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1


Kh^_j`Zgb_ <hijhku ............................... 7 §1. ...................................... 7 §2. ...................................... 7 §3. ...................................... 7 §4. ...................................... 7 §5. ...................................... 8 §6. ...................................... 8 §7. ...................................... 8 §8. ...................................... 9 §9. ...................................... 9 §10. ..................................... 9 §11. .................................... 10 §12. .................................... §13. .................................... §14. .................................... §15. .................................... §16. .................................... §18. .................................... §19. .................................... §20. .................................... §21. .................................... §22. .................................... §23. .................................... §24. .................................... §25. .................................... §26. .................................... §27. ....................................

11 11 12 12 12 13 13 13 14 14 14 15 15 16 16 2


§28. .................................... §29. .................................... §30. .................................... §31. .................................... §32. .................................... §33. .................................... §34. .................................... §35. .................................... §36. .................................... §37. .................................... §38. .................................... §39. .................................... §40. .................................... §42. .................................... §43. .................................... §44. .................................... §45. .................................... §46. .................................... §47. .................................... §48. .................................... §49. .................................... §50. .................................... §51. .................................... §52. .................................... §53. .................................... §54. .................................... §55. .................................... §56. .................................... §57. ....................................

17 17 17 18 18 19 19 19 20 20 21 21 21 21 22 23 23 24 25 25 25 26 27 27 27 28 28 29 30 3


ยง58. .................................... ยง59. .................................... ยง60. .................................... ยง61. .................................... ยง62. .................................... ยง63. .................................... ยง64. .................................... ยง65. .................................... ยง66. .................................... ยง67. .................................... ยง68. .................................... ยง69. .................................... ยง70. .................................... ยง72. ....................................

31 32 32 32 33 33 34 34 34 35 35 36 36 37

MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_

39 39 39 39 40 40 41 41 42 42 42 43 44 44

MijZ`g_gby ........................... 39  ...........................  ...........................  ...........................  ...........................  ...........................  ...........................  ...........................  ...........................  ...........................  ..........................  ..........................  ..........................  ..........................  ..........................

4


MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_

 ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................  ..........................

44 45 45 46 47 47 47 48 48 48 49 49 50 50 50 50 50 51 51 51 52 52 53 53 53 53 54 54 54 5


MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_

 ..........................  ..........................  ..........................  ..........................  ..........................

55 55 55 55 55

AZ^Zqbij_^eZ]Z_fu_ ^eyih\lhj_gby b ijb qZkZo nbabdb \g_^_ex .......... 56 EZ[hjZlhjgu_ jZ[hlu .................. 64 EZ[hjZlhjgZy EZ[hjZlhjgZy EZ[hjZlhjgZy EZ[hjZlhjgZy EZ[hjZlhjgZy EZ[hjZlhjgZy

jZ[hlZÂ&#x2039; ................. jZ[hlZÂ&#x2039; ................. jZ[hlZÂ&#x2039; ................. jZ[hlZÂ&#x2039; ................. jZ[hlZÂ&#x2039; ................. jZ[hlZÂ&#x2039; .................

64 67 67 68 69 70

6


<hijhku ยง1.

1. FZl_jbZevgZy lhqdZ h[eZ^Z_l fZkkhc gh bf__l ij_g_[j_`bfh fZeu_jZaf_ju 2. FZl_jbZevgZylhqdZ ยฒwlhZ[kljZdlgh_ihgylb_ 3. >eymijhs_gbyaZ^Zq 4. Dh]^Z\ mkeh\bbaZ^ZqbjZaf_jZfbwlh]hl_eZfh`ghij_g_[j_qv 5. AZ fZl_jbZevgmx lhqdm fh`gh ijbgylv Z\lhfh[bev ijb hij_^_e_gbb _]h kdhjhklb gZ fZjrjml_ ] Ijhl\bgh ยฑ ] Fhkd\Z Wlhl `_ Z\lhfh[bev g_evay kqblZlv fZl_jbZevghc lhqdhc ijb jZkq_l_^Z\e_gbyhdZau\Z_fh]hbfgZ^hjh]m 6. IjbihklmiZl_evghf^\b`_gbb 7. FZl_jbZevghc lhqdhc gZau\Z_lky l_eh jZaf_jZfb dhlhjh]h fh`ghij_g_[j_qv\ mkeh\byo^ZgghcaZ^Zqb 8. Ijbijyfhebg_cghf^\b`_gbbl_eZ 9. Kbkl_fZhlkq_lZhlghkbl_evghdhlhjhcjZkkfZljb\Zxl^\b`_gb_ ij_^klZ\ey_l kh[hc kh\hdmighklv kbkl_fu dhhj^bgZl ijb[hjZ ^ey baf_j_gby \j_f_gb b lhqdb hlkq_lZ k dhlhjhc k\yaZgZ kbkl_fZ dhhj^bgZl

ยง2.

1. G_l\k_aZ\bkblhlljZ_dlhjbb^\b`_gbyG_evaymagZlv]^_[m^_l Z\lhfh[bevq_j_a qZk_kebg_agZ_rvihdZdbf^hjh]Zfhgih_^_l 2. <_dlhjgZijZ\e_gguchllhqdbhlkq_lZgZqZeZ^\b`_gbyd lhqd_ hlkq_lZdhgpZ^\b`_gbyl_eZ 3. Fh`gh

ยง3.

1. <uqbke_gbyijhba\h^ylkhkdZeyjgufb\_ebqbgZfb 2. ?keb \_dlhj khgZijZ\e_g k hkvx lh _]h ijh_dpby gZ g__ [m^_l iheh`bl_evgZ b gZh[hjhl _keb \_dlhj ijhlb\hiheh`gh gZijZ\e_g hkblh_]hijh_dpbygZg__[m^_lhljbpZl_evgZ 3. o1 = o0 + so.

ยง4.

1. Kdhjhklvx jZ\ghf_jgh]h ijyfhebg_cgh]h ^\b`_gby gZau\Z_lky U Y ihklhygguc \_dlhj v  jZ\guc hlghr_gbx i_j_f_s_gby s l_eZ aZ Y U s ex[hcijhf_`mlhd\j_f_gbt d agZq_gbxwlh]hijhf_`mldZ v = . t 7


2. Ihnhjfme_sx = vxt. 3. Ijbijyfhebg_cghfjZ\ghf_jghf^\b`_gbb 4. Wlh\b^ghbajbkmq_[gbdZ 5. Hgb^\b`mlkyjZ\ghf_jgh\ jZaguogZijZ\e_gbyokhkdhjhklyfb jZ\gufbihfh^mex b dfq

§5.

1. D g_jZ\ghf_jghfm^\b`_gbx 2. Kdhjhklvl_eZ\ ^Zgghclhqd_\ ^Zggucfhf_gl\j_f_gb U 3. Mkdhj_gb_f jZ\ghmkdhj_ggh]h ^\b`_gby l_eZ a gZau\Z_lky U \_ebqbgZjZ\gZyhlghr_gbxbaf_g_gbykdhjhklbâ&#x2C6;&#x2020; v d ijhf_`mldm U U U U â&#x2C6;&#x2020;v v â&#x2C6;&#x2019; v 0 \j_f_gbtaZdhlhjucwlhbaf_g_gb_ijhbahreh a = = . t t 4. >\b`_gb_k ihklhyggufmkdhj_gb_f 5. HgihdZau\Z_l[ukljhlmbaf_g_gbyfh^mey\_dlhjZkdhjhklb 6. < kbkl_f_KBfk2. 7. M\_ebqb\Z_lky ijb iheh`bl_evghf mkdhj_gbb \ wlhf kemqZ_ \_dlhjkdhjhklbb \_dlhjmkdhj_gbykhgZijZ\e_gu mf_gvrZ_lky² ijb hljbpZl_evghf \ wlhf kemqZ_ \_dlhj kdhjhklb b \_dlhj mkdhj_gbyijhlb\hiheh`ghgZijZ\e_gu 

§6.

1. Z vx = v0x + axt[ vx = axt. 2. < h[hbokemqZyoijyfZy\ kemqZ_ ©Zª²ijhoh^ysZyq_j_agZqZeh kbkl_fudhhj^bgZl 3. Wlb ^\b`_gby jZ\ghmkdhj_ggu_ h^gZdh \ i_j\hf kemqZ_ mkdhj_gb_iheh`bl_evghZ \h\lhjhf²hljbpZl_evgh

§7.

1. Ijh_dpby\_dlhjZi_j_f_s_gby\uqbkey_lkyihnhjfme_ axt 2 . 2 Ih^klZ\bf\ wlmnhjfmem\ujZ`_gb_^eyijh_dpbbmkdhj_gby v â&#x2C6;&#x2019; v0 x ax = x . t Ihemqbf v â&#x2C6;&#x2019; v0 x t 2 v0 x + v x s x = v0 x t + x â&#x2039;&#x2026; = â&#x2039;&#x2026;t . t 2 2 s x = v0 x t +

8


LZddZdv0x = AO, vx = BC, t = OB kfjbkZ mq_[gbdZ lhfu AO + BC â&#x2039;&#x2026; OB ihemqZ_fqlhijh_dpby\_dlhjZi_j_f_s_gby s x = 2 jZ\gZiehsZ^bnb]mjuOACB ²ijyfhm]hevghcljZi_pbbk hkgh\ZgbyfbAO, BC b \ukhlhcOB. 2. s x = v0 x t +

axt 2 . 2

1. Ihnhjfme_ s x =

§8.

axt at 2 ²^eyijh_dpbbi_j_f_s_gby s = â&#x20AC;&#x201D; 2 2 ^eyfh^mey\_dlhjZi_j_f_s_gby 2. < n2 jZaihkdhevdms ~ t2 3.

2

s n a (nt1 ) 2 / 2 = = n2 . 2 st1 at1 / 2

4. DZdjy^ihke_^h\Zl_evguog_q_lguoqbk_e 5. >eyhij_^_e_gbyjZ\ghmkdhj_ggh]h^\b`_gby 1. < jZaguokbkl_fZohlq_lZwlb\_ebqbgubf_xljZagu_agZq_gbyb ihjZaghfmhjb_glbjh\Zggu 2. RZjbd iZ^Zxsbc gZ ihe ^\b`ms_]hky Z\lhfh[bey g_ bf__l ]hjbahglZevghc kdhjhklb hlghkbl_evgh g_]h Hlghkbl_evgh A_feb hgbf__lkdhjhklvjZ\gmxkdhjhklbZ\lhfh[bey 3. Kdhjhklv imlv ljZ_dlhjby b l^ jZaebqgu \ jZaguo kbkl_fZo hlkq_lZ 4. =_ebhp_gljbq_kdZy kbkl_fZ k\yaZgZ k Khegp_f ]_hp_gljbq_kdZy ²k A_fe_c 5. Kf_gZ^gyb ghqbh[tykgy_lky\jZs_gb_fA_feb\hdjm]k\h_chkb

§9.

1. JZ\ghf_jghb ijyfhebg_cghbebihdhblky 2. G_l 3. L_hjby :jbklhl_ey aZdexqZxsZyky \ lhf qlh ijb hlkmlkl\bb \g_rg_]h\ha^_ckl\byl_ehfh`_llhevdhihdhblvky 4. L_f qlh ih =Zebe_x l_eZ fh]ml jZ\ghf_jgh ^\b]Zlvky \ hlkmlkl\bb\g_rgbokbe 5. Hiul bah[jZ`_gguc gZ jbk  mq_[gbdZ ^hdZau\Z_l lh qlh ihfbfh bg_jpbZevguo kbkl_f hlkq_lZ \ dhlhjuo \uihegy_lky i_j\uc aZdhg GvxlhgZ  kms_kl\mxl kbkl_fu bgh]h oZjZdl_jZ Hg

§10.

9


khklhbl \ ke_^mxs_f GZ l_e_`d_ h^bg rZjbd e_`bl gZ ]hjbahglZevghc ih\_joghklb Z \lhjhc ih^\_rb\Z_lky gZ gblb KgZqZeZ l_e_`dZ ^\b`_lky ijyfhebg_cgh b jZ\ghf_jgh b \ wlhf kemqZ_ h[Z rZjbdZ gZoh^ylky \ ihdh_ hlghkbl_evgh l_e_`db Klhbl lhevdh ijb^Zlv l_e_`d_ mkdhj_gb_ eb[h __ ijblhjfhablv eb[h ih^lhedgmlv  dZd rZjbdb ijb^ml \ ^\b`_gb_ k mkdhj_gb_f hlghkbl_evghl_e_`dbLZdbfh[jZahfhlghkbl_evghl_e_`dbi_j\uc aZdhgGvxlhgZg_\uihegy_lky 6. Kms_kl\mxl kbkl_fu hlkq_lZ hlghkbl_evgh dhlhjuo l_eZ khojZgyxl k\hx kdhjhklv g_baf_gghc _keb gZ gbo g_ ^_ckl\mxl \g_rgb_ kbeu beb bo ^_ckl\b_ kdhfi_gkbjh\Zgh LZdb_ kbkl_fu gZau\Zxlkybg_jpbZevgufb 7. Bg_jpbZevgu_kbkl_fum^h\e_l\hjyxli_j\hfmaZdhgmGvxlhgZ g_bg_jpbZevgu_ยฒg_l 8. Fh`gh 9. G_l

ยง11.

1. Ijbeh`_ggZyd l_emkbeZ 2. Q_f [hevr_ fhsghklv Z\lhfh[bey Z khhl\_lkl\_ggh _]h kbeZ ly]bl_f[uklj__hgm\_ebqb\Z_lk\hxkdhjhklv 3. Hiul bah[jZ`_gguc gZ jbk  mq_[gbdZ ^hdZau\Z_l lh qlh ijbeh`_ggZy d l_em kbeZ y\ey_lky ijbqbghc mkdhj_gby >ey ijh\_^_gby^Zggh]hhiulZgZ^h\aylvl_e_`dmmklZgh\blvgZg_c^\Z h^bgZdh\hjZ[hlZxsbo\_glbeylhjZb dZi_evgbpm>eydhfi_gkZpbb kbeulj_gbyijbdj_ibfd l_e_`d_h^bgbadhgph\gblbi_j_dbgmlhc q_j_a [ehd Z d ^jm]hfm dhgpm gblb ih^\_kbf ]jma AZl_f hldjh_f djZg dZi_evgbpu b \dexqbf h[Z \_glbeylhjZ Ih^ ^_ckl\b_f kbeu \_glbeylhjh\ l_e_`dZ ijb^_l \ ^\b`_gb_ Ijb wlhf gZ klhe [m^ml iZ^Zlv dZieb q_j_a h^bgZdh\u_ ijhf_`mldb \j_f_gb L_i_jv _keb baf_jylvjZkklhygbyf_`^mkhk_^gbfbdZieyfblhfh`ghm[_^blvky qlh wlb jZkklhygby [m^ml hlghkblvky dZd jy^ ihke_^h\Zl_evguo g_q_lguo qbk_e LZdbf h[jZahf fh`gh aZdexqblv qlh l_e_`dZ ^\b]ZeZkvjZ\ghmkdhj_ggh kfยง IhkqblZ_fmkdhj_gb_ihnhjfme_ 2s a = 2  aZf_jb\ ijhc^_ggh_ l_e_`dhc jZkklhygb_ s b \j_fy __ t ^\b`_gby t ?keb mf_gvrblv kbem ^_ckl\mxsmx gZ l_e_`dm \ ^\Z jZaZ \udexq_gb_f h^gh]h ba \_glbeylhjh\  b kgh\Z ihkqblZlv mkdhj_gb_ lh hgh ihemqblky \ ^\Z jZaZ f_gvrbf q_f i_j\uc jZa ?keb l_i_jv m\_ebqblv fZkkm l_e_`db \ ^\Z jZaZ ^h[Z\e_gb_f d l_e_`d_ ]jmaZ fZkkhc jZ\ghc fZkk_ l_e_`db  b kgh\Z ihkqblZlv 10


mkdhj_gb_ lh hgh ihemqblky \ ^\Z jZaZ f_gvrbf q_f i_j\uc jZa LZdbf h[jZahf aZdexqZ_f qlh mkdhj_gb_ l_e_`db ijyfh ijhihjpbhgZevgh ijbeh`_gghc d g_c kbe_ b h[jZlgh ijhihjpbhgZevgh__ fZkk_ 4. Mkdhj_gb_ l_eZ ijyfh ijhihjpbhgZevgh jZ\gh^_ckl\mxs_c ijbeh`_gguo d g_fm kbe b h[jZlgh ijhihjpbhgZevgh _]h fZkk_ U U F a= . m d] โ‹… f 5. HgbkhgZijZ\e_gu 6. G 1 2 . k

ยง12.

1. Hiulubah[jZ`_ggu_gZjbkmq_[gbdZih^l\_j`^Zxl lj_lbc aZdhg GvxlhgZ <h \k_o wlbo hiulZo ijb ihfhsb ^\mo ^bgZfhf_ljh\ baf_jyxlky kbeu k dhlhjufb ^\Z l_eZ ^_ckl\mxl ^jm]gZ^jm]Z< i_j\hfhiul_\aZbfh^_ckl\b_l_eijhbkoh^blijb bo g_ihkj_^kl\_gghf dhglZdl_ \h \lhjhf ยฒ gZ jZkklhygbb \ lj_lv_f ยฒ \ ijhp_kk_ ^\b`_gby Ijb wlhf \ dZ`^hf kemqZ_ ihdZaZgby ^bgZfhf_ljh\ hdZau\Zxlky h^bgZdh\ufb LZdbf h[jZahf fh`gh k^_eZlv \u\h^ qlh ^\Z l_eZ ^_ckl\mxl ^jm] gZ ^jm]Z k kbeZfb jZ\gufb ih fh^mex b ijhlb\hiheh`gufb ih gZijZ\e_gbx 2. Kbeuk dhlhjufb\aZbfh^_ckl\mxl^\Zl_eZjZ\guihfh^mexb ijhlb\hiheh`guihgZijZ\e_gbx 3. Wlhmkdhj_gb_\\b^m[hevrhcfZkkuA_febij_g_[j_`bl_evghfZeh 4. GZijbf_j Khegp_ b EmgZ \aZbfh^_ckl\mxl ihkj_^kl\hf ]jZ\blZpbhgguokbe 5. Wlbkbeuijbeh`_gud jZagufl_eZf 1. >\b`_gb_ih^^_ckl\b_fkbeuly`_klb 2. GZ^h baf_jblv jZkklhygby dhlhju_ rZjbd ijhoh^bl aZ ihke_^h\Zl_evgu_ h^bgZdh\u_ ijhf_`mldb \j_f_gb b m[_^blvky \ lhf qlh ^Zggu_ jZkklhygby hlghkylky dZd jy^ ihke_^h\Zl_evguo g_q_lguo qbk_e Wlh b [m^_l y\eylvky ^hdZaZl_evkl\hf lh]h qlh k\h[h^gh_iZ^_gb_l_eZy\ey_lkyjZ\ghmkdhj_gguf^\b`_gb_f kf ยง8). 3. K p_evx ihdZaZlv qlh mkdhj_gb_ k\h[h^gh]h iZ^_gby h^bgZdh\h ^ey\k_ol_e 4. Mkdhj_gb_\ua\Zggh_^_ckl\b_fkbeuly`_klb 5. BaaZkbeukhijhlb\e_gby\ha^moZ

ยง13.

11


6. =Zebe_c

§14.

1. >ZhgZij_iylkl\m_l_]hih^t_fm 2. K mkdhj_gb_f g Ijb ^\b`_gbb l_eZ \\_jo _]h kdhjhklv mf_gvrZ_lky ih aZdhgm v(t) = v0 â&#x20AC;&#x201C; gt < \_jog_c lhqdb ljZ_dlhjbb kdhjhklv l_eZ jZ\gZ gmex b hgh gZqbgZ_l ^\b]Zlvky \gba m\_ebqb\ZykdhjhklvihaZdhgmv(t) = gt^hl_oihjihdZg_ miZ^_l gZa_fex 3. Hl\_ebqbgugZqZevghckdhjhklb 4. ?keb gZijZ\blv hkv \\_jo lh ijh_dpby \_dlhjZ kdhjhklb gZ wlm hkv iheh`bl_evgZ Z ijh_dpby mkdhj_gby k\h[h^gh]h iZ^_gby ² hljbpZl_evgZ

§15.

1. <aZbfgh_ ijbly`_gb_ \k_o l_e <k_e_gghc ]jZ\blZpbhggh_ \aZbfh^_ckl\b_l_e  2. =jZ\blZpbhggufb 3. BkZZdGvxlhg\ ;9,,\_d_ 4. >\Z l_eZ ijbly]b\Zxlky ^jm] d ^jm]m k kbehc ijyfh ijhihjpbhgZevghc ijhba\_^_gbx bo fZkk b h[jZlgh ijhihjpbhgZevghcd\Z^jZlmjZkklhygbyf_`^mgbfb mm 5. F = G 1 2 2  ]^_ F ² fh^mev ]jZ\blZpbhgghc kbeu m1, m2 â&#x20AC;&#x201D; r fZkku \aZbfh^_ckl\mxsbo l_e r ² jZkklhygb_ f_`^m gbfb G â&#x20AC;&#x201D; ]jZ\blZpbhggZyihklhyggZyjZ\gZy â&#x2039;&#x2026;10-11 Gâ&#x2039;&#x2026;f2d]2. 6. AZdhg\k_fbjgh]hly]hl_gbykijZ\_^eb\\ ke_^mxsbokemqZyo

^ey^\mol_ejZaf_judhlhjuoij_g_[j_`bfhfZeuk jZkklhygb_fr f_`^mgbfb _kebh^ghbal_ebf__lnhjfmrZjZjZ^bmkb fZkkZ dhlhjh]h \h fgh]h jZa [hevr_ q_f m \lhjh]h l_eZ ijhba\hevghc nhjfu    ^ey ^\mo h^ghjh^guo l_e rZjhh[jZaghc nhjfu ijb ex[uobojZaf_jZo 7. >Z 1. <_jgh 2. Mf_gvrZ_lky3. Fl = mg. 4. KbeZly`_klb[hevr_gZ ihexkZoldA_fey g_fgh]hkiexkgmlZ m ihexkh\ 5. Hghijb[ebabl_evgh\ jZaf_gvr_a_fgh]h

§16.

12


1. RZjbd ^\b`_lky hl lhqdb : d lhqd_ < ih^ ^_ckl\b_f kbeu U mijm]hklb F  WlZ kbeZ \hagbdeZ \ j_amevlZl_ jZkly`_gby rgmjZ Kdhjhklv mkdhj_gb_ rZjbdZ b ^_ckl\mxsZy gZ g_]h kbeZ gZijZ\e_gu hl lhqdb A d lhqd_ B RZjbd ^\b`_lky ijyfhebg_cgh l__]hljZ_dlhjbyยฒijyfZyebgby 2. KbeZmijm]hklb\ rgmj_\hagbdeZ\ j_amevlZl__]hjZkly`_gbyb hgZgZijZ\e_gZd lhqd_OKdhjhklvrZjbdZb ^_ckl\mxsZygZg_]h kbeZ gZijZ\e_gu ih ijyfuf i_j_k_dZxsbfky ih^ m]ehf  R . LjZ_dlhjby rZjbdZ ij_^klZ\ey_l kh[hc hdjm`ghklv l_ rZjbd ^\b`_lkydjb\hebg_cgh 3. ?keb kdhjhklv l_eZ b ^_ckl\mxsZy gZ g_]h kbeZ gZijZ\e_gu \^hev i_j_k_dZxsboky ijyfuo lh l_eh ^\b`_lky djb\hebg_cgh _keb\^hevh^ghcijyfhclhl_eh^\b`_lkyijyfhebg_cgh

ยง18.

1. Hiulih\uk_dZgbxbkdjubalhqbevgh]hdZfgy 2. Mkdhj_gb_ gZijZ\e_gh ih jZ^bmkm d p_gljm hdjm`ghklb b hgh gZau\Z_lkyp_gljhklj_fbl_evguf

ยง19.

3. Ihnhjfme_Zp =

v2 . r 4. Ih jZ^bmkm d p_gljm hdjm`ghklb ?_ fh^mev hij_^_ey_lky ih nhjfme_Fp =

mv 2 . r

ยง20.

1. H[jZs_gb_ieZg_l\hdjm]KhegpZb kimlgbdh\\hdjm]ieZg_l 2. Ld hg h[eZ^Z_l ^hklZlhqgh [hevrhc kdhjhklvx gZijZ\e_gghc ihdZkZl_evghcd ljZ_dlhjbb^\b`_gby 3. >Z ld lZdh_ ^\b`_gb_ ijhbkoh^bl lhevdh ih^ ^_ckl\b_f kbeu ly`_klb 4. Khh[sblv_fmi_j\mxdhkfbq_kdmxkdhjhklv 5. Zp =

v2 v2 ;g= ; v 2 = gr โ‡’ v = gr . IheZ]Zyr โ‰ˆ RAlhihemqZ_f r r

qlh v = gRA โ‰ˆ dfk 6. Ihweebilbq_kdhchj[bl_\hdjm]A_febihweebilbq_kdhchj[bl_ \hdjm]KhegpZ

13


§21.

1. Bfimevkhf l_eZ gZau\Z_lky nbabq_kdZy \_ebqbgZ jZ\gZy ijhba\_^_gbxfZkkul_eZgZ_]hkdhjhklv 2. Bfimevkb kdhjhklv^\b`ms_]hkyl_eZ\k_]^ZkhgZijZ\e_gu 3. < kbkl_f_KBd]â&#x2039;&#x2026;fk

§22.

1. Hiul bah[jZ`_gguc gZ jbkmgd_  mq_[gbdZ ijh\h^blky ke_^mxsbfh[jZahf;_jmlky^\ZrZjbdZih^\_r_ggu_gZgblyolZd qlh[u hgb dZkZebkv ^jm] ^jm]Z H^bg ba rZjbdh\ hldehgyxl gZ g_dhlhjuc m]he b hlimkdZxl RZjbd ^hklb]gm\ k\h_]h ij_`g_]h iheh`_gby m^Zjy_lky h \lhjhc b hklZgZ\eb\Z_lky Ijb wlhf \lhjhc rZjbd hldehgy_lky gZ lhl `_ m]he LZdbf h[jZahf ijb \aZbfh^_ckl\bbbfimevki_j\h]hrZjbdZmf_gvrbekygZklhevdhgZ kdhevdhm\_ebqbekybfimevk\lhjh]hWlhlhiulih^l\_j`^Z_laZdhg khojZg_gbybfimevkZ 2. Kbkl_fZl_egZau\Z_lkyaZfdgmlhc_kebgZwlbl_eZg_^_ckl\mxl \g_rgb_kbeu 3. <_dlhjgZykmffZbfimevkh\l_eaZfdgmlhckbkl_fuihklhyggZ\h \j_f_gbijbex[uo^\b`_gbyob \aZbfh^_ckl\byowlbol_e U U U U U U 4. m1v1â&#x20AC;² + m2 v â&#x20AC;²2 = m1v1 + m2 v2  ]^_ m1, m2 ² fZkku l_e v1 , v 2 ² bo U U kdhjhklb ^h \aZbfh^_ckl\by v1â&#x20AC;² , v 2â&#x20AC;² ² bo kdhjhklb ihke_ \aZbfh^_ckl\by

§23.

1. >\b`msbcky \ha^mo h[eZ^Z_l g_dhlhjuf bfimevkhf Ih aZdhgm khojZg_gby bfimevkZ rZjbd h[eZ^Z_l lZdbf `_ ih fh^mex gh ijhlb\hiheh`guf ih gZijZ\e_gbx bfimevkhf < j_amevlZl_ hg ^\b`_lkyijhlb\hiheh`ghkljm_\uoh^ys_]hbarZjbdZ\ha^moZ 2. >\b`_gb_ \h^hf_lguo ]b^jhfhlhpbdeh\ j_Zdlb\guo kZfhe_lh\ b jZd_l 3. <h_ggh_gZmqghbkke_^h\Zl_evkdh_ljZgkihjlgh_b l^ 4. =jmah\hc hlk_d ihe_aghc gZ]jmadb \ kemqZ_ bah[jZ`_gghf gZ jbkmgd_ wlh dhkfbq_kdbc dhjZ[ev  ijb[hjguc hlk_d [Zd k hdbkebl_e_f[Zdk ]hjxqbfgZkhkudZf_jZk]hjZgbykhieh 5. JZkkfhljbf ijbgpbi ^_ckl\by jZd_lu gZ ijbf_j_ h^ghklmi_gqZlhc K ihfhsvx gZkhkh\ lhieb\h b hdbkebl_ev ih^Zxlky\ dZf_jmk]hjZgby]^_hgbk]hjZyh[jZamxl]Za\ukhdhc l_fi_jZlmju b \ukhdh]h ^Z\e_gby < j_amevlZl_ \hagbdgh\_gby [hevrhc jZaghklb ^Z\e_gbc \ dZf_j_ k]hjZgby b \ dhkfbq_kdhf 14


ijhkljZgkl\_]ZaubadZf_juk]hjZgby\ulZedb\ZxlkygZjm`mq_j_a khieh k h]jhfghc kdhjhklvx < kbem aZdhgZ khojZg_gby bfimevkZ jZd_lZ ihemqZ_l bfimevk jZ\guc ih fh^mex b ijhlb\hiheh`gh gZijZ\e_ggucbfimevkm\ue_l_\r_ckljmb]ZaZ 6. Hlkdhjhklbbkl_q_gby]ZaZfZkkulhieb\ZlbiZlhieb\Zb l^ 7. Kihkh[ghklvjZa\b\Zlv[hevrmxkdhjhklv 8. Khiehf\gbald\ lZdhfkemqZ_j_Zdlb\gZykljmy]Zkblkdhjhklv jZd_lu 1. Dhe_[Zgb_fZylgbdZqZkh\kljmgu]blZju 2. >\b`_gb_ih\lhjy_lkyq_j_ahij_^_e_ggucijhf_`mlhd\j_f_gb 3. I_jbh^hf dhe_[Zgbc gZau\Z_lky ijhf_`mlhd \j_f_gb q_j_a dhlhjuc ^\b`_gb_ ih\lhjy_lky \j_fy kh\_jr_gby h^gh]h dhe_[Zgby  4. AZ\j_fyjZ\gh_i_jbh^mdhe_[ZgbcdZ`^h_babah[jZ`_gguogZ jbkmgd_  mq_[gbdZ l_e ^\Z`^u ijhoh^bl q_j_a iheh`_gb_ jZ\gh\_kby ^\b]Zykv\ ijhlb\hiheh`guogZijZ\e_gbyo 

ยง24.

ยง25.

1. KbeZmijm]hklb^_ckl\m_lgZrZjbd\ lhqdZo<, K, D, :lddh]^Z rZjbdgZoh^blky\ wlbolhqdZoijm`bgZ^_nhjfbjh\ZgZ jZklygmlZ beb k`ZlZ  < lhqd_ O kbeZ mijm]hklb gZ rZjbd g_ ^_ckl\m_l ld dh]^Z rZjbd gZoh^blky \ wlhc lhqd_ ijm`bgZ g_ ^_nhjfbjh\ZgZ LhqdZO gZau\Z_lkyiheh`_gb_fjZ\gh\_kbyrZjbdZ 2. Ih f_j_ ijb[eb`_gby rZjbdZ d lhqd_ O kdhjhklv l_eZ m\_ebqb\Z_lky ld kbeZ mijm]hklb b mkdhj_gb_ kh\iZ^Zxl ih gZijZ\e_gbx kh kdhjhklvx Ih f_j_ m^Ze_gby rZjbdZ hl lhqdb O kdhjhklv l_eZ mf_gvrZ_lky ld kbeZ mijm]hklb b mkdhj_gb_ ijhlb\hiheh`ghgZijZ\e_gukdhjhklb 3. Ld ex[h_ l_eh h[eZ^Z_l k\hckl\hf khojZgylv k\hx kdhjhklv _kebgZg_]hg_^_ckl\mxlkbeubeb^_ckl\b_kbekdhfi_gkbjh\Zgh Ijb ijhoh`^_gbb iheh`_gby jZ\gh\_kby gZ rZjbd g_ ^_ckl\m_l kbeZ mijm]hklb Z _]h kdhjhklv g_ jZ\gZ gmex b khojZgy_l k\h_ agZq_gb_b gZijZ\e_gb_ 4. Dhe_[ZgbygZau\Zxlkyk\h[h^gufb_kebhgbijhbkoh^yllhevdh aZkq_lgZqZevgh]haZiZkZwg_j]bbkbkl_fu 5. Dhe_[Zl_evgufbkbkl_fZfb gZau\Zxlkykbkl_ful_ekihkh[guo kh\_jrZlvk\h[h^gu_dhe_[Zgby 6. FZylgbdhf gZau\Z_lky l\_j^h_ l_eh kh\_jrZxs__ ih^ ^_ckl\b_f ijbeh`_gguo kbe dhe_[Zgby hdheh g_ih^\b`ghc lhqdb beb\hdjm]hkb 15


7. Ijm`bggucfZylgbdkhklhblbal_eZaZdj_ie_ggh]hgZijm`bg_ GblyghcfZylgbdkhklhblbal_eZih^\_r_ggh]hgZgblb

§26.

1. :fieblm^Z ² fZdkbfZevgh_ kf_s_gb_ dhe_[exs_]hky l_eZ hl iheh`_gbyjZ\gh\_kby:fieblm^Zh[hagZqZ_lky[md\hc©:ªb \KB baf_jy_lky\ f_ljZo f  I_jbh^ ² \j_fy kh\_jr_gby h^gh]h dhe_[Zgby I_jbh^ h[hagZqZ_lky[md\hc©Tªb \KBbaf_jy_lky\ k_dmg^Zo k  QZklhlZ ² dhebq_kl\h dhe_[Zgbc \ _^bgbpm \j_f_gb QZklhlZ h[hagZqZ_lky[md\hc©νªb \KBbaf_jy_lky\ ]_jpZo =p  2. H^ghihegh_dhe_[Zgb__klvdhe_[Zgb_aZi_jbh^ 3. K\yavf_`^mi_jbh^hfb qZklhlhc\ujZ`Z_lkynhjfmehcL = 1/ν bebν = 1/L. 4. Z Q_f[hevr_^ebgZgblbfZylgbdZl_ff_gvr_qZklhlZ[ q_f [hevr_^ebgZgblbfZylgbdZl_f[hevr_i_jbh^ 5. Kh[kl\_gghcqZklhlhcdhe_[Zl_evghckbkl_fugZau\Z_lkyqZklhlZ k\h[h^guodhe_[Zgbckbkl_fu 6. ?keb fZylgbdb dhe_[exlky \ ijhlb\hiheh`guo nZaZo lh bo kdhjhklb ijhlb\hiheh`gh gZijZ\e_gu _keb \ h^bgZdh\uo lh bo kdhjhklbkhgZijZ\e_gu

§27.

1. Hiul klZ\beky k p_evx ihdZaZlv qlh dhe_[Zgby ijm`bggh]h fZylgbdZy\eyxlky]Zjfhgbq_kdbfbHgaZdexqZ_lky\ lhfqlh]jma gZijbf_j \hjhgdZ k gZeblhc djZkys_c `b^dhklvx  mdj_ie_gguc gZ ijm`bg_ ijb k\h_f dhe_[Zl_evghf ^\b`_gbb hklZ\ey_l ke_^ ljZ_dlhjbb gZ ^\b`ms_cky k ihklhygghc kdhjhklvx [mfZ`ghc e_gl_ Ihemq_ggZy lZdbf kihkh[hf ljZ_dlhjby y\ey_lky kbgmkhb^hc 2. Kbgmkhb^hc Hlj_ahd OA khhl\_lkl\m_l Zfieblm^_ dhe_[Zgbc Z hlj_ahdOB ²i_jbh^m 3. =Zjfhgbq_kdbfb dhe_[Zgbyfb gZau\Zxlky dhe_[Zgby \ dhlhjuo baf_g_gb_dZdhceb[h nbabq_kdhc \_ebqbgu ijhbkoh^bl ih aZdhgm kbgmkZbebdhkbgmkZ 4. Qlhdhe_[Zgbygbl_\h]hfZylgbdZy\eyxlky]Zjfhgbq_kdbfb 5. FZl_jbZevgZy lhqdZ h[eZ^ZxsZy fZkkhc b dhe_[exsZyky gZ ihklhygghf jZkklhygbb hl lhqdb ih^\_kZ gZau\Z_lky fZl_fZlbq_kdbffZylgbdhf

16


6. Dhe_[Zgby gblygh]h fZylgbdZ fh`gh kqblZlv ]Zjfhgbq_kdbfb _keb^ebgZgblbfgh]h[hevr_jZaf_jh\ih^\_r_ggh]hgZg_cl_eZ gZijbf_j rZjbdZ  gblv hq_gv e_]dZy b fZehjZkly`bfZy kbeu lj_gby\ kbkl_f_hlkmlkl\mxlZfieblm^Zdhe_[ZgbcfZeZ 7. F_gyxlkyihaZdhgmkbgmkZbebdhkbgmkZ

ยง28.

1. Ijbmkeh\bbhlkmlkl\byihl_jvwg_j]bb 2. KmffZ dbg_lbq_kdhc b ihl_gpbZevghc wg_j]bc ihklhyggZ kh]eZkgh aZdhgm khojZg_gby wg_j]bb b jZ\gZ i_j\hgZqZevghfm aZiZkmihl_gpbZevghcwg_j]bbdhe_[Zl_evghckbkl_fu 3. G_l 4. Mf_gvrZ_lky 5. < \h^_ ld \ g_c gZ fZylgbd ^_ckl\m_l [hevrZy kbeZ khijhlb\e_gbyq_f\ \ha^mo_

ยง29.

1. G_lbaaZkhijhlb\e_gbykj_^u 2. Ijbeh`blvd dhe_[exs_fml_emi_jbh^bq_kdmx\g_rgxxkbem 3. Dhe_[ZgbygZau\Zxlky\ugm`^_ggufb_kebhgbijhbkoh^ylih^ ^_ckl\b_fi_jbh^bq_kdbbaf_gyxs_cky\g_rg_ckbeu 4. <ugm`^Zxs_c kbehc gZau\Z_lky i_jbh^bq_kdb baf_gyxsZyky \g_rgyykbeZ\uau\ZxsZydhe_[Zgby 5. Dh]^Z Zfieblm^Z b qZklhlZ \ugm`^_gguo dhe_[Zgbc i_j_klZxl f_gylvky 6. WlbqZklhlujZ\gu 7. Fh]mlgZijbf_jihjr_gvihfih\h]hgZkhkZ 8. >hl_oihjihdZ^_ckl\m_l\ugm`^ZxsZykbeZ

ยง30.

1. Hiul ijh\h^blky k p_evx ^_fhgkljZpbb y\e_gby j_ahgZgkZ >ey wlh]h [_jml ^\Z fZylgbdZ \bkysb_ gZ h[s_f rgmj_ >ebgZ fZylgbdZ  g_baf_ggZ b ke_^h\Zl_evgh _fm khhl\_lkl\m_l hij_^_e_ggZy qZklhlZ k\h[h^guo dhe_[Zgbc kh[kl\_ggZy qZklhlZ  >ebgm fZylgbdZ  fh`gh f_gylv ijb ihfhsb k\h[h^guo dhgph\ gbl_cIjbwlhff_gy_lky_]hkh[kl\_ggZyqZklhlZ?kebhldehgblv fZylgbdhliheh`_gbyjZ\gh\_kbyb ij_^hklZ\blvkZfhfmk_[_lh hg gZqg_l kh\_jrZlv k\h[h^gu_ dhe_[Zgby Wlh \uah\_l dhe_[Zgby rgmjZ \ j_amevlZl_ q_]h gZ fZylgbd  [m^_l ^_ckl\h\Zlv \ugm`^ZxsZy kbeZ k qZklhlhc jZ\ghc kh[kl\_gghc qZklhl_ 17


fZylgbdZ Ih^ ^_ckl\b_f wlhc kbeu fZylgbd  gZqg_l kh\_jrZlv \ugm`^_ggu_dhe_[Zgby?kebl_i_jvmf_gvrZlv^ebgmfZylgbdZ lh _]h qZklhlZ b qZklhlZ \ugm`^Zxs_c kbeu ^_ckl\mxs_c gZ fZylgbd  [m^ml m\_ebqb\Zlvky Ijb wlhf Zfieblm^Z mklZgh\b\rboky \ugm`^_gguo dhe_[Zgbc fZylgbdZ  [m^_l \hajZklZlv HgZ ^hklb]g_l fZdkbfZevgh]h agZq_gby ijb jZ\_gkl\_ ^ebg fZylgbdh\ Z khhl\_lkl\_ggh ijb jZ\_gkl\_ qZklhlu \ugm`^Zxs_c kbeu b kh[kl\_gghc qZklhlu fZylgbdZ  < wlhf b khklhblkmlvy\e_gbyj_ahgZgkZ 2. Y\e_gb_ j_ahgZgkZ aZdexqZ_lky \ j_adhf m\_ebq_gbb Zfieblm^u mklZgh\b\rboky \ugm`^_gguo dhe_[Zgbc ijb kh\iZ^_gbb qZklhlu kh[kl\_gguo dhe_[Zgbc kbkl_fu k qZklhlhc \ugm`^Zxs_ckbeu 3. ldbo^ebguZke_^h\Zl_evghb qZklhlujZ\gu 4. Lhevdhd \ugm`^_gguf 5. Ihe_agh_ y\e_gb_ \ fmaudZevguo bgkljmf_glZo <j_^gh_ y\e_gb_ ijb ijhoh`^_gbb khe^Zl ih fhklm \ gh]m \ j_amevlZl_ j_ahgZgkZfhklfh`_ljZajmrblvky 1. <hafms_gby jZkijhkljZgyxsb_ \ ijhkljZgkl\_ b m^Zeyxsb_ky hlf_klZbo\hagbdgh\_gbygZau\Zxlky\hegZfb 2. < gboijhbkoh^bli_j_ghkwg_j]bb[_ai_j_ghkZ\_s_kl\Z 3. G_lg_ijhbkoh^bl 4. Mijm]bfb \hegZfb gZau\Zxlky \hegu jZkijhkljZgyxsb_ky \ mijm]bokj_^Zo 5. We_dljhfZ]gblgu_\hegu

§31.

1. Ijh^hevgu_\hegu²wlhlZdb_\hegu\ dhlhjuodhe_[ZgbyqZklbp kj_^u kh\_jrZxlky \^hev gZijZ\e_gby jZkijhkljZg_gby \heg gZijbf_ja\mdh\u_\heguIhi_j_qgu_\hegu²wlhlZdb_\heguijb dhlhjuo dhe_[Zgby qZklbp kj_^u kh\_jrZxlky i_ji_g^bdmeyjgh gZijZ\e_gbxjZkijhkljZg_gby \heg gZijbf_j\hegu gZ ih\_joghklb \h^u 2. <hegZfb k^\b]Z y\eyxlky ihi_j_qgu_ \hegZfb k`Zlby ² ijh^hevgu_ 3. Ihi_j_qgu_ \hegu fh]ml jZkijhkljZgylvky lhevdh \ l\_j^hc kj_^_ijh^hevgu_²\ l\_j^hc`b^dhcbeb]Zahh[jZaghckj_^_ 4. Ld\ ]ZaZob `b^dhklyog_\hagbdZ_lmijm]bokbeijbk^\b]_

§32.

18


§33.

1. >ebghc\hegugZau\Z_lkyjZkklhygb_f_`^m^\mfy[eb`Zcrbfb lhqdZfb\hegudhe_[exsbfky\ h^bgZdh\uonZaZo 2. ;md\hc©λª qblZ_lky©eZf[^Zª  3. AZi_jbh^L h^gh]hihegh]hdhe_[Zgby 4. IhnhjfmeZfλ = vL b v = λ/L = λν. 5. F_`^mlhqdZfbb b  1. Wlb hiulu ^_fhgkljbjmxl dhe_[Zl_evguc oZjZdl_j \hagbdgh\_gby a\mdZ < i_j\hf hiul_ \ dZq_kl\_ bklhqgbdZ a\mdZ [_j_lky h[uqgZy ebg_cdZ aZ`ZlZy \ lbkdZo \h \lhjhf ² kljmgZ dhgpudhlhjhcaZdj_ie_gu\ lj_lv_f²dZf_jlhg?kebdZ`^mxba \ur_ i_j_qbke_gguo kbkl_f \u\_klb ba iheh`_gby jZ\gh\_kby b ^Zlv _c kh\_jrZlv k\h[h^gu_ dhe_[Zgby lh fu mkeurbf a\md LZdbf h[jZahf bklhqgbdZfb a\mdZ y\eyxlky dhe_[Zl_evgu_ kbkl_fu 2. Ex[hcbklhqgbda\mdZy\ey_lkydhe_[Zl_evghckbkl_fhc 3. Dhe_[Zgby k qZklhlhc hl  =p ^h  =p gZau\Zxlky a\mdh\ufbihkdhevdm\hkijbgbfZxlkyq_eh\_dhf 4. BgnjZa\mdh\ufb gZau\Zxlky dhe_[Zgby k qZklhlhc gb`_  =p mevljZa\mdh\ufb²k qZklhlhc\ur_=p

§34.

1. Hiul ijh\h^blky k p_evx \uykgblv aZ\bkbfhklv \ukhlu a\mdZ hl qZklhlu dhe_[Zgbc >ey ijh\_^_gby ^Zggh]h hiulZ [_jml ijb[hj khklhysbcbag_kdhevdboam[qZluof_lZeebq_kdbo^bkdh\bf_xsbo jZaebqgh_ qbkeh am[v_\ b aZdj_ie_gguo gZ h^ghc hkb AZl_f \k_ ^bkdb ijb\h^yl \h \jZs_gb_ b lhgdhc dZjlhgghc ieZklbgdhc ihhq_j_^gh dZkZxlky am[v_\ dZ`^h]h ba ^bkdZ Ijb wlhf fu mkeurbfjZagu_ih\ukhl_a\mdbFh`ghaZf_lblvqlhq_f [hevr_ qbkeh am[v_\ gZ ^bkd_ b khhl\_lkl\_ggh [hevr_ qZklhlZ dhe_[Zgbc dZjlhgghcieZklbgdbl_f [hevr_ [m^_l\ukhlZa\mdZ :gZeh]bqgmx aZ\bkbfhklvfh`gh \uy\blv bkihevamy \k_]h lhevdh h^bg ^bkd >ey wlh]hgZ^h m\_ebqb\Zlvkdhjhklv ^bkdZ Q_f [hevr_ kdhjhklv ^bkdZ l_f [hevr_ qZklhlZ dhe_[Zgbc dZjlhgghc ieZklbgdb b l_f \ur_ [m^_lba^Z\Z_fuca\md 2. Hiulijh\h^blkyk p_evx\uykgblvaZ\bkbfhklv\ukhlua\mdZhl qZklhlu dhe_[Zgbc >ey ijh\_^_gby ^Zggh]h hiulZ [_jml ^\Z dZf_jlhgZ ba^Zxsbo a\mdb jZaghc \ukhlu H[Z dZf_jlhgZ ijb\h^yl \ dhe_[Zl_evgh_ ^\b`_gb_ Ijb wlhf hkljby

§35.

19


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§36.

§37.

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^_j_\vy ]Zau `b^dhklb d ihjbkluf ยฒ \hcehd ihjhehg i_ghieZkl 4. Iml_fhl^_edbihf_s_gbca\mdhbaheypbhggufbfZl_jbZeZfb 1. K qZklhlhckhhl\_lkl\mxs_ca\mdm 2. Ijh^hevgmx\hegm\ h[hbokemqZyo 3. Q_j_ag_kdhevdhk_dmg^ihke_\kiurdbfhegbbfukeurbf]jhf 4. < f \_d_ njZgpmakdbfb mq_gufb [ueZ baf_j_gZ kdhjhklv a\mdZ< ^\moimgdlZojZkklhygb_f_`^mdhlhjufb[uehba\_klgh ijhba\h^beb \uklj_eu ba imr_d < h[hbo imgdlZo baf_jyeb hlj_adb \j_f_gb f_`^m \kiurdhc h]gy ijb \uklj_e_ b fhf_glhf dh]^Z [ue keurZg a\md \uklj_eZ Kdhjhklv a\mdZ hij_^_eyeb dZd hlghr_gb_ jZkklhygby f_`^m imgdlZfb d baf_j_gghfm hlj_adm \j_f_gb 5. v fk 6. >ZaZ\bkbl

ยง38.

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ยง39.

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ยง40.

1. Hiulihkeh`_gbxa\mdh\uo\heghl^\mobklhqgbdh\ijh\h^blky ke_^mxsbf h[jZahf < dZq_kl\_ bklhqgbdh\ a\mdZ [_jml ^\Z ]jhfdh]h\hjbl_ey=jb =jih^dexq_ggu_d a\mdh\hfm]_g_jZlhjm A= BaemqZ_fuc bfb a\md ihiZ^Z_l \ fbdjhnhg F ]^_ ihke_ ij_h[jZam_lky \ we_dljbq_kdb_ dhe_[Zgby Wlb dhe_[Zgby mkbeb\Zxlky mkbebl_e_f gbadhc qZklhlu MGQ b j_]bkljbjmxlky ]Zev\Zghf_ljhf = GZkljhbf ]_g_jZlhj gZ qZklhlm  =p l_ gZ ^ebgm \hegu ijb[ebabl_evgh jZ\gmx  kf =jhfdh]h\hjbl_eb mklZgh\bfgZjZkklhygbbf hlfbdjhnhgZ?kebl_i_jvdZ`^uc

ยง42.

21


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ยง43.

1. >\b`msbfbkywe_dljbq_kdbfbaZjy^Zfb 2. <gmlj_ggbfbwe_dljbq_kdbfblhdZfbfZ]gblZ 3. FZ]gblgufb ebgbyfb gZau\Zxlky \hh[jZ`Z_fu_ ebgbb \^hev dhlhjuo jZkiheh`bebkv [u fZ]gblgu_ klj_edb ihf_s_ggu_ \ fZ]gblgh_ihe_ 22


4. Khhl\_lkl\_gghijyfhebg_cghb djb\hebg_cgh 5. AZgZijZ\e_gb_fZ]gblghc ebgbb\ dZdhceb[hlhqd_ijbgbfZxl gZijZ\e_gb_ k_\_jgh]h ihexkZ fZ]gblghc klj_edb ihf_s_gghc \ wlmlhqdm 6. Q_fkbevg__ihe_l_f]ms_jZkiheh`_gu\ g_ffZ]gblgu_ebgbb 7. H gZijZ\e_gbbb \_ebqbg_fZ]gblgh]hihey

§44.

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§45.

23


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ยง46.

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7. < kemqZ_dh]^ZgZijZ\e_gb_lhdZ\ ijh\h^gbd_eb[hgZijZ\e_gb_ kdhjhklbqZklbpukh\iZ^Zxlk gZijZ\e_gb_ffZ]gblghcebgbbbeb iZjZee_evgu_c

ยง47.

1. FZ]gblgZy bg^mdpby ยฒ wlh \_dlhjgZy nbabq_kdZy \_ebqbgZ U oZjZdl_jbamxsZyfZ]gblgh_ihe_HgZh[hagZqZ_lkykbf\hehf < . 2. Fh^mev \_dlhjZ fZ]gblghc bg^mdpbb hij_^_ey_lky dZd hlghr_gb_ fh^mey kbeu ^_ckl\mxs_c gZ jZkiheh`_gguc i_ji_g^bdmeyjghfZ]gblgufebgbyfijh\h^gbdk lhdhfd kbe_lhdZ F b _]h^ebg_ B = . Il 3. < kbkl_f_KBLe qblZ_lkyยฉl_keZยช  4. EbgbyfbfZ]gblghcbg^mdpbbgZau\Zxlkyebgbb dZkZl_evgu_ d dhlhjuf \ dZ`^hc lhqd_ ihey kh\iZ^Zxl k gZijZ\e_gb_f \_dlhjZ fZ]gblghcbg^mdpbb 5. FZ]gblgh_ ihe_ h^ghjh^gh _keb \h \k_o _]h lhqdZo fZ]gblgZy U bg^mdpby < ihklhyggZ < ijhlb\ghf kemqZ_ fZ]gblgh_ ihe_ g_h^ghjh^gh 6. KbeZ^_ckl\mxsZygZfZ]gblgmxklj_edmbeb^\b`msbckyaZjy^ \ fZ]gblghf ihe_ [m^_l l_f [hevr_ q_f [hevr_ fh^mev \_dlhjZ fZ]gblghcbg^mdpbb\ ^Zgghclhqd_ihey

ยง48.

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ยง49.

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ijh\h^gbdhf iehsZ^v < i_j\hf hiul_ ]Zev\Zghf_lj j_]bkljbjm_l ihy\e_gb_ lhdZ \ aZfdgmlhc gZ g_]h dZlmrd_ ijb \klZ\e_gbb \ g__ fZ]gblZ <h \lhjhf hiul_ dZlmrdZ \dexq_ggZy \ p_iv bklhqgbdZ lhdZ \klZ\ey_lky \h \lhjmx dZlmrdm aZfdgmlmx gZ ]Zev\Zghf_lj IjbaZfudZgbbb jZafudZgbbp_ib]Zev\Zghf_ljkgh\Zj_]bkljbjm_l lhd 2. Ijbbaf_g_gbbfZ]gblgh]hihlhdZq_j_adZlmrdm 3. Y\e_gb_we_dljhfZ]gblghcbg^mdpbbaZdexqZ_lky\ \hagbdgh\_gbb we_dljbq_kdh]h lhdZ \ aZfdgmlhf ijh\h^gbd_ ijb baf_g_gbb fZ]gblgh]h ihlhdZ ijhgbau\Zxs_]h ho\Zq_ggmx ijh\h^gbdhf iehsZ^v 4. Y\e_gb_ we_dljhfZ]gblghc bg^mdpbb bkihevam_lky \ we_dljh]_g_jZlhjZoihemqb\rborbjhdh_jZkijhkljZg_gb_

§50.

1. We_dljbq_kdbc lhd i_jbh^bq_kdb f_gyxsbcky \h \j_f_gb ih fh^mex b ih gZijZ\e_gbx gZau\Z_lky i_j_f_gguf lhdhf I_j_f_gguc lhd fh`gh ihemqblv _keb \ dZlmrd_ aZfdgmlhc gZ ]Zev\Zghf_lj i_jbh^bq_kdb ^\b]Zlv fZ]gbl \\_jo b \gba Ijb wlhf klj_edZ ]Zev\Zghf_ljZ [m^_l i_jbh^bq_kdb hldehgylvky hl gme_\h]h agZq_gby lh \ h^gm klhjhgm lh \ ^jm]mx Wlh [m^_l k\b^_l_evkl\h\Zlv h lhf qlh b fh^mev kbeu bg^mdpbhggh]h lhdZ b _]h gZijZ\e_gb_ i_jbh^bq_kdb f_gyxlky \h \j_f_gb l_ \ dZlmrd_ h[jZam_lkyi_j_f_gguclhd 2. < we_dljhk_lyo 3. GZy\e_gb_we_dljhfZ]gblghcbg^mdpbb 4. =_g_jZlhj khklhbl ba klZlhjZ ² g_ih^\b`ghc qZklb \uihegyxs_cnmgdpbxaZfdgmlh]hdhglmjZjhlhjZ²\jZsZxs_cky qZklb \uihegyxsbc nmgdpbx fZ]gblZ \ ijhfure_gguo ]_g_jZlhjZo bkihevamxlky h[uqgh we_dljhfZ]gblu  Ijbgpbi ^_ckl\by ]_g_jZlhjZ hkgh\Zg gZ y\e_gbb we_dljhfZ]gblghc bg^mdpbbIjb\jZs_gbbjhlhjZ\g_rg_ckbehcf_gy_lkyfZ]gblguc ihlhdijhgbau\ZxsbcklZlhj\ j_amevlZl_q_]h\ g_fbg^mpbjm_lky i_j_f_gguclhd 5. GZ l_ieh\hc we_dljhklZgpbb jhlhj ]_g_jZlhjZ ijb\h^blky \h \jZs_gb_ iZjh\hc lmj[bghc gZ ]b^jhwe_dljhklZgpbb ² \h^yghc lmj[bghc 6. LZd dZd kdhjhklv \jZs_gby \h^yguo lmj[bg hlghkbl_evgh g_\ukhdZ lh ^ey kha^Zgby lhdZ klZg^Zjlghc qZklhlu ijbf_gyxl fgh]hihexkgu_jhlhju 7. =p 26


ยง51.

1. :g]ebckdbfmq_guf>DFZdk\_eehf  \ ]WlZ l_hjby \djZlp_ k\h^blky d lhfm qlh f_gyxs__ky \h \j_f_gb we_dljbq_kdh_ ihe_ ihjh`^Z_l i_j_f_ggh_ fZ]gblgh_ ihe_ b gZh[hjhl f_gyxs__ky \h \j_f_gb fZ]gblgh_ ihe_ ihjh`^Z_l i_j_f_ggh_we_dljbq_kdh_ihe_ 2. Bklhqgbdhfwe_dljhfZ]gblgh]hiheykem`ZlaZjy^u^\b`msb_ky k mkdhj_gb_f 3. Kbeh\u_ ebgbb \boj_\h]h we_dljbq_kdh]h ihey aZfdgmlu Z kbeh\u_ ebgbb we_dljhklZlbq_kdh]h ihey gZqbgZxlky gZ iheh`bl_evguoaZjy^Zob aZdZgqb\ZxlkygZhljbpZl_evguo

ยง52.

1. We_dljhfZ]gblgZy \hegZ ij_^klZ\ey_l kh[hc kbkl_fm ihjh`^Zxsbo ^jm] ^jm]Z b jZkijhkljZgyxsboky \ ijhkljZgkl\_ i_j_f_gguo we_dljbq_kdh]h b fZ]gblgh]h ihe_c i_ji_g^bdmeyjguo ^jm] ^jm]m We_dljhfZ]gblgu_ \hegu y\eyxlky ihi_j_qgufb lZd dZd iehkdhklv \ dhlhjhc e_`Zl dhe_[exsb_ky U U \_dlhju B b E  i_ji_g^bdmeyjgZ gZijZ\e_gbx jZkijhkljZg_gby \hegu Bklhqgbdhf we_dljhfZ]gblguo \heg y\eyxlky mkdhj_ggh ^\b`msb_ky we_dljbq_kdb_ aZjy^u Kdhjhklv jZkijhkljZg_gby we_dljhfZ]gblguo\heg\ \Zdmmf_jZ\gZkdhjhklbk\_lZl_ dfk U 2. <_dlhj gZijy`_gghklb we_dljbq_kdh]h ihey E b \_dlhj U fZ]gblghcbg^mdpbb B . 3. ฮป = cT = k/ฮฝ. U 4. >eywlh]hg_h[oh^bfhqlh[uqZklhlZฮฝ dhe_[Zgbc\_dlhjh\ B b U E [ueZ^hklZlhqgh[hevrhc 5. We_dljhfZ]gblgu_ \hegu \i_j\u_ m^Zehkv h[gZjm`blv =_gjbom =_jpm\ ] 6. <b^bfuck\_lmevljZnbhe_ljZ^bh\hegu 7. JZ^bhk\yavjZ^bhehdZpbyjZ^bhZkljhghfbyj_gl]_gb ^j 1. GZ kq_l k\_lZ kms_kl\h\Zeb ^\_ hkgh\guo l_hjbb dhjimkdmeyjgZyb \hegh\Zy< hkgh\_i_j\hce_`Zehml\_j`^_gb_h lhf qlh k\_l ยฒ wlh ihlhd qZklbp \ hkgh\_ \lhjhc ml\_j`^_gb_ h lhfqlhk\_lยฒwlh\hegZ

ยง53.

27


2. <  ] Zg]ebckdbc mq_guc LhfZk Xg] ihdZaZe qlh k\_lm ijbkms_ k\hckl\h bgl_jn_j_gpbb Wlh ^hdZau\Zeh lh qlh k\_l h[eZ^Z_l\hegh\ufbk\hckl\Zfb 3. GZ ijh\hehqgh_ dhevph k jmqdhc aZlygmlh_ fuevghc ie_gdhc \ aZl_fg_gghc dhfgZl_ gZijZ\eyeky k\_l gZijbf_j `_elh]h p\_lZ Ijb wlhf gZ ie_gd_ h[jZah\u\Zebkv q_j_^mxsb_ky `_elu_ b l_fgu_ihehku 4. K\_l iZ^Zy gZ ie_gdm qZklbqgh hljZ`Z_lky hl i_j_^g_c ih\_joghklb \ lhqd_ : Z qZklbqgh ijhoh^bl \gmljv ie_gdb b hljZ`Z_lky hl aZ^g_c ih\_joghklb \ lhqd_ < ihke_ q_]h \uoh^bl ba ie_gdb \ lhqd_ K <hegu \uoh^ysb_ ba lhq_d : b K y\eyxlky dh]_j_glgufb ld hgb h[jZamxlky hl h^gh]h b lh]h `_ bklhqgbdZ JZaghklv oh^Z ^ebg \heg aZ\bkbl hl lhesbgu ie_gdb dhlhjZy \ jZaguo lhqdZo jZaebqgZ ?keb lhesbgZ ie_gdb hdZ`_lky lZdhc qlh \hegu[m^ml\uoh^blvbalhq_d: b Kbf_yh^bgZdh\u_nZaulhwlb \hegu ijb keh`_gbb mkbeyl ^jm] ^jm]Z < j_amevlZl_ \hagbdg_l fZdkbfmf bgl_jn_j_gpbhgghc dZjlbgu ² `_elZy ihehkZ ?keb lhesbgZie_gdbhdZ`_lkylZdhcqlh\hegu[m^ml\uoh^blvbalhq_d : b K \ ijhlb\hiheh`guo nZaZo lh wlb \hegu ijb keh`_gbb [m^ml ]Zkblv ^jm] ^jm]Z < j_amevlZl_ \hagbdg_l fbgbfmf bgl_jn_j_gpbhgghcdZjlbgu²l_fgZyihehkZ 5. Wlhlhiul^hdZau\Z_llhqlhk\_lh[eZ^Z_l\hegh\ufbk\hckl\Zfb 6. QZklhlu beb^ebgu k\_lh\uo\hegjZaguop\_lh\jZaebqgu

§54.

1. < \b^_mijm]bo\hegih^h[gha\mdh\uf 2. L_fqlhk\_ljZkijhkljZgy_lkyb \\Zdmmf_ 3. FZdk\_ee ij_^iheh`be qlh k\_l ² wlh qZklguc kemqZc we_dljhfZ]gblguo \heg Hkgh\Zgb_f ^ey wlh]h ihkem`beh lh qlh k\_lh\u_ b we_dljhfZ]gblgu_ \hegu y\eyxlky ihi_j_qgufb b h[eZ^Zxlh^bgZdh\hckdhjhklvxjZkijhkljZg_gby 4. QZklbpZwe_dljhfZ]gblgh]hbaemq_gbygZau\Z_lkynhlhghf

§55.

1. Hldjulb_ ;_dd_j_ey khklhyeh \ lhf qlh g_dhlhju_ \_s_kl\Z kZfhijhba\hevgh baemqZxl g_\b^bfu_ emqb gZa\Zggu_ \ihke_^kl\bbjZ^bhZdlb\gufbaemq_gb_f 2. JZ^bhZdlb\ghklvx 3. <  ] Wjg_kl J_a_jnhj^ hiulguf iml_f h[gZjm`be qlh jZ^bhZdlb\gh_ baemq_gb_ jZ^by g_h^ghjh^gh b bf__l keh`guc khklZ\ < lheklhkl_gguc k\bgph\uc khkm^ hg ihf_sZe djmibgdm 28


jZ^by Imqhd jZ^bhZdlb\gh]h baemq_gby jZ^by ijhoh^be kd\hav madh_ hl\_jklb_ b ihiZ^Ze gZ nhlhieZklbgdm Ihke_ ijhy\e_gby nhlhieZklbgdb gZ g_c h[gZjm`behkv h^gh iylgh AZl_f hiul \b^hbaf_gyeb L_i_jv imqhd baemq_gby ijhoh^be q_j_a h[eZklv fZ]gblgh]h ihey ij_`^_ q_f ihiZklv gZ nhlhieZklbgdm < j_amevlZl_ fZ]gblgh_ ihe_ jZa^_eyeh wlhl imqhd gZ ljb b gZ nhlhieZklbgd_ ihke_ ijhy\e_gby h[gZjm`b\Zehkv ljb iylgZ ² h^gh ih p_gljm ^\Z k[hdm hl g_]h Wlh ]h\hjbl h lhf qlh imqhd baemq_gby khklZ\eyeb iheh`bl_evgh aZjy`_ggu_ αqZklbpu  hljbpZl_evgh aZjy`_ggu_ βqZklbpu  b g_cljZevgu_ γqZklbpu

qZklbpu 4. αqZklbpZ ij_^klZ\ey_l kh[hc iheghklvx bhgbabjh\Zgguc Zlhf ]_eby k aZjy^hf jZ\guf fh^mex m^\h_ggh]h aZjy^Z we_dljhgZ βqZklbpZ ² we_dljhg γqZklbpZ ² h^bg ba ^bZiZahgh\ we_dljhfZ]gblgh]hbaemq_gby 5. H keh`ghfkljh_gbbZlhfZ

§56.

1. Kh]eZkgh fh^_eb ij_^eh`_gghc Lhfkhghf Zlhf ij_^klZ\eye rZj ih \k_fm h[t_fm dhlhjh]h jZ\ghf_jgh jZkij_^_e_g iheh`bl_evguc aZjy^ <gmljb wlh]h gZoh^ylky we_dljhgu dZ`^uc badhlhjuodhe_[e_lkyhdhehk\h_]hiheh`_gbyjZ\gh\_kby 2. < k\bgph\uc khkm^ K ihf_sZeky jZ^bhZdlb\guc we_f_gl J baemqZxsbc αqZklbpu Ba wlh]h khkm^Z αqZklbpu \ue_lZeb kh kdhjhklvx  dfk b ihke_ ihiZ^Zeb gZ wdjZg W ]^_ hgb j_]bkljbjh\Zebkv WdjZg [ue ihdjul ki_pbZevguf \_s_kl\hf [eZ]h^Zjy q_fm \ f_klZo ihiZ^Zgby gZ g_]h αqZklbp \hagbdZeb \kiurdb dhlhju_ j_]bkljbjh\Zebkv ijb ihfhsb fbdjhkdhiZ F LZdhc kihkh[ j_]bkljZpbb gZau\Z_lky f_lh^hf kpbglbeeypbc \kiur_d  Ihke_ \ky wlZ mklZgh\dZ ihf_sZeZkv \ khkm^ ba dhlhjh]h [ue hldZqZg \ha^mo b ijh\h^beky hiul ?keb gZ imlb αqZklbpg_lgbdZdboij_]jZ^lhhgbihiZ^ZebgZwdjZgmadbfke_]dZ jZkrbjyxsbfky imqdhf Ijb wlhf gZ wdjZg_ gZ[ex^Z_lky g_[hevrh_ k\_lh\h_ iylgh ?keb `_ l_i_jv ihklZ\blv gZ imlb αqZklbp lhgdmx nhev]m N lh ijb \aZbfh^_ckl\bb k \_s_kl\hf hgb [m^mljZkk_b\Zlvkyih\k_fgZijZ\e_gbyfgZjZagu_m]euHkgh\gZy qZklv αqZklbp ijhreZ kd\hav nhev]m fZeh baf_gb\ k\h_]h i_j\hgZqZevgh]h gZijZ\e_gby Gh g_[hevrZy qZklv αqZklbp jZkk_yeZkvgZm]euihjy^dZ°Z g_dhlhju_^Z`_gZm]eu ihjy^dZ 180°. 29


3. J_a_jnhj^ ijbr_e d \u\h^m qlh klhev kbevgh_ hldehg_gb_ αqZklbp \hafh`gh lhevdh lh]^Z dh]^Z \gmljb ZlhfZ bf__lky hq_gv kbevgh_we_dljbq_kdh_ihe_LZdh_kbevgh_ihe_lhevdhfh]eh[ulv kha^Zgh aZjy^hf kdhgp_gljbjh\Zgguf \ hq_gv fZehf h[t_f_ ih kjZ\g_gbx k h[t_fhf ZlhfZ Bkoh^y ba \k_]h wlh]h J_a_jnhj^ ij_^eh`be ieZg_lZjgmx fh^_ev ZlhfZ Kh]eZkgh wlhc fh^_eb \ p_glj_ ZlhfZ gZoh^blky iheh`bl_evgh aZjy`_ggh_ y^jh dhlhjh_ b [ueh ijbqbghc kbevgh]h hldehg_gby αqZklbp <hdjm] y^jZ ^\b`mlkywe_dljhgufZkkZdhlhjuofgh]hf_gvr_fZkkuy^jZ 4. Kh]eZkgh y^_jghc fh^_eb \ p_glj_ ZlhfZ gZoh^blky iheh`bl_evgh aZjy`_ggh_ y^jh <hdjm] y^jZ ^\b`mlky we_dljhgu fZkkZdhlhjuofgh]hf_gvr_fZkkuy^jZ 5. ?keb αqZklbpZ ijhe_lZ_l hq_gv [ebadh d y^jm lh hgZ kbevgh hldehgy_lky hl i_j\hgZqZevgh]h gZijZ\e_gby ^\b`_gby dmehgh\kdhc kbehc Ld jZaf_ju y^jZ hq_gv fZeu ih kjZ\g_gbx k jZaf_jZfbZlhfZlhhkgh\gZyqZklvαqZklbpijhe_lZ_l^hklZlhqgh ^Ze_dhhly^jZb g_bkiulu\Z_lkbevgh]hhldehg_gby

§57.

1. JZ^bcij_\jZsZ_lky\ jZ^hg 2. Ijhbkoh^blij_\jZs_gb_h^gh]hobfbq_kdh]hwe_f_glZ\ ^jm]hc 3. Y^jh 222 4 4 226 4. 226 88 Rd â&#x2020;&#x2019; 86 Rn + 2 He  ]^_ 2 He â&#x20AC;&#x201D; αqZklbpZ 88 Rd ² y^jh

jZ^by 222 86 Rn ²y^jhjZ^hgZ 5. <_jog__qbkeh²fZkkh\h_qbkehgb`g__²aZjy^h\h_qbkeh 6. FZkkh\h_qbkehy^jZZlhfZ^Zggh]hobfbq_kdh]hwe_f_glZjZ\gh k lhqghklvx^hp_euoqbkemZlhfguo_^bgbpfZkkukh^_j`Zsboky \ fZkk_ wlh]h y^jZ AZjy^h\h_ qbkeh y^jZ ZlhfZ ^Zggh]h obfbq_kdh]h we_f_glZ jZ\gh aZjy^m y^jZ \ujZ`_gghfm \ we_f_glZjguowe_dljbq_kdboaZjy^Zo 222 4 7. 226 88 Rd â&#x2020;&#x2019; 86 Rn + 2 He Ba^Zgghcj_Zdpbb\b^ghqlh\uihegyxlky aZdhgu khojZg_gby fZkkh\h]h qbkeZ b aZjy^Z >_ckl\bl_evgh fZkkh\h_qbkeh  b aZjy^  jZkiZ^Zxs_]hkyy^jZZlhfZjZ^by jZ\gu khhl\_lkl\_ggh kmff_ fZkkh\uo qbk_e       b kmff_ aZjy^h\       h[jZah\Z\rboky \ j_amevlZl_ jZkiZ^Z Zlhfh\jZ^hgZb ]_eby 8. Y^jZZlhfh\bf__lkeh`gh_kljh_gb_ 9. JZ^bhZdlb\ghklvxgZau\Zxlkihkh[ghklvy^_jZlhfh\g_dhlhjuo obfbq_kdbo we_f_glh\ kZfhijhba\hevgh ij_\jZsZlvky \ ^jm]b_ y^jZk bkimkdZgb_fqZklbp 30


§58.

1. Kq_lqbd =_c]_jZ khklhbl ba ]_jf_lbqghc kl_deygghc ljm[db aZiheg_gghc jZaj_`_gguf ]Zahf gZijbf_j Zj]hghf < g__ \iZygu we_dljh^u dZlh^ b Zgh^  ih^dexq_ggu_ q_j_a khijhlb\e_gb_ R d bklhqgbdm \ukhdh]h gZijy`_gby Ijbgpbi kq_lqbdZ =_c]_jZ ke_^mxsbc Ijb ijhe_l_ \gmljb ljm[db dZdhcgb[m^v [ukljhc qZklbpu kihkh[ghc bhgbabjh\Zlv Zlhfu ]ZaZ h[jZam_lky g_dhlhjh_ qbkehwe_dljhgbhgguoiZjWe_dljhgugZqbgZxl^\b]Zlvkyd Zgh^mZ iheh`bl_evgu_ bhgu ² d dZlh^m ?keb gZijy`_gghklv ihey ^hklZlhqgh\_ebdZlhwe_dljhgmkdhjyykvfh`_lijbh[j_klbwg_j]bx ^hklZlhqgmx ^ey bhgbaZpbb Zlhfh\ ]ZaZ <gh\v h[jZah\Z\rb_ we_dljhgumkdhjyxlkyihe_fb \k\hxhq_j_^vijhba\h^ylbhgbaZpbx ^Z\Zy gZqZeZ gh\uf we_dljhgZf b bhgZf < ljm[d_ h[jZam_lky lZd gZau\Z_fZy we_dljhgghbhggZy eZ\bgZ < j_amevlZl_ wlh]h \ ljm[d_ \hagbdZ_l jZajy^ b \ p_ib kq_lqbdZ ijhbkoh^bl djZldh\j_f_ggh_ b j_adh_ \hajZklZgb_ kbeu lhdZ dhlhjh_ j_]bkljbjm_lky ki_pbZevguf mkljhckl\hf JZajy^ ^eblky ijbf_jgh fbdjhk_dmg^m b aZl_f ij_djZsZ_lky ld hkgh\gZy qZklv gZijy`_gby iZ^Z_l gZ khijhlb\e_gbb R b \ j_amevlZl_ wlh]h gZijy`_gb_ f_`^m dZlh^hf b Zgh^hfj_adhmf_gvrZ_lky 2. >eyj_]bkljZpbbwe_dljhgh\b γd\Zglh\ 3. DZf_jZ <bevkhgZ khklhbl ba pbebg^jZ KK kh kl_deygghc djurdhcLL<gmljbpbebg^jZfh`_li_j_f_sZlvkyihjr_gvPGZ ^g_ dZf_ju e_`bl q_jgZy ijhiblZggZy kf_kvx \h^u kh kibjlhf ldZgv FF [eZ]h^Zjy dhlhjhc \ dZf_j_ \ha^mo gZkus_g < dZf_j_ hlkmlkl\mxl y^jZ dhg^_gkZpbb Ijbgpbi ^_ckl\by dZf_ju <bevkhgZke_^mxsbc< j_amevlZl_j_adh]h^\b`_gbyihjrgy\gba l_fi_jZlmjZ \ g_c iZ^Z_l b iZju \gmljb klZgh\ylky i_j_kus_ggufb l_ hgb l_i_jv fh]ml e_]dh dhg^_gkbjh\Zlvky gZ y^jZo dhg^_gkZpbb gZijbf_j gZ bhgZo Q_j_a lhgdh_ hdhrdh dZf_ju \imkdZ_lky imqhd bkke_^m_fuo qZklbp dhlhjuc ijhe_lZy q_j_a ]Za kha^Z_l gZ k\h_f imlb bhgu y^jZ dhg^_gkZpbb  IZju dhg^_gkbjmxlky gZ bhgZo b \ blh]_ \^hev ljZ_dlhjbb ^\b`_gby qZklbpu h[jZam_lky \b^bfuc ke_^ ba dZi_e_d iZjZ lj_d  LZdbf h[jZahf k ihfhsvx dZf_ju <bevkhgZ fu fh`_f magZlv ljZ_dlhjbx^\b`_gbyqZklbpu 4. ?kebdZf_jm<bevkhgZihf_klblv\ fZ]gblgh_ihe_lhhij_^_eb\ ljZ_dlhjbx ^\b`_gby qZklbpu fu fh`_f hij_^_eblv agZd aZjy^Z qZklbpu ih gZijZ\e_gbx ba]b[Z  __ fZkkm wg_j]bx aZjy^ ih jZ^bmkmdjb\baguljZ_dlhjbb 

31


5. Imaujvdh\Zy dZf_jZ h[eZ^Z_l [hevrbf [ukljh^_ckl\b_f \ hlebqb_ hl dZf_ju <bevkhgZ Imaujvdh\Zy dZf_jZ hlebqZ_lky hl dZf_ju <bevkhgZ l_f qlh \ g_c \f_klh i_j_kus_ggh]h iZjZ ijbf_gy_lkyi_j_]j_lZy\ur_lhqdbdbi_gby`b^dhklv 1. Hiul aZdexqZ_lky \ bkke_^h\Zgbb \aZbfh^_ckl\by ฮฑqZklbp k y^jZfbZlhfh\ZahlZE_lysZyk [hevrhckdhjhklvxฮฑqZklbpZ ijb ihiZ^Zgbb \ y^jh ZlhfZ ZahlZ \u[b\ZeZ ba g_]h y^jh ZlhfZ \h^hjh^Zdhlhjh_J_a_jnhj^gZa\Zeijhlhghf 2. H lhfqlh\ j_amevlZl_\aZbfh^_ckl\byฮฑqZklbpk y^jZfbZlhfh\ ZahlZh[jZah\Zebkvy^jZdbkehjh^Zb \h^hjh^Z 3. Y^jh ZlhfZ \h^hjh^Z 11 G bgZq_ gZau\Z_lky ijhlhghf b

ยง59.

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ยง60.

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ยง61.

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ยง68.

35


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ยง69.

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ยง70.

36


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t

5. >eyl_eZ,Z fk2^eyl_eZ,,Z fk2. 1. >Zgh t=5c Zo fk2 v0o dfq fk GZclbsx. 2. >Zgh t = 20 c Zo fk2 v0o fk GZclbsx. 1. >Zgh s3 f t1 k GZclb s1, a. 2. >Zgh s5 f t1 k t5 k

MijZ`g_gb_ 

J_r_gb_ sx = v0 o t +

axt 2 2

fk â&#x2039;&#x2026; k

f Hl\_lsx f

0,5 fk 2 â&#x2039;&#x2026; (5 k ) = 2 2

J_r_gb_

axt 2 v v t2 v t ; ao = â&#x2C6;&#x2019; 0 x â&#x2021;&#x2019; sx = v0 o t â&#x2C6;&#x2019; 0 x = 0 x = 2 t 2t 2 fk â&#x2039;&#x2026; k  f Hl\_lsx f sx = v0 o t +

MijZ`g_gb_ 

J_r_gb_ s1 : s2 : s3 = 1 : 3 : 5; s1 : 2 f = 1 : 5 â&#x2021;&#x2019; s1 = 2 f 5 = 0,4 f; at12 2s 2 â&#x2039;&#x2026; 0,4 f = 0,8 f/k2. â&#x2021;&#x2019; a = 21 = 2 2 t1 (1 k) Hl\_ls1 fa fk2. s1 =

J_r_gb_ s1 : s2 : s3 : s4 : s5 = 1 : 3 : 5 : 7 : 9; s1 : 6,3 f = 1 : 9 â&#x2021;&#x2019; â&#x2021;&#x2019; s1 = 6,3 f 5 = 0,7 f; at12 2s 2 â&#x2039;&#x2026; 0,7 f = 1,4 f/k2; â&#x2021;&#x2019; a = 21 = 2 t1 (1 k)2 v5 = at5 fk2 â&#x2039;&#x2026; k fk Hl\_lv5 fk s1 =

GZclbv5.

41


MijZ`g_gb_ 

1. fk 2. G_l ihkdhevdm b ^_j_\h b \hdaZe `_kldh k\yaZgu k ^jm]hc kbkl_fhchlkq_lZ²A_fe_c 3. Ijbmkeh\bbg_ih^\b`ghklbwlbol_ehlghkbl_evgh^jm]^jm]Z 4. dfq fk 5*. >Zgh J_r_gb_ v1 dfq fk v\ = v1 + v2 fk fk fk v2 fk va = v2 â&#x20AC;&#x201C; v1 fk ±fk fk GZclbv\, va. Hl\_lv\ fkva fk

MijZ`g_gb_ 

AZdhgbg_jpbb\uihegy_lky\ kbkl_f_hlkq_lZk\yaZgghck A_fe_cb \ kbkl_f_ hlkq_lZ k\yaZgghc k ih_a^hf \h \j_fy _]h ijyfhebg_cgh]h b jZ\ghf_jgh]h ^\b`_gby g_ \uihegy_lky \ kbkl_f_ hlkq_lZ k\yaZgghc k ih_a^hf \h \j_fy _]h lhjfh`_gby Bg_jpbZevghckbkl_fhcfh`ghkqblZlva_fexZ ih_a^²g_evay

MijZ`g_gb_

1. >Zgh J_r_gb_ Z fk2 IhhfmaZdhgmGvxlhgZ m d] F = ma d]â&#x2039;&#x2026; fk2 G GZclbF. Hl\_lF G 2. >Zgh J_r_gb_ t = 20 c F = ma ²hcaZdhgGvxlhgZ v fk v mv 1,84 â&#x2039;&#x2026; 10 5 d] â&#x2039;&#x2026; 4 fk 5 = = = = a â&#x2021;&#x2019; F m l â&#x2039;&#x2026;10 d] 20 k t t G dG GZclbF. Hl\_lF dG 3. >Zgh J_r_gb_ IhhfmaZdhgmGvxlhgZ m1 = m2 a1 fk2 F1 = m1a1; F2 = m2a2. Ldm1 = m2lhihemqZ_f a2 fk2 F1 F2 a F 0,64 fk 2 â&#x2039;&#x2026; 1,2 G = â&#x2021;&#x2019; F2 = 2 1 = = 9,6 H. F1 = 1,2 H a1 a 2 a1 0,08 fk 2 GZclbF2.

Hl\_lF2 G

42


4. >Zgh m = 0,5 d] FA = 10 H FL = 5 H FC = 2 H

J_r_gb_ IhhfmaZdhgmGvxlhgZF = ma. F = FA â&#x20AC;&#x201C; FL â&#x20AC;&#x201C; FC â&#x2021;&#x2019; FA â&#x20AC;&#x201C; FL â&#x20AC;&#x201C; FC = ma â&#x2021;&#x2019; F â&#x2C6;&#x2019; FL â&#x2C6;&#x2019; FC 10 H â&#x2C6;&#x2019; 5 H â&#x2C6;&#x2019; 2 H fk2. â&#x2021;&#x2019;a = A = m 0,5 d] GZclbF2. Hl\_la fk2. 5. Ijb ^\b`_gbb \\_jo kdhjhklv b i_j_f_s_gb_ ijhlb\hiheh`gh gZijZ\e_gu k kbehc ly`_klb mkdhj_gb_ ² khgZijZ\e_gh Ijb ^\b`_gbb\gbakdhjhklvi_j_f_s_gb_b mkdhj_gb_khgZijZ\e_guk kbehcly`_klb 6. Mkdhj_gb_ \k_]^Z khgZijZ\e_gh k jZ\gh^_ckl\mxs_c ijbeh`_gguo d l_em kbe Kdhjhklv b i_j_f_s_gb_ fh]ml [ulv dZd khgZijZ\e_gu k jZ\gh^_ckl\mxs_c ijbeh`_gguo d l_em kbe lZd b ijhlb\hiheh`ghgZijZ\e_gu

MijZ`g_gb_

U U 1. GZ l_eh ^_ckl\mxl kbeZ ly`_klb Fl b kbeZ j_Zdpbb hihju N kfjbk  U N

U Fl

2. G_ ij_\ukbl ld jZ\gh^_ckl\mxsZy ijbeh`_gguo kbe gZ ^bgZfhf_ljjZ\gZ 3. >Zgh J_r_gb_  IhhfmaZdhgmGvxlhgZ m1 d] m2 d] F2x = m2ax d]â&#x2039;&#x2026; fk2 G a fk2 IhfmaZdhgmGvxlhgZF1x = â&#x20AC;&#x201C;F2x ±G  IhhfmaZdhgmGvxlhgZ F1x = m1ax d]â&#x2039;&#x2026; fk2 G IhfmaZdhgmGvxlhgZF2x = â&#x20AC;&#x201C;F1x ±G   < i_j\hf kemqZ_ gblv f_`^m l_e_`dZfb gZlygmlZ kbevg__  IhhfmaZdhgmGvxlhgZ Fx = (m1 + m2)ax  d]d] â&#x2039;&#x2026; fk2 G GZclb F1x, Hl\_l F1x ±GF2x G F1x GF2x = ±G \ i_j\hfkemqZ_ Fx G F2x, Fx. 43


1. >Zgh g â&#x2030;&#x2C6; fk2 t=2c

J_r_gb_

gt 2 10 fk 2 â&#x2039;&#x2026; (2 k ) = 2 2 Hl\_lh f

2

h=

GZclbh. 2. >Zgh g â&#x2030;&#x2C6; fk2 h = 80 cf f GZclbt. 3. >Zgh g â&#x2030;&#x2C6; fk2 h = 45 f t1 = 1 c â&#x2C6;&#x2020;t = 1 c

GZclb t, s1, s2. >Zgh v fk v1 = 0 g fk2 GZclbt, s.

MijZ`g_gb_ f

J_r_gb_

gt 2 2h 2 â&#x2039;&#x2026; 0,8 f â&#x2021;&#x2019;t= = = 0,4 k. 2 g 10 fk 2 Hl\_lt k h=

J_r_gb_ h=

gt 2 2h 2 â&#x2039;&#x2026; 45 f â&#x2021;&#x2019;t= = 2 g 10 fk 2

k

gt12 10 fk 2 â&#x2039;&#x2026; (1 k )2 = = 5 f; 2 2 2 gt 2 g (t â&#x2C6;&#x2019; ût ) s2 = â&#x2C6;&#x2019; = 2 2 2 2 10 fk 2 â&#x2039;&#x2026; (3 k ) 10 fk 2 â&#x2039;&#x2026; (3 c â&#x2C6;&#x2019; 1 c ) = â&#x2C6;&#x2019; =5f 2 2 Hl\_lt ks1 fs2 f s1 =

MijZ`g_gb_

J_r_gb_ v â&#x2C6;&#x2019; v1 v v 9,8 fk g= = â&#x2021;&#x2019;t= = =1 c; t t g 9,8 fk 2

gt 2 9,8 fk 2 â&#x2039;&#x2026; (1k ) fk â&#x2039;&#x2026; k ± 2 2 Hl\_lt ks f

2

s = vt â&#x2C6;&#x2019;

f

MijZ`g_gb_

1. <k_l_eZiZ^ZxlgZa_fexih^^_ckl\b_fkbeuly`_klb 2. KlZgpby m^Zey_lky hl A_feb ijb[eb`Zykv d Emg_ BaaZ baf_g_gbc jZkklhygbc f_`^m ieZg_lZfb b klZgpb_c kbeZ __ ijbly`_gby d A_fe_ mf_gvrZ_lky Z kbeZ ijbly`_gby d Emg_ 44


m\_ebqb\Z_lky Dh]^Z klZgpby gZoh^blky gZ k_j_^bg_ hgZ kbevg__ ijbly]b\Z_lkyd A_fe_ldfZkkZA_feb[hevr_fZkkuEmgu 3. G_l 4. Z ^_ckl\h\ZeZ[ ijbly`_gb_A_feb\ baaZ^_ckl\bykbeuly`_klb 5. >Zijbly]b\Z_lky ghwlZkbeZ]hjZa^hf_gvr_kbeuly`_klb ba aZjZkklhygbcEmgZlZd`_ijbly]b\Z_lkyd wlhfmq_eh\_dm 1. >Zgh g â&#x2030;&#x2C6; fk2 m1 d] m2 ] d] m3 l d] m4 l d]

GZclb Fl1, Fl2, Fl3, Fl4. 2. >Zgh g â&#x2030;&#x2C6; fk2; m d] GZclbFl. 3. >Zgh g â&#x2030;&#x2C6; fk2; Fl G

MijZ`g_gb_

J_r_gb_ Fl = mg â&#x2021;&#x2019; Fl fk2 â&#x2039;&#x2026; d] G Fl fk2 â&#x2039;&#x2026; d] G Fl fk2 â&#x2039;&#x2026; d] G dG Fl fk2 â&#x2039;&#x2026; d] â&#x2039;&#x2026;105 G dG Hl\_lGGdGdG J_r_gb_ Fl = mg d]â&#x2039;&#x2026; fk2 G Hl\_lFl G J_r_gb_

Fl 819,3 G d] = g 10 fk 2 GZclbFl. Hl\_lm d] 4. G_lihkdhevdm\ukhlZihe_lZkjZ\gbfZk jZaf_jZfbA_febKbem F a mj ly`_klb fh`gh jZkkqblZlv ih nhjfme_ Fl = G  ]^_ h â&#x20AC;&#x201D; ( Ra + h) 2 \ukhlZgZ^A_fe_c 5. GZyklj_[Z^_ckl\m_lkbeZly`_klbb _kebhgkeh`bldjuevylh hgmiZ^_lgZA_fex 1 6. GZjZkklhygbbRa; 3Ra (Ra ²jZ^bmkA_feb ihkdhevdmFl~ (Ra + h)2 Fl = mg â&#x2021;&#x2019; m =

MijZ`g_gb_

U 1. KbeZ F fh]eZ^_ckl\h\Zlvlhevdh\ gZijZ\e_gbb 2. KbeZ ^_ckl\h\ZeZ gZ rZjbd gZ mqZkldZo     RZjbdih\hjZqb\Zekyih^^_ckl\b_f\g_rgbokbe 3. KbeZ^_ckl\h\ZeZgZl_ehgZ\_jgydZgZmqZkldZo:<&'GZl_eh fh]eZ^_ckl\h\ZlvkbeZb gZhklZevguomqZkldZo 45


MijZ`g_gb_

1. >Zgh r kf f v fk GZclba. 2. >Zgh R kf f T k

GZclba. 3. Z1 =

J_r_gb_

v 2 (20 fk )2 = â&#x2030;&#x2C6; fk2. r 0,21 f Hl\_lZ â&#x2030;&#x2C6; fk2. Z=

J_r_gb_ Z=

v2 l 2Ï&#x20AC;R 4Ï&#x20AC; 2 R 2 4Ï&#x20AC; 2 R ;v= = â&#x2021;&#x2019;Z= 2 = 2 = R T T T R T 2 4 â&#x2039;&#x2026; (3,14 ) â&#x2039;&#x2026; 0,02 f = â&#x2030;&#x2C6; 2â&#x2039;&#x2026;10-4 fk2. (60 k )2 Hl\_lZ â&#x2030;&#x2C6; 2â&#x2039;&#x2026;10-4 fk2.

v2 v2 v2 ; Z2 = = 2a1 â&#x2021;&#x2019; ml\_j`^_gb_\_jgh = 2â&#x2039;&#x2026; r r/2 r

4. >Zgh T1 k T2 k

J_r_gb_ v 2 (2Ï&#x20AC;R T1 )2 4Ï&#x20AC; 2 R 4Ï&#x20AC; 2 R a1 = 1 = . :gZeh]bqgh a 2 = . = 2 R R T1 T22 Ke_^h\Zl_evgh

GZclb

a1 . a2

Hl\_l

5. >Zgh Fa = 6â&#x2039;&#x2026;1024 d] Fe = 6â&#x2039;&#x2026;1022 d]

G â&#x2039;&#x2026; f2

d] 2 r = df = 3,84â&#x2039;&#x2026;108 f G=6,67â&#x2039;&#x2026;10-11

GZclbF]j, Zp, v.

2

a1  T1   3600 c  =   =   = 3600. a 2  T2   60 c  2

a1 = 3600. a2

J_r_gb_ Z F]j = G Ã&#x2014;

F aF e 2

= 6,67â&#x2039;&#x2026;10-11

r 6 â&#x2039;&#x2026; 10 24 d] â&#x2039;&#x2026; 7 â&#x2039;&#x2026;10 22 d] (3,84 â&#x2039;&#x2026; 10 8 f 2

[ Zp =

F]j

Fa

=

G â&#x2039;&#x2026; f2 d] 2

Ã&#x2014;

â&#x2030;&#x2C6; 1,9â&#x2039;&#x2026;1020 G

1,9 â&#x2039;&#x2026; 10 20 G 6 â&#x2039;&#x2026; 10 24 d]

â&#x2030;&#x2C6; 3,17â&#x2039;&#x2026;10-5 fk2;

\ v = ap r = 3,17 â&#x2039;&#x2026;10â&#x2C6;&#x2019;5 fk2 â&#x2039;&#x2026; 3,84â&#x2039;&#x2026;108 f â&#x2030;&#x2C6;fk Hl\_lF]j â&#x2030;&#x2C6; 1,9â&#x2039;&#x2026;1020 Gv â&#x2030;&#x2C6; fk Zp = 3,17â&#x2039;&#x2026;10-5 fk2.

46


MijZ`g_gb_ 1. >Zgh h df â&#x2039;&#x2026;106 f Fa = 6â&#x2039;&#x2026;1024 d] Ra = 6,4â&#x2039;&#x2026;106 f G = 6,67â&#x2039;&#x2026;10-11

G â&#x2039;&#x2026; f2 d] 2

J_r_gb_ Ma vâ&#x2030;&#x2C6; G = Ra + h = 6,67 â&#x2039;&#x2026; 10â&#x2C6;&#x2019;11

G â&#x2039;&#x2026; f2 d] 2

â&#x2039;&#x2026;

6 â&#x2039;&#x2026; 1024 d]

(2,6 â&#x2039;&#x2026; 106 f + 6,4 â&#x2039;&#x2026; 106 f

fk dfk GZclbv. Hl\_lv dfk 2. >Zgh J_r_gb_ v dfk â&#x2039;&#x2026;103 fk v2 v2 1,67 â&#x2039;&#x2026;10 3 fk re = â&#x2021;&#x2019; re = = ge â&#x2030;&#x2C6; fk2 re ge 1,6 fk 2 = 1,7â&#x2039;&#x2026;106 f â&#x2039;&#x2026;103 df GZclb re. Hl\_lre = 1,7â&#x2039;&#x2026;103 df

(

)

=

2

=

MijZ`g_gb_ 1. >Zgh v1x = â&#x20AC;&#x201C;v2x fk m = 0,2 d] GZclb p1x, p2x. 2. >Zgh v1 dfq fk v2 dfq fk m l d] GZclb â&#x2C6;&#x2020;p.

J_r_gb_ p1x = mv1x d]â&#x2039;&#x2026; fk d]â&#x2039;&#x2026;fk p2x = â&#x20AC;&#x201C; p1x ±d]â&#x2039;&#x2026;fk <_dlhjubfimevkh\fZrbgg_jZ\guldhgb ijhlb\hiheh`gh gZijZ\e_gu Fh^meb \_dlhjh\bfimevkh\jZ\gu Hl\_lp1x d]â&#x2039;&#x2026;fkp2x ±d]â&#x2039;&#x2026;fk J_r_gb_ â&#x2C6;&#x2020;j = mâ&#x2C6;&#x2020;v = m(v2 â&#x20AC;&#x201C; v1) = d]â&#x2039;&#x2026; fk ± fk  d]â&#x2039;&#x2026;fk Hl\_lâ&#x2C6;&#x2020;p d]â&#x2039;&#x2026;fk

MijZ`g_gb_

1. Ih aZdhgm khojZg_gby bfimevkZ eh^dZ gZqg_l ^\b]Zlvky \ klhjhgmijhlb\hiheh`gmx^\b`_gbxq_eh\_dZ 47


2. >Zgh m1 l m2 l v2 fk GZclb v1. 1. >Zgh ve fk m\ d] v\ fk me d]

J_r_gb_ AZibr_faZdhgkhojZg_gbybfimevkZ m + m2 v2 = m1v1 = (m1 + m2)v2 â&#x2021;&#x2019; v1 = 1 m1 35 l + 28 l = â&#x2039;&#x2026; 0,5 fk fk 35l Hl\_lv1 fk J_r_gb_ AZibr_faZdhgkhojZg_gbybfimevkZ ( m + m\ ) v e + m\ v \ (me + m\)ve + m\v\ = mev â&#x2021;&#x2019; v = e = me (200 d] + 5 d] )â&#x2039;&#x2026; 2 fk + 5 d] â&#x2039;&#x2026; 8 fk fk = 200 d] Hl\_lv fk

GZclb v. 2. >Zgh mj ] d] mi ] d] vi fk GZclb vj.

MijZ`g_gb_

J_r_gb_ AZibr_faZdhgkhojZg_gbybfimevkZ m v 0,1 d] â&#x2039;&#x2026; 100 fk mjvj=miviâ&#x2021;&#x2019;vj= i i = â&#x2030;&#x2C6; fk mj 0,3 d] Hl\_lvj â&#x2030;&#x2C6; fk

MijZ`g_gb_

1. Dhe_[Zl_evgufb kbkl_fZfb y\eyxlky [ ] _ G_ y\eyxlky dhe_[Zl_evgufbZ\^ 2. Z Ih^^_ckl\b_fkbemijm]hklbrgmjh\[ g_l\ rgmju^bkd ] ^Zy\ey_lky

MijZ`g_gb_

1. :fieblm^Z : qZklhlZ ν i_jbh^ L ² ihklhyggu_ F, v â&#x20AC;&#x201D; i_j_f_ggu_ 2. >Zgh J_r_gb_ 1 1 ν = =p T= = = 0,5 k ν 2 =p GZclb T. Hl\_lT k 48


3. >Zgh T k GZclb ν. 4. >Zgh n = 600 t fbg k

J_r_gb_ 1 1 ν= = = 2 =p T 0,5 c Hl\_lν =p

J_r_gb_ 1 t n 600 ν= ; T = â&#x2021;&#x2019;ν= = = 10 =p T n t 60 c GZclb ν. Hl\_lν =p 5. kfkfkfkf 6. >Zgh J_r_gb_ A = 10 kf 1 1 T = = = 2 c AZ  k l_eh kh\_jrZ_l ihegh_ ν = 0,5 =p ν 0,5 =p t k dhe_[Zgb_b ijhc^_limlvS = 4: kf GZclb S. Hl\_lS kf 7. Dhe_[exlky \ h^bgZdh\uo nZaZo \ kemqZyo [  ^  Dhe_[exlky \ ijhlb\hiheh`guonZaZo\ kemqZyoZ \ ] _ 

MijZ`g_gb_

GZijZ\ e_gb_ ^\b`_gby fZylgbdZ Hl< d H

mf_gv

Hl: d H

mf_gv

1.

HlH d : HlH d <

Fmij

m\_e m\_e

v m\_e

mf_gv . m\_e mf_gv .

?i

?d

mf_gv

m\_e

mf_gv

m\_e

m\_e m\_e

mf_gv mf_gv

?ihe K lj_ ;_a lj_ gb_f gby mf_gv mf_gv mf_gv mf_gv

g_ baf_g g_ baf_g g_ baf_g g_ baf_g

2. Z   >`  >` [   >`  >`  >` \   >` \h \k_o kemqZyo

MijZ`g_gb_

1. Kihkh[gu kh\_jrZlv k\h[h^gu_ dhe_[Zgby l_eZ [  _  \ugm`^_ggu_dhe_[Zgby²\k_l_eZ 2. Z ^ZgZijbf_jkljmgZfmaudZevgh]hbgkljmf_glZ[ g_l 49


MijZ`g_gb_

1. Z <ugm`^_ggu_[ [eZ]h^Zjydhe_[ZgbxfZylgbdZ\ qZklhlZ fZylgbdZ jZ\gZ qZklhl_ fZylgbdZ  m fZylgbdZ  qZklhlZ [hevr_ q_fm fZylgbdZm fZylgbdZqZklhlZf_gvr_q_fm fZylgbdZ]

ldbo^ebgub khhl\_lkl\_gghkh[kl\_ggu_qZklhlukh\iZ^Zxl 2. FZevqbdb \h^ZgZqbgZxldhe_[Zlvky\ ijhlb\hnZa_ 3. Q_j_ak L = 1/ν k  1. >Zgh λ f T k

GZclb v. 2. >Zgh ν =p v fk GZclb λ. 3. 2. >Zgh v fk λ f GZclbT.

MijZ`g_gb_

J_r_gb_ λ 270 f v= = = 20 fk T 13,5 k Hl\_lv fk

J_r_gb_ v 340 fk λ= = = 1,7 f ν 200 =p Hl\_lλ f J_r_gb_ λ 6f v= = = 4 k T 1,5 fk Hl\_lT = 4 c.

MijZ`g_gb_

E_lysZyilbpZkha^Z_lbgnjZa\mdh\u_\hegu

MijZ`g_gb_

1. DhfZjA\mdkha^Z\Z_fucbfkZfuc\ukhdbc 2. Mf_gvrblkyihkdhevdmqZklhlZ__ \jZs_gbylZd`_mf_gvrblky 3. Ijb ih\ur_gbb l_fi_jZlmju kljmgZ jZkly]b\Z_lky i_jbh^ __ dhe_[Zgbc m\_ebqb\Z_lky qZklhlZ b khhl\_lkl\_ggh \ukhlZ a\mqZgbymf_gvrZ_lky

MijZ`g_gb_

1. G_lf_`^mA_fe_cb Emghcg_lmijm]hckj_^uihdhlhjhcfh`_l jZkijhkljZgylvkya\md 2. A\mdh\u_\hegujZkijhkljZgyxlkyihgblb 50


1. >Zgh λ f T k

GZclb v. 2. >Zgh v1 fk v2 fk v3 fk ν =p

MijZ`g_gb_

J_r_gb_ λ 2,9 f v= = = 1450 fk T 0,002 k Hl\_lv fk

J_r_gb_ v 340 fk v 1483fk λ1 = 1 = â&#x2030;&#x2C6; 0,47 f; λ 2 = 2 = â&#x2030;&#x2C6; 2,05 f; 725 =p ν 725 =p ν v 5500 fk λ3 = 3 = â&#x2030;&#x2C6; 7,59 f. 725 =p ν GZclbλ1, λ2, λ3. Hl\_lλ1 â&#x2030;&#x2C6; fλ2 â&#x2030;&#x2C6; fλ3 â&#x2030;&#x2C6; f 3. A\md [m^_l jZkijhkljZgylvky b ih f_lZeem b ih \ha^mom b q_eh\_dmkeurbl^\Zm^ZjZ 4. >Zgh J_r_gb_ ta\ k Sa\ = va\ta\; SiZj = viZjtiZj; Sa\ = SiZj; va\ta\ = viZjtiZj â&#x2021;&#x2019; va\ fk v t 340 fk â&#x2039;&#x2026; 2 k â&#x2021;&#x2019; viZj = a\ a\ = = 20 fk tiZj k t iZj 34 k Sa\ = SiZj GZclbviZj. Hl\_lviZj fk 5. Dh]^Z\b^bfu_b keurbfu_m^ZjugZqbgZxlkh\iZ^Zlvkgh\Zlh wlhagZqblqlhq_eh\_dkeurblij_^u^msbci_j_^\b^bfufm^Zj

MijZ`g_gb_

1. Kms_kl\m_l 2. FZ]gblgh_ ihe_ [m^_l ^_ckl\h\Zlv gZ klj_edm k gZb[hevr_c kbehc \ lhqd_ N k gZbf_gvr_c ² \ lhqd_ F K jZkklhygb_f fZ]gblgh_ihe_hkeZ[_\Z_l

MijZ`g_gb_

1. Z ?klvwlhlhqdbD b K[ \ lhqd_:. 2. GZ iZju lhq_d P â&#x2C6;&#x2019; Q, X â&#x2C6;&#x2019; Y kh klhjhgu g_h^ghjh^gh]h fZ]gblgh]h ihey ^_ckl\mxl kbeu h^bgZdh\u_ , dZd ih fh^mex lZd b ih gZijZ\e_gbx ld PO = QO, XO = , YO.

3 2 ;

<

4

51


MijZ`g_gb_ 1.

2.

3. K_\_jguc ihexk gZoh^blky kijZ\Z Z x`guc ke_\Z Bo iheh`_gb_fh`ghbaf_gblvihf_gy\iheyjghklvkhe_ghb^Z 4. Lhd[m^_ll_qvhllhqdbS d lhqd_N. 5. KijZ\Z ² k_\_jguc ihexk ke_\Z ± x`guc ih ijZ\bem ijZ\hc jmdb  6. < i_j\hf kemqZ_ \aZbfh^_ckl\b_ h[mkeh\e_gh fZ]gblgufb kbeZfb\h\lhjhf±dmehgh\kdbfb

MijZ`g_gb_

1. IhijZ\beme_\hcjmdbhij_^_ey_fqlh\ijZ\h 2. Ih ijZ\bem e_\hc jmdb hij_^_ey_f qlh lhd l_q_l hl lhqdb B d lhqd_ A b ke_^h\Zl_evgh \_jogbc ihexk bklhqgbdZ lhdZ ih^dexq_g d hljbpZl_evghfm ihexkm Z gb`gbc ² d iheh`bl_evghfm

52


3. GZ e_\hf jbkmgd_ e_\uc ijh\h^gbd ^\b`_lky \\_jo ijZ\uc ijh\h^gbd²\gbaGZijZ\hfjbkmgd_e_\ucijh\h^gbd^\b`_lky \gbaijZ\ucijh\h^gbd²\\_jo 4.

U v

U F

5. Ih ijZ\bem e_\hc jmdb hij_^_ey_f qlh wlh iheh`bl_evgh aZjy`_ggZyqZklbpZ 1. >Zgh I = 4 A; F = 0,2 H l kf f

MijZ`g_gb_

J_r_gb_ F 0,2 G B= = = 0,5 Le Il 0,1 f â&#x2039;&#x2026; 4 : GZclbB. Hl\_lB Le 2. FZ]gblgZy bg^mdpby g_ baf_gy_lky hgZ ihklhyggZy \_ebqbgZ Baf_gy_lkylhevdhkbeZ^_ckl\mxsZygZijh\h^gbd²hgZlZd `_ dZdb lhdmf_gvrZ_lky\ jZaZ

MijZ`g_gb_

FZ]gblguc ihlhd ijhgbau\Zxsbc dZlmrdm D2 fh`gh f_gylv iml_fbaf_g_gby\aZbfghchjb_glZpbbdZlmr_db baf_g_gb_fkbeu lhdZj_hklZlhfR bebaZfudZgb_fjZafudZgb_fdexqZD

MijZ`g_gb_

1. Baf_gblvfZ]gblgucihlhdq_j_adZlmrdmD2 iml_fhibkZgguf\ mijZ`g_gbb 2. Bg^mdpbhgguclhd\hagbdZ_l\ kemqZ_] g_\hagbdZ_l\ kemqZyo Z [ \ ^  1. >Zgh

J_r_gb_

MijZ`g_gb_

53


ν =p

1 1 = = 0,02 k ν 50 =p GZclb T. Hl\_lT k 1 1 1 =p 2. Ih]jZnbdmgZoh^bfqlhT= k , ν= = 60 T (1 60 )c : f: T=

MijZ`g_gb_

Wlbiheygbq_fg_hlebqZxlkyb kms_kl\h\Zeb[u[_adZlmrdbK

MijZ`g_gb_ 1. >Zgh T = 10-7 c GZclbν. 2. >Zgh t = 8,3â&#x2039;&#x2026;10-7 c c = 3â&#x2039;&#x2026;108 fk GZclb S. 3. >Zgh λ f c = 3â&#x2039;&#x2026;108 fk

J_r_gb_ 1 1 ν = = â&#x2C6;&#x2019;7 = 10 7 =p T 10 c Hl\_lν = 107 =p

J_r_gb_ S = ct = 3â&#x2039;&#x2026;108 fk â&#x2039;&#x2026; 8,3â&#x2039;&#x2026;10-7 k f Hl\_lS = 249 f

J_r_gb_ c 3 â&#x2039;&#x2026; 108 fk ν= = = 5 â&#x2039;&#x2026; 105 =p 600 f λ GZclbν. Hl\_lν = 5â&#x2039;&#x2026;105 =p 4. AgZy kdhjhklv jZkijhkljZg_gby kb]gZeZ k hgZ jZ\gZ kdhjhklb k\_lZ  b \j_fy _]h jZkijhkljZg_gby t g_ljm^gh jZkkqblZlv ijhc^_ggh_ jZkklhygb_ S AZ \j_fy t kb]gZe ijhc^_l jZkklhygb_ S lm^Zb h[jZlghbke_^h\Zl_evghS = ct/2. 5. G_la\mdh\u_\hegug_jZkijhkljZgy_lky\ \Zdmmf_

MijZ`g_gb_

1. 126 K ²Z_f 63 Li ²Z_f 40 20 Ca ²Z_f 2. 6, 3, 20.

54


6 Z_f jZa 1 Z_f 4. Z [ Z_f\ \ jZa] ^ _ `  5. 146 K â&#x2020;&#x2019; 146â&#x2C6;&#x2019;+01O + â&#x2C6;&#x2019;01 _ â&#x2021;&#x2019;147 O =147 N ²Zahl 3. < n =

MijZ`g_gb_

14 4 17 1 7 N + 2 He â&#x2020;&#x2019; 8 O +1 H  Bf__f   

       Ke_^h\Zl_evgh aZdhgkhojZg_gbyaZjy^Z\uihegy_lky

MijZ`g_gb_

1. < y^j_ ZlhfZ [_jbeeby 94 Be gmdehgh\ ²  ijhlhgh\ ²  g_cljhgh\²N = A + Z = 9 â&#x20AC;&#x201C; 4 = 5.   [  Np = Z   \  Q   \ we_f_glZjguo 2. 39 19 D  Z  Z we_dljbq_kdboaZjy^Zo ] Ne = Np ^ _ ` : a N = Aâ&#x20AC;&#x201C;Z= ±  b m Z_f 3. Qbkeh ijhlhgh\ khhl\_lkl\_ggh we_dljhgh\  \ Zlhf_ jZ\gh _]h ihjy^dh\hfm ghf_jm \ lZ[ebp_ F_g^_e__\Z ke_^h\Zl_evgh Z

eblbc[ nlhj

MijZ`g_gb_

Wlb Zlhfu bf_xl h^bgZdh\u_ fZkku gh bo obfbq_kdb_ k\hckl\Z jZaebqguWlhh[tykgy_lkyl_fqlh m gbojZagu_aZjy^h\u_ qbkeZ ZagZqblb dhebq_kl\hwe_dljhgh\

MijZ`g_gb_

1.

238 234 4 92 U â&#x2020;&#x2019; 90Th + 2 He . 234 234 0 0 ~ 234 234 0 0~ 90Th â&#x2020;&#x2019; 91Pa + â&#x2C6;&#x2019;1 e+ 0  ; 91Pa â&#x2020;&#x2019; 92 U + â&#x2C6;&#x2019;1 e+ 0  

2. j_amevlZl_^\moβjZkiZ^h\

Ke_^h\Zl_evgh \

MijZ`g_gb_

Ld gmdehgu bf_xl fZkkm lh f_`^m gbfb ^_ckl\mxl kbeu ]jZ\blZpbhggh]hijbly`_gby

55


AZ^Zqbij_^eZ]Z_fu_^eyih\lhj_gby b ijbqZkZonbabdb\ g_^_ex

U 1. >ey\_dlhjZ a bf__fZ     [ Zy ± ±\ _Zy| = U ]  | a | = (0,5 â&#x2C6;&#x2019; 0,5) 2 + (2 â&#x2C6;&#x2019; 5) 2 = 3. U >ey\_dlhjZ b bf__fZ     [ by ±  \ _by_ ]

U | b | = (4 â&#x2C6;&#x2019; 1) 2 + (4 â&#x2C6;&#x2019; 0) 2 = 5. U >ey\_dlhjZ c bf__fZ     [ cy   ±   \  _cy_  ]

U | c | = (6 â&#x2C6;&#x2019; 4) 2 â&#x2C6;&#x2019; (1 â&#x2C6;&#x2019; 1) 2 = 2. U >ey\_dlhjZ d bf__fZ    ± [ dy ±± ±\ _dy_ ]

U | d | = (3 â&#x2C6;&#x2019; 6) 2 + (â&#x2C6;&#x2019;4 â&#x2C6;&#x2019; 0) 2 = 5 >ey\_dlhjZ e bf__fZ  ±   [ ey ±± ±  \

U |ey_ ]  | e | = (0,5 â&#x2C6;&#x2019; 0,5) 2 + (â&#x2C6;&#x2019;1 â&#x2C6;&#x2019; (â&#x2C6;&#x2019;4)) 2 = 3. U U 2. ax = 0, bx = | b | , cx = 0, dx = â&#x2C6;&#x2019; | d | . 3. Z A (0;2), B ± [ sx = 12 â&#x20AC;&#x201C; 0 = 12, sy ±±  ±\ _sx| = 12, U |sy| = 5; ]  | s | = (12 â&#x2C6;&#x2019; 0) 2 + (â&#x2C6;&#x2019;3 â&#x2C6;&#x2019; 2) 2 = 13. â&#x2020;&#x2019;

4. y



B

 



sAB = ( 4 â&#x2C6;&#x2019; ( â&#x2C6;&#x2019;8)) + (3 â&#x2C6;&#x2019; ( â&#x2C6;&#x2019;2))





 x



A 2



2

 LZd dZd imlv g_ fh`_l ij_\ukblv

i_j_f_s_gby fh^mevdhlhjh]h_klvgZbf_gvr__jZkklhygb_f_`^m gZqZevghcb dhg_qghclhqdZfbimlb lhhgfh`_l[ulveb[hjZ\_g eb[h[hevr_i_j_f_s_gbyghgb \dh_fkemqZ_g_f_gvr__]h 5. Ijyfhebg_cguf jZ\ghf_jguf ^\b`_gb_f gZau\Z_lky lZdh_ ^\b`_gb_ ijb dhlhjhf aZ h^bgZdh\u_ ijhf_`mldb \j_f_gb l_eh kh\_jrZ_l h^bgZdh\u_ i_j_f_s_gby \^hev g_dhlhjhc hkb lZd dZd ^\b`_gb_ ijyfhebg_cgh_  Ihwlhfm sx = vxt ]^_ vx ² ihklhyggZy 56


\_ebqbgZ oZjZdl_jbamxsZy kdhjhklv i_j_f_s_gby Bkoh^y ba mjZ\g_gbyo = o0 + sxihemqbfx = x0 + vxt. 6. >Zgh J_r_gb_ vx fkx0 f x(t) = x0 + vxt â&#x2021;&#x2019; x(t) = 3 + 5t. GZclbx(t). Hl\_lx(t) = (3 + 5t f 7. xl xi <hdaZe x\ X       >Zgh J_r_gb_ xi = 260 â&#x20AC;&#x201C; 10t < gZqZevgucfhf_glgZ[ex^_gby xl = â&#x20AC;&#x201C;100 + 8t xi = 260 â&#x20AC;&#x201C; 10 â&#x2039;&#x2026; 0 = 260; xl = â&#x20AC;&#x201C;100 + 8 â&#x2039;&#x2026; 0 = â&#x20AC;&#x201C;100. < fhf_gl\klj_qbxi = xl beb±t = â&#x20AC;&#x201C;100 + 8t. Hlkx^ZgZoh^bffhf_gl\j_f_gb\klj_qbt = 20 c. x\ = 260 â&#x20AC;&#x201C; 10 â&#x2039;&#x2026; 20 = â&#x20AC;&#x201C;100 + 8 â&#x2039;&#x2026;  f GZclb xi, Hl\_lxi = 260, xl = â&#x20AC;&#x201C;100, t = 20 c, x\ f xl, t, x\. 8. Kh]eZkgh]jZnbdmiehl[uekims_ggb`_klhygdbgZf_ljh\ Ih]jZnbdmhij_^_ebfo0 = â&#x20AC;&#x201C;10; vx fk fko = â&#x20AC;&#x201C;10 + 2t. 9. >Zgh J_r_gb_ t=2c v â&#x2C6;&#x2019; v0 v v v t 4,5 fk â&#x2039;&#x2026; 2 k = ; t1 = 1 = 1 = = 3 c; a= v0 = 0 3 fk t t a v v fk at 2 vv 2 t 2 v 2 t (4,5 fk )2 â&#x2039;&#x2026; 2 k v1 fk = 6,75 f s= 1 = 1 2 = 1 = 2 2v 2 â&#x2039;&#x2026; 3 fk 2tv GZclbt1, s. Hl\_l: t1 = 3 c, s = 6,75 f. U U U U U U U U v +v at 2  U at  t U 10. s = v0 t + = t  v0 +  = (v0 + (v0 + at )) = 0 t. 2 2 2 2  U U U U U U U U U (v â&#x2C6;&#x2019; v 0 )t 2 v 0 + v a t 2 U v â&#x2C6;&#x2019; v0 U U t; 11. s = v0 t + = ; a= ; s = v0 t + 2 2t 2 t U U U U U2 U2 (aU, sU) =  v â&#x2C6;&#x2019; v0 , v0 + v t  = 1 â&#x2039;&#x2026; (vU, vU0 ) + vU2 â&#x2C6;&#x2019; vU02 â&#x2C6;&#x2019; (vU0 , vU) = v â&#x2C6;&#x2019; v0 â&#x2021;&#x2019; 2 2  t  2 U2 U2 U v â&#x2C6;&#x2019; v0 â&#x2021;&#x2019;a= U . 2s

(

12. >Zgh tx = 0,3 k

)

J_r_gb_ 57


s f

s 0,43 f = â&#x2030;&#x2C6; 1,43 fk t 0,3 k 2s 2 s 2 â&#x2039;&#x2026; 0,43 f a = 2 ; v = at = â&#x2030;&#x2C6; 2,87 f/k. = t 0,3 k t GZclbvkj, v. Hl\_lvkj â&#x2030;&#x2C6; fkv â&#x2030;&#x2C6; fk 2 a t a t 2 3a t 2 13. so[ = o[ ; sFd = cd = o[ = 3sh[. â&#x2021;&#x2019; < jZaZ[hevr_ 2 2 2 vkd = acdt = 3ah[t = 3vh[. â&#x2021;&#x2019; < jZaZ[hevr_ 14. vkj =

>eykdhjhklgh]h ebnlZ

vx

>eyh[uqgh]h ebnlZ

0

t

15. >Zgh vx(t) = 10 + 0,5t

J_r_gb_ v0x = vx(0) = 10 + 0,5 â&#x2039;&#x2026;  fka fk2. K l_q_gb_f \j_f_gb fh^mev \_dlhjZ kdhjhklb Z\lhfh[bey\hajZklZ_l lZddZdZ!b v0>0). Hl\_lv0x fk

GZclbv0x.

16. Ihke_ m^ZjZ mkdhj_gb_ rZc[u gZijZ\e_gh ijhlb\ kdhjhklb Dh]^Z kdhjhklv h[jZsZ_lky \ gmev mkdhj_gb_ lh`_ klZgh\blky (5 â&#x2C6;&#x2019; t ) fk 0 â&#x2030;¤ t â&#x2030;¤ 5; jZ\gufgmex | v x (t ) |=  t > 5. 0 fk 

vx

 

   















t

58


17. o = o0 + sx JZg__ [ueh ^hdZaZgh qlh ijb jZ\ghmkdhj_gghf ^\b`_gbbk mkdhj_gb_fZo b gZqZevghckdhjhklvx v0x i_j_f_s_gb_ a t a t jZ\ghsx = v0xt + x ihwlhfmo = o0+ v0xt + x . 2 2 18. >Zgh J_r_gb_ ax fk2 vx(t) = v0x + axt = 0,1t \ fk2). v0x = 0 a t2 0,1 â&#x2039;&#x2026; t 2 x(t) = x0 + v0xt + x = = 0,05t2. x0 = 0 2 2 GZclbvx(t), x(t). Hl\_lv0x fk 19. >Zgh J_r_gb_ |v\_ dfq |vf| = ||v\| â&#x20AC;&#x201C; |v\|| ijb v\ â&#x2020;&#x2018;â&#x2020;&#x2018; vf beb |vf| = ||v\| + |v\|| Z |vhlg| = 0 ijb v\ â&#x2020;&#x2018;â&#x2020;&#x201C; vf. [ |vhlg_ dfq Z) v\ â&#x2020;&#x2018;â&#x2020;&#x2018; vf b v\ â&#x2020;&#x2018;â&#x2020;&#x201C; vf â&#x2021;&#x2019; |vf| = |40 df/q Âą 0 df/q| = \ |vhlg_ dfq = 40 df/q. ] |vhlg_ dfq [) v\ â&#x2020;&#x2018;â&#x2020;&#x2018; vf â&#x2021;&#x2019; |vf| = |40 df/q â&#x20AC;&#x201C; 10 df/q| = 30 df/q. v\ â&#x2020;&#x2018;â&#x2020;&#x201C; vf â&#x2021;&#x2019; |vf| = |40 df/q + 10 df/q| = 50 df/q. \ v\ â&#x2020;&#x2018;â&#x2020;&#x2018; vf â&#x2021;&#x2019; |vf_ _dfq Âądfq_  v\ â&#x2020;&#x2018;â&#x2020;&#x201C; vf â&#x2021;&#x2019; |vf_ _dfq dfq_ dfq ] v\ â&#x2020;&#x2018;â&#x2020;&#x2018; vf â&#x2021;&#x2019; |vf_ _dfq dfq_ dfq v\ â&#x2020;&#x2018;â&#x2020;&#x201C; vf â&#x2021;&#x2019; |vf_ _dfq Âądfq_ dfq GZclbvf. Hl\_l Z   dfq [   dfq beb  dfq \   bebdfq[ dfq bebdfq 20. KdhjhklvdZl_jZhlghkbl_evgh[_j_]Zihl_q_gbxvd = = vd + vl = 6vl a^_kvvd ²kdhjhklvdZl_jZhlghkbl_evgh\h^uvl â&#x20AC;&#x201D; kdhjhklv l_q_gby \h^u hlghkbl_evgh [_j_]Z  kdhjhklv dZl_jZ hlghkbl_evgh [_j_]Z ijhlb\ l_q_gby vd = vd â&#x20AC;&#x201C; vl = 4vl LZdbf v 6 h[jZahf d + = = 1,5. vd â&#x2C6;&#x2019; 4 m 3,87 â&#x2039;&#x2026; 10 â&#x2C6;&#x2019;3 d]  d]f3 Fu \b^bf qlh iehlghklv = V 3 â&#x2039;&#x2026; 10 â&#x2C6;&#x2019;3 f 3 rZjbdZjZ\gZiehlghklb\ha^moZZke_^h\Zl_evgh\ulZedb\ZxsZy kbeZ ^_ckl\mxsZy gZ rZjbd jZ\gZ _]h kbe_ ly`_klb AgZqbl ih i_j\hfm aZdhgm GvxlhgZ rZjbd hklZg_lky \ khklhygbb ihdhy ld _]h hlimklbeb [_a gZqZevghc kdhjhklb bgZq_ [u hg jZ\ghf_jgh b ijyfhebg_cghi_j_f_sZeky  22. Kh]eZkghlj_lv_fmaZdhgmGvxlhgZkbeu^_ckl\mxsb_gZrZju jZ\guKh]eZkgh\lhjhfmaZdhgmGvxlhgZbomkdhj_gbyjZ\gu 21. Ď =

59


a m F F  Hlkx^Z c = a  < j_Zevguo nbabq_kdbo , ZZ = mc ma a a mc aZ^ZqZo dh]^Z fZkku rZjh\ g_ jZ\gu gmex  fh^mev mkdhj_gby klZevgh]h rZjZ g_ fh`_l jZ\gylvky gmex Hg fh`_l [ulv dZd [hevr_ lZd b f_gvr_ fh^mey mkdhj_gby Zexfbgb_\h]h rZjZ qlh aZ\bkblebrvhlkhhlghr_gbyfZkkrZjh\ 23. Ba nhjfmeu ^ey g0 ihemqZ_f GM3 = g 0 R32  Ih^klZ\eyy \ Zk =

nhjfmem^eygihemqZ_fg =

g 0 R32 ( R3 + h) 2

.

v2 v2 1 1 1 ; a1 = = a1 ; L1 = ma1 ; L2 = ma 2 = ma1 = L 1 . r 2r 2 2 2 DZd mkdhj_gb_lZd b kbeZ^_ckl\mxsZy gZ \lhjhc rZjbd \ jZaZ f_gvr_ZgZeh]bqguo\_ebqbg^ey\lhjh]hrZjbdZ 25. GZ \ukhl_ h hlghkbl_evgh a_feb r = R3 + h; mapk = mg; 24. a1 =

g 0 R32 g 0 R32 v2 = â&#x2021;&#x2019; v = ( R3 + h) ( R3 + h) 2 R3 + h 26. >Zgh J_r_gb_ <hkihevam_fkynhjfmehc ihemq_gghc \ R df â&#x2039;&#x2026; 106 f ij_^u^ms_caZ^Zq_ g0 fk2 h df â&#x2039;&#x2026; 106 f g 0 R32 9,8 fk â&#x2039;&#x2026; (6,4 â&#x2039;&#x2026;10 6 f 2 v=v= = â&#x2030;&#x2C6; R3 + h 6,4 â&#x2039;&#x2026; 10 6 f + 3,6 â&#x2039;&#x2026;10 6 f â&#x2030;&#x2C6; fk Hl\_lv â&#x2030;&#x2C6; fk

GZclbv. 27. vx = gt.

vx, fk

 

  



28. >Zgh l d]











t, c



J_r_gb_ â&#x2C6;&#x2020;p = mâ&#x2C6;&#x2020;v = mgâ&#x2C6;&#x2020;t. 60


v0 = 0 Ldâ&#x2C6;&#x2020;v1 = â&#x2C6;&#x2020;v2 jZ\ghmkdhj_ggh_^\b`_gb_ lh t k â&#x2C6;&#x2020;p1 = â&#x2C6;&#x2020;p2 = â&#x2C6;&#x2020;p d]â&#x2039;&#x2026;fk2 â&#x2039;&#x2026; 1 c d]â&#x2039;&#x2026;fk â&#x2C6;&#x2020;t = 1c GZclbv. Hl\_lâ&#x2C6;&#x2020;p1 = â&#x2C6;&#x2020;p2 = â&#x2C6;&#x2020;p d]â&#x2039;&#x2026;fk 29. Ld m ² ihklhyggZy \_ebqbgZ lh baf_g_gb_ bfimevkZ [m^_l hij_^_eylvky lhevdh baf_g_gb_f kdhjhklb Ih ]jZnbdm kf aZ^Zqm  \b^ghqlh_kebâ&#x2C6;&#x2020;t1 = â&#x2C6;&#x2020;t2lhb â&#x2C6;&#x2020;v1 = â&#x2C6;&#x2020;v2bagZqblâ&#x2C6;&#x2020;p1 = â&#x2C6;&#x2020;p2. 30. < mkeh\byo k\h[h^gh]h iZ^_gby kdhjhklb h[hbo rZjbdh\ \ ex[hc fhf_gl \j_f_gb [m^ml h^bgZdh\u b ke_^h\Zl_evgh hlghr_gb_ bo bfimevkh\ [m^_l aZ\bk_lv ebrv hl hlghr_gby bo fZkk LZd dZd ih mkeh\bx h[t_fu h^bgZdh\u hgh [m^_l jZ\gh Ď f 8,9 â&#x2039;&#x2026; 10 3 d]f 3 = â&#x2030;&#x2C6; 3,3. Ď Z 2,7 â&#x2039;&#x2026;10 3 d]f 3 BlZd \ ex[hc fhf_gl \j_f_gb f_^guc rZjbd bf__l bfimevk ijbf_jgh\ jZaZ[hevr_q_fZexfbgb_\uc 31. ^hklhedgh\_gby X 1 2 hlghr_gbxiehlghkl_cf_^bb Zexfbgby

ihke_klhedgh\_gby 1

2

X

^hklhedgh\_gby 1

2

X

2

X

>Zgh v1x fk v2x fk v1â&#x20AC;˛ x fk GZclbv. 32.

J_r_gb_ Ih aZdhgm khojZg_gby bfimevkZ gZ hkv O): mv1x + mv2 x = mv1â&#x20AC;˛ x + mvâ&#x20AC;˛2 x â&#x2021;&#x2019; v â&#x20AC;˛2 x = v1x + v 2 x â&#x2C6;&#x2019; v1â&#x20AC;˛ x = fk fk Âąfk fk Hl\_l v â&#x20AC;˛2 x fk

ihke_klhedgh\_gby 1

>Zgh v1x fk v2x Âąfk v1â&#x20AC;˛ x = â&#x20AC;&#x201C;fk GZclbv.

J_r_gb_ Ih aZdhgm khojZg_gby bfimevkZ gZ hkv O): mv1x + mv2 x = mv1â&#x20AC;˛ x + mvâ&#x20AC;˛2 x â&#x2021;&#x2019; v â&#x20AC;˛2 x = v1x + v 2 x â&#x2C6;&#x2019; v1â&#x20AC;˛ x = fk  Âąfk Âą Âąfk  fk Hl\_l v â&#x20AC;˛2 x fk

33. E=

(

)

(

)

mv12x mv22x m 2 mv â&#x20AC;˛ 2 mv â&#x20AC;˛22x m + = â&#x2039;&#x2026; v1x + v 22x ; E â&#x20AC;˛ = 1x + = â&#x2039;&#x2026; v1â&#x20AC;˛ x2 + v â&#x20AC;˛22x ; 2 2 2 2 2 2 61


v12x + v22x  fk 2 + ±fk 2 = 0,05 f2k2; v1â&#x20AC;²x2 + vâ&#x20AC;²22x  ±fk 2 +

+ fk = 0,05 f k â&#x2021;&#x2019; v1x + v2 x = v1â&#x20AC;² x + vâ&#x20AC;²2 x â&#x2021;&#x2019; E = Eâ&#x20AC;². 2

2

2

2

2

2

34. Ih ]jZnbdm hij_^_ey_f qlh L

2

  k b ν =

1 1   =p = T 2c Ex[Zy^jm]ZylhqdZbaf_gy_lkdhjhklvk lhc`_kZfhcqZklhlhc 35. <havf_f aZ t   fhf_gl dh]^Z hldehg_gb_ kj_^g_c lhqdb kljmgujZ\ghgmex =jZnbdg_]h^blky^ey^jm]bolhq_dkljmguldZfieblm^ZbohlebqgZ hlZfieblm^ukj_^g_clhqdb>eykj_^gbolhq_dkljmg ^jm]bo Zjnhg l_f[he__g_]h^blkylZddZdhgbbf_xlbgu_qZklhludhe_[Zgbc ;ff    

  







WfF





36. GZ^h ^\Z h^bgZdh\uo dZf_jlhgZ jZkiheh`blv gZ g_dhlhjhf jZkklhygbb ^jm] hl ^jm]Z lZd qlh[u bo j_ahgZlhjgu_ ysbdb [ueb h[jZs_gu ^jm] d ^jm]m ?keb l_i_jv m^Zjblv ih h^ghfm ba gbo b q_j_ag_dhlhjh_\j_fyaZ]emrblvijbdhkgm\rbkvjmdhcd g_fmlh fu mkeurbf a\md hl \lhjh]h dZf_jlhgZ < hkgh\_ ^Zggh]h hiulZ e_`bly\e_gb_a\mdh\h]hj_ahgZgkZ 37. Ihevamykv ]jZnbdhf hij_^_ey_f Z  ijb  =p Zfieblm^Z mklZgh\b\rboky dhe_[Zgbc [m^_l [hevr_ q_f ijb  =p [  qlh[u Zfieblm^Z mklZgh\b\rboky dhe_[Zgbc [ueZ fZdkbfZevghc dZq_eb gZ^hih^lZedb\Zlvk qZklhlhc=p\ kh[kl\_ggZy qZklhlZ dZq_e_c jZ\gZqZklhl_\ugm`^Zxs_ckbeul_=p 38. >Zgh: J_r_gb_ l kf f mg 0,002 d] â&#x2039;&#x2026; 9,8 fk 2 = = m ] d] Fl = Ff; mg = BIl â&#x2021;&#x2019; I = Bl 4 â&#x2039;&#x2026;10 â&#x2C6;&#x2019;2 Le â&#x2039;&#x2026; 0,1 f B = 4 â&#x2039;&#x2026; 10-2 Le = 4,9 A. GZclbI. Hl\_l: I = 4,9 A. 39. < ^Zgghf kemqZ_ jhev p_gljhklj_fbl_evghc kbeu \uihegy_l kbeZ k dhlhjhc fZ]gblgh_ ihe_ ^_ckl\m_l ^\b`msbcky we_dljhg IhevamykvijZ\behfe_\hcjmdbhij_^_ey_fqlhwe_dljhg\e_l_e\ dZf_jm\ lhqd_<. 62


40. >Zgh v = 3 ⋅ 107 fk |_| = 1,6 ⋅ 10-19 De m = 9,1 ⋅ 10-31 d] B = 8,5 ⋅ 10-3 Le

J_r_gb_ Fpk = Ff;

mv 2 mv = B|_|v ⇒ r = = r B|e|

9,1 ⋅ 10 −31 d] ⋅ 3 ⋅10 7 fk

8,5 ⋅ 10 −3 Le ⋅ 1,6 ⋅10 -19 De GZclbr. Hl\_lr = 2 ⋅ 10-2 f 41. < j_amevlZl_βjZkiZ^Z 146 C → 147 N + -01 e . 42. 43.

=

27 1 24 4 13 Al+ 0 n → 11 N + 2 He . 10 7+ 4−10 7 4 5 Al+ 3+ 2−5 X → 3 N + 2 He

7 + 4−10 3+ 2−5 X

= 2 ⋅ 10-2 f

= 01 n ²g_cljhg

63


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Bkke_^h\Zgb_jZ\ghmkdhj_ggh]h^\b`_gby[_agZqZevghckdhjhklb

<ZjbZgl P_evjZ[hlum[_^blvky\ jZ\ghmkdhj_gghfoZjZdl_j_^\b`_gby [jmkdZb hij_^_eblv_]hmkdhj_gb_b f]gh\_ggmxkdhjhklv < ^Zgghf\ZjbZgl_jZ[hlubkke_^mxloZjZdl_j^\b`_gby[jmkdZ ih gZdehgghc iehkdhklb K ihfhsvx ijb[hjZ bah[jZ`_ggh]h gZ jbk  Z  mq_[gbdZ fh`gh baf_jylv fh^meb \_dlhjh\ i_j_f_s_gbckh\_jr_gguo[jmkdhfaZijhf_`mldb\j_f_gbt1, t2 = 2t1, t3 = = 3t1,â&#x20AC;¦, tn = nt1hlkqblu\Z_fuohlfhf_glZgZqZeZ^\b`_gby?keb aZibkZlv^ey^Zgguofh^me_c\_dlhjh\i_j_f_s_gbcbo\ujZ`_gby

at 2 a (3t1 ) at12 at 2 a (2t1 ) 22 32 s1 , s3 = 3 = s3 ,â&#x20AC;¦, , s 2 = 2 == = = 2 2 2 2 2 2 2 at 2 a (nt1 )2 n 2 sn = n = s1 , = 2 2 2 lhfh`ghaZf_lblvke_^mxsmxaZdhghf_jghklv s1 : s2 : s3 : â&#x20AC;¦ : sn = 12 : 22 : 32 :â&#x20AC;¦: n2 = 1 : 4 : 9 :â&#x20AC;¦: n2. ?keb wlZ aZdhghf_jghklv \uihegy_lky ^ey baf_j_gguo \ jZ[hl_ fh^me_c \_dlhjh\ i_j_f_s_gbclh wlhb [m^_l ^hdZaZl_evkl\hf lh]h qlh ^\b`_gb_ [jmkdZ ih gZdehgghc iehkdhklb y\ey_lky jZ\ghmkdhj_gguf Ijbf_j\uiheg_gbyjZ[hlu. AZ^Zgb_  Bkke_^h\Zgb_ oZjZdl_jZ ^\b`_gby [jmkdZ ih gZdehgghc iehkdhklb 2

2

t, c

0

0,02

0,04

0,06

0,08

0,10

0,12

0,14

0,16

0,18

0,20

0,22

0,24

0,26

0,28

0,30

sff

0

1

3

7

15

24

36

50

65

82

102

126

146

170

198

227

s1 =

<uqbke_gby. s s s 2 3 ff s 7 ff 15 ff 24 ff = = 3, 3 = = 7, 4 = = 15, 5 = = 24, s1 1 ff s1 1 ff s1 1 ff s1 1 ff 64


s 6 36 ff s s s 50 ff 65 ff 82 ff = = 36, 7 = = 50, 8 = = 65, 9 = =82, s1 1 ff s1 1 ff s1 1 ff s1 1 ff s 11 126 ff s10 102 ff s s 146 ff = = 102, = = 126, 12 = = 146, 13 = ff ff s1 1 ff 1 s 1 s1 s1 1

s s 170 ff 198 ff 227 ff = 170, 14 = = 198, 15 = = 227. 1 ff s1 1 ff s1 1 ff Hlkx^ZgZoh^bf s1 : s2 : s3 : s4 : s5 : s6 : s7 : s8 : s9 : s10 : s11 : s12 : s13 : s14 : s15 = = 1 : 3 : 7 : 15 : 24 : 36 : 50 : 65 : 82 : 102 : 126 : 146 : 170 : 198 : 227. WlZ aZdhghf_jghklv g_ hq_gv kbevgh hlebqZ_lky hl l_hj_lbq_kdhc aZdhghf_jghklb ^ey jZ\ghmkdhj_ggh]h ^\b`_gby LZdbf h[jZahf fh`gh kqblZlv qlh ^\b`_gb_ [jmkdZ ih gZdehgghc iehkdhklb y\ey_lkyjZ\ghmkdhj_gguf AZ^Zgb_ Hij_^_e_gb_mkdhj_gby^\b`_gby[jmkdZ 2s Mkdhj_gb_[m^_f\uqbkeylvihnhjfme_a = 2 . t 2 â&#x2039;&#x2026; 0,102 f t10 = 0,2 c; s10 = 102 ff = 0,102 f; a1 = = 5,1 f/k2. 2 (0,2 k) 2 â&#x2039;&#x2026; 0,227 f t15 = 0,3 c; s15 = 227 ff = 0,227 f; a1 = â&#x2030;&#x2C6; 5,04 f/k2. (0,3 k)2 =

a1 + a 2 5,1 fk 2 + 5,04 fk 2 fk2. = 2 2 AZ^Zgb_  Hij_^_e_gb_ f]gh\_gghc kdhjhklb [jmkdZ \ jZagu_ fhf_glu \j_f_gb b ihkljh_gb_ ]jZnbdZ aZ\bkbfhklb f]gh\_gghc kdhjhklbv hl\j_f_gbt. AgZq_gb_f]gh\_gghckdhjhklb[m^_f\uqbkeylvihnhjfme_v = at. t = 0,1 c; v fk2 â&#x2039;&#x2026; k fk t = 0,2 c; v fk2 â&#x2039;&#x2026; k fk t = 0,3 c; v fk2 â&#x2039;&#x2026; k fk =jZnbdaZ\bkbfhklbf]gh\_gghckdhjhklbv hl\j_f_gbt. akj =

65


v, fc 

 

 









 t, c

>hihegbl_evgh_ aZ^Zgb_ Ihkljh_gb_ ]jZnbdZ aZ\bkbfhklb dhhj^bgZlu x [jmkdZ hl \j_f_gb t. x0 = 0, t0 = 0, xi(ti) = si, i = 1,2,3,â&#x20AC;¦,15. x, ff    















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JZkklhygb_ sf

<j_fy ^\b`_gby t, c

0,9

1,5

t, c

Mkdhj_gb_

a=

2s t2

fk

0,8

2

F]gh\_ggZy kdhjhklv v = atfk 1,2

66


<uqbke_gby. t = 0,5 c â&#x2039;&#x2026; 3 = 1,5 c; a =

2 â&#x2039;&#x2026; 0,9 f

(1,5 k )2

fk2; v fk2 â&#x2039;&#x2026; k fk

EZ[hjZlhjgZyjZ[hlZÂ&#x2039;

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<uqbke_gby.

Imlvsff

Imlvsf

400

0,4

n = 14; t = 14 â&#x2039;&#x2026; 0,02 c = 0,28 c; gwdki =

2 â&#x2039;&#x2026; 0,4 f

(0,28 k )2

Mkdhj_gb_k\h[h^gh]h iZ^_gbyg = 2s/t2fk2

â&#x2030;&#x2C6;fk2.

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67


t 1 N , ν= = . N T t Baf_jyy i_jbh^ b qZklhlm ijb jZaguo agZq_gbyo ^ebgu fZylgbdZ ful_fkZfufihemqZ_faZ\bkbfhklvi_jbh^Zb qZklhluhl^ebgu Ijbf_j\uiheg_gbyjZ[hlu. T=

Â&#x2039; hiulZ Nba\_e

lkf N t, c T, c ν, =p

1

2

3

4

5

5 30 13 0,43 2,31

20 30 27 0,9 1,11

45 30 40 1,33 0,75

80 30 53 1,77 0,57

125 30 67 2,23 0,45

Ba ^Zgguo \ lZ[ebp_ fh`gh aZf_lblv lZdmx aZdhghf_jghklv q_f [hevr_ ^ebgZ fZylgbdZ l_f [hevr_ i_jbh^ b f_gvr_ qZklhlZ b gZh[hjhl >hihegbl_evgh_aZ^Zgb_. P_ev aZ^Zgby \uykgblv dZdZy fZl_fZlbq_kdZy aZ\bkbfhklv kms_kl\m_lf_`^m^ebghcfZylgbdZb i_jbh^hf_]hdhe_[Zgbc T2 â&#x2030;&#x2C6;2 T1

T3 â&#x2030;&#x2C6;3 T1

T4 â&#x2030;&#x2C6; 4 T1

T5 â&#x2030;&#x2C6;5 T1

l2 =4 l1

l3 =9 l1

l4 = 16 l1

l 2 = 25 l1

Ba ^Zgguo \ lZ[ebp_ ohjhrh ijhkfZljb\Z_lky k\yav f_`^m i_jbh^hf dhe_[ZgbcfZylgbdZb _]h^ebghc b 

Tk = T1

lk l1

]^_k fh`_lijbgbfZlv

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69


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70


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