A
E
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r = R/ 2
r = R/ 2
r = R/ 2
R
r h
= 0,5
h
= 0,5
h
= 0,5
R
r
R
r
= R/ 2
= R/ 2
= R/ 2
R h
= 0,5
h
= 0,5
h
= 0,5
R
R
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r/c
r
c
r/c
r
c
r
r/c
r
r/c
r
c
r/c c
r/c c
r c
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r/c
r
c
r/c
r
c
r
r/c
r
r/c
r
c
r/c c
r/c c
r c
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A
B
C
D
S 1 S 2 S 3 S 4 A B C
4
S 1 S 2 S 3 S 4
3
2 1 1
2
3
4
P
P
P
S 5
D
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r/c
r
c
r/c
r
c
r
r/c
r
r/c
r
c
r/c c
r/c c
r c
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A
A B C S 1 S 2 S 3 S 4 S 5
4 3
2 1 1
2
3
4
P
P
P
D
B
C
D
S 1 S 2 S 3 S 4
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300 200 200
A
A
A
100 100
A
A
A
A
A
A
τ = 1, 1 ,5 τ g = 9,8
/
A
h
A
A
2
B A A K
M = M = 100
A A
A
A A
A
A
A
A
A
A
A
A
S h2
G h1 = 30
h1
h2 = 40
h3 A
G
h3 = 65
A A
N = 1000 N
A
A
A
A
A A
C
S K
r = 1
τ = 0 ,3 ∆T = 1 C c = 4200 /( · C) g = 10 /
t
◦
= 10 1000 00
/
x
ρ=
◦
3
2
h = 30
100% n = 3
n
R = 100 R RBC
B E = 24
B
C
α
C sin2α sin2 α =
− tg 2 tg α 1 − tg2 α , cos2α cos2α = , 2 1 + tg α 1 + tg 2 α
tg 2α =
2 tg α . 1 − tg2 α − tg
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P
N I N A N B1 N B2 r1
P 0
N
P 0
N B3 N V 0
B2
r2 (r1 + r 2 )/2
r2
r1
k = r1 /r2
B3
γ = C P P /C V V R
0
ρ
P ((V P V )) = aV + b
ai
ρ0 = = 1000
/
N I
3
N B1 N B2
P V n = const ri G ′
I x Ax N I x Ax
′
vi
ri
j ρ0
ρ0 ρ0 rmax
η
N B2
N N Bx n
I
r0
C 3
n = (C − C − C P − C V P )/(C − C V )
N I N A Bx
C
N B2 αV 0
A
NIAN
αV
N
C
H = const H
τ
aa NA
N B3
C 1 C 2
vi = H H ri
V 0
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r2
r1
U E E B R R0 R(B ) µ
E
v = = µE µE
B r2
r1
B
U
U
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P N I N A N B1 N B2 N
N B3 r1
r2 (r1 +
P 0
+ r2 )/2 k = r1 /r2
N
B2
V 0
r2
r1
ρ
P 0
B3 γ = C P P /C V V
0
R ρ0 = 1000 kg/m3
P ((V ) = aV + b P N I N B1 C 2
NA N B2
V 0
αV
ai N
aa
N B3
C 3 P
vi = Hri
ri
= const
n = (C − C − C P − C V P )/(C − C V )
C
H = H = const
N I N A G
N B2
vi
N N Bx N B2 I
ri
′
′
j
C ρ0 η
ρ0 ρ0 rmax r0 τ
I x Ax N I x Ax A
Bx n αV 0
NIAN
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r2 r1 U E E B R R0
R( B )
µ E v = = µE µE
B r2
r1
B
U
U
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XV Международная олимпиада Туймаада. Физика Задача 4. Заземлённый контур
Колебательный контур, состоящий из катушки индуктивно r стью L и конденсатора ёмкостью C , заземлили через резистор малым сопротивлением R сопротивлением R (рис. 6). Ко второму выводу контура подключили проводящую сферу радиусом r радиусом r.. Конденсатор заря дили до напряжения U 0 и замкнули ключ. Непосредственно пе ред замыканием ключа колебаний в цепи не было. Конденсатор C U 0 и сфера находятся далеко друг от друга. L 1. Определите период T T колебаний колебаний в цепи. 2. Найдите максимальную силу тока I max max в катушке в про цессе колебаний. 3. Вычислите добротность Q добротность Q колебательной системы. R Примечание. По определению добротность Q = 2πW/ ∆W T T , где W где W полная энергия, запасённая в системе, ∆W T T потери этой энергии за период. Рис. 6
XV Международная олимпиада Туймаада. Физика
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XV International olympiad "Tuymaada". Physics Problem 4. Earthed circuit
An oscillatory circuit consisting of a coil with inductance L and r a condenser with capacity C C was earthed through a resistor with small resistance R (fig. 8). A conductive sphere with radius r is connected conne cted to the second term terminal inal of the circuit. The conde condenser nser was charged up to the voltage U 0 , then a key was closed. Immediately before the key was closed there were no oscillations in the circuit. C U 0 The condenser and the sphere are far from each other. L 1. Determine Determine the period T T of of oscillations in the circuit. 2. Fin Find d the max maxim imum um cur curren rentt I max thee co coil il du duri ring ng th thee max in th oscillations. 3. Calculate the quality factor Q of the oscillating system. R Note. By definition quality factor is Q = 2πW/ ∆W T T , where W is full energy stored in a system, ∆W T T losses of this energy over a period. Fig. 8
XV International olympiad "Tuymaada". Physics
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а г и л я
� d е � , я н а а р о к р з я о и о и и е н н т т т я о р о ё я о г е а к т , м й в с е с т ь а я е ц т р и и � и ы т н с п и н б а с о я к б ъ а х н T б ь е л л ы ж й О е о . л т к н н а о и н н е ё з н д б а у г ы и а . е н р л � ь д г ц о е м л и к о я и с п о я и и т , с н х ь н н у ы я л ы р а к с о а н е б с к к ь л е ь а о и л п е л т м п т и о а й и р т р к
й о = н l д е и м к ы о н л о и . в л д о д и р т в п о ё е T е н и л й е т и и д н и а л е р б е д е п л р о к п T й х О . и ы ) н н а ь d б л м е и о л x
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� а � и . � ю и а а к и г о н и м м о ц з и ц я р л а о в р а в о о д м п м в ф с р , е р о а д о у о р ь м ф л ф п л и я а , е с а е у р г д о а д щ и д к о ф т � л в й . м т е ю о д е а г с а у F н г е у в ь в е и а ь т о е ы л м � л м т с к т у , у с и у т θ д а б ы я ы т а п п а о с П е , м л с с . а я . р и о и θ м а ) т а в н п а ю F S о ч и и а р и м р й н а ё и р , е г т о = т е д е ъ и й л м а е б н м т и м п о н G е е с и а н н д и е с о п я р е л х в г я р з л е и р о г о е п и и П г л е н е й м е в о
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я л о п о г о н т и . н й г а ы м н . ж а й е ю к и т щ й о и н ю к я а г к . а л в а е м а т , т о с г й й о о у ы н к с н с ь й р о н е е о б н в о е л ь
� о д е н р н п е в е т ы с е н т щ и у с н г а т г м у е о м ы ) н . н е р д ж о и л о в и п т с а а р т ш о , к з а и к
� , а е т с ч , т о и н ь г т к с и , а н ы м ц а я а и в к н т с н е ж о о т н щ , , е в а ь к а к т и й т е с и н о н и н т г о а л , л м м П х м . и 5 а к к ь 3 о ч н е н о н л е и а р м з
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e u g a e
e a s d e d t r u e o t a s r r n n g i r e a i e e ff t c v g t o a s n e s i ’ v r T d h t n r m I u d o o r . c r y a ) f o c d i w 9 o . r n . , e e a a g m h n p t i fi u l n i l c ( m n u u u l e o o e s d t u h p t n d t i n a t a n e i n l s d l e n i i o s p d n s a c m p s n l a n s u t a o i o d i c s r h o e i t i t r m p a b s i a s y u l l f n i o e l u s l h i h i u p t e q s u n c s i n n g d e e o a l e t o i n n e t t n p w d x a i
t n o h g i a t i r t s t o a l p t e g : o e c t n e r e d d n e r o p e i d n s t e e a h t i n d r e z o i o r a c
, h c t a w p o t . s , m r c l e 5 u 6 r , = d l n a t r o s f , t s i n o o i t t a l d l e i c h s o c a t m t a x
. d o r e h t m o r f
e u g a e
e a s d e d t r u e o t a s r r n n g i r e a i e e ff t c v g t o a s n e s i ’ v r T d h t n r m I o r d o . u c r y a ) f o c d i w 0 o . r n 1 a e e a . m h g , i p n t u m l c fi n u l i ( l n u u e o o s d e u h i p t t t n d n a i a n e t n d l l o s e i i s p d p n n s a c s m n l a n s a t o u i e o d c s i i h o p r t i t s a r s m a y n b i u l f e l o l u s l h i i h i p u t e q s u n c s i n n g d e e o a l e n n t o i e t t n p w d x a i
t n o h g i a t i r t s t o a l p t e g : o e c t n e r e d d n e r o p e i d n s t e e a h t i n d r e z o i o r a c
, h c t a w p o t . s , m r c l e 5 u 6 r , = d l n a t r o s f , t s i n o o i t t a l d l e i c h s o c a t m t a x
. d o r e h t m o r f
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t m h . u g r e u m i o r p a x a b p m e d e . e r l d t h n u c i o t a F t d s , . h n r e x a g o ) t e b u o r C s k b m m b c d h a e n o l r n b a a o , k e s B ) h h t b o , R t i n n A d w i k ( n s y a s l r x i t a o u a n t b c o i R m 3
e u g a e
2
t m h . u g r e u m i o r p a x a b p m e d e . e r l d t h n u c i o t a F t d s , . h n r e x a g o ) t e b u o r C s k b m m b c d h a e n o l r n b a a o , k e s B ) h h t b o , R t i n n A d w i k ( n s y a s l r x i t a o u a n t b c o i R m 3
e u g a e
2
t m h . u g r e u m i o r p a x a b p m e d e . e r l d t h n u c i o t a F t d s , . h n r e x a g o ) t e b u o r C s k b m m b c d h a e n o l r n b a a o , k e s B ) h h t b o , R t i n n A d w i k ( n s y a s l r x i t a o u a n t b c o i R m 3
e u g a e
2
t m h . u g r e u m i o r p a x a b p m e d e . e r l d t h n u c i o t a F t d s , . h n r e x a g o ) t e b u o r C s k b m m b c d h a e n o l r n b a a o , k e s B ) h h t b o , R t i n n A d w i k ( n s y a s l r x i t a o u a n t b c o i R m 3
e u g a e
2
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e u g a e
l e a m r c u p i l p u t r d o c e v n e a t p n a a o f � � o g e l l s n u r e n h o i b i e w b t l a a l m l d e d u i e n s d c a o n � l a n a a o n h t i f i i t i o o w s s r s o d o p n t e t l o e i c t t t e a a a n g l n n o
. e . ) r y t l d l e n a e x c fi c i t n r g o e n i s o e i e n h e t b p d s e c u h s n t i e n d w e ( e n e l w p t e h e d b t e g d h n e e l t c e n n i r i a a w t l s i p s d x u s E s u . r s d e
, , e a ) a d c e m 2 r s 1 t c e s o i o f . 0 L p . a S g 5 . x , fi e i s n s m ( i ≈ c s o n i F i l y 5 l t t a ) o . a i 5 h i i t c t s r i g m = t e e r a n s t g o m e a a n f r l l l e a : e o m h h f t t e ) c h n c d i i g f o g d o t e i n w n f i s t e r l a m i e t o a l r n u n . i e e l e e fi e r h θ l o i s f e g d F S w v v e , w t o n r r r t a y e a a p h u = l t h b o d n b i ( G u h r w d a w t n s , i i . y e a s s p r i w s f i y i T e ( e θ i t a r p e n c d p a c m p a l x
x
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c i l l a t e m , . s d r
r l , e i c p a n p e p f , o r e e l i p
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а к и з и Ф . � а д а а м й у Т � а д а и п м и л о я а н д о р а н у д ж е М X I X
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� е � н е а в т о ч е и т О р к а т . я а в д о 1 р 0 л К а а у . т з п а 0 к е й , н 0 и л в д а к с о н г = н р у е е ч н а р ϕ п з у а к д и р и л д и е ь в з , ы м п м и т я а ы н а и т т Ф е р с т е . о м о ы в ж � т к п с о 2 а о , с л д к й о с 0 о а о л и п у а = п т д д е м я с а ж a у о р й и и у н р е у д ж о р Т е м м н ж м п е � и л 1 о л м л й ж а а г д ϕ а д к о в а р = у т р о , е а и т х е л е п О D я г з н м . т м у т л о и 4 м с и о в , о л о о г с о а р к л о й а с е и т н ч я к о н н а а е р л е а ы м н е н д п а д ж н а и х з р г о а З д ы ы у р а р в т з а р д о я а н т в н ь с у л д е и а л н т N
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! й о б о с с е т и с о н у я и в о л с У
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а к и з и Ф . � а д а а м й у Т � а д а и п м и л о я а н д о р а н у д ж е М X I X
) и . ы ы н м н т б е 5 н , и л о р 0 р г д = т ф ( х и h о v и а а и н г а , т б к с е м е р и о р е з 0 р и е г 5 б о и к Ф р у с е = з о г . и р � л й е λ б о а м б в д а у в а н я о а н у и р з а м ы м л о ф о й г д у н о м ь и а т Т л л , с о л � о ) е н о в п z и а м k д у м ( и б и у а е м с h л и и ы t ы Г п н о в м н g k а м ж я л ? ◦ з и е р о 5 ( л п в р о б к 1 и = д м = и я с и v т а и 0 α р в н р у е д 0 д П 7 л п т й о с е . о = о р и е г а 4 д д м у о н а п H м н и у о н д ч
! й о б о с с е т и с о н у я и в о л с У
� , � и я й б и о у ц к л к о г н б у у � л г . z ф � z , � о а g л н √ с h t : и с и ≈ ч н и е е с v г о р в е ) λ о н а п н т с л и й о д z в и к а и с н � е о р п λ ч к ( . и / л x x а π о − − з е д 2 б о e e и а в р = е ч − + k п x x у � л й , и я г e e с о к и а = е л н , ы е е x н е д к h ь м � а ч t л п о а е т н д о е г ; о й р k н о п / м д g ь е й о т б а о
! й о б о с с е т и с о н у я и в о л с У
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s c i s y h P . " a d a a m y u T " d a i p m y l o l a n o i t a n r e t n I X I X
. r o n t m a i o n t n m e r u e l e F r e m l . a i m m b 2 h g o o x t u / e r c a n o S i e p 2 n d . m h s x a 1 n t P i − e h 0 e 0 p a t 1 n ? h . r n o 0 e m i W e n ≈ p s e . t o x t = s s c i i i s i r s s s y ϕ o y o s t o a r h p g d c r r s n p e i i P n , a i o e m h d x . i t s " d b m e n ≈ a e n o h s d c 2 t i s e . c x a a l n 0 f o a n r n o p a e i g o l = s r d i m e t p y c r e n s u e a e a e d n u ≈ T s a n t l e h u " fl o x p t m h e n n g t d n a . m a R 1 n n e t e i a e e e e r . = e l p 4 a r r e f w b t e u m t t o w d y h e t D i l t s m g i e s b h o e r b i l s n g l e i l i ϕ l e o x s a b t r e c n e h l e n o o l t a g o r r y + m f i r g n a 1 t a i n n o P i a a a a m d e m l c e n r e ≈ r f e a u e o h t h r s t n t n n
! t s i l m e l b o r p s i h t u o y h t i w e k a T
! t s i l m e l b o r p s i h t u o y h t i w e k a T
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� и л и л и 2 м k , р , 1 т е k м и о т м с . а Н н � о к к т с и д 5 и ё , о щ ж B д я и и й о й � л A и ы а р к и с е ь м с и т я . � щ я н н а в и й о и ж . г р и г ж е я я и о к т т у н с с р с р е е е а п о с л ч � с п р м е о и ё н у н � р н а м к и к ж в х е я о щ е х м с я я л с М ю х й д ы и ы н . 1 у щ ы т и р ш е н а й а С е ж у ж ч е м � р р а т е с е . л П д о д е а о и э . , е З р п с н а и г х а а н е ё т в м а р и т о у ч л д б е е з у д и р я м е и о а й б р в р п о о р О П О д т ж е а к м 3
а г и л я а ш д а л М
3
k
и 2
k
,
1
k
и т с � о к к т с и ё щ ж я й и ы � р а к
� и л л и м , р т е м о м . а Н н и д 5 , о д B й и о л A и и с
� и л и л и 2 м k , р , 1 т е k м и о т м с . а Н н � о к к т с и д 5 и ё , о щ ж B д я и и й о й � л A и ы а р к и с е ь м с и т я . � щ я н н а в и й о и ж . г р и г ж е я я и о к т т у н с с р с р е е е а п о с л ч � с п р м е о и ё н у н � р н а м к и к ж в х е я о щ е х м с я я л с М ю х й д ы и ы н . 1 у щ ы т и р ш е н а й а С е ж у ж ч е м � р р а т е с е . л П д о д е а о и э . , е З р п с н а и г х а а н е ё т в м а р и т о у ч л д б е е з у д и р я м е и о а й б р в р п о о р О П О д т ж е а к м 3
k
а г и л я а ш д а л М
3
k
и 2
k
,
1
k
и т с � о к к т с и ё щ ж я й и ы � р а к
� и л л и м , р т е м о м . а Н н и д 5 , о д B й и о л A и и с
� и л и л и 2 м k , р , 1 т е k м и о т м с . а Н н � о к к т с и д 5 и ё , о щ ж B д я и и й о й � л A и ы а р к и с е ь м с и т я . � щ я н н а в и й о и ж . г р и г ж е я я и о к т т у н с с р с р е е е а п о с л ч � с п р м е о и ё н у н � р н а м к и к ж в х е я о щ е х м с я я л с М ю х й д ы и ы н . 1 у щ ы т и р ш е н а й а С е ж у ж ч е м � р р а т е с е . л П д о д е а о и э . , е З р п с н а и г х а а н е ё т в м а р и т о у ч л д б е е з у д и р я м е и о а й б р в р п о о р О П О д т ж е а к м 3
k
а г и л я а ш д а л М
3
k
и 2
k
,
1
k
и т с � о к к т с и ё щ ж я й и ы � р а к
� и л л и м , р т е м о м . а Н н и д 5 , о д B й и о л A и и с
� и л и л и 2 м k , р , 1 т е k м и о т м с . а Н н � о к к т с и д 5 и ё , о щ ж B д я и и й о й � л A и ы а р к и с е ь м с и т я . � щ я н н а в и й о и ж . г р и г ж е я я и о к т т у н с с р с р е е е а п о с л ч � с п р м е о и ё н у н � р н а м к и к ж в х е я о щ е х м с я я л с М ю х й д ы и ы н . 1 у щ ы т и р ш е н а й а С е ж у ж ч е м � р р а т е с е . л П д о д е а о и э . , е З р п с н а и г х а а н е ё т в м а р и т о у ч л д б е е з у д и р я м е и о а й б р в р п о о р О П О д т ж е а к м 3
k
k
а г и л я а ш д а л М
3
k
и 2
k
,
1
k
и т с � о к к т с и ё щ ж я й и ы � р а к
� и л л и м , р т е м о м . а Н н и д 5 , о д B й и о л A и и с
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2
k
,
1
k
e u g a e l r o i n u J
, r e p a p h p a r g , r e t e m o m a n y d ,
2
k
,
s e t a r n o i t c . e N fl e 5 � d o x d t o n p b a u y � e e c r x r o g b B f o � y d g l e n n a r a i c g y i l A n � e s p p a h a h t d c s o e f . r g o s n i M e i h n t i r . p a 1 m t w s e n e h o � h m c s t c e t x o h l i b s b t c e t s o l y g r p n e e r r t P i m i s r G s p y � s a e f . h m t o t n e h e e n n c a i m O e . m p e f r i o e . t u t 3 q s o e k N D d E p m a n l a c
2
k
,
1
k
s e t a r n o i t c e fl e � d x d o b n a y e � x
, r e p a p h p a r g , r e t e m o m a n y d
1
k
e u g a e l r o i n u J
2
k
,
s e t a r n o i t c . e N fl e 5 � d o x d t o n p b a u y � e e c r x r o g b B f o � y d g l e n n a r a i c g y i l A n � e s p p a h a h t d c s o e f . r g o s n i M e i h n t i r . p a 1 m t w s e n e h o � h m c s t c e t x o h l i b s b t c e t s o l y g r p n e e r r t P i m i s r G s p y � s a e f . h m t o t n e h e e n n c a i m O e . m p e f r i o e . t u t 3 q s o e k N D d E p m a n l a c
2
k
,
1
k
. N 5 o t p u e c
, r e p a p h p a r g , r e t e m o m a n y d ,
s e t a r n o i t c e fl e � d x d o b n a y e � x
, r e p a p h p a r g , r e t e m o m a n y d
1
k
e u g a e l r o i n u J
2
k
,
s e t a r n o i t c . e N fl e 5 � d o x d t o n p b a u y � e e c r x r o g b B f o � y d g l e n n a r a i c g y i l A n � e s p p a h a h t d c s o e f . r g o s n i M e i h n t i r . p a 1 m t w s e n e h o � h m c s t c e t x o h l i b s b t c e t s o l y g r p n e e r r t P i m i s r G s p y � s a e f . h m t o t n e h e e n n c a i m O e . m p e f r i o e . t u t 3 q s o e k N D d E p m a n l a c
2
k
,
1
k
. N 5 o t p u e c
, r e p a p h p a r g , r e t e m o m a n y d ,
s e t a r n o i t c e fl e � d x d o b n a y e � x
, r e p a p h p a r g , r e t e m o m a n y d
1
k
e u g a e l r o i n u J
s e t a r n o i t c . e N fl e 5 � d o x d t o n p b a u y � e e c r x r o g b B f o � y d g l e n n a r a i c g y i l A n � e s p p a h a h t d c s o e f . r g o s n i M e i h n t i r . p a 1 m t w s e n e h o � h m c s t c e t x o h l i b s b t c e t s o l y g r p n e e r r t P i m i s r G s p y � s a e f . h m t o t n e h e e n n c a i m O e . m p e f r i o e . t u t 3 q s o e k N D d E p m a n l a c
2
k
,
1
k
. N 5 o t p u e c
, r e p a p h p a r g , r e t e m o m a n y d ,
s e t a r n o i t c e fl e � d x d o b n a y e � x
, r e p a p h p a r g , r e t e m o m a n y d
. N 5 o t p u e c
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Туймаада-2016 Туймаада-2016 Черный ящик ( ящик (младшая младшая лига) лига)
Неустроев Е.П.
В черном ящике находится источник постоянного тока. 1. Определите характеристики источника тока: внутренне сопротивление, ЭДС, силу тока короткого замыкания. 2. Постройте зависимость полезной мощности от сопротивленияP(R). Из зависимости P(R) определите внутреннее сопротивление источника и сравните со значением, полученным в первом задании. 3. Оените погре!ности измерений
О"орудование: черный ящик, амперметр, на"ор сопротивлений с известными значениями, соединительные провода (по тре"овани# участников) Внимание: Внимание: для из"е$ания короткого замыкания запрещается подсоединять амперметр непосредственно к выводам черного ящика!
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Black box (junior league)
E. P. Neustroev
There is a source of direct current in the black box. 1. Determine characteristics of source of current: internal resistance, an electromotive force, a current intensity of short circuit. 2. Plot the dependence P(R) of net power P on the resistance R. Determine from the function P(R) the internal resistance of the source and compare with the value obtained in the first task. 3. Estimate errors of measurements Equipment: a black box, an ammeter, a set of resistors with known values, connecting wires (at a request of participants). Caution: Caution: to avoid a short circuit it is forbidden to connect the ammeter directly to terminals of black box!
Density and voidage (junior league)
Zamyatnin M. Yu.
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. о м а я р и т о ч о т н т , э а а с б и е к а н т р е л п д о к и ь н с о е л а у к и н а к л и о и щ и з г в н о ю и е д а к з Ф х а м с . р о у р з и � т л а а о п з о д т з з а е н а а н а с и н е р м н м е л о к й е ы д ь у е е д н л Т н щ м н о я � о о е к ь в т а к с т н с д с е о а й о б ч В и ы с , о . с о з п н е и а м р р т и а у о р т я л д н n в о о н о р о х е в я а К к с и н . м о м о ь с д о н 4 р а о в н п л р а а ь , а ч л и р и ч н а е т и у а т с д д а а о р л е б н о в ж т в у ? е З е л а и с о М к т н й й и к е и I н I у д н м а а д о н н б б X н и о е е X к
� й v � с а ы ю с а р н ь р ? о т а м ь н д ь ы л а с г о о л н ч р с а а к у н о , к м к с т и о в н н й , е ф к о м и к е о м з с о ч а к м м у н ы е т и з ж С и о л н . и й ы т н е в л и з в ж к я й ь н и а к а р н и е л е щ л ч б н у о е е ю а р ж з а ж р м т е и а и a н и м р б е ц н ы м б о н с е м е о ь ж и з й н о а л и о е к р е с т е б р е к н и о ч и о о з в к и т н с т и т е и у п я с р с м о с й е о о ы в т д е к я о с й ж о н г н с и У к й е я в и . с о е и д 5 ч т ш с в и w а т о и м п о м о ч к а п с к е о и д й т о н ч а о ё п е у З н з и р ж л н о у в д а о п е м к ж
! й о б о с с е т и с о н у я и в о л с У
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2 Младшая лига Задача 1. Задача 1. Длина изоленты
Вычислить с максимальной точностью длину изоленты в рулоне и ее толщину, толщину, не разматывая не разматывая рулон рулон.. Оборудование: рулон изоленты, изоленты, линейка длиной 20-30 длиной 20-30 см с наклеенной по всей длине полоской изоленты. изоленты. Задача 2. Задача 2. Плотность кристалла соли
Вычислить плотность кристалла пищевой поваренной соли (соль мочить нельзя). нельзя). Оборудование: шприцы 10 мл и 20 мл с колпачками для отверстий, отверстий, пластилин, пластилин, пластиковая трубка длиной 1 м (от капельницы), капельницы), сосуд с покрашенной водой, водой, сосуд с солью, солью, линейка, линейка, скотч, скотч, пробка для трубки. трубки.
Рис. 1 %о""ициент пропорциональности κ называется модулем кручения линейки. линейки. &одуль кручения определяется геометрическими параметрами линейки и упругими свойствами материала, материала, из которого изготовлена линейка. линейка. !ак, !ак, для тонкой линейки длиной ℓ , шириной b и толщиной δ, изготовленной из материала с модулем сдвига G, модуль кручения мо'ет быть рассчитан быть рассчитан по "ормуле: "ормуле:
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5 модуля кручения κ , поло'ив безразмерный ко""ициент β = 1/3. 7. Придумайте и проведите ксперимент, ксперимент, позволяющий с помощью имеющегося оборудования определить численное значение модуля кручения κ для одной из алюминиевы# планок. планок. алюминия. 8. Рассчитайте модуль сдвига G алюминия.
6
M k ϕ . =
torsion of The coefficient of proportionality κ is is called a modulus a modulus of torsion of ruler.
Junior league Problem 1. Length of insulating tape
Compute with maximum accuracy a length of insulating tape in a roll and its thickness without unwinding the roll. Equipment: the roll of insulating tape, a ruler with a length of 20-30 cm with a strip of insulating tape, which is glued on along the whole length of ruler.
Fi . 1
The modulus of torsion determines geometric parameters of ruler and
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9 7. Design and conduct an experiment that enables with the use of existing equipment to determine the numerical value of modulus of torsion κ for for one of aluminium laths. 8. Calculate the shear modulus G of aluminium.
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