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Исследования микромира и микрокосмоса

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Aeieaia a?aiy eacaeinue, /oi naiia eioa?aniia a Oeceea – yoi
enneaaeiaaiey iee?iie?a e iee?ieiniina. Eiaiii oai iuoaeenue iaeoe
ioaaou ia iaaieaa aaaeiua, ooiaeaiaioaeueiua aii?inu, iauyniethuea
ono?ienoai ie?oaeathuaai ie?a. A nae/an ia?aciaaeny o?aoee o?iio
enneaaeiaaiee – eco/aiea oa??aeuo oae.

Ii/aio aea oae aaaeii enneaaeiaaoue oa??aeua oaea?

Ia?iiioth ?ieue, eiia/ii, ea?aao naeanue i?aeoe/aneay
aeayoaeueiinoue /aeiaaea. Oa??aeua oaea – yoi iaoaeeu e aeeyeaeo?eee,
aac eioi?uo iaiuneeia yeaeo?ioaoieea, yoi – iieoi?iaiaeieee, eaaeauee a
iniiaa nia?aiaiiie yeaeo?iieee, iaaieou, naa?o i?iaiaeieee,
eiino?oeoeeiiiua iaoa?eaeu. Neiaii, iiaeii ooaa?aeaeaoue, /oi
iao/ii-oaoie/aneee i?ia?ann a cia/eoaeueiie ia?a iniiaai ia
eniieueciaaiee oa??aeuo oae.

Ii ia oieueei i?aeoe/aneay noi?iia aeaea aaaeia i?e eo eco/aiee. Naia
aioo?aiiyy eiaeea ?acaeoey iaoee – oeceee oa??aeiai oaea – i?eaaea e
iiieiaieth aaaeiiai cia/aiey eieeaeoeaiuo naienoa aieueoeo nenoai.

Oa??aeia oaei ninoieo ec ieeeea?aea /anoeoe, eioi?ua
acaeiiaeaenoaotho iaaeaeo niaie. Yoi iaoneiaeeaaao iiyaeaiea
ii?aaeae?iiiai ii?yaeea a nenoaiia e iniauo naienoa anaai eiee/anoaa
iee?i/anoeoe.Oae, eieeaeoeaiua naienoaa yeeaeo?iiia ii?aaeaeytho
yeaeo?ii?iaiaeiinoue oa??aeue oae, a niiniaiinoue oaea iiaeiuaoue oaiei
– oaiei?ieinoue – caaeneo io oa?aeoa?a eieeaeoeaiuo eieeaaaiee aoiiia
i?e oaieiaii aeaeaeaiee. Eieeaeoeaiua naienoaa iauyniytho ana iniiaiua
caeiiiia?iianoe iiaaaeaiey oa??aeuo oae.

No?oeoo?a oa??aeuo oae iiiaiia?acia. Oai ia iaiaa ec iiaeii
?acaeaeeoue ia aeaa aieueoeo eeanna: e?enoaeeu e aii?oiua oaea.

?en. 1

E?enoaeeu – yoi oa??aeua oaea, aoiiu eee iieaeoeu eioi?uo caieiatho
ii?aaeae?iiua, oii?yaei/aiiua iieiaeaiey a i?ino?ainoaa. Iiyoiio
e?enoaeeu eiatho ieineea a?aie. Iai?eia? e?oieiea iau/iie iiaa?aiiie
niee eiaao ieineea a?aie, ninoaaeythuea ae?oa n ae?oaii i?yiua oaeu
(?en. 1). Yoi iiaeii caiaoeoue, ?anniao?eaay nieue n iiiiuueth eoiu.
No?iaay ia?eiaee/iinoue a ?aniieiaeaiee aoiiia i?eaiaeeo e nio?aiaieth
ii?yaeea ia aieueoeo ?annoiyieyo (a oaeii neo/aa aiai?yo, /oi eiaaony
aeaeueiee ii?yaeie). A eae aaiiao?e/anee i?aaeeueia oi?ia niaaeeiee! A
iae oaeaea io?aaeaia aaiiao?e/aneay i?aaeeueiinoue aioo?aiiaai no?iaiey
e?enoaeee/aneiai oa??aeiai oaea – eueaea.

Iaeiaei, i?aaeeueiay aiaoiyy oi?ia ia aaeeinoaaiiia e aeaaea ia naiia
aeaaiia neaaenoaea oii?yaei/aiiiai no?iaiey e?enoaeea. Aeaaiia – yoi
caaeneiinoue oece/aneeo naienoa io aua?aiiiai a e?enoaeea iai?aaeaiey.
I?aaeaea anaai a?inaaony a aeaca ?acee/iay iaoaie/aneay i?i/iinoue
e?enoaeeia ii ?aciui iai?aaeaieyi. Iai?eia? eonie nethaeu eaaei
?anneaeaaaony a iaeiii ec iai?aaeaiee ia oiieea ieanoeiee, ii ?aci?aaoue
aai a iai?aaeaiee, ia?iaiaeeeoey?iii ieanoeieai, ai?acaei o?oaeiaa. Oae
aea eaaei ?anneaeaaaony a iaeiii iai?aaeaiee e?enoaee a?aoeoa. Eiaaea au
ieoaoa ea?aiaeaoii, oaeia ?anneiaiea i?ienoiaeeo iai?a?uaii e oiieea
neie a?aoeoa inoathony ia aoiaaa. Yoi i?ienoiaeeo iioiio /oi
e?enoaeee/aneay ?ao?oea a?aoeoa eiaao neienooth no?oeoo?o. Neie
ia?aciaaiu ?yaeii ia?aeeaeueiuo naoie, ninoiyueo ec aoiiia oaea?iaea.
Aoiiu ?aniieiaathony a aa?oeiao i?aaaeueiuo oanoeoaieueieeia. ?annoiyiea
iaaeaeo neiyie n?aaieoaeueii aaeeei – i?eia?iia a aeaa ?aca aieueoa, /ai
aeeeia noi?iiu oanoeoaieueieea, iiyoiio nayce iaaeaeo neiyie iaiaa
i?i/iu, /ai nayce aioo?e ieo. Iiiaea e?enoaeeu ii-?aciiio i?iaiaeyo
oaieioo e yeaeo?e/aneee oie a ?acee/iuo iai?aaeaieyo. Io iai?aaeaiey
caaenyo e iioe/aneea naienoaa e?enoaeeia. Oae, e?enoaee eaa?oea ii
?aciiio i?aeiieyao naao a caaeneiinoe io iai?aaeaiey iaaeathueo ia iaai
eo/ae.

Caaeneiinoue oece/aneeo naienoa io iai?aaeaiey aioo?e e?enoaeea
iacuaatho aiecio?iieae. Ana e?enoaeee/aneea oaea aiecio?iiiu.

E?enoaee/aneoth no?oeoo?o eiatho iaoaeeu. Eiaiii iaoaeeu i?aeiouanoaaii
eniieuecothony a ianoiyuaa a?aiy aeey ecaioiaeaiey i?oaeee o?oaea,
?acee/iuo iaoei e iaoaieciia.

Anee acyoue n?aaieoaeueii aieueoie eonie iaoaeea, oi ia ia?aue acaeyae
aai e?enoaee/aneay no?oeoo?a ieeae ia i?iyaeyaony ie ai aiaoiai aeaea
eonea ie a aai oece/aneeo naienoaao. Iaoaeeu a iau/iii ninoiyiee ia
iaia?oaeeaatho aiecio?iiee.

Aeaei caeanue a oii, /oi iaoaee iau/ii ninoieo ec ia?iiiiai eiee/anoaa
n?inoeony ae?oa n ae?oaii e?enoaeeeia. Iiae iee?ineiiii eee aeaaea n
iiiiuueth eoiu eo iao?oaeii ?anniio?aoue, iniaaiii ia naaaeai eceiia
iaoaeea.Naienoaa eaaeaeiai e?enoaeeeea caaenyo io iai?aaeaiey, ii
e?enoaeeeee i?eaioe?iaaiiu ii ioiioaieth ae?oa e ae?oao aanii?yaei/ii. A
?acoeueoaoa a iau?ia, cia/eoaeueii i?aauoathuai iau?i ioaeaeueiuo
e?enoaeeeeia ana iai?aaeaiey aioo?e iaoaeeia ?aaiii?aaiu e naienoaa
iaoaeeia iaeeiaeiau ii anai iai?aaeaieyi.

Oa??aeia oaei, ninoiyuaa ec aieueoiai /enea iaeaiueeeo e?enoaeeeeia,
iacuaatho iiiie?enoaeeaie.

Niaethaeay aieueoea i?aaeinoi?iaeiinoe, iiaeii au?anoeoue
iaoaeee/aneee e?enoaee aieueoeo ?acia?ia – iiiie?enoaee. A iau/iuo
oneiaeyo iieee?enoaeee/aneia oaei ia?acoaony a ?acoeueoaoa oiai, /oi
ia/aaoeeny ?ino iiiaeo e?enoaeeia i?iaeieaeaaony aei oao ii? iiea iie ia
i?eoiaeyo a nii?eeiniiaaiea ae?oa n ae?oaii, ia?acoy aaeeiia oaei.

E iieee?enoaeeai ioiinyony ia oieueei iaoaeeu. Eonie naoa?a,
iai?eia?, oaeaea eiaao iieee?enoaeee/aneoth no?oeoo?o.

Aieueoeinoai e?enoaeee/aneeo oae – iieee?enoaeeu, oae eae iie ninoiyo
ec iiiaeanoaa n?inoeony e?enoaeeia. Iaeeii/iua e?enoaeeu – iiiie?enoaeeu
eiatho i?aaeeueioth aaiiao?e/aneoth oi?io, e eo naienoaa ?acee/iu ii
?aciui iai?aaeaieyi (aiecio?iiey).

Ia ana oa??aeua oaea – e?enoaeeu. Nouanoaoao iiiaeanoai
aii?oiuo oae. *ai iie ioee/athony io e?enoaeeia?

O aii?oiuo oae iao no?iaiai ii?yaeea a ?aniieiaeaiee aoiiia. Oieueei
aeeaeaeoea aoiiu – ninaaee ?aniieiaathony a iaeioi?ii ii?yaeea. Ii
no?iaie iai?aaeyaiinoe ii ana iai?aaeaieyi iaeiiai e oiai aea yeaiaioa
no?oeoo?u, eioi?ay oa?aeoa?ia aeey e?enoaeeia a aii?oiuo oaeao, iao.

*anoi iaeii e oi aea aauanoai iiaeao iaoiaeeoueny eae a
e?enoaee/aneii, oae e a aii?oiii ninoiyiee. Iai?eia?, eaa?oe SiO2,
iiaeao auoue eae a e?enoaee/aneie, oae e a aii?oiie oi?ia (e?aiiacai).
E?enoaeee/aneoth oi?io eaa?oea noaiaoe/anee iiaeii i?aaenoaaeoue a aeaea
?ao?oee ec i?eaeeueiuo oanoeoaieueieeia. Aii?oiay no?oeoo?aeaa?oea
oaeaea eiaao aeae ?ao?oee, ii ia?iaaeueiie oi?iu. Ia?yaeo n
oanoeoaieueieeaie a iae ano?a/athony iyoe e naieoaieueieee.

A 1959 a. aiaeeeneee oecee Ae. Aa?iae i?ia?e eioa?aniua iiuou: ii
acye iiiai iaeaiueeeo ieanoeeeiiauo oa?eeia iaeeiaeiaiai ?acia?a,
iaaieye eo a iaeiaie ioae?a e ni?aniaae a aieueoie eii. A ?acoeueoaoa
oa?eee aeaoi?ie?iaaeenue a iiiaia?aiieee. Ieacaeinue, /oi i?e yoii
ia?aciauaaeenue i?aeiouanoaaiii iyoeoaieueiua a?aie, a iiiaia?aiieee a
n?aaeiai eiaee 13,3 a?aie. Oae /oi eaeie-oi ii?yaeie a aii?oiuo
aauanoaao ii?aaeae?iii anoue.

Naienoaa Aii?oiuo oae. Ana aii?oiua oaea ecio?iiiu, o.a. eo
oece/aneea naienoaa iaeeiaeiau ii anai iai?aaeaieyi. E aii?oiui oaeai
ioiinyony noaeei, niiea, eaieoieue, naoa?iue eaaeaiaoe e ae?.

I?e aiaoieo aicaeaenoaeyo aii?oiua oaea iaia?oaeeaatho iaeiia?aiaiii
oi?oaea naienoaa, iiaeiaii oa??aeui oaeai, e oaeo/anoue, iiaeiaii
oeaeeinoe. Oae, i?e e?aoeia?aiaiiuo aicaeaenoaeyo (oaea?ao) iie aaaeoo
naay eae oa??aeua oaea e i?e neeueiii oaea?a ?aneaeuaathony ia eonee.Ii
i?e i/aiue i?iaeieaeeoaeueiii aicaeaenoaee aii?oiua oaea oaeoo.
I?ineaaeei ca eoneii niieu, eioi?ue eaaeeo ia aeaaeeie iiaa?oiinoe.
Iinoaiaiii niiea ii iae ?anoaeaaony, e , /ai auoa oaiia?aaoo?a niieu,
oai auno?aa yoi i?ienoiaeeo.

Aoiiu eee iieaeoeu aii?oiuo oae, iiaeiaii iieaeoeai aeeaeeinoe,
eiatho ii?aaeae?iiia a?aiy “in?aeeie aeecie” – a?aiy eieaaaiee ieiei
iieiaeaiey ?aaiiaaney. Ii a ioee/aa io aeeaeeinoae yoi a?aiy o ieo
aanueia aaeeei. Oae, aeey aa?a i?e t = 20oC a?aiy “in?aeeie aeecie” 0,1
n. A yoii ioiioaiee aii?oiua oaea aeecee e e?enoaeee/aneei, oae eae
ia?aneiee aoiiia ec iaeiiai iieiaeaiey ?aaiiaaney a ae?oaia i?ienoiaeyo
?aaeei.

Aii?oiua oaea i?e ieceeo oaiia?aoo?ao ii naiei naienoaai iaiiieiatho
oa??aeua oaea. Oaeo/anoueth iie ii/oe ia iaeaaeatho, ii ii ia?a
iiauoaiey oaiia?aoo?u iinoaiaiii ?aciya/athony e eo naienoaa an? aieaa e
aieaa i?eaeeaeathony e naienoaai aeeaeeinoae. Yoi i?ienoiaeeo iioiio,
/oi n ?inoii oaiia?aoo?u iinoaiaiiio/auathony ia?aneiee aoiiia ec
iaeiiai iieiaeaiey a ae?oaia. Ii?aaeae?iiie oaiia?aoo?u oae o aii?oiuo
oae, a ioee/aa io e?enoaeee/aneeo, iao.

Oeceea oa??aeiai oaea. *?eiaa/anoai anaaaea eniieueciaaei e aoaeao
eniieueciaaoue oa??aeua oaea. Ii anee ?aiueoa oeceea oa??aeiai oaea
ionoaaaea io ?acaeoey oaoiieiaee, iniiaaiiie ia iaiin?aaenoaaiiii iiuoa,
oi oaia?ue iieiaeaiea ia?aiaieeinue. Oai??aoe/aneea enneaaeiaaiey
i?eaiaeyo e nicaeaieth oa??aeuo oae, nai?noaa eioi?uo niaa?oaiii
iaiau/iu. Iieo/eoue oaeea oaea iaoiaeii i?ia e ioeaie auei au
iaaiciiaeii. Niocaeaiea o?aicenoi?ia, i eioi?uo iieae?o ?a/ue a
aeaeueiaeoai, – y?eee i?eia? oiai, eae iiieiaiea no?oeoo?u oa??aeuo oae
i?eaaei e ?aaiethoeee ai anae ?aaeeioaoieea.

Iieo/aiea iaoa?eaeeia n caaeaiiuie iaoaie/aneeie, iaaieoiuie,
yeaeo?e/aneeie e ae?oaeie naienoaaie – iaeii ec iniiaiuo iai?aaeaiee
nia?aiaiiie oeceee oa??aeiai oaea.

Aii?oiua oaea caieiatho i?iiaaeooi/iia iieiaeaiea iaaeaeo
e?enoaeee/aneeie oa??aeuie oaeaie e aeeaeeinoyie. Eo aoiiu eee iieeaeoeu
?aniieiaathony a ioiineoaeueiii ii?yaeea. Iiieiaiea no?oeoo?u oa??aeuo
oae (e?enoaeee/aneeo e aii?oiuo) iicaieyao nicaeaaaoue iaoa?eaeu n
caaeaiiuie naienoaaie.

Aeaoi?iaoeey oa??aeiai oaea – eciaiaiea aai oi?iu eee iau?ia. ?anoyieoa
?aceiiaue oio? ca eiioeu. I/aaeaeii, o/anoee oio?a nianoyony ae?oa
ioiineoaeueii ae?oaa; oio? ieaaeaony aeaoi?ie?iaaiiui – noaiao aeeeiiaa
e oiiueoa. Aeaoi?iaoeey aicieeaao anaaaea, eiaaea ?acee/iua /anoe oaea
iiae aeaenoaeai nee ia?aiauathony iaiaeeiaeiai.

Oio?, iinea i?ae?auaiey aeaenoaey ia iaai nee, aica?auaaony a
enoiaeiia ninoiyiea. Aeaoi?iaoeee, eioi?ua iieiinoueth en/acatho iinea
i?ae?auaiey aeaenoaey aiaoieo nee iacuaathony oi?oaeie. E?iia ?aceiiaiai
oio?a, oi?oaea aeaoi?iaoeee eniuouaatho i?oaeeia, noaeueiua oa?eee i?e
noieeiiaaiee e o.ae.

Oaia?ue niaeieoa eoni/ae ieanoeeeia. A aaoeo ?oeao ii eaaei i?eiao
ethaoth oi?io. Ia?aiia/aeueiay oi?ia ieanoeeeia ia ainnoaiiaeony naia
niaie. Ieanoeeei “ia iiiieo” eaeay oi?ia au o iaai nia/aea.
Aeaoi?iaoeee, eioi?ua ia en/acatho iinea i?ae?auaiey aeaenoaey aiaoieo
nee, iacuaathony ieanoe/aneeie. Ieanoe/aneoth aeaoi?iaoeeth, i?e
iaaieueoeo, ii ia e?aoeia?aiaiiuo aicaeaenoaeyo eniuouaatho aine, eeeia,
naeiaoe.

?en.2

F1= -F
F

Aeaoiiaoeey ?anoyaeaiey (naeaoey). Anee e iaeiiio noa?aeith,
cae?aie?iiiio iaeiei eiioeii, i?eeiaeeoue neeo F aaeieue ine noa?aeiy a
iai?aaeaiee io yoiai eiioea (?en. 2), oi noa?aeaiue iiaeaa?aiaony
aeaoiiaoeee ?anoyuaiey. Aeaoiiaoeeth ?anoyaeaiey oa?aeoa?ecotho
aaniethoiui oaeeeiiaieai.

(l = l – l0

e ioiineoaeueiui oaeeeiaieai

( = (l / l0

aaea l0 – ia/aeueiay aeeeiia, a l – eiia/iay aeeeiia noa?aeiy.

Aeaoi?iaoeeth ?anoyaeaiey iniuouaatho o?inu, eaiaou, oeaie a
iiaeu?iiuo ono?ienoaao, noyaeee iaaeaeo aaaiiaie e o.ae.

I?e iaeuo ?anoyaeaieyo (l0(( l), aeaoi?iaoeee aieueoeinoaa oae
oi?oaea.

?en. 3

F1= -F F

Anee ia oio aea noa?aeaiue iiaeaenoaiaaoue neeie F, iai?aaeaiiie e
cae?aie?iiiio eiioeo (?en. 3), oi noa?aeaiue iiaeaa?aiaony aeaoi?iaoeee
naeaoey. A yoii neo/aa ioiineoaeueiay aeaoi?iaoeey io?eoeaoaeueia: (( 0.

I?e?anoyaeaiee eee naeaoee eciaiyaony ieiuaaeue iiia?a/iiai na/aiey
oaea. Yoi iiaeii iaia?oaeeoue, anee ?anoyiooue ?aceiiaoth o?oaeo, ia
eioi?oth i?aaeaa?eoaeueii iaaeaoi iaoaeee/aneia eieueoei. I?e
aeinoaoi/ii neeueiii ?anoyaeaiee eieueoei iaaeaao. I?e naeaoee,
iaiai?io, ieiuaaeue iiia?a/iiai na/aiey oaea oaaee/eaaaony.

?en. 4

B C B
C F

a b a
b

c d c
d

(

A D A D

a b

Aeaoi?iaoeey naeaeaa. Aicuei?i ?aceiiaue a?onie n ia/a?/aiiuie ia aai
iiaa?oiinoe ai?eciioaeueiie e aa?oeeaeueiuie eeieyie e cae?aiei ia noiea
(?en. 4, a). Naa?oo e a?oneo i?ee?aiei ?aeeo e i?eeiaeei e iae
ai?eciioaeueioth neeo (?en. 4, a). Neie a?onea ab, cd e ae?.
Naeaeioony,inoa-aaynue ia?aeeaeueiuie, a aa?oeeaeueiua a?aie, inoaaaynue
ieineeie, iaeeiiyony ia oaie ( .

Aeaoi?iaoeeth, i?e eioi?ie i?ienoiaeeo niauaiea nei?a oaea ae?oa
ioiineoaeueii ae?oaa, iacuaatho aeaoi?iaoeeae naeaeaa.

Anee neeo F oaaee/eoue a aeaa ?aca, oi e oaie ( oaaee/eony a 2 ?aca.
Iiuou iieacuaatho, /oi i?e oi?oaeo aeaoi?iaoeeyo oaie naeaeaa ( i?yii
i?iii?oeeaiaeai iiaeoeth F i?eeiaeaiiie neeu.

Iaaeyaeii aeaoi?iaoeeth naeaeaa iiaeii iieacaoue ia iiaeaee oa??aeiai
oaea, eioi?ia ninoieo ec ?yaea ia?aeeaeueiuo ieanoei, niaaeei?iiuo
iaaeaeo niaie i?oaeeiaie. Ai?eciioaeueiay neea naeaeaaao ieanoeiu ae?oa
ioiineoaeueii ae?oaa aac eciaiaiey iau?ia oaea. O ?aaeueiuo oa??aeuo oae
i?e aeaoi?iaoeee naeaeaa iau?i oaeaea ia iaiyaony.

Aeaoi?iaoeeyi naeaeaa iiaeaa?aeaiu ana aaeee a ianoao iii?, caee?iee
e aieou, ne?aieythuea aeaoaee e o.ae. Naeaea ia aieueoea oaeu iiaeao
i?eaanoe e ?ac?ooaieth oaea – n?aco. N?ac i?ienoiaeeo i?e ?aaioa
iiaeieoe, aeieioa, coaaea, coaueaa ieeu.

Ecaea e e?o/aiea. Aieaa neiaeiuie aeaeaie aeaoi?iaoeee yaeythony
ecaea e e?o/aiea. Aeaoi?iaoeeth ecaeaa eniuouaaao, iai?eia?,
iaa?oaeaiiay aaeea. E?o/aiea i?ienoiaeeo i?e caa??ouaaiee aieoia,
a?auaiee aaeia iaoei, na??e e o.ae. Yoe aeaoi?iaoeee naiaeyony e
iaiaeii?iaeiiio ?anoyaeaieth eee naeaoeth e iaiaeii?iaeiiio naeaeao.

Ana aeaoi?iaoeee oa??aeuo oae naiaeyony e ?anoyaeaieth (naeaoeth) e
naeaeao. I?e oi?oaeo aeaoi?iaoeeyo oi?ia oaea ainnoaiaaeeaaaony, a i?e
ieanoe/aneeo ia ainnoaiaaeeaaaony.

Oaieiaia aeaeaeaiea aucuaaao eieaaaiey aoiiia (eee eiiia), ec eioi?uo
ninoieo oa??aeia oaei. Aiieeooaea eieaaaiee iau/ii iaea ii n?aaiaieth n
iaaeaoiiiuie ?annoiyieyie, e aoiiu ia iieeaeatho naieo iano. Iineieueeo
aoiiu a oa??aeii oaea naycaiu iaaeaeo niaie, eo eieaaaiey i?ienoiaeyo
niaeaniaaiii, oae /oi ii oaeo n ii?aaeae?iiie nei?inoueth
?ani?ino?aiyaony aieia. Aeey iienaiey eieaaaiee a oa??aeuo oaeao i?e
ieceeo oaiia?aoo?ao /anoi eniieuecotho i?aaenoaaeaiey i eaace/anoeoeao –
oiiiiao.

Ii naiei yeaeo?iiiui naienoaai oa??aeua oaea ?acaeaeythony ia
iaoaeeu, aeeyeaeo?eee e iieoi?iaiaeieee. E?iia oiai, i?e ieceeo
oaiia?aoo?ao aiciiaeii naa?oi?iaiaeyuaa ninoiyiea, a eioi?ii
nii?ioeaeaiea yeaeo?e/aneiio oieo ?aaii ioeth.

?en. 5 Iaoaee

(

Aeaeaeaiea iee?i/anoeoe iiae/eiyaony caeiiai eaaioiaie iaoaieee. O
naycaiiuo yeaeo?iiia, iai?eia? a aoiia, yia?aey iiaeao i?eieiaoue
oieueei ii?aaeae?iiua e a a i o i a a i i u a c i a / a i e y. A
oa??aeii oaea yoe o?iaie y?aiaee iauaaeeiythony a ciiu, ?acaeae?iiua
cai?au?iiuie iaeanoyie yia?aee (?en. 5). A neeo i?eioeeia Iaoee
yeaeo?iiu ia neaieeaathony ia ieaeiai o?iaia, a caieiatho o?iaie n
?aciuie yia?aeyie. A ?acoeueoaoa iiaeao ieacaoueny, /oi ana o?iaie
yia?aee a ciia aoaeoo iieiinoueth caiieiaiu. Oaeia oa??aeia oaei
yaeyaony aeeyeaeo?eeii. Oaeia oa??aeia oaei yaeyaony aeeyeaeo?eeii.
Eciaieoue yia?aeth yeaeo?iia iiaeii oieueei n?aco ia aieueooth eiia/ioth
aaee/eio (oe?eio cai?au?iiie iaeanoe, eee, eae aiai?yo, yia?aeoe/aneie
uaee). Iiyoiio yeaeo?iiu a aeeyeaeo?eea ia iiaoo onei?youeny a
yeaeo?e/aneii iiea, e i?iaiaeeiinoue i?e ioeaaie oaiia?aoo?a (eiaaea iao
oaieiauo aicaoaeaeaiee) ?aaia ioeth(nii?ioeaeaiea aaneiia/ii).

A iaoaeea, iai?ioea, aa?oiee caiieiaiiue o?iaaiue yia?aee eaaeeo
aioo?e ciiu, yia?aey yeaeo?iiia iiaeao iaiyoueny ii/oe iai?a?uaii, e
yeeo?e/aneia iiea nicaea?o oie. Eii?yaei/aiiia aeaeaeaiea yeaeo?iiia
aaeieue iiey iaeeaaeuaaaony ia eioaineaiia oaioe/aneia aeaeaeaiea.
Iaeneiaeueiay yia?aey yeaeo?iiia ii?aaeaeyaony eo eiiaoeaio?aoeeae. A
oeie/iuo iaoaeeao yoi aaee/eia ii?yaeea yeaeo?iiaieueo. Niioaaonoaothuay
oaeie yia?aee oaiia?aoo?a ( 104E! Oae /oi aeaaea i?e aaniethoiii ioea
/anoue yeaeo?iiia a iaoaea yia?ae/ii aeaeaeaony e eiaao ia?iiioth
yooaeoeaioth oaiia?aoo?o.

?en. 6

ciia i?iaiaeeiinoe

cai?aoiay ciia

ciia aaeaioiinoe

aicaoaeaeaiea yeaeo?iiia a iieoi?iaiaeieea

Iieoi?iaiaeiee – yoi oio aea aeeyeaeo?ee, ii n iaeie aaee/eiie
yia?aeoe/aneie uaee. Oaieiaia aeaeaeaiea iiaeao “caa?anuaaoue” yeaeo?iiu
a naiaiaeioth ciio (iia iacuaaaony ciiie i?iaiaeeiinoe a ioee/aa io
caiieiaiiie aaeaioiie ciiu), aaea iie oaea onei?ythony yeaeo?e/aneei
iieai (?en. 6). Iiyoiio iieoi?iaiaeieee iau/ii eiatho iaaieueooth
i?iaiaeeiinoue, ?acei caaenyuoth io oaiia?aoo?u.Ia i?iaiaeeiinoue
iieoiiaiaeieeia iiaeii oaeaea aeeyoue, aaiaey niaoeeaeueiua i?eiane.

Iieoi?iaiaeieeiaua e?enoaeeuiicai-eytho nicaeaaaoue neiaeiua
iieoi?iaiaeiee-iaua i?eai?u, a oii /enea oae iacuaaaiua eioaa?aeueiua
noaiu. Nae/an aeinoeaiooa oaeay noaiaiue eioaa?aoeee, /oi ieeeeiiu
ioaeaeueiuo yeaiaioia oiauathony ia ieiuaaee ?acia?ii a 1 ni2! Oaeia
ono?ienoai eae au yaeyaony aaeeiui e?enoaeeii, e iiaoth iaeanoue oaoieee
ia c?y iacuaatho oaa?aeioaeueiie yeaeo?iieeie.

Ia?iiiia cia/aiea aeey nia?aiaiiie oaoieee eiatho iaaieoiua
iaoa?eaeu. Aoiiu (eee /anoue aoiiia), ec eioi?uo ninoieo iaaieoiia oaei,
iiaoo iaeaaeaoue iaaieoiui iiiaioii. Anee acaeiiaeaenoaea iaaeaeo
iaaieoiuie iiiaioaie aaeeei, oi iie auno?aeaathonyi i?aaeae?iii ia?acii
e oa??aeia oaei ia?aciaeeo a oa??iiaaieoiia eee aioeoi??iiaaieoiia
ninoiyiea.

Iaoaie/aneea naienoaa oa??aeuo oae.

Aeeaa?aiia ?anoyaeaiey. Aaee/eia, oa?aeoa?ecothuay nioiyiea
aeaoi?ia?iaaiiiai oaea, iacuaaaony iaoaie/aneei iai?yaeaieai. A ethaii
na/aiee aeaoi?ie?iaaiiiai oaea aeaenoaotho neeu
oi?oainoe,i?aiyonoaothuea ?ac?uao yoiai oaea ia /anoe. Iai?yaeaieai eee,
oi/iaa, iaoaie/aneei iai?yaeaieai iacuaatho ioiioaiea iiaeoey neeu
oi?oainoe F e ieiuaaee iiia?a/iiai na/aiey S oaea.

( =F/S

A NE ca aaeeieoeo iai?yaeaiey i?eieiaaony 1 Ia= 1 I/i2, eae e aeey
aeaaeaiey.

A neo/aa naeaoey noa?aeiy iai?yaeaiea aiaeiae/ii aeaaeaieth a aacao e
aeeaeeinoyo. Aeey enneaaeiaaiey aeaoi?iaoeee ?anoyaeaiey noa?aeaiue i?e
iiiiue niaoeeaeueiuo ono?ienoaiiaeaa?aatho ?anoyaeaieth, a caoai
ecia?ytho oaeeeiaiea ia?acoea e aicieeathuaa a i?i iai?yaeaiea. Ii
?acoeueoaoai iiuoia au/a?/eaatho a?aoee caaeneiinoe iai?yaeaiey ( io
ioiineoaeueiiai oaeeeiaiey (, iieo/eaoee iacaaiea aeeaa?aiiu
?anoyaeaiey.

Caeii Aoea. Iiuo iieacuaaao: i?e iaeuo aeaoi?iaoeeyo iai?yaeaiea (
i?yii i?iii?oeeaiaeueiiioiineoaeueii ioiineoaeueiiio oaeeeiaieth (
(o/anoie OA aeeaa?aiiu). Yoa caaeneiinoue, iacuaaaiay caeiiii Aoea,
caienuaaaony oae:

( = E |(| (1)

Ioiineoaeueiia oaeeeiaiea ( a oi?ioea (1) acyoi ii iiaeoeth, oae eae
caeii Aoea ni?aaaaeeea eae aeey aeaoi?iaoeee ?anoyaeaiey, oae e aeey
aeaoi?iaoeee naeaoey, eiaaea ( < 0.Eiyooeoeaio i?iii?oeeaiaeueiinoe E, aoiaeyuee a caeii Aoea, iacuaaaony iiaeoeai oi?oainoe eee iiaeoeai THiaa. Iiaeoeue THiaa i?aaeaeytho ii oi?ioea (1), ecia?yy iai?yaeaiea ( e ioiineoaeueiia oaeeeiaiea ( i?e iaeuo aeaoi?iaoeeyo.Aeey aieueoeinoaa oe?iei ?ani?ino?ai?iiuo iuoa?eaeia iiaeoeue THiaa ii?aaeae?i yenia?eiaioaeueii. Oae, aeey o?iiiieeaeaaie noaee E=2,1(1011 Ia, a aeey aeethieiey E=7(1010 Ia. *ai aieueoa iiaeoeue THiaa, oai iaiueoa aeaoi?ie?aony noa?aeaiue i?e i?i/eo ?aaiuo oneiaeyo (iaeeiaeiauo F,S,l0). Iiaeoeue THiaa oa?aeoa?ecoao nii?ioeaeyaiinoue iaoa?eaea oi?iaie aeaoi?iaoeee ?anoyaeaiey eee naeaoey.Caeii Aoea, caienaiiue a oi?ioea (1), eaaei i?eaanoe e aeaeo, ecaanoiiio ec eo?na oeceee IX eeanna.Aeaenoaeoaeueii, iiaenoaaea a oi?ioeo (1) ( = F/S e ( = |(l|/l0 , iieo/ei:F/S=E ( |(l|/l0IonthaeaF = SE/l0 ( |(l|. (2)Iaicia/eiSE/l0=k, oiaaeaF=k|(l |. (3)Oaeei ia?acii, aeanoeinoue k noa?aeiy i?yii i?iii?oeeaiaeueia i?iecaaaeaieth iiaeoey THiaa ia ieiuaaeue iiia?a/iiai na/aiey noa?aeiy e ia?aoii i?iii?oeeaiaeueia aai aeeeia.I?aaeaeu i?iii?oeeaiaeueiinoe e oi?oainoe. Iu oaea aiai?eee,/oi caeii Aoea auiieiyaony i?e iaaieueoeo aeaoi?iaoeeyo, a neaaeiaaoaeueii, i?e iai?yaeaieyo, ia i?aainoiaeyueo iaeioi?iai i?aaeaea. Iaeneiaeueiia iai?yaeaiea (i (ni. ?en. 7), i?e eioi?ii au? auiieiyaony caeii Aoea, iacuaatho i?aaeaeii i?iii?oeeaiaeueiinoe.Anee oaaee/eaaoue iaa?oceo, oi aeaoi?iaoeey noaiiaeony iaeeiaeiie, iai?yaeaiea ia?anoaiao auoue i?yii i?iii?oeeaeueiui ioiineoaeueiiio oaeeeiaieth. Oai ia iaiaa i?e iaaieueoeo iaeeiaeiuo aeaoi?iaoeeyo iinea niyoey iaa?ocee oi?ia e ?acia?u oaea i?aeoe/anee ainnoaiaaeeaathony. Iaeneiaeueiia iai?yaeaiea, i?e eioi?ii au? ia aicieeatho caiaoiua inoaoi/iua aeaoi?iaoeee(ioiineoaeueiay inoaoi/iay aeaoi?iaoeey ia i?aauoaao 0,1%), iacuaatho i?aaeaeii oi?oainoe (oi. I?aaeae oi?oainoe i?aauoaao i?aaeae i?iii?oeeiiaeueiinoe eeoue ia nioua aeiee i?ioeaioa.?en. 7(E(i/ KC D(oiB(i AO Q P (I?aaeae i?i/iinoe. Anee aiaoiyy iaa?ocea oaeiaa, /oi iai?yaeaiea a iaoa?eaea i?aauoaao i?aaeae oi?oainoe, oi iinea niyoey iaa?ocee ia?acaoe, oiyo iaiiiai e oei?a/eaaaony, ii ia i?eiaiaao i?aaeieo ?acia?ia, a inoa?ony aeaoi?ie?iaaiiui.Ii ia?a oaaee/aiey iaa?ocee aeaoi?iaoeey ia?anoaao an? auno?aa e auno?aa. I?e iaeioi?ii cia/aiee iai?yaeaiey , niioaaonoaothuai ia aeeaa?aiia oi/ea C, oaeeeiaiea ia?anoaao i?aeoe/anee aac oaaee/aiey iaa?ocee. Yoi yaeaiea iacuaatho oaeo/anoueth iaoa?eaea (o/anoie CD). E?eaay ia aeea?aiia eae?o ie? yoii ii/oe ai?eciioaeueii. Aeaeaa n oaaee/aieai aeaoi?iaoeee e?eaay iai?yaeaiee ia/eiaao iaiiiai aic?anoaoue e aeinoeaaao iaeneioia a oi/ea E. Caoai iai?yaeaiea ?acei niaae?o e ia?acaoe ia?ooaaony (oi/ea K). Oaeei ia?acii, ?ac?ua i?ienoiaeeo iinea oiai, eae iai?yaeaiea aeinoeaaao iaeneiaeueiiai cia/aiey (i/, iacuaaaiiai i?aaeaeiii?i/iinoe (ia?caoe ?anoyaeaaaony aac oaaee/aiey aiaoiae iaa?ocee aieioue aei ?ac?ooaiey). Yoa aaee/eia caaeneo io iaoa?eaea ia?acoea e ea/anoaa aai ia?aaioee.Nii?oaeaiey eee eiino?oeoeee iaae?aeiu, anee aicieeathuea a ieo i?e yenieoaoaoeee iai?yaeaiey a ianeieueei ?ac iaiueoa i?aaeaea i?i/iinoe.Enneaaeiaaiey ?anoyaeaiey (naeaoey) oa??aeiai oaea iicaieytho onoaiiaeoue, io /aai caaeneo eiyooeoeaio aeanoeinoe a caeiia Aoea. Aeeaa?aiia ?anoyaeaiey, iieo/aiiay yenia?eiaioaeueii, aea?o aeinoaoi/ii iieioth eioi?iaoeeth i iaoaie/aneeo naienoaao iaoa?eaea e iicaieyao ioeaieoue aai i?i/iinoue.Ieanoe/iinoue e O?oieinoue.Oi?oainoue. Oaei ec ethaiai iaoa?eaea i?e iaeuo aeaoi?iaoeeyo aaae?o naay, eae oi?oaia. Aai ?acia?u e oi?ia ainnoaiaaeeaathony i?e niyoee iaa?ocee. A oi aea a?aiy ana oaea a oie eee eiie ia?a iiaoo eniuouaaoue ieanoe/eneea aeaoi?iaoeee.Iaoaie/aneea naienoaa iaoa?eaeia ?aciiia?aciu. Oaeea iaoa?eaeu, eae ?aceia eee noaeue iaia?oaeeaatho oi?oaea naienoaa i?e n?aaeieoaeueii aieueoeo iai?yaeaieyo e aeaoi?iaoeeyo. Aeey noaee, iai?eia?, caeii Aoea auiieiyaony aieioue aei ( = 1%, a aeey ?aceiu - aei aeanyoeia i?ioeaioia. Iiyoiio oaeea iaoa?eaeu iacuaatho oi?oaeie.Ieanoe/iinoue. O iie?ie aeeiu, ieanoeeeia eee naeioea iaeanoue oi?oaeo aeaoi?iaoeee iaea. Iaoa?eaeu, o eioi?uo iacia/eoaeueiua iaa?ocee aucuaatho ieanoe/aneea aeaoi?iaoeee, iacuaatho ieanoe/iuie.Aeaeaiea iaoa?eaeia ia oi?oaea e ieanoe/iua a cia/eoaeueiie ia?a oneiaii. A caaeneiinoeio aicieeathueo iai?yaeaiee iaeei e oio aea iaoa?eae aoaeao aanoe naay eee eae oi?oaee, eee eae ieanoe/iue. Oae, i?e i/aiue aieueoeo iai?yaeaieyo noaeue iaia?oaeeaaao ieanoe/iua naienoaa. Yoi oe?iei eniieuecotho i?e ooaiiiaea noaeueiuo ecaeaeee n iiiiuueth i?anna, nicaeithuaai ia?iiioth iaa?oceo.Oieiaeiay noaeue eee aeaeaci n o?oaeii iiaeaeathony eiaea iieioii. Ii iinea neeueiiai iaa?aaa ei eaaei i?eaeaoue iin?aaenoaai eiaee ethaoth oi?io. Naeiaoe ieanoe/iue e i?e eiiiaoiie oaiia?aoo?a, ii i?eia?aoaao y?ei au?aaeaiiua oi?oaea naienoaa, anee aai ioeaaeeoue aei oaiia?aoo?u ieaea -100 C0.O?oieinoue. Aieueoia cia/aiea ia i?eeoeea eiaao naienoai oa??aeuo oae, iacuaaaiia o?oieinoueth. Iaoa?eae iacuaatho o?oieei, anee ii ?ac?ooaaony i?e iaaieueoeo aeaoi?iaoeeyo. Ecaeaeey ec noaeea e oi?oi?a e?oieea, oae eae iie ?acaeaathony ia eonee i?e iaaeaiee ia iie aeaaea n iaaieueoie auniou. *oaoi, i?aii?, yioa?ue oaeaea iaeaaeatho iiauoaiiie o?oieinoueth, e, iaiai?io, noaeue, iaaeue, naeiaoe ia yaeythony o?oieeie.O anao o?oieeo iaoa?eaeia iai?yaeaiea i/aiue auno?i ?ano?o n oaaee/aieai aeaoi?iaoeee, iie ?ac?ooathony i?e aanueia iaeuo aeaoi?iaoeeyo. Oae, /oaoi ?ac?ooaaony i?e ioiineoaeueiii oaeeeiaiee ( ( 0,45%. O noaee aea i?e ( ( 0,45% aeaoi?iaoeey inoa?ony oi?oaie e ?ac?ooaiea i?ienoiaeeo i?e ( ( 15%.Ieanoe/iua naienoaa o o?oieeo iaoa?eaeia i?aeoe/anee ia i?iyaeythony.Aeaiu aieaa eee iaiaa oi/iua ii?aaeaeaiey oi?oainoe, ieanoe/iinoe e o?oieinoe iaoa?eaeia. Iu oaia?ue eo/oa i?aaenoaaeyai, /oi iaicia/atho yoe neiaa, ia?aaeei ano?a/athueany a iaeoiaeiie aeecie.I?EIA? ?AOAIEss CAAeA*Ieoa noeaieai n o?aeoi?ii noaeueiui o?inii. Aeiionoeiia iai?yaeaiea iaoa?eaea o?ina ( = 20 AIa. Eaeie aeieaeia auoue ieiuaaeue iiia?a/iiai na/aiey o?ina, anee nii?ioeaeaiea ii/au aeaeaeaieth ieoaa ?aaii1,6(105 H?Aeaii: Ne: ?aoaiea:F = 1,6(105I S = F/(( = 20 AIa 20 000 000 000 S = 1,6/200000=8(10-6S = 8(10-6S - ?2. Eaeei aeieaeai auoue iiaeoeue neeu, i?eeiaeaiiie e noa?aeith aaeieue aai ine, /oiau a noa?aeia aicieeei iai?yaeaiea 1,5(108 Ia? Aeeaiao? noa?aeiy ?aaai 0,4ni.Aeaii: ?aoaiea:d = 0,0004i. S = ((R2=(((d/2)2=(((0,0002)2=(((0,00000004)= ((4(10-8;( = 1,5(108Ia F = ((S;F - ? F = 1,5(108(((4(10-8= 6(Eaeia iai?yaeaiea aicieeaao o iniiaaiey ee?ie/iie noaiu aunioie 20i ? Ieioiinoue ee?ie/a ?aaia 1800 ea/i2. Iaeeiaeiaie ee aeieaeia auoue i?i/iinoue ee?ie/ae o iniiaaiey noaiu e a aa?oiae a? /anoe?Aeaii: ?aoaiea:g(10 ( = F/S;h0=0i F = mg = hspg;h1=20i ( = hSpg/S = hpg;(=1800ea/ni3 (1 = h1pg ( 20(1800(10 ( 360000 ( 360 eIa;(2 = h0pg ( 0(1800(10 = 0 Ia.(1 - ?Ioaao: 1) iai?yaeaiea o iniiaaiey noaiu ( 360 eIa.2) iaiaeeiaeiaia, o.e. a aa?oiae /anoe iai?yaeaiea ioeaaia.4. Eaeoth iaeiaiueooth aeeeio aeieaeia eiaoue naiaiaeii iiaeaaoaiiay ca iaeei eiiaoe noaeueiay i?iaieiea, /oiau iia ?aci?aieanue iiae aeaenoaeai neeu oyaeanoe? I?aaeae i?i/iinoe noaee ?aaai 3,2(108 Ia, ieioiinoue - 7800ea/i3.Aeaii: ?aoaiea:( = 3,2(108 Ia F = mg = (lsg;( = 7800 ea/i3 ( = F/S;g ( 10 F = ((s(lsg = ((s | :sl - ? (lg = (;l = (/(g = 3,2(108/7800(10 = 3,2(105/78 ni.5. Iiae aeaenoaeai neeu 100I i?iaieiea aeeeiie 5i e ieiuaaeueth iiia?a/iiai na/aiey 2,5 ii2 oaeeeieeanue ia 1ii. Ii?aaeaeeoa iai?yaeaiea, eniuouaaaiia i?iaieieie, e iiaeoeue THiaa.Aeaii:F = 100Il0 = 5iS = 2,5ii2(l =*ai neiaeiaa ono?iaii oa??aeia oaei, oai o?oaeiaa auyaeoue eieeaeoeaiua yooaeou. Iniaaiii neiaeii ono?iaiu i?aaie/aneea oa??aeua oaea, oioy e a ieo eiaaony ii?aaeae?iiay no?oeoo?a. Eae eiaiii aicieeaao naeanue oii?yaei/aiea, e eaeei eieeaeoeaiui naienoaai iii i?eaiaeeo - ia yoe aii?inu iaoea au? i?aaenoieoue ioaaoeoue. Ii ynii, /oi eiaiii ia yoii iooe eaaeeo eeth/ e iiieiath oaei aeeaie i?e?iaeu.

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