Taller 1 de Fisica.

 

BÃ[IKN DHLHQNF KÛGID@5 >==7>; Nlhx` 1 B`rcnt` Wnrhn >

Wnrhn >- Xligng > ‛ Chgikiûl y kilhcîtikn.

]rhshltng` nf tut`r (n)5 Yugi Hsthr Qncirhz Knfghr`l

Hltrhdng` p`r fn hstuginlth5 Ynrfhygis Ahrri` Hsk`anr Kûgid`5 78828>=4

Drup`5 >==7>;P;=4

XLIRHQ[IGNG LNKI@LNF NAIHQWN Y N GI[WNLKIN - XLNG H[KXHFN GH KIHLKIN[ AÎ[IKN[ WHKL@F@DÃN H ILDHLIHQÃN >1 />=/ 1=1= Knrtndhln.

 

ILWQ@GXKKIÛL Hf thcn gh chgikiûl y kilhcîtikn nanrkn hltrh sus suathcns hf gh vhkt`rhs y fns cndlitughs, ghskriah hf c`vicihlt` p`r chgi` gh vhkt`rhs f`s kunfhs puhghl gnr fn uaiknkiûl y trnyhkt`rin. trnyhkt`rin. [ihlg` hf ghspfnzncihlt` ghspfnzncihlt` uln uln cndlitug vhkt` vhkt`rinf rinf sh ficitn prilkipnfchlth prilkipnfchl th nf hstugi` gh fn trnyhkt`rin hl trnyhkt`rin hl bulkiûl ghf tihcp`, tihcp`, utifizn vhf`kignghs y vhf`kignghs y nkhfhrnki`lhs k`l nkhfhrnki`lhs  k`l fns kunfhs sh ghskriahl kûc` kncain fn p`sikiûl hl bulkiûl ghf tihcp`, Fn vhf`kigng kncain vhf`kigng kncain gh p`sikiûl k`l rhsphkt` nf tihcp` utifizng`, cihltrns quh fn nkhfhrnkiûl hs nkhfhrnkiûl hs hf kncai` gh vhf`kigng hl hf tihcp` utifizng`

 

GH[NQQ@FF@ GH FN WNQHN > ‖CHGIKIÛL Y KILHCÎWIKN– Rhf`kigng gh > c/s

Rhf`kigng gh 1 c/s

Wihcp ` (s)

Nkhfhrnkiûl (c/s1)

Rhf`kign g (c/s)

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]`sikiûl Nkhfhrnkiûl Rhf`kigng ]`sikiûl (c) (c/s1) (c/s) (c)

-1

Nkhfhrnkiûl gh =,1 c/s1 Wihcp ` (s)

1

->,9>4

Nkhfhrnkiûl gh =,8 c/s1 Rhf`kig ng (c/s)

]`sikiû l (c)

=,8

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>,=19

-9,11>

-? -?,,79? 79? -4,8=7

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>. Wnafn gh rhs rhspuhst puhstns ns ghf ghf hehrkiki hehrkiki` ` >. ]rhdultns quh ghah rhsp`lghr hl hf vãgh` y eustibiknr utifiznlg` hf sicufng`r Rhribiknr ul` gh f`s rhsuftng`s gh fn p`sikiûl gh fn tnafn 7 k`l hf rhsuftng` thûrik` gh fn N. hkunkiûl (>)

Qhspuhstn5 f`s rhsuftng`s s`l idunf quh fn tnafn. Rhribiknr ul` gh f`s rhsuftng`s gh fn vhf`kigng gh fn tnafn 8 k`l hf rhsuftng` thûrik` gh fn hkunkiûl (1) A.

K.

G.

Qhspuhstn5 gnl hf cisc` rhsuftng`. °^ué sukhgh k`l fn vhf`kigng si fn nkhfhrnkiûl hl hf CXN hs p`sitivn0 Qhspuhstn5 fn vhf`kigng vn hl nuchlt`. °^ué sukhgh k`l fn vhf`kigng si fn nkhfhrnkiûl hl hf CXN hs lhdntivn0 °Fn knãgn fiarh gh uln phf`tn n uln nfturn s`arh fn suphrbikih gh fn tihrrn hs ul CXN ` CQX0 Qhspuhstn5 kunlg` fn nkhfhrnkiûl nkhfhrnkiûl hs lhdntivn fn p phf`tn hf`tn vn gisciluyhlg gisciluyhlg` ` su vhf`kigng, hs CXN yn quh fn trnyhkt`rin hs uln fãlhn rhktn y fn nkhfhrnkiûl hs k`ltnlth.

Hskrian hl hsth hspnki` fn prhdultn quh b`rcufû n sus k`cpnþhr`s gh drup`.

 _ b 3 _ i+ R  x t    c  _ b 3∑? c + >   ( 1 s ) s  _ b 3∑? c + 1

 c s

1

 _ b 3∑2 c R  xb 3R  xi + n x t  c c R  xb 3=,8  + =,1 1 ( >) s s c c R  xb 3=,8  + =,1 1 s s R  xb 3=,4

c s

Wnafn >. Qhspuhstns n fns prhdultns ghf hehrkiki` >.

1. Ghsnrr` Ghsnrr`ff` ff` g gh h f`s hehrkiki`s hehrkiki`s 1 1,, ; y 7. 7. Hehrkiki` 1. c`vicihlt` uligichlsi`lnf Xl nviûl ghah nfknlznr uln rnpighz gh ?>,8 c/s pnrn ilikinr su ghsphduh. Ghltr` gh f`s rhquisit`s gh fn pistn, hstî uln f`lditug cîxicn gh 1,2= jc pnrn f`drnrf`. n) °Kuîf °Ku îf hs vnf`r vnf`r nkhfh nkhfhrnk rnkiûl iûl cãlicn cãlicn pnrn ffhdnr ffhdnr n fn vhf`kign vhf`kigng g gh ghsphdu ghsphduh, h, kunlg` hf hf nviûl on gh pnrtig` ghf rhp`s`0

 

a) [i nf ffhdnr n f`s 1,2= jc nphlns nfknlzn uln vhf`kigng gh 82,9 c/s, ghah npfiknr uln ghsnkhfhrnkiûl ghsnkhfhrnk iûl (brhlng`) k`lstnlth gh -1,;? c/s1, °kuîf hs fn p`sikiûl bilnf kunlg` hf nviûl sh ghtihlh0

N k`ltilunkiûl, prhshlth fns vnrinafhs bãsikns, prilkipi` bãsik`, ghbiliki`lhs y/` k`lkhpt`s utifizng`s hl hf ghsnrr`ff` ghf hehrkiki`. Rnrinafhs bãsikns5 Gistnlkin Wihcp` Nkhfhrnkiûl vhf`kigng

]rilkipi` bãsik`5puhgh shr fn Fn nkhfhrnkiûl ciscn phr` n chgign quh nuchltn fn vhf`kigng tncaiél nuchltn fn gistnlkin s`l pr`p`rki`lnfhs.

G hbiliki`lhs y/` k`lkhpt`s5 Fn vh vhf` f`ki kign gng g kn knca cain in gh p`sikiûl k`l rhsphkt` nf tihcp`. Fn nkhfhrnkiûl hs ul kncai` hl fn vhf`kigng.

Ghsnrr`ff` ghf hehrkiki` c`vicihlt` uligichlsi`lnf5 N. Gnt`s Ri3 =,= c/s

Rb3?>,8c/s

G3 1,2= jc 3 12==c 1 Rbx ∑Rix 31 ∂ x  b`rcufn `ridilnf. Ausknc`s ghsphenr fn nkhfhrnkiûl 1

1

1

Rbx ∑Rix   3n 1∂ x 1 1 Rbx ∑Rix vhf`kigng ilikinf hs khr` quitnc`s quitnc`s hsn pnrth gh fn b`rcufn. b`rcufn.   3 n  k`c` fn vhf`kigng 1∂ x 1 Rbx 3n   uaiknc`s f`s vnf`rhs. 1∂x (?>,8 c / s )1 3n 1 ( 12== ) c 1 1 2,271 c s 81== c   3 n >,144° n   A.

GNW@[

Rb3= Ri382,9c/s n3 -1,;?c/s 1 1 Rbx ∑Rix 31 ∂ x  b`rcufn k`l fn quh v`y n trnanenr. 1

1

Rbx ∑Rix hficil` l` gh fn `phrnkiûl n rhnfiznr.   3 ∂ x   fn vhf`kigng lnf hs = p`r f` tnlt` fn hfici 1n ∑Rix 1   3 ∂ x  pnsnc`s n rhhcpfnznr f`s vnf`rhs. 1n ∑(82,9 c/ s )1 3∂ x  1 (∑1,;? c / s )

 

∑;1;4,2> c1 s 1   3∂ x ∑ 7,42 c / s 2?=,>4c° ∂ x 2?=,>4c +12== 3 ;1?=,>4

Nlîfisis gh f`s Hf vnf`r gh fn nkhfhrnkiûl cãlicn hs gh >,144c/ s1  pnrn p`ghr rhsuftng`s `athlig`s ghsphdnr, y kunlg` hf nviûl sh ghtihlh on rhk`rrig` ;1?=,>4 c Wnafn 1. Ghsnrr`ff` ghf hehrkiki` 1.

Hehrkiki` ;. knltignghs hsknfnrhs y vhkt`rinfhs Xl ilshkt` sh uaikn hl t`gn fn citng gh uln rhdfn gh 1== kc quh hstî s`arh ul cur` vhrtiknf, y fuhd` rhnfizn vnri`s rhk`rrig`s s`arh hffn. ]richr` rhk`rrh >2,; kc onkin nane`, ilchgintnchlth knciln 82,= kc onkin nrrian, hl shduign knciln ;,== kc onkin nane`. Ghspués k`ltilõn 18,= kc onkin nane` y pnrn bilnfiznr sh cuhvh >9,= kc onkin nrrian. n) Qhnfikh uln uln rhprhshltnkiûl rhprhshltnkiûl drîbikn ghf c`vicihlt` c`vicihlt` ghf ghf ilshkt`. ilshkt`. a) Hlkuhltrh Hlkuhltrh hf vhkt`r ghspfnzncihl ghspfnzncihlt` t` t`tnf k`l rhsphkt` nf khltr` gh fn rhdfn. Hlkuhltrh Hlkuhlt rh fn p`sikiûl bilnf ghf ilshkt` rhsphkt` n fn pnrth cîs nftn gh fn rhdfn

N k`ltilunkiûl, prhshlth fns vnrinafhs bãsikns, prilkipi` bãsik`, ghbiliki`lhs y/` k`lkhpt`s utifizng`s hl hf ghsnrr`ff` ghf hehrkiki`. Rnrinafhs bãsikns5 Rnrinafhs bãsikns5 Ghsp Gh spfn fnzn znci cih hlt lt`5 `5 rh rhst stn n Cn Cndl dlit itug ughs hs vhkt vhkt`r `rin infh fhs5 s5 hltrh fn p`sikiûl bilnf y fn k` k`ls lstn tnl l gh ul cû cûgu guf` f` y ilikinf. uln girhkkiûl. Fns cndlitugh cndlitughss hsknf hsknfnrhs nrhs s`l fns quh k`lstnl gh ul lõchr` y uln uligng.

Rnrinafhs bãsikns5 Ghspfn Ghs pfnznc zncihl ihlt` t` bilnf bilnf hs fn sucn gh t`g`s f`s ghspfnzncihlt`s.

Ghsnrr`ff` ghf hehrkiki` ;. Knltignghs hsknfnrhs y vhkt`rinfhs5

 

N. A.

∂ x 3 b ∑ = ∂ x 3>;=,4 ∑>== ∂ x 3;=,4 c/ s K.⃔= 3( = ↞+ >==  e ) kc  N 3( = ↞∑>2,;  e ) kc A3( = ↞ + 82,=  e ) kc K 3( = ↞∑;,==   e ) kc  G3 ( = ↞ ∑18,=  e ) kc  H 3( = ↞+ >9,=  e ) kc  B 3( = ↞ + >;=,4  e ) kc

⃔

⃔

⃔

⃔

Nlîfisis

gh

f`s ]rhshlth nquã ul arhvh nlîfisis gh f`s rhsuftng`s `athlig`s hl hf

;.Ghsnrr`ff` Knltignghs hsknfnrhs y vhkt`rinfhs5 Wnafn ;. ghf hehrkiki` ;. rhsuftng`s `athlig`s hehrkiki`

Hehrkiki` 7. c`vicihlt` aigichlsi`lnf Hf R`fkîl Dnfhrns fnlzn uln r`kn k`l uln rnpighz gh 24,> c/s, hl ul îlduf` gh ;9,>½ s`arh hf heh x. Fn r`kn t`kn hf suhf` n >48= c p`r ghane` gh fn nfturn ilikinf. [i sh ghsprhkin fn rhsisthlkin ghf nirh y k`lsighrnlg` ul vnf`r k`lstnlth gh nkhfhrnkiûl ghaign n fn drnvhgng gh 9,?> c/s1. n) °Kuîf °Kuîf hs hf tihcp` tihcp` hl k`cpfh k`cpfhtnr tnr fn trnyhkt` trnyhkt`rin0 rin0 a) °Kuîf °Kuîf hs hf vhkt`r vhf`kigng vhf`kigng nf c`chlt` c`chlt` ghf icpnkt`0 icpnkt`0 Hsphkib Hsphkibiknr iknr fns k`cp` k`cp`lhl lhlths ths o`riz`ltnf y vhrtiknf gh fn vhf`kigng. k) °Kuîf °Kuîf hs fn cndlitu cndlitug g ghf vhkt`r vhkt`r vhf`ki vhf`kigng gng bilnf0 bilnf0

 

N k`ltilunkiûl, prhshlth fns vnrinafhs bãsikns, prilkipi` bãsik`, ghbiliki`lhs y/` k`lkhpt`s utifizng`s hl hf ghsnrr`ff` ghf hehrkiki`. Rnrinafhs bãsikns5 K`cp`l K`c p`lhlt hlths hs o`r o`riz` iz`ltn ltnf5 f5 s`l s` l f`s f`s v vhk hkt` t`rhs rhs hl fn fnss k``rghlngns hl x.

Rnrinafhs bãsikns5 Cndlit Cnd litug ug gh fn vhf vhf`ki `kigng gng.. Qhfnki`ln fn gistnlkin k`l hf tihcp`.

Rnrinafhs bãsikns5 Drnv Dr nvh hgn gng5 g5 buhr buhrzn zn qu quh h hehrkh fn tihrrn s`arh ul kuhrp` hs gh 9,?> c / s >

K`cp K`cp`lhlt vhrtiknf5 f`s `lhlth vhkt`hrhsvhrti hknf5 l s`l fns k``rghlngns hl y. Ghsnrr`ff` ghf hehrkiki` 7. c`vicihlt` aigichlsi`lnf5 Wihcp` pnrn k`cpfhtnr fn trnyhkt`rin. B`rcufn > 1

 y 3 yi + v iy t ∑ d t  1

∑>48= 3= + 24,> c

> c   sil ;9,> ;9,> t ∑ ° 1 s >

= 3>48= + 24,> s   .=,2; t ∑ 1 ° 1 = 3>48= + 71,1=2 ∑7,9=8. t  [h hlh5 t >,13 n3 -7.9=

∑a ¾ ∕ a 1∑7 nk  

1n a371,1> k3 >48=

∑71,1> ¾ ∕ (71,1> )1∑7 (∑ 7,9=)( >48= ) t >,13 1 (∑7.9= ) >4?>,2? ∑;7,;== ∑71,1> ¾ ∕ >4?>,2? ∑ 9,?= ;18>9,;1 ∑71,1> ¾ ∕ ;18>9,;1 t >,13 ∑9,?= t 13∑>7,=98 s t >311,2?248 s Fn rhspuhstn hs hf t >311,2?248  s

t >,13

°Kuîf hs hf vhkt`r vhf`kigng nf c`chlt` ghf icpnkt`0 Hsphkiknr fns k`cp`lhlths o`riz`ltnf y vhrknf gh fn vhf`kigng. v x 3 v x ⟹ v i k`s ο

 c  c v x 324,>   k`s;9,>381,=4 s s c  c v y 3v iy ∑° ⟹ v y 3 24,>   sil sil ;9,> ;9,>∑9,?> 1 t  s s c c v y 324,>   =,219 ∑9 , ?> 1 ( 11,29 ) s s  c v y 371,1=89 ∑111,8?93∑>?=,;?;> s

 

 c  k`cp`lhlth o`riz`ltnf s c ∑>?=,;?;> K`cp`lhlth vhrknf. s Rhkt`r vhf`kigng 3 ( 81,=4 i ∑ >?=,;?;>  e ) c/ s 81,=4

Cndlitug ghf vhkt`r vhf`kigng lnf.

|v|3 ∕ v + v  x  y |v|3 ∕ ° ° 1

∕ | |3

|v|3 v

1

14>>,1?

 c  c + ;18;?,=2 1 1 s s

;8179,;8 ∕ ;8179,;8

|v|3>?4,48

Nlîfisis gh f`s Hf tihcp` quh ghc`r` fn r`kn pnrn k`cpfhtnr fn trnyhkt`rin hs gh rhsuftng`s `athlig`s 11 11,2 ,29 9 sh shd, d, hf vhkt vhkt`r `r vhf` vhf`ki kign gng g nf c`ch c`chlt lt` ` ghf ghf icpn icpnkt kt` ` hs hstn tn uaikng` hl 81,=4i ->?=,;? e y fn cndlitug ghf vhkt`r bilnf hs gh >?4,48. Wnafn 7. Ghsnrr`ff` ghf hehrkiki` 7. Wnafn 8. Ghsnrr`ff` ghf hehrkiki` 8 nsidlng`.

;. Wnafn k` k`l l f`s hlf hlfnkhs nkhs gh f` f`ss vigh` vigh`ss gh f`s heh hehrkiki rkiki`s `s > y 8. Hlfnkh ghf vigh`

Ghskripkiû l ghf k`lthlig` ghf k`lthlig` ghf vigh`.

Hehrkiki `>

ottps5//www.f``c.k`c/sonrh/nkn=h;b>;?;k71?ga1k?h8gnk>hb2;; 2 

Hl hf vi vigh gh` ` sh gn rhspu rhs puhst hstn n n fns prhdultns s`arh hf o`carh cûvif hf kunf sirviû gh a nl sh ffh nr

pnf`rn s

 

kungr`s 1 y ; Wnafn 2. Hlfnkhs gh f`s vigh`s gh f`s hehrkiki`s > y 8.

7. k` k`lk lkfu fusi si`l `lhs hs.. ]nrn p`ghr onffnr hf ghspfnzncihlt` gh ul `aeht` ghahc`s rhstnr fn p`sikiûl bilnf k`l fn ilikinf f` kunf gn k`c` rhsuftng`. Kunlg` fn nkhfhrnkiûl hs k`lstnlth fn trnyhkt`rin hs uln fãlhn rhktn, nf nuchltnr fn nkhfhrnkiûl ony ul kncai` gh vhf`kigng hs ghkir s`l pr`p`rki`lnfhs, pnrn quh nuchlth fn vhf`kigng ghah nuchltnr fn nkhfhrnkiûl. Fns k``rghlngns rhktnldufnrhs b`rcnl ul îlduf` gh 9=½ hf kunf hltrh uaikng` hltrh hf heh x quh hs hf gh fns naskisns y hf heh y quh s`l fns f ns `rghlngns.

 

8. Qhb Qhbhrhl hrhlkin kinss aiafi` aiafi`drî drîbik bikns. ns. Anuhr, T. y Thstbnff, G. (1=>7). Bãsikn pnrn ildhlihrãns y kihlkins R`f. >. (1n. hg.) CkDrnw-Oiff Ilthrnchriknln. Ilthrnchriknln. (pp. 7> n fn 7;, 78 n fn 79 y 81 n fn 21). W`cng` gh ottp5//www.ha``js4-17. ottp5//www.h a``js4-17.k`c.aiafi`thk k`c.aiafi`thknvirtunf.ulng.h nvirtunf.ulng.hgu.k`/0if34= gu.k`/0if34== = Righ` # >5 K`lkhpt`s gh p`sikiûl, rnpighz, vhf`kigng chgin, vhf`kigng ilstnltîlhn, nkhfhrnkiûl chgin h ilstnltîlhn. ^uikj Wut`rinfs (=9/=1/1=>2). C`vicihlt` uligichlsi`lnf pnrth > (vigh`). Qhkuphrng` gh ottps5//y`utu.ah/@XE>HXhO7O=  Qhpr`gukkiûl Rãgh`   Righ` # 15 CXQ, CXN y nlîfisis gh drîbikn Kurs` gh bisikn (>=/=9/1=1=) Kurs` gh Bãsikn. Whcn >5 C`vicihlt`. >.> C`vicihlt` hl >G (vigh`) Qhkuphrng` gh ottps5//y`utu.ah/q[te9=KyRQ`  ottps5//y`utu.ah/q[te9=KyRQ`  Qhpr`gukkiûl Rãgh`

 

Anuhr, T. y Thstbnff, G. (1=>7). Bãsikn pnrn ildhlihrãns y kihlkins R`f. >. (1n. hg.) CkDrnw-Oiff Ilthrnchriknln. Ilthrnchriknln. (pp. 17 n fn 1? y ;> n fn ;1). Qhkuphrng` ottp5//www.ha``js4-17.k a``js4-17.k`c.aiafi`thk `c.aiafi`thknvirtunf.ulng.h nvirtunf.ulng.hgu.k`/0if34= gu.k`/0if34== = gh ottp5//www.h Righ` # ;5 K`cp`lhlths rhktnldufnrhs gh ul vhkt`r hl 1 gichlsi`lhs Ahlithz, H. (1=1=, nd`st`f) K`cp`lhlths rhktnldufnrhs gh ul vhkt`r hl 1 gichlsi`lhs ZNrkoiv` gh vigh`S. Qhkuphrng` gh ottps5//y`utu.ah/Lo1_wi>eLgC  ottps5//y`utu.ah/Lo1_wi>eLgC  Qhpr`gukkiûl Rãgh` Righ` # 75 Rhkt`rhs Cndlitug y Girhkkiûl Ahlithz, H. (1=>4, cnrz`) Rhkt`rhs Cndlitug y Girhkkiûl ZNrkoiv` gh vigh`S. Qhkuphrng` ghottps5//y`utu.ah/Q>GsqO^oLpC Qhpr`gukkiûl Rãgh` Righ` # 85 [ucn gh Rhkt`rhs p`r k`cp`lhlths rhktnldufnrhs Ahlithz, H. (1=>4, cnrz`) [ucn gh Rhkt`rhs p`r k`cp`lhlths rhktnldufnrhs ZNrkoiv` gh vigh`S. Qhkuphrng` gh ottps5//y`utu.ah/E8DiogtkdDC  ottps5//y`utu.ah/E8DiogtkdDC  Qhpr`gukkiûl Rãgh` Righ` # 25 [ucn Rhkt`rhs Dh`dharn II Ahlithz, H. (1=>4, cnrz`) [ucn Rhkt`rhs Dh`dharn II ZNrkoiv` gh vigh`S. Qhkuphrng` gh ottps5//y`utu.ah/iA@^kG[beW=  ottps5//y`utu.ah/iA@^kG[beW=  Qhpr`gukkiûl Rãgh` Anuhr, T. y Thstbnff, G. (1=>7). Bãsikn pnrn ildhlihrãns y kihlkins R`f. >. (1n. hg.) CkDrnw-Oiff Ilthrnchriknln. Ilthrnchriknln. (pp. 49 n fn ?7). Qhkuphrng` gh ottp5//www.ha``js417.k`c.aiafi`thknvirtunf.u 17.k`c.a iafi`thknvirtunf.ulng.hgu.k` lng.hgu.k`/0if34== /0if34== Righ` # 45 dhlhrnfignghs ghf c`vicihlt` Aigichlsi`lnf. Ahlithz, H. (1=>4, narif) C`vicihlt` Aigichlsi`lnf Aigichlsi`lnf (Dhlhrnfignghs) ZNrkoiv` gh vigh`S. Qhkuphrng` gh ottps5//y`utu.ah/iA@^kG[beW=  ottps5//y`utu.ah/iA@^kG[beW=  Qhpr`gukkiûl Rãgh` Righ` # ?5 Qhsuchl gh bûrcufns usngns hl hf nlîfisis ghf c`vicihlt` gh pr`yhktifhs ` tir` pnrnaûfik`. Ohrlnl puhlths (1=>1, `ktuarh). `ktuarh). B`rcufns C`vicihlt` hl ul ]fnl` - Wir` ]nrnaûfik` - Fnlzncihlt` gh ]r`yhktifhs - Righ` >;1 (vigh`) Qhkuphrng` gh ottps5//y`utu.ah/oDeyE1opaRN  ottps5//y`utu.ah/oDeyE1opaRN  Qhpr`gukkiûl Rãgh` Ahlithz, H. (1=>4, narif) Wir` pnrnaûfik` (Hehrkiki`) (Hehrkiki`) ZNrkoiv` gh vigh`S. Qhkuphrng` Qhkuphrng` ghottps5//y`utu.ah/TsErGFWXx^7 Qhpr`gukkiûl Rãgh`

 

Rnrdns, [. (1=>4, shptihcarh) C`vicihlt` Kirkufnr Xlib`rch C.K.X. (K`lkhptunfiznkiûl) ZNrkoiv` gh vigh`S. Qhkuphrng` gh ottps5//y`utu.ah/UzpW8l8wfBN   ottps5//y`utu.ah/UzpW8l8wfBN Qhpr`gukkiûl Rãgh` Rnrdns, [. (1=>4, shptihcarh) C.K.X. Hehrkiki` gh npfiknkiûl ZNrkoiv` gh vigh`S. Qhkuphrng` Qhkuphrng ` ghottps5//y`utu.ah/ti1DI]nb ghottps5//y`utu.ah/ti1DI]nbYOw YOw