . . 1994.9 . . . . . . . . 1994.10 . . . . . . . . . . . . . . . . . . . . . . . 2014.11 t = t0. . . . . . . . . . . . . . . . . . . 2034.12 t = 0.2s. . . . . . . . . . . . . . . . . 2054.13 t = 0.3s. . . . . . . . . . . . . . . . . . 2064.14 t = t0. . . . . . . . . . . . . . . . . . 2084.15 . . 2124.16 t. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2155.1 t. . . . . . . 2175.2 t. . . . . . 2195.3 t. . 2205.4 t. . . . . . . . . . . . . . 2215.5 . . . . . . . . . . . . . . . . . 2225.6 . . 2235.7 Bz t. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2265.8 E t. . . . . . 2285.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2295.10 S B. . . . . 2305.11 . . . . . . . . . . . 2315.12 . . . . . . . . . . . . . . . . . . . . . . . 2325.13 . . . . . . . . . . . . . . . . . 2355.14 . . . . . . . . . . . . . 2375.15 , I, v. . . . . . 239249 . 5.16 . . . . . . . . . . . . . 2405.17 Biot-Savart. . . . . 243250 . 3.1 m, x0, k. . . . . . . . . . . . . . . . . . . . . 1183.2 X0. m, k . . . . . . . . . . . . . . . . . 1203.3 m. X0, k . . . . . . . . . . . . . 1203.4 k. m, X0 . . . . . . . . . . . . . . . . . 1203.5 g . . . . 1223.6 g . . . . . . . . . . . . . . . . . . . . . . . . . . . 1233.7 g . . . . 1253.8 . . . . . . . . . . 1253.9 . . . . . . . . . 1263.10 . . . . 1263.11 . . . . . . . . . . 1503.12 . . . . . . . . . . . . . . . 155251 252 . [1] . , . (1997), , 7, [2] . , . (1998): , - 7, -[3] . , . (1987): 2, 3, -[4] . , . , . (2001): , , -[5] . , . , . , . (2001):, , [6] . , . , . , . , ., . , . , . , . . , . , . , . , . ,. (2007): , , [7] Tom Duncan (1973):Advanced Physics, 5thEdition, London HodderMurray, a member of the Hodder Murray Headline Group[8] Mark Ellse, Chris Honeywill (2003):Waves and our Universe, RevisedEdition, Nelson and Thornes Cheltenham, United Kingdom[9] Harvey J. Greenberg (2004): ASimpliedIntroductiontoLaTEX, Uni-versity of Colorado, Denver253[10] Tobias Oetiker, Hubert Partl, Irene Hyna and Elisabeth Schlegl (2000):The Not So Short Introduction to LaTEX2254 .