3 v = t x v mv mv = 0 x = 1.5 t ml x = M + m = 1.0 t L = v t o

v w r 6 r 488. 10 355 / T 4 60 60

5 w 7.7 10 / T F mv / r v R = = F GMm / R GMr 6 355 ( 637. 10 ) = 11 4 6 6. 67 10 598. 10 488. 10

t s t nr t nr v = t t s t AB CD AB CD - 3

s v 0t 1 at s v v t v s AbB t t

1 5 1 v1 x 5 / t 1 x 3 48 v t 4 v = v + v 0 t s v = t AB AaB = t t

v a = t v t v t v v t a = t t

v a = t v = gt t = t a = v ai = lim 0 t F = ma = -kx a = k m x v = v + at t 0 s = v t + 1 at 0

v = v + as t 0 1 v0t + at s v v at v = = 1 0 + 0 + = v0 + at = t t v0 + v v = t s = 1 at 1 s1 = v0t + at 1 s = v1t + at v 1 = v 0 + at s = s - s = at 1 t 1 = v a = s = d + s1 - s = d + vt 1 1 at = 4 1

s va + v B v = = t s t = va + v A v a tg t = α = a = tga = ( / ) v v v = 0 + t v v t/ =

1 s = v0t + at 1 a v v s = v t at = t 0 0 0 ( ) + a a t = v v s a0 = 0 m a s v = t AB A t GMm = mg r GM GM g = = r ( R + h) GM g = R

1 s = v0t + gt v = v + gt v t = v 0 t 0 + gs v0 + v v = t v1 v 1 = v0 - gt t = h h = g 1 v v t gt v g v 1 1 1 v1 g g g v v1 + = + ( ) = ( + ) 1 gt s

v s = v t = + v t = 0 v v v t = = g g v vt v t = = t = t g g 1 h1 = gt 1 h = v0t gt 1 1 h1 + h = gt + v0t gt = v0t H t = = ( ) v0 h = 60 H t = v 0 = 80 40 =

F = GMm 11 4 6. 67 10 5. 976 10 = m R 6 637816. 10 = 9. 79m 0. 034m 9. 79m = 0 00347 F = GMm r R F = GMm r F = m r r r F1 AB OAB F R AB = F R 1 = 0 0034R F tg AOD AD R sin40 sin40 = = = OD R cos40 AB cos 40 0. 0034 0. 64 8 = = 0. 849 0. 766 AOD = 40 13

1 F = k x k = k 1 F k F = k x 1 = kx k = k F = 1 kx A W = F x = 1 kx 1 E p = kx = f N

m g a = µ 1 1 m g m = µ 1 1 a = F ( m + m ) g µ m + m 1 1

m1g mg a = m1 + m m1m g T = m + m 1

(5) OB T = mg cosa T = mg cosa T - mgcos = m v (l = OB) l

T = 1 4 M + m g ( )

T = F 3 5

1 F = F + F + F F cosθ F 1

AO F = L 1 1 T L BO L L G F = L T L L = L G 3 3 3 = 1 3 F = F x + F tgϕ = F y F x y

a 1 m

F = ma = m v n n R F = G m m 1 r F = k q q 1 r

U = U t + 1 at 0

f max a = = 3 / 0 m A a = F - 1 µ ( ma + mb) g 1 =.0 / m + m A B f = m a a = f m =.5 A A A

a = F f µ ( ma + mb ) g B mb = 4.0 /

F x = F OA + F OB+ F OC 1 3

m1g OC = mgoa mgob = m1goc + mgod mgob = m goa + mgod = mg l

OB l = m m l m m g + mg OB = mgl G AP G OA 1 0 G l 0 G = 1 G OA 0 G0l = AP l b l b l l l G ( b + ) + G ( a ) 0 ag Gl G 0l G( a l) G 0l G = b + l b + 1 lg0 b l G( a l) lg0 b + 1

v s t = v s r =

a = v t t 0 v t A h = v0t 1 gt t = v v 0 0 h 1 = v0t = g g h = 1 v gt = 1 v 0 H = h = 0 1 h g g

y θ = arctg a a = a + a t = a 0 x y x a = a + a x y 1 y = gt

1 g y = x v 0 1 y s s = x + y = v t + g t 4 0 4 v t = v + ( gt) 0 v = arctg gt 0 v0 t = h g h x = v0t = v0 g 1 x = v0cos t y = v0sin t gt

y = ssin = v0sin t 1 gt () s α α s sin = v0sinθ g s cos 1 cos v0 cosθ v cos θ 0 sgcos = v cos sin cos - v cos sin s 0 s = v0 cosθsin( θ α) g cos α 0 v sinθ 0 = 0 s = g v = s t v = πr T ϕ = t = π T s πr v = = t T

r = r O A = 1 r 1 1 1 AC CB CD (1) ( vt ) = CB CB r () CB << r CB + r r ( vt ) = CB r (3) CB = 1 v r t 1 a t = v a = = ω r (4) r O 180 ϕ a = ( 1) t 0 ϕ 0 90 v v A v AB = ( ) v r v v = AB (3) r v AB = t t v (4) r

t 0 (4) AB t v a = = ω r ( 5) r a = v = r r mv F = ma = m r = r F = mgctg = m r = m v r 5k( R t) A 4mR

m R = k R l 0 k(r - l) 0 = mr 5k( R l) = 4mR cos = g ω l mg F = mg / cos = = m l g / ω l π cos = g / l T = π lcos θ / g ω l cosθ l

3 a T = k k F G m m 1 = r F = F Mm M R R 4π r F = ma n = m r = m (1) T 3 r 3 T = k T (1)

km F = 4 π () r m F = µ (3) r a = 4 π R (4) T g = R (5) g R 0 M F' = µ ' 6 r µ ' M µ r = m (7) r µ ' = µ ( 8) m M F = G Mm (9) r

G Mm 4π = m r r T M = 4 r 3 π T r M GT M m mg G R R g M 6.0 10 4 G M M ρ = = V 4 3 πr 3 M = 4 r 3 π GT 6 6 3 4 314. ( 0. 11 10 + 174. 10 ) = 11 6. 67 10 ( 10. 5 60) = 7 19 10 M 719. 10 ρ = = 4 3 4 6 3 πr 314. ( 174. 10 ) 3 3 4π r 3 T M = r GT m 4π r3/ GT 3π ρ = = = v 4 3 πr GT 3

3π ρt = T G π ρ = 3 GT 3 314. = 11 6. 67 10 ( 84. 4 60) mv mg = R0 6 3 v = R g = 6. 4 10 9. 8 = 7. 9 10 = 8( / ) 0 Mm mv G = ( R + h) r + h 0 0 GM v = R 0 + h v = GM 6. 67 10 6 10 = 6 R + h ( 64. + 14. ) 10 0 11 4 3 = 7. 16 10

G mm mv P = l R OP G mm mv = l R OQ Q v v = l l P Q OQ OP 4π mm m T (R 0 + h) = G (R + h) GMT R 0 + h = = 4π 3 3 667. 10 60. 10 86400 4 314. 0 11 4

(R + h) v = = 7 π 0 314. 4. 3 10 T 86400 GM v = = = G mm M R0 R 0 E = E = G mm K P 1 mv R 0 = G mm R v = GM = v 1 = 11. / R 0 0 1 R 0

P = W t 1 = 1 1 W = Fscos P = W t Fscosθ p = = F vcos t v F 1 P = mgv = mg 0 + gt / = mg t v = P F = P f = 100 735 m 10 10 3 10 0. 05

W = 100% W = W W = P 100 P m = V Q = v t Q = P η gh ρ 1 E K = mv

1 E = mv K W AC = mgaccos 90 = mgacsin

1 x W = kx (3) () (3) E = W = 1 p p kx (4)

1 W = mv 1 m mv G 1 () 1 1 (1) () mv + mgh = mv + mgh (3) 1 1 mv B mg = ( 1) R B mgh = mgr + 1 mv () B 5 (1) () h = R

1 mv mv

p = mv

1 1 W = E K = mv = 50 1 = 5 W P = = 5 = 5 t 1 p F = = mv- 0 = mv t t

gl v V V m m M V m = + m + M gl mgl = 1 mv = 1 m + M v + mg l - lcos 1 m = cos m + M

1 m v + 1 m v = 1 m 1 v + 0 (1) 1 1 1 v 1 = m m 1 m + m v 1 1 m1 v = m + m v 1 1 k a = m x

1 1 mv = mv + E 1 P E = 1 P m( v v ) 1 1 Ep = 1 5 - ) Ep = 8( ) m T = T k

a = F m = ω m x ω = k m π m T = = π ω k m T = k x 5 sin = l mg F = x l mg mg F = x k = F = kx l l m k T = k T = l g

T g l = g = 9 801 4π 9. 801 l = = 0.993 4 31416. 1 E = ka = 1 m A T = 1 f = 1 f T π π = T = T ω

= f = π T x = A cos t + ϕ v = Asin t + ϕ a = Acos t + ϕ 0 0 0 t + ϕ 0 ϕ 0 t + ϕ - t + ϕ 0 0 1 ( ωt + ϕ ) = ϕ ϕ = ϕ 01 0 01 0 (1) ϕ = / ϕ n n ϕ (n 1)

T l cosθ g l cos30 T T 1 8 g t ϕ 0 π 1.0 5 T kx a m x t B C x ϕ 0 x Acos t ϕ 0

v v x vmsin t ϕ 0 Asin t ϕ0 a a mcos t ϕ0 Acos t ϕ0 a A m a Acos t ϕ 0 F m Acos t ϕ k m 0 k T = π ω m m T = π k m ϕ 0 0 A 1 T 3 14 k 1 k 0.68 ω = = 10 a m 100 m Oa = x = 1 A x 1 arc cos( ) arc cos( ) t A π = = ω 10 30 v Asin t ϕ 0 π 10 1 sin(10 0 8.66 30 E = 1 mv K = 1 mv A sin ( ωt + ϕ) E = E E P + K 1 = mω A [sin ( ωt + ϕ) + cos ( ωt + ϕ)]

1 mω A 1 ka 1 E ka k ϕ t ϕ0 π ( k + 1) k 0 1 3 sinϕ 1 cosϕ 0 E = 1 K ka E P 0 ϕ t ϕ0 sinϕ 0 cosϕ 1 EK 0 E P = 1 ka

s v = = λ λ f t T 1.5 t T v '= t 3 6.67 / t T t nt T 4 s

t n t T ( n + 075. ) λ λ( n + 0. 75) v' = = = 0. 36( n + 0. 75) T t

π A 0cos r r 1 (1) λ ( ) λ r r (k 1) ( k 0 1 ) 1

1 10

T = π l g g 4π l g = l T

x x 100%

a = s s j i s j si = ( j > i) ( j i) T j i)[( n + 1) 0. 0

s1 + s s + s3 s3 + s4 v1 = v = v 3 = t 1 = ( n + 1) T T T T = π l g l g 4 π T l tga 4 g g = 4 π T - l tgα T 1 l T tga = l g = 4 π tgα

l g = 4 g T g1 + g + + g n g n T nt(s) T(s) T (s ) l / l(m) g = 4π l T n /l 5 ( m / s ) T n /T 5 1 3 4 5 mv ( M m )v (1) 1 (M m)v 1 ( M m ) v = ( M + m) gh v = gh () M + m v = gl( 1 cos θ) ( 3) m

T = π l g

3 1 71 3 1 7

h V πr V d πr

ab AB ab AB ab r ab r AB R AB R K AB R = ab r O 3 N A 3 3 M M m i N A M NA mi m i = N A

3 18. 0 10 / 6 m i = =. 99 10 3 1 6. 0 10 V i V = N A l V 3 i 3 3. 4 10 / 6 3 V i = = 37. 10 3 1 6. 0 10 l = 3 3 = 6 3 9 3. 7 10 = 3. 34 10 V i

ε ε = 3 kt R k k = R N N A A

1 1 W f = ( m M ) V mv W f = f s s Q = fl = 1 mv 1 m M V ( ) V = m m + M v V = 4 / 1 1 Q = mv ( m + M) v Wf Q f = = f = 960 l l 4 5 Q = cm t 4 Q t = 5 t = 9.8 cm

W I RT I RT JQ J J = = Q Q

h = h = α ρgr

p = 1 n( mv 3 1 n mv 1 mv 1 n T mv m R m pv = RT p = M M V T p = R M ρt

pv m RT (l) M p = 3 n( 1 mv ) () 1 n mv m N = m M N ( N 1 3 R mv = N T R k k N A k = R N = 8.31 / = 1.38 10 3 / A 60 10 3. 1 1 εmv ε = 3 kt A A A

3 kt p1 = V 1 p V p V = p V = = 1 1 1 136. 3 1 3 500 500 500. 0685 3 1 3 1 1000 1000

1 1 0 73 p t = p 1 1 0 ( + t) 73 p1 = T p p T T = p 1 1 T = = 1 1 73 p0 p t p t = p0 + t p t t 73 p0 p 0 73 p0 73 p 0 73 P = p 0 p0 T T pt T 73 73

1 (1967 7316. 1 73 V t = V 1 1 0( + t) 73 V1 T1 V1 V = = = = V T T T 1 V0 V - t V t = V0 t Vt t 73 ( ) V 0 73 V 0 73 73 (1) V V = V 0 73 T V T V 0 (1) T T 73 V 0

m pv RT M p1v1 pv pv = = T T T 1 m pv = RT M p = m p1 p = V ρ1t1 ρ T R p = M ρt

p V T 0 0 0 R N A k k = N A p1v1 p V = T T 1 p1v1 p V p V pv = m RT T T M 1

m M pv m = m 1 + m pv = RT M R T = M p V R T + M p V pv = p V + P V p = p V 1 1 1 1 + p V 1 1 R T V P l S = ( P + F )( S l l + x ) S 0 0 0 0

P T p T 1 1 P T T p 83 = P p 1 = 0 = 1 10 0 73 73 P1 ' T1 ' T ' P P T T p 303 = P P ' = 1 ' = 0 = 1 10 0 ' ' ' 93 93 1 1

N N v 8RT v M v 8kT R = = k = m = M π πm N A N A m v T

F mv v 1x vx u Nx = 1x + mv x + + mv Nx l l l p = F l = m + v v + + ( v 3 l 1 x x N x ( v + v + + v ) N 1 N m x x p = = x 3 l N X v x v = v + v + v 1 1 1 1 x y z v = v + v + v x y z v = v + v + v z N N x N y v = v + v + v x y z 1 vx = vu = v z = v 3 N m p = 3 1 v l 3 n n = N l 3 p = 1 nmv 3 p = 1 n( mv ) 3 1 n mv 1000 1.5

1 n mv 1 p n mv p = 1 N n mv p 3 = 1 3 V mv ( ) ( ) 1 3 mv = kt 1 N mv pv = 3 N 1 mv N p = 3 n(1 mv ) N p = 1 3 V mv ( ) 1 3 mv = kt p N = N 1 3 V mv P N A T

p = 1 N n mv p 3 = 1 3 V mv ( ) ( ) 1 3 mv = kt 1 N T mv V N = N 1 3 p mv V N A T m pv R T T P V R M RT p V V m m ( 1) ( 1 M M

( c m 1 + c m )( ) 0 t1 c t m

( c m 1 + c m t 0)( θ 1) L = c ( t ) θ m

p 9 B = 100 = 100 = 66 P 13.63

B = p 100 = 10. 5 100 = 60 P 17. 54

1 e e e e 3 3

F k Q Q 1 9 = k k = 8. 988 10 / r Q 5Q C A C B C B C 4 r 5 A B A B F 4 A k 4Q Q = k + Q 4Q Q C (l + x) l

4Q B k k Q Q C Q C l x 4Q Q C k = k Q Q C C (l + x) x Qq + Q F 1 = k Qq cosθ F O cosθ = l l x kqq l F l' x l x = kx l F 3 E = F E q q

Q E = k Q r F (1) q F E = q (3) E = U U d

q C k ( R + l / ) E = F q E = k Q r E = U d U = k Q Q U r F (1) E = q

E = U ab d ab

(1) a U = W AP a W ap a q U = W ap a = 8 10. WbP =. 0 U = = 9 b q 50. 10 q 8. 0 10 = 4. 0 U a U b a 9 50. 10

qu qu = 1 1 ab ab mv b mva v eu = 1 1 U1 l mv 1 x = v t 0 1 1 qe y at m t 1 qu = = = md t vx = v0 qe v at m t qu md t y = = =, L t = v 1 qu L qu L y = v = v + 0 ( ) md v md v vy qul v v 0 ϕ tgϕ = = v mdv 0 0 x 0 0

U F E = q W E = qu d A t d = 1 at 1 eu0 md t = t = md eu 0 T t T = 1 f eu 0 f 8md 1 qex 0 mv0 1 qex0 fs = 0 mv 0 0 s = mv + qex 0 f 1 U1 v 0 eu 1 = mv 0

t = l y1 v 0 y 1 1 1 eu l = at = ( ) md v vy eu l U l ϕ tgϕ = = = v mdv U d x y = y + y () y = Dtg = U ld U d 1 y = U l l 1 ( + D) = ( + D) tgϕ U d 1 0 0 1 1 ϕ Q Q U U C C = Q C U R C C = C 1 K Q C = C 1 C U εs C = 4πKd

E = U Q E Q S d d S 1 1 1 1 = + + + C C C C 1 3

q I = q t q I = t 0 t ( ) r e I = ve πr

a X = X a b b + x A X X = L U I U I I = U R U I = U I tgϕ = 1 R

I U I R = U R I R = U I 1 R = S S = R R l l 1 a = 0.00367 a 0.4% 73

R = ρ L R = R (1 at R 0 0 S

U R = U R = U 1 3 R R 1 3 3 I U R R = U I I P1 P3 = P = I P P = IU = I R = U = R1 R R3 R 1 1 I1 I I 3 = R R 1 R I R I R = I R 1 1 3 3 = U 3 1 U R R = U I I 1 R 1 1 1 = + + + R R R = R R 1 1 R R R R + R 1 3 1 1 1 1 P1 P P3 P1R 1 = R R R 1 3 P = IU = I R = U R

R1 R = R 1 R + R R R R U = U U = R 3 1 3 1 R R U R3 U R U 3 = R U = R 1 1 cd R c d R U R 1 L cd R U ab R1R L R 1 + RL R L R1 ( R R1) U' cd = (R R ) + R R 1 L 1 R + R R1Uab R + R ( R R ) / R 1 1 L 1 L Uab Uab R R I R I I R R I I R R I 1 = = 3 = 1 1 R R r R n 1 = r 3 L =

R R r n x 1 R n x 1 = / n x = n -1 r q = It W = qu = ItU P = W = IU t U P = IU = I R = P U I R P = IU P = I R = U P = I ε R + I R P = I + I R ε R = P R = I U I

I = Ir = ε ε r Ir = ε ε + r R r

U U 1 0. 4 = = 0. I I 1 U U I r = = 0.4 I = 0. ε r I = R + r r 0 ε = ε r = 0 n I I = I 0 n ε = nε 0 r = n r 1 m

I I = I 0 m U1 ε = U + R r 1 1 U ε = U + R r ε = I1R1 + I1r ε = I R + I r εx U AD RAD RAD = = ε x = ε s AB RAD RAC ε U R R s AC AC LAD LAD LAC ε x = ε s L AC AC R = U U I U R = U R x x I I U U I R = R R x R I U R x x / v

() () R = U x I U IR A U = RA R R R R x x x A I I ε Rd Ig = R r + R R g + d ε ε I = Rx = R R + R I x U ac U ad R1 R3 R3 U ac = U U = U = = R = U U R R R R ad cb db 1 cb db R3 R R1 R1 R R 3 L1 R L L1 R L R 1 = 4 4 4 4

ε U d = 0 I = = d c R R + R + r 1 R R R R = R r + R R 0 0 1 R + R0 ε R 0 I R I = I = R + r R + R 0 ε R ( R + r R) R + r + R0 R + r y R (R r R ) = R + rr + RR R = y R r y = ( + ) m a R = R y = Rr b R = 0 4

ε a I = R + r + Rr 0.53 a R0 R = R + r ε = 6Ω I I min = ( R + r) R + r + 4R ε b I = 0.3 R + r RV R1 RV R1 R R R + R RV R1 1 K R V R R1 = Rr R + R 4 U R = 5V5W 6V3W 5 1 P ε K ( ) 19 475 19 + 1 K I I 19 = 385 U = 386 19 = ε I 1 I 1 1 1 I I I I U R I R 0 0 P I U I R x = V 0 1 0 v 1

F B B = m F Il m

π π ( B n ) ( Wb)

I B = k I r r

1 mv mgh Q = I t = m gh Bl (3) B F ( π π ) F F1 = Fcos( α ) = IlBsin α. F1 mgsin IlBsin a = mgsin B = mgsin θ Ilsinα = NIL L B = NL L B 1 1 I = CI I k

f = qvb = m v r r = mv T = πm qb qb mvsinθ B r = T = π m qb qb h = vcos T = πmv cos θ qb

t = m ( π θ) qb P x = OP = r sinθ = 0 mv (sin θ) qb qe = qub u = E B v = E B c W W = 1 mv 1 mv0 d E = 1 mv 1 1 1 K 0 W = mv 0 ( mv 1 mv 0 ) = mv 0 mv

E B v = E 1 1 1 B 1 m B r = mv m q = B r qb q u = B B r 1 q r m E 1 E v = =.5 10 / r = m v 1 5 1 1 B qb 1 7 5 63 166. 10. 5 10 = = 0.33 r 19 = 0.34 160. 10 050. 1 mv = NqU mv πm r = T T = qb qb

I = nedhv U = IB U U = R HIB / b R H neb 1 1 RH = R H = ne nq v = E B mv e r = = E E B r eb m rb e m = 10 11 /

I = nedhv U = IB U U = R HIB / b R H neb R = 1 R = 1 H H ne nq 0 v r mv 0 πr πm r = t = = 1 eb v eb mv0 v0 eet = mv0 t = ee 0

r v = = t + t 1 v0e πe + v B 1 n n = mv n = nqu v n = nqu m R B qvu B = m v n n n R B = mv n n = 1 nmu qr R q ε i I i R R 0

l l l v = 0 + ω ω π ω = (v B) εi Bl 1 Bl ω

ωl sinθ ωlsin θ 1 v = ε i = ( Bsin θ) l ( ) = Bωl sin θ i t B S BS (B B)xr ε = i t = πr ( B' B) t ε i t t t t ε i

T t 0 4 T t1 0 1 0 t 90 4 π T π 1 NBl l T t 1 εi ω 4 ω t NωBl1l π

ε i a I i adcba i 0. 0.5 6. 0 = R + R 1 a cd Rcd 0.1.0 0. I = 0.4 R + R cd ε icd mgcos IlB = B L v mgsin mgcos + R B L v vm mgsin µ cosθ R B L v m R v = mgr(sin θ µ cos) m B L BLum I R P I R R

Bdv1 Bdv bacdb I cd IdB R Bd( v1 v ) Rf 0. 1 0. IdB f db f v v 1 = / R B d 0. 0. 4 U U i BLv E Bv mg qe qbv B mg L qu u mu uv πr u R T R qb g v g L R L L 4R 4uv 7.5 u g 3 v T R uv 3 3π = v gt v = 3π / 4 g 4

ε ε I 0 = R + r R + r ε Φ i L I t t L ε I i t

l εi ab = Bl1vsinθ = Blω sinωt cd l ε i = Bl ω ωt ε ω c d 1 = sin i = Bl1l sin t S N ε i = NBS ε r R i = R + r = ε m sinωt = I m sinωt I m u = ir R + r

I = I m U 0.707I U = m ε 0.07U m m ε = m 0707. εm 0 0 311 1 T = f = 1 f T T f f = π T

ω u t U m f = π 1 u t U m T f = T t = 0 u = U sin = arcsin u 0 m U U = 3U U = 0 U U1 U U 3 = = U 1 U U 3 = N 1 N N N 1 U U = U = N N N1 N U = 440 1 N1 I 0N1 = I N I = I 0 = 0.5 N U R = = 880 R 880 I 3 0 m

P = U I I = P 1 U = 00 I R = 1 1 1 1 N 1 I 1 P1 4% I = 5 = = N I 40 1 P P = (1-4% P1 U 3 = = 9600 I N 3 U3 480 = = N U 11 4 4 1 0

T = LC f 1 = L C T f L C π LC

v c n v = c n LC = v f = v LC

Φ Ω cd 1 = 1 / 1

O f f = 1 OC d 0. 6λ f

sinα sinα 1 1 v v n = sin α 1 sin n sinα1 v1 n 1 n sinα v 1

n 1. 33 n = = = 089. n 1. 5 sinα sinα 1 sinc v1 n sin90 v n v1 n sinc v n 1 1

v 1 sinc c n π α ' arcsin n b n sinα sin α ' = n g n ng ng π sinα = sin = sin n b arcsin n a n a ng ng nb = cos arcsin = a b n n n n a α = arcsin 1 ng n b n a g a g 1 b a A arcsin 1 ng n b n a

u v uf f v = = u f f 1 u f u (1 v u f u 1 u f v u v = u f f u v u v = u 1 u f u 1 1 f u

m l v = = l u K m = m m α ' α m = d d f f

1 α' 1 m = = f f1 f α f m = α' α tgα' A B A1B1 f = = tgα f f f 1 1

A 1B1 A1B1 a a a a tga a tgα = f f α f m = = α f 1 1 = 0.61 λ n sinu n

1 10cm 50cm + 1 v = 1 v = -1.5cm u f 1 D D f f 1 1 1 1 D = + f u v 0. 5

c v

λ d = L d L nl

Dλ y = D A B d S 1 S d

1 e U 0 = mv m e U 0 1 mv hv = 1 mv A

n = c v = εµ c v hv p = mc = p = h h c h p = v

a θ b = ctg b a a a = Z Z e 1 Z1 Z E σ( θ) = ( a 1 ) 4 θ sin

4 3 N A r πr 3 4 3 A / 1 πr N A 3 4 A πr3n A = 3 ρ 3A r = 3 4πρN A ο -8 1A = 10 cm S 1 1S 4 π Z e me En = ( n = 1,, 3 ) h n

E1 E v = h

λ = B n n 4 B B = 3645.6 A n n = 3 4 5 6 1 1 1 v = = R( )( n = 3 4 5 6 ) λ n 1 1 1 v = = R H ( ) = T( m) T( n) λ m n = 6563 A 1853 A

A Z X N

A Z X A 4 Z Y + α ve A A Z X Z 1Y + e + ve A + X + Y + e + ve A Z Z 1 X e + e + + v A Z i e

W m = m m W c 38 U 06 3 08 Pb Th Pb 35 9 8 90 U Pb Pu 07 8 41 94 09 Bi 83 dn / dt λ = N N0 λt = N0e 1/ ln 0. 693 T1 / = = λ λ 9 8

4 ( He) m x = 4.001506u mp = 10076. u

v m = m0 1 c

K = Pf σ σf t σ t =.47 = 1.0 p = 0.89 f = 0.88 = 0.54 σ t

( )( ) ( U ) = Z1e Ze max ( R + R ) 4πε 0 1 (U ) 360keV max

1 6 4 H + Li Hc +. 4McV 3

m H = h m n

30 0 P e 15 1 30 13 7 ( Si) ( C) ( 14 6 13