физика 9кл перышкин гутник_2001_ответы и решения

1. >hfZrgyy jZ[hlZ ihnbabd_ aZ deZkk d mq_[gbdm ©NbabdZdeMq_[^eyh[s_h[jZahZlmq_[aZ_^_gbcª :I_jurdbg?F=mlgbd±_ ba^kl_j_hlbi± F©jhnZª ] 1

2. 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. .................................... 11 §13. .................................... 11 §14. .................................... 12 §15. .................................... 12 §16. .................................... 12 §18. .................................... 13 §19. .................................... 13 §20. .................................... 13 §21. .................................... 14 §22. .................................... 14 §23. .................................... 14 §24. .................................... 15 §25. .................................... 15 §26. .................................... 16 §27. .................................... 16 2

3. §28. .................................... 17 §29. .................................... 17 §30. .................................... 17 §31. .................................... 18 §32. .................................... 18 §33. .................................... 19 §34. .................................... 19 §35. .................................... 19 §36. .................................... 20 §37. .................................... 20 §38. .................................... 21 §39. .................................... 21 §40. .................................... 21 §42. .................................... 21 §43. .................................... 22 §44. .................................... 23 §45. .................................... 23 §46. .................................... 24 §47. .................................... 25 §48. .................................... 25 §49. .................................... 25 §50. .................................... 26 §51. .................................... 27 §52. .................................... 27 §53. .................................... 27 §54. .................................... 28 §55. .................................... 28 §56. .................................... 29 §57. .................................... 30 3

4. §58. .................................... 31 §59. .................................... 32 §60. .................................... 32 §61. .................................... 32 §62. .................................... 33 §63. .................................... 33 §64. .................................... 34 §65. .................................... 34 §66. .................................... 34 §67. .................................... 35 §68. .................................... 35 §69. .................................... 36 §70. .................................... 36 §72. .................................... 37 MijZ`g_gby ........................... 39 MijZ`g_gb_ ........................... MijZ`g_gb_ ........................... 39 MijZ`g_gb_ ........................... 39 MijZ`g_gb_ ........................... 39 MijZ`g_gb_ ........................... 39 MijZ`g_gb_ ........................... 40 MijZ`g_gb_ ........................... 40 MijZ`g_gb_ ........................... 41 MijZ`g_gb_ ........................... 41 MijZ`g_gb_ .......................... 42 MijZ`g_gb_ .......................... 42 MijZ`g_gb_ .......................... 42 MijZ`g_gb_ .......................... 43 MijZ`g_gb_ .......................... 44 44 4

5. MijZ`g_gb_ .......................... MijZ`g_gb_ .......................... 44 MijZ`g_gb_ .......................... 45 MijZ`g_gb_ .......................... 45 MijZ`g_gb_ .......................... 46 MijZ`g_gb_ .......................... 47 MijZ`g_gb_ .......................... 47 MijZ`g_gb_ .......................... 47 MijZ`g_gb_ .......................... 48 MijZ`g_gb_ .......................... 48 MijZ`g_gb_ .......................... 48 MijZ`g_gb_ .......................... 49 MijZ`g_gb_ .......................... 49 MijZ`g_gb_ .......................... 50 MijZ`g_gb_ .......................... 50 MijZ`g_gb_ .......................... 50 MijZ`g_gb_ .......................... 50 MijZ`g_gb_ .......................... 50 MijZ`g_gb_ .......................... 51 MijZ`g_gb_ .......................... 51 MijZ`g_gb_ .......................... 51 MijZ`g_gb_ .......................... 52 MijZ`g_gb_ .......................... 52 MijZ`g_gb_ .......................... 53 MijZ`g_gb_ .......................... 53 MijZ`g_gb_ .......................... 53 MijZ`g_gb_ .......................... 53 MijZ`g_gb_ .......................... 54 MijZ`g_gb_ .......................... 54 54 5

6. MijZ`g_gb_ .......................... MijZ`g_gb_ .......................... 55 MijZ`g_gb_ .......................... 55 MijZ`g_gb_ .......................... 55 MijZ`g_gb_ .......................... 55 55 AZ^Zqbij_^eZ]Z_fu_ ^eyihlhj_gby b ijb qZkZo nbabdb g_^_ex .......... 56 EZ[hjZlhjgu_ jZ[hlu .................. 64 EZ[hjZlhjgZy jZ[hlZ‹ ................. EZ[hjZlhjgZy jZ[hlZ‹ ................. 64 EZ[hjZlhjgZy jZ[hlZ‹ ................. 67 EZ[hjZlhjgZy jZ[hlZ‹ ................. 67 EZ[hjZlhjgZy jZ[hlZ‹ ................. 68 EZ[hjZlhjgZy jZ[hlZ‹ ................. 69 70 6

7. hijhku §1. 1. FZl_jbZevgZy lhqdZ h[eZ^Z_l fZkkhc gh bf__l ij_g_[j_`bfh fZeu_jZaf_ju 2. FZl_jbZevgZylhqdZ ²wlhZ[kljZdlgh_ihgylb_ 3. eymijhs_gbyaZ^Zq 4. Dh]^Z mkehbbaZ^ZqbjZaf_jZfbwlh]hl_eZfh`ghij_g_[j_qv 5. AZ fZl_jbZevgmx lhqdm fh`gh ijbgylv Zlhfh[bev ijb hij_^_e_gbb _]h kdhjhklb gZ fZjrjml_ ] Ijhlbgh ± ] FhkdZ Wlhl `_ Zlhfh[bev g_evay kqblZlv fZl_jbZevghc lhqdhc ijb jZkq_l_^Ze_gbyhdZauZ_fh]hbfgZ^hjh]m 6. IjbihklmiZl_evghf^b`_gbb 7. FZl_jbZevghc lhqdhc gZauZ_lky l_eh jZaf_jZfb dhlhjh]h fh`ghij_g_[j_qv mkehbyo^ZgghcaZ^Zqb 8. Ijbijyfhebg_cghf^b`_gbbl_eZ 9. Kbkl_fZhlkq_lZhlghkbl_evghdhlhjhcjZkkfZljbZxl^b`_gb_ ij_^klZey_l kh[hc khhdmighklv kbkl_fu dhhj^bgZl ijb[hjZ ^ey baf_j_gby j_f_gb b lhqdb hlkq_lZ k dhlhjhc kyaZgZ kbkl_fZ dhhj^bgZl §2. 1. G_lk_aZbkblhlljZ_dlhjbb^b`_gbyG_evaymagZlv]^_[m^_l Zlhfh[bevq_j_a qZk_kebg_agZ_rvihdZdbf^hjh]Zfhgih_^_l 2. _dlhjgZijZe_gguchllhqdbhlkq_lZgZqZeZ^b`_gbyd lhqd_ hlkq_lZdhgpZ^b`_gbyl_eZ 3. Fh`gh §3. 1. uqbke_gbyijhbah^ylkhkdZeyjgufb_ebqbgZfb 2. ?keb _dlhj khgZijZe_g k hkvx lh _]h ijh_dpby gZ g__ [m^_l iheh`bl_evgZ b gZh[hjhl _keb _dlhj ijhlbhiheh`gh gZijZe_g hkblh_]hijh_dpbygZg__[m^_lhljbpZl_evgZ 3. o1 = o0 + so. §4. 1. Kdhjhklvx jZghf_jgh]h ijyfhebg_cgh]h ^b`_gby gZauZ_lky 7 ; ihklhygguc _dlhj v jZguc hlghr_gbx i_j_f_s_gby s l_eZ aZ ; 7 s ex[hcijhf_`mlhdj_f_gbt d agZq_gbxwlh]hijhf_`mldZ v = . t 7

8. 2. Ihnhjfme_sx = vxt. 3. Ijbijyfhebg_cghfjZghf_jghf^b`_gbb 4. Wlhb^ghbajbkmq_[gbdZ 5. Hgb^b`mlkyjZghf_jgh jZaguogZijZe_gbyokhkdhjhklyfb jZgufbihfh^mex b dfq §5. 1. D g_jZghf_jghfm^b`_gbx 2. Kdhjhklvl_eZ ^Zgghclhqd_ ^Zggucfhf_glj_f_gb 7 3. Mkdhj_gb_f jZghmkdhj_ggh]h ^b`_gby l_eZ a gZauZ_lky 7 _ebqbgZjZgZyhlghr_gbxbaf_g_gbykdhjhklb∆ v d ijhf_`mldm 7 7 7 7 ∆v v − v 0 j_f_gbtaZdhlhjucwlhbaf_g_gb_ijhbahreh a = = . 4. b`_gb_k ihklhyggufmkdhj_gb_f t t 5. HgihdZauZ_l[ukljhlmbaf_g_gbyfh^mey_dlhjZkdhjhklb 6. kbkl_f_KBfk2. 7. M_ebqbZ_lky ijb iheh`bl_evghf mkdhj_gbb wlhf kemqZ_ _dlhjkdhjhklbb _dlhjmkdhj_gbykhgZijZe_gu

9. mf_gvrZ_lky² ijb hljbpZl_evghf wlhf kemqZ_ _dlhj kdhjhklb b _dlhj mkdhj_gbyijhlbhiheh`ghgZijZe_gu

10. §6. 1. Z

11. vx = v0x + axt[

12. vx = axt. 2. h[hbokemqZyoijyfZy kemqZ_ ©Zª²ijhoh^ysZyq_j_agZqZeh kbkl_fudhhj^bgZl 3. Wlb ^b`_gby jZghmkdhj_ggu_ h^gZdh i_jhf kemqZ_ mkdhj_gb_iheh`bl_evghZ hlhjhf²hljbpZl_evgh §7. 1. Ijh_dpby_dlhjZi_j_f_s_gbyuqbkey_lkyihnhjfme_ axt 2 s x = v0 x t + . Ih^klZbf wlmnhjfmemujZ`_gb_^eyijh_dpbbmkdhj_gby 2 v − v0 x ax = x . Ihemqbf t v − v0 x t 2 v0 x + v x s x = v0 x t + x ⋅ = ⋅t . t 2 2 8

13. LZddZdv0x = AO, vx = BC, t = OB kfjbkZ

14. mq_[gbdZ

15. lhfu ihemqZ_fqlhijh_dpby_dlhjZi_j_f_s_gby s x = AO + BC ⋅ OB jZgZiehsZ^bnb]mjuOACB ²ijyfhm]hevghcljZi_pbbk 2 hkghZgbyfbAO, BC b ukhlhcOB. axt 2 2. s x = v0 x t + . 2 §8. 1. Ihnhjfme_ s x = ²êyijh_dpbbi_j_f_s_gby s = 2 axt at 2 — êyfh^mey_dlhjZi_j_f_s_gby 2 2 2. n2 jZaihkdhevdms ~ t2 s n a (nt1 ) 2 / 2 3. = 2 = n2 . st1 4. DZdjyîhke_^hZl_evguog_q_lguoqbk_e at1 / 2 5. eyhij_^_e_gbyjZghmkdhj_ggh]h^b`_gby 1. jZaguokbkl_fZohlq_lZwlb_ebqbgubf_xljZagu_agZq_gbyb §9. ihjZaghfmhjb_glbjhZggu 2. RZjbd iZ^Zxsbc gZ ihe ^b`ms_]hky Zlhfh[bey g_ bf__l ]hjbahglZevghc kdhjhklb hlghkbl_evgh g_]h Hlghkbl_evgh A_feb hgbf__lkdhjhklvjZgmxkdhjhklbZlhfh[bey 3. Kdhjhklv imlv ljZ_dlhjby b l^ jZaebqgu jZaguo kbkl_fZo hlkq_lZ 4. =_ebhp_gljbq_kdZy kbkl_fZ kyaZgZ k Khegp_f ]_hp_gljbq_kdZy ²k A_fe_c 5. Kf_gZ^gyb ghqbh[tykgy_lkyjZs_gb_fA_febhdjm]kh_chkb 1. JZghf_jghb ijyfhebg_cghbebihdhblky §10. 2. G_l 3. L_hjby :jbklhl_ey aZdexqZxsZyky lhf qlh ijb hlkmlklbb g_rg_]hha^_cklbyl_ehfh`_llhevdhihdhblvky 4. L_f qlh ih =Zebe_x l_eZ fh]ml jZghf_jgh ^b]Zlvky hlkmlklbbg_rgbokbe 5. Hiul bah[jZ`_gguc gZ jbk mq_[gbdZ ^hdZauZ_l lh qlh ihfbfh bg_jpbZevguo kbkl_f hlkq_lZ dhlhjuo uihegy_lky i_juc aZdhg GvxlhgZ

16. kms_klmxl kbkl_fu bgh]h oZjZdl_jZ Hg 9

17. khklhbl ke_^mxs_f GZ l_e_`d_ h^bg rZjbd e_`bl gZ ]hjbahglZevghc ih_joghklb Z lhjhc ih^_rbZ_lky gZ gblb KgZqZeZ l_e_`dZ ^b`_lky ijyfhebg_cgh b jZghf_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

18. dZd rZjbdb ijb^ml ^b`_gb_ k mkdhj_gb_f hlghkbl_evghl_e_`dbLZdbfh[jZahfhlghkbl_evghl_e_`dbi_juc aZdhgGvxlhgZg_uihegy_lky 6. Kms_klmxl kbkl_fu hlkq_lZ hlghkbl_evgh dhlhjuo l_eZ khojZgyxl khx kdhjhklv g_baf_gghc _keb gZ gbo g_ ^_cklmxl g_rgb_ kbeu beb bo ^_cklb_ kdhfi_gkbjhZgh LZdb_ kbkl_fu gZauZxlkybg_jpbZevgufb 7. Bg_jpbZevgu_kbkl_fum^he_lhjyxli_jhfmaZdhgmGvxlhgZ g_bg_jpbZevgu_²g_l 8. Fh`gh 9. G_l §11. 1. Ijbeh`_ggZyd l_emkbeZ 2. Q_f [hevr_ fhsghklv Zlhfh[bey Z khhl_lkl_ggh _]h kbeZ ly]bl_f[uklj__hgm_ebqbZ_lkhxkdhjhklv 3. Hiul bah[jZ`_gguc gZ jbk mq_[gbdZ ^hdZauZ_l lh qlh ijbeh`_ggZy d l_em kbeZ yey_lky ijbqbghc mkdhj_gby ey ijh_^_gby^Zggh]hhiulZgZ^haylvl_e_`dmmklZghblvgZg_c^Z h^bgZdhhjZ[hlZxsbo_glbeylhjZb dZi_evgbpmeydhfi_gkZpbb kbeulj_gbyijbdj_ibfd l_e_`d_h^bgbadhgphgblbi_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^ ^_cklb_f kbeu _glbeylhjh l_e_`dZ ijb^_l ^b`_gb_ Ijb wlhf gZ klhe [m^ml iZ^Zlv dZieb q_j_a h^bgZdhu_ ijhf_`mldb j_f_gb L_i_jv _keb baf_jylvjZkklhygbyf_`^mkhk_^gbfbdZieyfblhfh`ghm[_^blvky qlh wlb jZkklhygby [m^ml hlghkblvky dZd jy^ ihke_^hZl_evguo g_q_lguo qbk_e LZdbf h[jZahf fh`gh aZdexqblv qlh l_e_`dZ ^b]ZeZkvjZghmkdhj_gghkf§

19. IhkqblZ_fmkdhj_gb_ihnhjfme_ a = 2 aZf_jb ijhc^_ggh_ l_e_`dhc jZkklhygb_ s b j_fy __ 2s ^b`_gby t ?keb mf_gvrblv kbem ^_cklmxsmx gZ l_e_`dm ^Z t jZaZ udexq_gb_f h^gh]h ba _glbeylhjh

20. b kghZ ihkqblZlv mkdhj_gb_ lh hgh ihemqblky ^Z jZaZ f_gvrbf q_f i_juc jZa ?keb l_i_jv m_ebqblv fZkkm l_e_`db ^Z jZaZ ^h[Ze_gb_f d l_e_`d_ ]jmaZ fZkkhc jZghc fZkk_ l_e_`db

21. b kghZ ihkqblZlv 10

22. mkdhj_gb_ lh hgh ihemqblky ^Z jZaZ f_gvrbf q_f i_juc 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 jZgh^_cklmxs_c ijbeh`_gguo d g_fm kbe b h[jZlgh ijhihjpbhgZevgh _]h fZkk_ 7 7 F a= . d] ⋅ f m 5. HgbkhgZijZe_gu 6. G 1 2 . k §12. 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 ^_cklmxl ^jm]gZ^jm]Z i_jhfhiul_aZbfh^_cklb_l_eijhbkoh^blijb bo g_ihkj_^kl_gghf dhglZdl_ h lhjhf ² gZ jZkklhygbb lj_lv_f ² ijhp_kk_ ^b`_gby Ijb wlhf dZ`^hf kemqZ_ ihdZaZgby ^bgZfhf_ljh hdZauZxlky h^bgZdhufb LZdbf h[jZahf fh`gh k^_eZlv uh^ qlh ^Z l_eZ ^_cklmxl ^jm] gZ ^jm]Z k kbeZfb jZgufb ih fh^mex b ijhlbhiheh`gufb ih gZijZe_gbx 2. Kbeuk dhlhjufbaZbfh^_cklmxl^Zl_eZjZguihfh^mexb ijhlbhiheh`guihgZijZe_gbx 3. Wlhmkdhj_gb_b^m[hevrhcfZkkuA_febij_g_[j_`bl_evghfZeh 4. GZijbf_j Khegp_ b EmgZ aZbfh^_cklmxl ihkj_^klhf ]jZblZpbhgguokbe 5. Wlbkbeuijbeh`_gud jZagufl_eZf 1. b`_gb_ih^^_cklb_fkbeuly`_klb §13. 2. GZ^h baf_jblv jZkklhygby dhlhju_ rZjbd ijhoh^bl aZ ihke_^hZl_evgu_ h^bgZdhu_ ijhf_`mldb j_f_gb b m[_^blvky lhf qlh ^Zggu_ jZkklhygby hlghkylky dZd jy^ ihke_^hZl_evguo g_q_lguo qbk_e Wlh b [m^_l yeylvky ^hdZaZl_evklhf lh]h qlh kh[h^gh_iZ^_gb_l_eZyey_lkyjZghmkdhj_gguf^b`_gb_fkf 3. K p_evx ihdZaZlv qlh mkdhj_gb_ kh[h^gh]h iZ^_gby h^bgZdhh §8). ^eyk_ol_e 4. Mkdhj_gb_uaZggh_^_cklb_fkbeuly`_klb 5. BaaZkbeukhijhlbe_gbyha^moZ 11

23. 6. =Zebe_c §14. 1. ZhgZij_iylklm_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 – gt _jog_c lhqdb ljZ_dlhjbb kdhjhklv l_eZ jZgZ gmex b hgh gZqbgZ_l ^b]Zlvky gba m_ebqbZykdhjhklvihaZdhgmv(t) = gt^hl_oihjihdZg_ miZ^_l gZa_fex 3. Hl_ebqbgugZqZevghckdhjhklb 4. ?keb gZijZblv hkv _jo lh ijh_dpby _dlhjZ kdhjhklb gZ wlm hkv iheh`bl_evgZ Z ijh_dpby mkdhj_gby kh[h^gh]h iZ^_gby ² hljbpZl_evgZ §15. 1. aZbfgh_ ijbly`_gb_ k_o l_e k_e_gghc ]jZblZpbhggh_ aZbfh^_cklb_l_e

24. 2. =jZblZpbhggufb 3. BkZZdGvxlhg ;9,,_d_ 4. Z l_eZ ijbly]bZxlky ^jm] d ^jm]m k kbehc ijyfh ijhihjpbhgZevghc ijhba_^_gbx bo fZkk b h[jZlgh ijhihjpbhgZevghcdZ^jZlmjZkklhygbyf_`^mgbfb 5. F = G 1 2 2 ]^_ F ² fh^mev ]jZblZpbhgghc kbeu m1, m2 — mm fZkku aZbfh^_cklmxsbo l_e r ² jZkklhygb_ f_`^m gbfb G — r ]jZblZpbhggZyihklhyggZyjZgZy ⋅10-11 G⋅f2d]2. 6. AZdhgk_fbjgh]hly]hl_gbykijZ_^eb ke_^mxsbokemqZyo

25. ^ey^mol_ejZaf_judhlhjuoij_g_[j_`bfhfZeuk jZkklhygb_fr f_`^mgbfb

26. _kebh^ghbal_ebf__lnhjfmrZjZjZ^bmkb fZkkZ dhlhjh]h h fgh]h jZa [hevr_ q_f m lhjh]h l_eZ ijhbahevghc nhjfu

27. ^ey ^mo h^ghjh^guo l_e rZjhh[jZaghc nhjfu ijb ex[uobojZaf_jZo 7. Z 1. _jgh 2. Mf_gvrZ_lky3. Fl = mg. §16. 4. KbeZly`_klb[hevr_gZ ihexkZoldA_fey g_fgh]hkiexkgmlZ m ihexkh 5. Hghijb[ebabl_evgh jZaf_gvr_a_fgh]h 12

28. 1. RZjbd ^b`_lky hl lhqdb : d lhqd_ ih^ ^_cklb_f kbeu §18. 7 mijm]hklb F WlZ kbeZ hagbdeZ j_amevlZl_ jZkly`_gby rgmjZ Kdhjhklv mkdhj_gb_ rZjbdZ b ^_cklmxsZy gZ g_]h kbeZ gZijZe_gu hl lhqdb A d lhqd_ B RZjbd ^b`_lky ijyfhebg_cgh l__]hljZ_dlhjby²ijyfZyebgby 2. KbeZmijm]hklb rgmj_hagbdeZ j_amevlZl__]hjZkly`_gbyb hgZgZijZe_gZd lhqd_OKdhjhklvrZjbdZb ^_cklmxsZygZg_]h kbeZ gZijZe_gu ih ijyfuf i_j_k_dZxsbfky ih^ m]ehf 4 . LjZ_dlhjby rZjbdZ ij_^klZey_l kh[hc hdjm`ghklv l_ rZjbd ^b`_lkydjbhebg_cgh 3. ?keb kdhjhklv l_eZ b ^_cklmxsZy gZ g_]h kbeZ gZijZe_gu ^hev i_j_k_dZxsboky ijyfuo lh l_eh ^b`_lky djbhebg_cgh _keb^hevh^ghcijyfhclhl_eh^b`_lkyijyfhebg_cgh 1. Hiulihuk_dZgbxbkdjubalhqbevgh]hdZfgy §19. 2. Mkdhj_gb_ gZijZe_gh ih jZ^bmkm d p_gljm hdjm`ghklb b hgh gZauZ_lkyp_gljhklj_fbl_evguf 3. Ihnhjfme_Zp = v2 . 4. Ih jZ^bmkm d p_gljm hdjm`ghklb ?_ fh^mev hij_^_ey_lky ih r nhjfme_Fp = mv 2 . r §20. 1. H[jZs_gb_ieZg_lhdjm]KhegpZb kimlgbdhhdjm]ieZg_l 2. Ld hg h[eZ^Z_l ^hklZlhqgh [hevrhc kdhjhklvx gZijZe_gghc ihdZkZl_evghcd ljZ_dlhjbb^b`_gby 3. Z ld lZdh_ ^b`_gb_ ijhbkoh^bl lhevdh ih^ ^_cklb_f kbeu ly`_klb 4. Khh[sblv_fmi_jmxdhkfbq_kdmxkdhjhklv 5. Zp = ; v 2 = gr ⇒ v = gr . IheZ]Zyr ≈ RAlhihemqZ_f v2 v2 ;g= r r qlh v = gRA ≈ dfk 6. Ihweebilbq_kdhchj[bl_hdjm]A_febihweebilbq_kdhchj[bl_ hdjm]KhegpZ 13

29. §21. 1. Bfimevkhf l_eZ gZauZ_lky nbabq_kdZy _ebqbgZ jZgZy ijhba_^_gbxfZkkul_eZgZ_]hkdhjhklv 2. Bfimevkb kdhjhklv^b`ms_]hkyl_eZk_]^ZkhgZijZe_gu 3. kbkl_f_KBd]⋅fk §22. 1. Hiul bah[jZ`_gguc gZ jbkmgd_ mq_[gbdZ ijhh^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 kh_]h ij_`g_]h iheh`_gby m^Zjy_lky h lhjhc b hklZgZebZ_lky Ijb wlhf lhjhc rZjbd hldehgy_lky gZ lhl `_ m]he LZdbf h[jZahf ijb aZbfh^_cklbbbfimevki_jh]hrZjbdZmf_gvrbekygZklhevdhgZ kdhevdhm_ebqbekybfimevklhjh]hWlhlhiulih^l_j`^Z_laZdhg khojZg_gbybfimevkZ 2. Kbkl_fZl_egZauZ_lkyaZfdgmlhc_kebgZwlbl_eZg_^_cklmxl g_rgb_kbeu 3. _dlhjgZykmffZbfimevkhl_eaZfdgmlhckbkl_fuihklhyggZh j_f_gbijbex[uo^b`_gbyob aZbfh^_cklbyowlbol_e 7 7 7 7 7 7 4. m1v1 + m2 v ′ = m1v1 + m2 v2 ]^_ m1, m2 ² fZkku l_e v1 , v 2 ² bo 7 7 ′ kdhjhklb ^h aZbfh^_cklby v1 , v 2 ² bo kdhjhklb ihke_ 2 ′ ′ aZbfh^_cklby §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 ijhlbhiheh`guf ih gZijZe_gbx bfimevkhf j_amevlZl_ hg ^b`_lkyijhlbhiheh`ghkljm_uoh^ys_]hbarZjbdZha^moZ 2. b`_gb_ h^hf_lguo ]b^jhfhlhpbdeh j_Zdlbguo kZfhe_lh b jZd_l 3. h_ggh_gZmqghbkke_^hZl_evkdh_ljZgkihjlgh_b l^ 4. =jmahhc hlk_d ihe_aghc gZ]jmadb kemqZ_ bah[jZ`_gghf gZ jbkmgd_ wlh dhkfbq_kdbc dhjZ[ev

30. ijb[hjguc hlk_d [Zd k hdbkebl_e_f[Zdk ]hjxqbfgZkhkudZf_jZk]hjZgbykhieh 5. JZkkfhljbf ijbgpbi ^_cklby jZd_lu gZ ijbf_j_ h^ghklmi_gqZlhc K ihfhsvx gZkhkh lhiebh b hdbkebl_ev ih^Zxlky dZf_jmk]hjZgby]^_hgbk]hjZyh[jZamxl]Zaukhdhc l_fi_jZlmju b ukhdh]h ^Ze_gby j_amevlZl_ hagbdgh_gby [hevrhc jZaghklb ^Ze_gbc dZf_j_ k]hjZgby b dhkfbq_kdhf 14

31. ijhkljZgkl_]ZaubadZf_juk]hjZgbyulZedbZxlkygZjm`mq_j_a khieh k h]jhfghc kdhjhklvx kbem aZdhgZ khojZg_gby bfimevkZ jZd_lZ ihemqZ_l bfimevk jZguc ih fh^mex b ijhlbhiheh`gh gZijZe_ggucbfimevkmue_l_r_ckljmb]ZaZ 6. Hlkdhjhklbbkl_q_gby]ZaZfZkkulhiebZlbiZlhiebZb l^ 7. Kihkh[ghklvjZabZlv[hevrmxkdhjhklv 8. Khiehfgbald lZdhfkemqZ_j_ZdlbgZykljmy]Zkblkdhjhklv jZd_lu 1. Dhe_[Zgb_fZylgbdZqZkhkljmgu]blZju §24. 2. b`_gb_ihlhjy_lkyq_j_ahij_^_e_ggucijhf_`mlhdj_f_gb 3. I_jbh^hf dhe_[Zgbc gZauZ_lky ijhf_`mlhd j_f_gb q_j_a dhlhjuc ^b`_gb_ ihlhjy_lky j_fy kh_jr_gby h^gh]h dhe_[Zgby

32. 4. AZj_fyjZgh_i_jbh^mdhe_[ZgbcdZ`^h_babah[jZ`_gguogZ jbkmgd_ mq_[gbdZ l_e ^Z`^u ijhoh^bl q_j_a iheh`_gb_ jZgh_kby^b]Zykv ijhlbhiheh`guogZijZe_gbyo

33. §25. 1. KbeZmijm]hklb^_cklm_lgZrZjbd lhqdZo, K, D, :lddh]^Z rZjbdgZoh^blky wlbolhqdZoijm`bgZ^_nhjfbjhZgZjZklygmlZ beb k`ZlZ

34. lhqd_ O kbeZ mijm]hklb gZ rZjbd g_ ^_cklm_l ld dh]^Z rZjbd gZoh^blky wlhc lhqd_ ijm`bgZ g_ ^_nhjfbjhZgZ LhqdZO gZauZ_lkyiheh`_gb_fjZgh_kbyrZjbdZ 2. Ih f_j_ ijb[eb`_gby rZjbdZ d lhqd_ O kdhjhklv l_eZ m_ebqbZ_lky ld kbeZ mijm]hklb b mkdhj_gb_ khiZ^Zxl ih gZijZe_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_ ijhlbhiheh`ghgZijZe_gukdhjhklb 3. Ld ex[h_ l_eh h[eZ^Z_l khcklhf khojZgylv khx kdhjhklv _kebgZg_]hg_^_cklmxlkbeubeb^_cklb_kbekdhfi_gkbjhZgh Ijb ijhoh`^_gbb iheh`_gby jZgh_kby gZ rZjbd g_ ^_cklm_l kbeZ mijm]hklb Z _]h kdhjhklv g_ jZgZ gmex b khojZgy_l kh_ agZq_gb_b gZijZe_gb_ 4. Dhe_[ZgbygZauZxlkykh[h^gufb_kebhgbijhbkoh^yllhevdh aZkq_lgZqZevgh]haZiZkZwg_j]bbkbkl_fu 5. Dhe_[Zl_evgufbkbkl_fZfb gZauZxlkykbkl_ful_ekihkh[guo kh_jrZlvkh[h^gu_dhe_[Zgby 6. FZylgbdhf gZauZ_lky l_j^h_ l_eh kh_jrZxs__ ih^ ^_cklb_f ijbeh`_gguo kbe dhe_[Zgby hdheh g_ih^b`ghc lhqdb bebhdjm]hkb 15

35. 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`_gbyjZgh_kby:fieblm^Zh[hagZqZ_lky[mdhc©:ªb KB baf_jy_lky f_ljZof

36. I_jbh^ ² j_fy kh_jr_gby h^gh]h dhe_[Zgby I_jbh^ h[hagZqZ_lky[mdhc©Tªb KBbaf_jy_lky k_dmg^Zok

37. QZklhlZ ² dhebq_klh dhe_[Zgbc _^bgbpm j_f_gb QZklhlZ h[hagZqZ_lky[mdhc©νªb KBbaf_jy_lky ]_jpZo=p

38. 2. H^ghihegh_dhe_[Zgb__klvdhe_[Zgb_aZi_jbh^ 3. Kyavf_`^mi_jbh^hfb qZklhlhcujZ`Z_lkynhjfmehcL = 1/ν bebν = 1/L. 4. Z

39. Q_f[hevr_^ebgZgblbfZylgbdZl_ff_gvr_qZklhlZ[

40. q_f [hevr_^ebgZgblbfZylgbdZl_f[hevr_i_jbh^ 5. Kh[kl_gghcqZklhlhcdhe_[Zl_evghckbkl_fugZauZ_lkyqZklhlZ kh[h^guodhe_[Zgbckbkl_fu 6. ?keb fZylgbdb dhe_[exlky ijhlbhiheh`guo nZaZo lh bo kdhjhklb ijhlbhiheh`gh gZijZe_gu _keb h^bgZdhuo lh bo kdhjhklbkhgZijZe_gu §27. 1. Hiul klZbeky k p_evx ihdZaZlv qlh dhe_[Zgby ijm`bggh]h fZylgbdZyeyxlky]Zjfhgbq_kdbfbHgaZdexqZ_lky lhfqlh]jma gZijbf_j hjhgdZ k gZeblhc djZkys_c `b^dhklvx

41. mdj_ie_gguc gZ ijm`bg_ ijb kh_f dhe_[Zl_evghf ^b`_gbb hklZey_l ke_^ ljZ_dlhjbb gZ ^b`ms_cky k ihklhygghc kdhjhklvx [mfZ`ghc e_gl_ Ihemq_ggZy lZdbf kihkh[hf ljZ_dlhjby yey_lky kbgmkhb^hc 2. Kbgmkhb^hc Hlj_ahd OA khhl_lklm_l Zfieblm^_ dhe_[Zgbc Z hlj_ahdOB ²i_jbh^m 3. =Zjfhgbq_kdbfb dhe_[Zgbyfb gZauZxlky dhe_[Zgby dhlhjuo baf_g_gb_dZdhceb[h nbabq_kdhc _ebqbgu ijhbkoh^bl ih aZdhgm kbgmkZbebdhkbgmkZ 4. Qlhdhe_[Zgbygbl_h]hfZylgbdZyeyxlky]Zjfhgbq_kdbfb 5. FZl_jbZevgZy lhqdZ h[eZ^ZxsZy fZkkhc b dhe_[exsZyky gZ ihklhygghf jZkklhygbb hl lhqdb ih^_kZ gZauZ_lky fZl_fZlbq_kdbffZylgbdhf 16

42. 6. Dhe_[Zgby gblygh]h fZylgbdZ fh`gh kqblZlv ]Zjfhgbq_kdbfb _keb^ebgZgblbfgh]h[hevr_jZaf_jhih^_r_ggh]hgZg_cl_eZ gZijbf_j rZjbdZ

43. gblv hq_gv e_]dZy b fZehjZkly`bfZy kbeu lj_gby kbkl_f_hlkmlklmxlZfieblm^Zdhe_[ZgbcfZeZ 7. F_gyxlkyihaZdhgmkbgmkZbebdhkbgmkZ §28. 1. Ijbmkehbbhlkmlklbyihl_jvwg_j]bb 2. KmffZ dbg_lbq_kdhc b ihl_gpbZevghc wg_j]bc ihklhyggZ kh]eZkgh aZdhgm khojZg_gby wg_j]bb b jZgZ i_jhgZqZevghfm aZiZkmihl_gpbZevghcwg_j]bbdhe_[Zl_evghckbkl_fu 3. G_l 4. Mf_gvrZ_lky 5. h^_ ld g_c gZ fZylgbd ^_cklm_l [hevrZy kbeZ khijhlbe_gbyq_f ha^mo_ §29. 1. G_lbaaZkhijhlbe_gbykj_^u 2. Ijbeh`blvd dhe_[exs_fml_emi_jbh^bq_kdmxg_rgxxkbem 3. Dhe_[ZgbygZauZxlkyugm`^_ggufb_kebhgbijhbkoh^ylih^ ^_cklb_fi_jbh^bq_kdbbaf_gyxs_ckyg_rg_ckbeu 4. ugm`^Zxs_c kbehc gZauZ_lky i_jbh^bq_kdb baf_gyxsZyky g_rgyykbeZuauZxsZydhe_[Zgby 5. Dh]^Z Zfieblm^Z b qZklhlZ ugm`^_gguo dhe_[Zgbc i_j_klZxl f_gylvky 6. WlbqZklhlujZgu 7. Fh]mlgZijbf_jihjr_gvihfihh]hgZkhkZ 8. hl_oihjihdZ^_cklm_lugm`^ZxsZykbeZ §30. 1. Hiul ijhh^blky k p_evx ^_fhgkljZpbb ye_gby j_ahgZgkZ ey wlh]h [_jml ^Z fZylgbdZ bkysb_ gZ h[s_f rgmj_ ebgZ fZylgbdZ g_baf_ggZ b ke_^hZl_evgh _fm khhl_lklm_l hij_^_e_ggZy qZklhlZ kh[h^guo dhe_[Zgbc kh[kl_ggZy qZklhlZ

44. ebgm fZylgbdZ fh`gh f_gylv ijb ihfhsb kh[h^guo dhgph gbl_cIjbwlhff_gy_lky_]hkh[kl_ggZyqZklhlZ?kebhldehgblv fZylgbdhliheh`_gbyjZgh_kbyb ij_^hklZblvkZfhfmk_[_lh hg gZqg_l kh_jrZlv kh[h^gu_ dhe_[Zgby Wlh uah_l dhe_[Zgby rgmjZ j_amevlZl_ q_]h gZ fZylgbd [m^_l ^_cklhZlv ugm`^ZxsZy kbeZ k qZklhlhc jZghc kh[kl_gghc qZklhl_ 17

45. fZylgbdZ Ih^ ^_cklb_f wlhc kbeu fZylgbd gZqg_l kh_jrZlv ugm`^_ggu_dhe_[Zgby?kebl_i_jvmf_gvrZlvêbgmfZylgbdZ lh _]h qZklhlZ b qZklhlZ ugm`^Zxs_c kbeu ^_cklmxs_c gZ fZylgbd [m^ml m_ebqbZlvky Ijb wlhf Zfieblm^Z mklZghbrboky ugm`^_gguo dhe_[Zgbc fZylgbdZ [m^_l hajZklZlv HgZ ^hklb]g_l fZdkbfZevgh]h agZq_gby ijb jZ_gkl_ êbg fZylgbdh Z khhl_lkl_ggh ijb jZ_gkl_ qZklhlu ugm`^Zxs_c kbeu b kh[kl_gghc qZklhlu fZylgbdZ wlhf b khklhblkmlvye_gbyj_ahgZgkZ 2. Ye_gb_ j_ahgZgkZ aZdexqZ_lky j_adhf m_ebq_gbb Zfieblmû mklZghbrboky ugm`^_gguo dhe_[Zgbc ijb khiZ^_gbb qZklhlu kh[kl_gguo dhe_[Zgbc kbkl_fu k qZklhlhc ugm`^Zxs_ckbeu 3. ldboêbguZke_^hZl_evghb qZklhlujZgu 4. Lhevdhd ugm`^_gguf 5. Ihe_agh_ ye_gb_ fmaudZevguo bgkljmf_glZo j_^gh_ ye_gb_ ijb ijhoh`^_gbb khe^Zl ih fhklm gh]m j_amevlZl_ j_ahgZgkZfhklfh`_ljZajmrblvky 1. hafms_gby jZkijhkljZgyxsb_ ijhkljZgkl_ b m^Zeyxsb_ky §31. hlf_klZbohagbdgh_gbygZauZxlkyhegZfb 2. gboijhbkoh^bli_j_ghkwg_j]bb[_ai_j_ghkZ_s_klZ 3. G_lg_ijhbkoh^bl 4. Mijm]bfb hegZfb gZauZxlky hegu jZkijhkljZgyxsb_ky mijm]bokj_^Zo 5. We_dljhfZ]gblgu_hegu 1. Ijh^hevgu_hegu²wlhlZdb_hegu dhlhjuodhe_[ZgbyqZklbp §32. kj_û kh_jrZxlky ^hev gZijZe_gby jZkijhkljZg_gby heg gZijbf_jamdhu_heguIhi_j_qgu_hegu²wlhlZdb_heguijb dhlhjuo dhe_[Zgby qZklbp kj_û kh_jrZxlky i_ji_g^bdmeyjgh gZijZe_gbxjZkijhkljZg_gby heg gZijbf_jhegu gZ ih_joghklb hû 2. hegZfb k^b]Z yeyxlky 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]_ 18

46. §33. 1. ebghchegugZauZ_lkyjZkklhygb_f_`^m^mfy[eb`Zcrbfb lhqdZfbhegudhe_[exsbfky h^bgZdhuonZaZo 2. ;mdhc©λªqblZ_lky©eZf[^Zª

47. 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 §34. hagbdgh_gby amdZ i_jhf hiul_ dZq_kl_ bklhqgbdZ amdZ [_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 jZgh_kby b ^Zlv _c kh_jrZlv kh[h^gu_ dhe_[Zgby lh fu mkeurbf amd LZdbf h[jZahf bklhqgbdZfb amdZ yeyxlky dhe_[Zl_evgu_ kbkl_fu 2. Ex[hcbklhqgbdamdZyey_lkydhe_[Zl_evghckbkl_fhc 3. Dhe_[Zgby k qZklhlhc hl =p ^h =p gZauZxlky amdhufbihkdhevdmhkijbgbfZxlkyq_eh_dhf 4. BgnjZamdhufb gZauZxlky dhe_[Zgby k qZklhlhc gb`_ =p mevljZamdhufb²k qZklhlhcur_=p 1. Hiul ijhh^blky k p_evx uykgblv aZbkbfhklv ukhlu amdZ hl §35. qZklhlu dhe_[Zgbc ey ijh_^_gby ^Zggh]h hiulZ [_jml ijb[hj khklhysbcbag_kdhevdboam[qZluof_lZeebq_kdbo^bkdhbf_xsbo jZaebqgh_ qbkeh am[v_ b aZdj_ie_gguo gZ h^ghc hkb AZl_f k_ ^bkdb ijbh^yl h jZs_gb_ b lhgdhc dZjlhgghc ieZklbgdhc ihhq_j_^gh dZkZxlky am[v_ dZ`^h]h ba ^bkdZ Ijb wlhf fu mkeurbfjZagu_ihukhl_amdbFh`ghaZf_lblvqlhq_f [hevr_ qbkeh am[v_ gZ ^bkd_ b khhl_lkl_ggh [hevr_ qZklhlZ dhe_[Zgbc dZjlhgghcieZklbgdbl_f [hevr_ [m^_lukhlZamdZ :gZeh]bqgmx aZbkbfhklvfh`gh uyblv bkihevamy k_]h lhevdh h^bg ^bkd ey wlh]hgZ^h m_ebqbZlvkdhjhklv ^bkdZ Q_f [hevr_ kdhjhklv ^bkdZ l_f [hevr_ qZklhlZ dhe_[Zgbc dZjlhgghc ieZklbgdb b l_f ur_ [m^_lba^ZZ_fucamd 2. Hiulijhh^blkyk p_evxuykgblvaZbkbfhklvukhluamdZhl qZklhlu dhe_[Zgbc ey ijh_^_gby ^Zggh]h hiulZ [_jml ^Z dZf_jlhgZ ba^Zxsbo amdb jZaghc ukhlu H[Z dZf_jlhgZ ijbh^yl dhe_[Zl_evgh_ ^b`_gb_ Ijb wlhf hkljby 19

48. aZdj_ie_ggu_ gZ gbo hklZeyxl gZ ^b`ms_cky kl_deygghc ieZklbgd_ke_^u?kebkjZgblvwlbke_^ulhfh`ghm[_^blvkyqlh qZklhlZdhe_[Zgbc[hevr_m dZf_jlhgZk [he__ukhdbfamdhf 3. HlqZklhludhe_[Zgby 4. Qbkluf lhghf gZauZ_lky amd bklhqgbdZ kh_jrZxs_]h ]Zjfhgbq_kdb_dhe_[Zgbykljh]hhij_^_e_gghcqZklhlu 5. Amd hij_^_e_gghc ukhlu khhl_lklmxsbc kZfhc gbadhc qZklhl_ keh`gh]h amdZ khhdmighklb g_kdhevdbo qbkluo lhgh

49. gZauZ_lky hkghguf lhghf h[_jlhgu beb ukrb_ ]Zjfhgbq_kdb_ lhgu²k_hklZevgu_lhgukeh`gh]hamdZ 6. DZq_klh amdZ hij_^_ey_fh_ khhdmighklvx h[_jlhgh keh`gh]hamdZgZauZ_lkyl_f[jhf 7. ukhlZamdZhij_^_ey_lkyqZklhlhchkghgh]hlhgZ 8. L_f[jamdZhij_^_ey_lkykhhdmighklvx_]hh[_jlhgh 1. Hiulijhh^blkyk p_evxuykgblvaZbkbfhklv]jhfdhklbamdZ §36. hl Zfieblmû dhe_[Zgbc ey ijh_^_gby ^Zggh]h hiulZ [_jml dZf_jlhg AZl_f _]h ijb ihfhsb fhehlhqdZ ijbh^yl dhe_[Zl_evgh_ ^b`_gb_ kgZqZeZ k h^ghc Zfieblm^hc ihke_ k [hevr_c Ijb wlhf dZf_jlhg dh]^Z dhe_[e_lky k [hevr_c Zfieblm^hcamqbl]jhfq_ 2. =jhfdhklvlZd`_mf_gvrblky 3. AmdqZklhlu=p]jhfq_ 4. Hl_ebqbguZfieblmûdhe_[Zgbc 5. kbkl_f_KB^; 6. Kemoq_eh_dZmom^rZ_lky §37. 1. Hiul ijhh^blky k p_evx ihdZaZlv qlh Zdmmf_ amd g_ jZkijhkljZgy_lky ey wlh]h ahghd ihf_sZxl ih^ dhehdhe ha^mrgh]h gZkhkZ b dexqZxl _]h AZl_f baih^ dhehdheZ gZqbgZxl hldZqbZlv ha^mo Ih f_j_ jZaj_`_gby ha^moZ amd keur_gk_lbr_b lbr_bgZdhg_pij_djZsZ_lkykhk_f?keb`_ ha^mo gZqZlv ghv imkdZlv lh amd klZghblky keur_g k_ ]jhfq_b ]jhfq_LZdbfh[jZahfamd [_aha^mrghfijhkljZgkl_ g_jZkijhkljZgy_lky 2. Z fh`_l Ijbf_ju jZkijhkljZg_gby amdZ l_jûo l_eZo ² jZkijhkljZg_gb_ amdZ ih `_e_agh^hjh`guf j_evkZf `b^dhklyo ²[jhr_ggucih^h^mdZf_gv ]ZaZo²]jhf 3. Mijm]b_ l_eZ yeyxlky emqrbfb ijhh^gbdZfb amdZ q_f ihjbklu_ D mijm]bf l_eZf hlghkylky [hevrbgklh f_lZeeh 20

50. ^_j_vy ]Zau `b^dhklb d ihjbkluf ² hcehd ihjhehg i_ghieZkl 4. Iml_fhl^_edbihf_s_gbcamdhbaheypbhggufbfZl_jbZeZfb 1. K qZklhlhckhhl_lklmxs_camdm §38. 2. Ijh^hevgmxhegm h[hbokemqZyo 3. Q_j_ag_kdhevdhk_dmgîhke_kiurdbfhegbbfukeurbf]jhf 4. f _d_ njZgpmakdbfb mq_gufb [ueZ baf_j_gZ kdhjhklv amdZ ^moimgdlZojZkklhygb_f_`^mdhlhjufb[uehba_klgh ijhbah^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 amd uklj_eZ Kdhjhklv amdZ hij_^_eyeb dZd hlghr_gb_ jZkklhygby f_`^m imgdlZfb d baf_j_gghfm hlj_adm j_f_gb 5. v fk 6. ZaZbkbl 1. j_amevlZl_hljZ`_gbyamdZhljZaebqguoij_]jZ^ §39. 2. fZe_gvdhc dhfgZl_ hljZ`_gguc amd hi_juo kebZ_lky k hkghgufbhlhjuoohjhrhih]ehsZ_lkyf_[_evx 3. Kl_guaZeZke_^m_lhl^_eZlvamdhih]ehsZxsbffZl_jbZehf 4. Ldamdhu_hegu jmihj_h[jZamxlmadhgZijZe_ggucimqhd 1. DhjimkZ]blZju[ZeZeZcdb §40. 2. eym_ebq_gby]jhfdhklb 3. BogZagZq_gb_²mkbe_gb_amdZb kha^Zgbyl_f[jZ 4. =hehkhu_kyadb 5. HlnhjfujZaf_jZfZl_jbZeZj_ahgZlhjZ 1. Hiulihkeh`_gbxamdhuoheghl^mobklhqgbdhijhh^blky §42. ke_^mxsbf h[jZahf dZq_kl_ bklhqgbdh amdZ [_jml ^Z ]jhfdh]hhjbl_ey=jb =jih^dexq_ggu_d amdhhfm]_g_jZlhjm A= BaemqZ_fuc bfb amd ihiZ^Z_l fbdjhnhg F ]^_ ihke_ ij_h[jZam_lky we_dljbq_kdb_ dhe_[Zgby Wlb dhe_[Zgby mkbebZxlky mkbebl_e_f gbadhc qZklhlu MGQ b j_]bkljbjmxlky ]ZevZghf_ljhf = GZkljhbf ]_g_jZlhj gZ qZklhlm =p l_ gZ êbgm hegu ijb[ebabl_evgh jZgmx kf =jhfdh]hhjbl_eb mklZghbfgZjZkklhygbbf hlfbdjhnhgZ?kebl_i_jvdZ`ûc 21

51. ]jhfdh]hhjbl_ev ihhq_j_^gh ih^dexqblv d ]_g_jZlhjm lh fh`gh aZf_lblv qlh ihdZaZgby ]ZevZghf_ljZ = h[hbo kemqZyo [m^ml h^bgZdhu LZdbf h[jZahf amdhu_ hegu h^bgZdhhc qZklhlu [m^ml bf_lv h^bgZdhu_ Zfieblmû ?keb l_i_jv ih^dexqblv ^Z ]jhfdh]hhjbl_ey h^ghj_f_ggh lh ihdZaZgby ]ZevZghf_ljZ m_ebqZlky ijbf_jgh ^Z jZaZ ih kjZg_gbx kh kemqZyfb dh]^Z dZ`ûc ba gbo ih^dexqZeky hl^_evghklb Wlh ]hhjbl h lhf qlh hegukdeZûZykvmkbebZxl^jm]^jm]Zl_Zfieblm^Zdhe_[Zgbc kmffZjghcamdhhcheg_[hevr_q_f h^ghc?kebl_i_jvh^bg ba ]jhfdh]hhjbl_e_c ihkl_i_ggh ijb[eb`Zlv d fbdjhnhgm lh fh`gh gZclb lZdb_ _]h iheh`_gby dh]^Z ihdZaZgby ]ZevZghf_ljZ [m^ml jZgu gmex hegu ]Zkyl ^jm] ^jm]Z

52. b dh]^Z hgb [m^ml fZdkbfZevgu hegu mkbebZxl ^jm] ^jm]Z

53. i_jhf kemqZ_ wlb iheh`_gby [m^ml khhl_lklhZlv jZkklhygbyf f_`^m i_j_^b]Z_fuf ]jhfdh]hhjbl_e_f b fbdjhnhghf ijhihjpbhgZevgufkfihehbg_^ebguhegu

54. hlhjhfkemqZ_ wlhjZkklhygb_ijhihjpbhgZevghkf^ebg_hegu

55. 2. JZaghklv jZkklhygbc ijhc^_gguo ^mfy hegZfb hl bklhqgbdh ^hdhgdj_lghclhqdbgZauZ_lkyjZaghklvxoh^Z^moheg 3. aZbkbfhklbhljZaghklboh^Zhegj_amevlbjmxsb_dhe_[Zgby eb[hmkbebZxlkyeb[hhkeZ[_Zxl 4. hegu gZauZxlky dh]_j_glgufb _keb hgb bf_xl h^bgZdhmx qZklhlmb ihklhyggmxhj_f_gbjZaghklvnZa 5. G_ f_gyxsZyky h j_f_gb dZjlbgZ jZkij_^_e_gby ijhkljZgkl_fbgbfmfhb fZdkbfmfhZfieblm^j_amevlbjmxsbo dhe_[Zgbc gZauZ_lky bgl_jn_j_gpbhgghc dZjlbghc Bgl_jn_j_gpbhggZy dZjlbgZ ihemqZ_lky lhevdh hl dh]_j_glguo bklhqgbdh 6. Ye_gb_keh`_gby ijhkljZgkl_ heg ijb dhlhjhf ihemqZ_lky ihklhyggh_ h j_f_gb jZkij_^_e_gb_ Zfieblm^ j_amevlbjmxsbo dhe_[ZgbcgZauZ_lkybgl_jn_j_gpb_c 7. GZ^h ijbdju h^gh moh gZdehgylvky jZagu_ klhjhgu aZbkbfhklb hl lh]h ihiZ^_l moh h[eZklv bgl_jn_j_gpbhggh]h fZdkbfmfZ beb fbgbfmfZ fu [m^_f khhl_lkl_ggh keurZlv mkbe_gb_bebhkeZ[e_gb_]jhfdhklbamdZ 8. eyk_ob^hheg §43. 1. b`msbfbkywe_dljbq_kdbfbaZjy^Zfb 2. gmlj_ggbfbwe_dljbq_kdbfblhdZfbfZ]gblZ 3. FZ]gblgufb ebgbyfb gZauZxlky hh[jZ`Z_fu_ ebgbb ^hev dhlhjuo jZkiheh`bebkv [u fZ]gblgu_ klj_edb ihf_s_ggu_ fZ]gblgh_ihe_ 22

56. 4. Khhl_lkl_gghijyfhebg_cghb djbhebg_cgh 5. AZgZijZe_gb_fZ]gblghc ebgbb dZdhceb[hlhqd_ijbgbfZxl gZijZe_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 gZijZe_gbbb _ebqbg_fZ]gblgh]hihey §44. 1. FZ]gblgu_ ebgbb ihehkhh]h fZ]gblZ uoh^yl ba k__jgh]h ihexkZ oh^yl x`guc gmljb fZ]gblZ hgb gZijZe_gu hl x`gh]hihexkZd k__jghfmM fZ]gblguoebgbcg_lgbgZqZeZgb dhgpZ hgb eb[h aZfdgmlu eb[h b^ml ba [_kdhg_qghklb [_kdhg_qghklv Ebgbb ihey ihehkhh]h fZ]gblZ bkdjbe_gu M ihexkhfZ]gblZhgbjZkiheh`_gu[he__]mklhq_f^Zebhlgbo 2. hdjm] fZ]gblZ b ijhh^gbdZ h[jZam_lky g_h^ghjh^gh_ fZ]gblgh_ihe_gmljbkhe_ghb^Z²h^ghjh^gh_ 3. h^ghjh^ghf fZ]gblghf ihe_ wlZ kbeZ dZ`^hc lhqd_ ihey ihklhyggZ b ih fh^mex b ih gZijZe_gbx g_h^ghjh^ghf fZ]gblghfihe_hgZ jZaguolhqdZoiheyfh`_l[ulvjZaebqghc b ihfh^mexb ihgZijZe_gbx 4. h^ghjh^ghf fZ]gblghf ihe_ fZ]gblgu_ ebgbb iZjZee_evgu b jZkiheh`_guk h^bgZdhhc]mklhlhc g_h^ghjh^ghffZ]gblghfihe_ fZ]gblgu_ebgbbbkdjbe_gub jZkiheh`_guk jZaebqghc]mklhlhc 5. Dj_klbdZfbb lhqdZfb 1. GZ^haylvijhh^gbdb ijhimklblvihg_fmlhdkgZqZeZ h^ghf §45. gZijZe_gbbZ aZl_f ^jm]hfIjbbaf_g_gbbgZijZe_gbylhdZgZ ijhlbhiheh`gh_ jy^hf jZkiheh`_ggZy k ijhh^gbdhf fZ]gblgZy klj_edZih_jg_lkygZ°LZdbfh[jZahfgZijZe_gb_fZ]gblguo ebgbckyaZghk gZijZe_gb_flhdZ 2. ?keb gZijZe_gb_ ihklmiZl_evgh]h ^b`_gby [mjZqbdZ khiZ^Z_l k gZijZe_gb_f lhdZ ijhh^gbd_ lh gZijZe_gb_ jZs_gby jmqdb [mjZqbdZ khiZ^Z_l k gZijZe_gb_f ebgbc fZ]gblgh]hiheykha^Zggh]hwlbflhdhf 3. AgZy gZijZe_gb_ lhdZ fh`gh hij_^_eblv gZijZe_gb_ ebgbc fZ]gblgh]h ihey b gZh[hjhl agZy gZijZe_gb_ fZ]gblguo ebgbc fh`ghhij_^_eblvgZijZe_gb_lhdZ 4. ?keb h[oZlblv khe_ghb^ eZ^hgvx ijZhc jmdb b gZijZblv q_luj_iZevpZihgZijZe_gbxlhdZ g_flh hlklZe_gguc gZ ° 23

57. [hevrhc iZe_p [m^_l mdZauZlv gZijZe_gb_ ebgbc fZ]gblgh]h iheygmljbkhe_ghb^Z 5. AgZy gZijZe_gb_ lhdZ khe_ghb^_ fh`gh hij_^_eblv gZijZe_gb_ ebgbc fZ]gblgh]h ihey gmljb g_]h b gZh[hjhl agZy gZijZe_gb_ fZ]gblguo ebgbc gmljb khe_ghb^Z fh`gh hij_^_eblvgZijZe_gb_lhdZ §46. 1. ;_j_lkyijhh^gbdb ih^_rbZ_lkygZ]b[dboijhh^Zodhlhju_ q_j_aj_hklZlih^dexq_gud bklhqgbdmlhdZIjhh^gbdihf_sZxl fZ]gblgh_ ihe_ ih^dhhh[jZagh]h fZ]gblZ ?keb aZfdgmlv p_iv lhijhh^gbdk lhdhfijb^_l ^b`_gb_?keb`_fZ]gblm[jZlvb aZfdgmlv p_iv lh k ijhh^gbdhf ijhbkoh^blv gbq_]h g_ [m^_l LZdbf h[jZahf gZ ijhh^gbd k lhdhf ihf_s_gguf fZ]gblgh_ ihe_^_cklm_lkbeZ 2. FZ]gblgh_ihe_h[gZjm`bZ_lkykhbf^_cklb_fgZijhh^gbdk lhdhf 3. GZijZe_gb_ wlhc kbeu aZbkbl hl gZijZe_gby lhdZ ijhh^gbd_b gZijZe_gbyfZ]gblguoebgbc 4. eyijhh^gbdZ_kebe_ZyjmdZjZkiheh`_gZlZdqlh__ q_luj_ iZevpZgZijZe_guihgZijZe_gbxlhdZZ fZ]gblgu_ebgbboh^yl eZ^hgv i_ji_g^bdmeyjgh d g_c lh hlklZe_gguc [hevrhc iZe_p mdZ`_lgZijZe_gb_^_cklmxs_cgZijhh^gbdkbeu ey^b`ms_ckyaZjy`_gghcqZklbpu_kebe_ZyjmdZjZkiheh`_gZ lZd qlh __ q_luj_ iZevpZ jZkiheh`_gu ijhlb gZijZe_gby ^b`_gby hljbpZl_evghc qZklbpu ih gZijZe_gbx ^b`_gby iheh`bl_evghc

58. Z fZ]gblgu_ ebgbb oh^yl eZ^hgv i_ji_g^bdmeyjgh d g_c lh hlklZe_gguc [hevrhc iZe_p mdZ`_l gZijZe_gb_^_cklmxs_cgZwlmqZklbpmkbeu 5. AZ gZijZe_gb_ lhdZ h g_rg_c qZklb p_ib ijbgbfZxl gZijZe_gb_^b`_gbyhliheh`bl_evgh]hihexkZbklhqgbdZlhdZd hljbpZl_evghfm 6. Ih ijZbem e_hc jmdb fh`gh hij_^_eblv gZijZe_gb_ kbeu ^_cklmxs_c gZ ijhh^gbd k lhdhf fZ]gblghf ihe_ beb gZijZe_gb_ kbeu ^_cklmxs_c gZ aZjy`_ggmx qZklbpm ^b`msmxky fZ]gblghf ihe_ LZd`_ ihevamykv wlbf ijZbehf fh`ghhij_^_eblvgZijZe_gb_lhdZ ijhh^gbd__kebagZ_fdZd gZijZe_gu fZ]gblgu_ ebgbb b kbeZ ^_cklmxsZy gZ ijhh^gbd

59. gZijZe_gb_ fZ]gblguo ebgbc _keb agZ_f dZd gZijZe_g lhd ijhh^gbd_b kbeZ^_cklmxsZygZg_]h

60. agZdaZjy^Z^b`ms_cky qZklbpu _keb agZ_f dZd gZijZe_gu fZ]gblgu_ ebgbb kdhjhklv ^b`_gbyqZklbpub kbeZ^_cklmxsZygZg__

61. b l^ 24

62. 7. kemqZ_dh]^ZgZijZe_gb_lhdZ ijhh^gbd_eb[hgZijZe_gb_ kdhjhklbqZklbpukhiZ^Zxlk gZijZe_gb_ffZ]gblghcebgbbbeb iZjZee_evgu_c §47. 1. FZ]gblgZy bg^mdpby ² wlh _dlhjgZy nbabq_kdZy _ebqbgZ 7 oZjZdl_jbamxsZyfZ]gblgh_ihe_HgZh[hagZqZ_lkykbfhehf . 2. Fh^mev _dlhjZ fZ]gblghc bg^mdpbb hij_^_ey_lky dZd hlghr_gb_ fh^mey kbeu ^_cklmxs_c gZ jZkiheh`_gguc i_ji_g^bdmeyjghfZ]gblgufebgbyfijhh^gbdk lhdhfd kbe_lhdZ b _]h^ebg_ B = . F 3. kbkl_f_KBLeqblZ_lky©l_keZª

63. Il 4. EbgbyfbfZ]gblghcbg^mdpbbgZauZxlkyebgbb dZkZl_evgu_ d dhlhjuf dZ`^hc lhqd_ ihey khiZ^Zxl k gZijZe_gb_f _dlhjZ fZ]gblghcbg^mdpbb 5. FZ]gblgh_ ihe_ h^ghjh^gh _keb h k_o _]h lhqdZo fZ]gblgZy 7 bg^mdpby ihklhyggZ ijhlbghf kemqZ_ fZ]gblgh_ ihe_ g_h^ghjh^gh 6. KbeZ^_cklmxsZygZfZ]gblgmxklj_edmbeb^b`msbckyaZjy^ fZ]gblghf ihe_ [m^_l l_f [hevr_ q_f [hevr_ fh^mev _dlhjZ fZ]gblghcbg^mdpbb ^Zgghclhqd_ihey §48. 1. FZ]gblgucihlhdijhgbauZxsbciehkdbcdhglmj fZ]gblghf ihe_ aZbkbl hl fh^mey _dlhjZ fZ]gblghc bg^mdpbb iehsZ^b dhglmjZ b hjb_glZpbb dhglmjZ ih hlghr_gbx d gZijZe_gbx fZ]gblguoebgbc 2. M_ebqbZ_lky n jZa ihkdhevdm fZ]gblguc ihlhd ijyfh ijhihjpbhgZe_gfh^mex_dlhjZfZ]gblghcbg^mdpbb 3. FZ]gblguc ihlhd fZdkbfZe_g _keb iehkdhklv dhglmjZ i_ji_g^bdmeyjgZ d gZijZe_gbx fZ]gblguo ebgbc b jZ_g gmex _kebiehkdhklvdhglmjZiZjZee_evgZfZ]gblgufebgbyf 4. Zf_gy_lky §49. 1. k_ hiulu ^_fhgkljbjmxl ye_gb_ we_dljhfZ]gblghc bg^mdpbb aZdexqZxs__ky hagbdgh_gb_ lhdZ aZfdgmlhf ijhh^gbd_ ijb baf_g_gbb fZ]gblgh]h ihlhdZ ijhgbauZxs_]h hoZq_ggmx 25

64. ijhh^gbdhf iehsZ^v i_jhf hiul_ ]ZevZghf_lj j_]bkljbjm_l ihye_gb_ lhdZ aZfdgmlhc gZ g_]h dZlmrd_ ijb klZe_gbb g__ fZ]gblZ h lhjhf hiul_ dZlmrdZ dexq_ggZy p_iv bklhqgbdZ lhdZ klZey_lky h lhjmx dZlmrdm aZfdgmlmx gZ ]ZevZghf_lj IjbaZfudZgbbb jZafudZgbbp_ib]ZevZghf_ljkghZj_]bkljbjm_l lhd 2. Ijbbaf_g_gbbfZ]gblgh]hihlhdZq_j_adZlmrdm 3. Ye_gb_we_dljhfZ]gblghcbg^mdpbbaZdexqZ_lky hagbdgh_gbb we_dljbq_kdh]h lhdZ aZfdgmlhf ijhh^gbd_ ijb baf_g_gbb fZ]gblgh]h ihlhdZ ijhgbauZxs_]h hoZq_ggmx ijhh^gbdhf iehsZ^v 4. Ye_gb_ we_dljhfZ]gblghc bg^mdpbb bkihevam_lky we_dljh]_g_jZlhjZoihemqbrborbjhdh_jZkijhkljZg_gb_ §50. 1. We_dljbq_kdbc lhd i_jbh^bq_kdb f_gyxsbcky h j_f_gb ih fh^mex b ih gZijZe_gbx gZauZ_lky i_j_f_gguf lhdhf I_j_f_gguc lhd fh`gh ihemqblv _keb dZlmrd_ aZfdgmlhc gZ ]ZevZghf_lj i_jbh^bq_kdb ^b]Zlv fZ]gbl _jo b gba Ijb wlhf klj_edZ ]ZevZghf_ljZ [m^_l i_jbh^bq_kdb hldehgylvky hl gme_h]h agZq_gby lh h^gm klhjhgm lh ^jm]mx Wlh [m^_l kb^_l_evklhZlv h lhf qlh b fh^mev kbeu bg^mdpbhggh]h lhdZ b _]h gZijZe_gb_ i_jbh^bq_kdb f_gyxlky h j_f_gb l_ dZlmrd_ h[jZam_lkyi_j_f_gguclhd 2. we_dljhk_lyo 3. GZye_gb_we_dljhfZ]gblghcbg^mdpbb 4. =_g_jZlhj khklhbl ba klZlhjZ ² g_ih^b`ghc qZklb uihegyxs_cnmgdpbxaZfdgmlh]hdhglmjZjhlhjZ²jZsZxs_cky qZklb uihegyxsbc nmgdpbx fZ]gblZ ijhfure_gguo ]_g_jZlhjZo bkihevamxlky h[uqgh we_dljhfZ]gblu

65. Ijbgpbi ^_cklby ]_g_jZlhjZ hkghZg gZ ye_gbb we_dljhfZ]gblghc bg^mdpbbIjbjZs_gbbjhlhjZg_rg_ckbehcf_gy_lkyfZ]gblguc ihlhdijhgbauZxsbcklZlhj j_amevlZl_q_]h g_fbg^mpbjm_lky i_j_f_gguclhd 5. GZ l_iehhc we_dljhklZgpbb jhlhj ]_g_jZlhjZ ijbh^blky h jZs_gb_ iZjhhc 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

66. §51. 1. :g]ebckdbfmq_gufDFZdk_eehf

67. ]WlZ l_hjby djZlp_ kh^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. Kbehu_ ebgbb boj_h]h we_dljbq_kdh]h ihey aZfdgmlu Z kbehu_ ebgbb we_dljhklZlbq_kdh]h ihey gZqbgZxlky gZ iheh`bl_evguoaZjy^Zob aZdZgqbZxlkygZhljbpZl_evguo §52. 1. We_dljhfZ]gblgZy hegZ ij_^klZey_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 yeyxlky ihi_j_qgufb lZd dZd iehkdhklv dhlhjhc e_`Zl dhe_[exsb_ky 7 7 _dlhju B b E i_ji_g^bdmeyjgZ gZijZe_gbx jZkijhkljZg_gby hegu Bklhqgbdhf we_dljhfZ]gblguo heg yeyxlky mkdhj_ggh ^b`msb_ky we_dljbq_kdb_ aZjy^u Kdhjhklv jZkijhkljZg_gby we_dljhfZ]gblguoheg Zdmmf_jZgZkdhjhklbk_lZl_ dfk 7 2. _dlhj gZijy`_gghklb we_dljbq_kdh]h ihey E b _dlhj 7 fZ]gblghcbg^mdpbb B . 3. λ = cT = k/ν. 7 4. eywlh]hg_h[oh^bfhqlh[uqZklhlZν dhe_[Zgbc_dlhjh B b 7 E [ueZ^hklZlhqgh[hevrhc 5. We_dljhfZ]gblgu_ hegu i_ju_ m^Zehkv h[gZjm`blv =_gjbom =_jpm ] 6. b^bfuck_lmevljZnbhe_ljZ^bhhegu 7. JZ^bhkyavjZ^bhehdZpbyjZ^bhZkljhghfbyj_gl]_gb ^j 1. GZ kq_l k_lZ kms_klhZeb ^_ hkghguo l_hjbb §53. dhjimkdmeyjgZyb heghZy hkgh_i_jhce_`Zehml_j`^_gb_h lhf qlh k_l ² wlh ihlhd qZklbp hkgh_ lhjhc ml_j`^_gb_ h lhfqlhk_l²wlhhegZ 27

68. 2. ] Zg]ebckdbc mq_guc LhfZk Xg] ihdZaZe qlh k_lm ijbkms_ khcklh bgl_jn_j_gpbb Wlh ^hdZauZeh lh qlh k_l h[eZ^Z_lheghufbkhcklZfb 3. GZ ijhhehqgh_ dhevph k jmqdhc aZlygmlh_ fuevghc ie_gdhc aZl_fg_gghc dhfgZl_ gZijZeyeky k_l gZijbf_j `_elh]h p_lZ Ijb wlhf gZ ie_gd_ h[jZahuZebkv 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 yeyxlky dh]_j_glgufb ld hgb h[jZamxlky hl h^gh]h b lh]h `_ bklhqgbdZ JZaghklv oh^Z ^ebg heg aZbkbl hl lhesbgu ie_gdb dhlhjZy jZaguo lhqdZo jZaebqgZ ?keb lhesbgZ ie_gdb hdZ`_lky lZdhc qlh hegu[m^mluoh^blvbalhq_d: b Kbf_yh^bgZdhu_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`_lkylZdhcqlhhegu[m^mluoh^blvbalhq_d : b K ijhlbhiheh`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^hdZauZ_llhqlhk_lh[eZ^Z_lheghufbkhcklZfb 6. QZklhlubeb^ebgu

69. k_lhuohegjZaguop_lhjZaebqgu §54. 1. b^_mijm]bohegih^h[ghamdhuf 2. L_fqlhk_ljZkijhkljZgy_lkyb Zdmmf_ 3. FZdk_ee ij_^iheh`be qlh k_l ² wlh qZklguc kemqZc we_dljhfZ]gblguo heg HkghZgb_f ^ey wlh]h ihkem`beh lh qlh k_lhu_ b we_dljhfZ]gblgu_ hegu yeyxlky ihi_j_qgufb b h[eZ^Zxlh^bgZdhhckdhjhklvxjZkijhkljZg_gby 4. QZklbpZwe_dljhfZ]gblgh]hbaemq_gbygZauZ_lkynhlhghf §55. 1. Hldjulb_ ;_dd_j_ey khklhyeh lhf qlh g_dhlhju_ _s_klZ kZfhijhbahevgh baemqZxl g_b^bfu_ emqb gZaZggu_ ihke_^klbbjZ^bhZdlbgufbaemq_gb_f 2. JZ^bhZdlbghklvx 3. ] Wjg_kl J_a_jnhj^ hiulguf iml_f h[gZjm`be qlh jZ^bhZdlbgh_ baemq_gb_ jZ^by g_h^ghjh^gh b bf__l keh`guc khklZ lheklhkl_gguc kbgphuc khkm^ hg ihf_sZe djmibgdm 28

70. jZ^by Imqhd jZ^bhZdlbgh]h baemq_gby jZ^by ijhoh^be kdhav madh_ hl_jklb_ b ihiZ^Ze gZ nhlhieZklbgdm Ihke_ ijhye_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_ ijhye_gby h[gZjm`bZehkv ljb iylgZ ² h^gh ih p_gljm ^Z k[hdm hl g_]h Wlh ]hhjbl h lhf qlh imqhd baemq_gby khklZeyeb iheh`bl_evgh aZjy`_ggu_ αqZklbpu

71. hljbpZl_evgh aZjy`_ggu_ βqZklbpu

72. b g_cljZevgu_ γqZklbpu

73. qZklbpu 4. αqZklbpZ ij_^klZey_l kh[hc iheghklvx bhgbabjhZgguc Zlhf ]_eby k aZjy^hf jZguf fh^mex m^h_ggh]h aZjy^Z we_dljhgZ β- qZklbpZ 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_^klZeye rZj ih k_fm h[t_fm dhlhjh]h jZghf_jgh jZkij_^_e_g iheh`bl_evguc aZjy^ gmljb wlh]h gZoh^ylky we_dljhgu dZ`^uc badhlhjuodhe_[e_lkyhdhehkh_]hiheh`_gbyjZgh_kby 2. kbgphuc khkm^ K ihf_sZeky jZ^bhZdlbguc 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_]bkljbjhZebkv WdjZg [ue ihdjul ki_pbZevguf _s_klhf [eZ]h^Zjy q_fm f_klZo ihiZ^Zgby gZ g_]h αqZklbp hagbdZeb kiurdb dhlhju_ j_]bkljbjhZebkv ijb ihfhsb fbdjhkdhiZ F LZdhc kihkh[ j_]bkljZpbb gZauZ_lky f_lh^hf kpbglbeeypbc kiur_d

74. Ihke_ ky wlZ mklZghdZ ihf_sZeZkv khkm^ ba dhlhjh]h [ue hldZqZg ha^mo b ijhh^beky hiul ?keb gZ imlb α- qZklbpg_lgbdZdboij_]jZ^lhhgbihiZ^ZebgZwdjZgmadbfke_]dZ jZkrbjyxsbfky imqdhf Ijb wlhf gZ wdjZg_ gZ[ex^Z_lky g_[hevrh_ k_lhh_ iylgh ?keb `_ l_i_jv ihklZblv gZ imlb α- qZklbp lhgdmx nhev]m N lh ijb aZbfh^_cklbb k _s_klhf hgb [m^mljZkk_bZlvkyihk_fgZijZe_gbyfgZjZagu_m]euHkghgZy qZklv αqZklbp ijhreZ kdhav nhev]m fZeh baf_gb kh_]h i_jhgZqZevgh]h gZijZe_gby Gh g_[hevrZy qZklv αqZklbp jZkk_yeZkvgZm]euihjy^dZ°Z g_dhlhju_^Z`_gZm]eu ihjy^dZ 180°. 29

75. 3. J_a_jnhj^ ijbr_e d uh^m qlh klhev kbevgh_ hldehg_gb_ α- qZklbp 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_gljbjhZgguf hq_gv fZehf h[t_f_ ih kjZg_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_jhgZqZevgh]h gZijZe_gby ^b`_gby dmehghkdhc kbehc Ld jZaf_ju y^jZ hq_gv fZeu ih kjZg_gbx k jZaf_jZfbZlhfZlhhkghgZyqZklvαqZklbpijhe_lZ_l^hklZlhqgh ^Ze_dhhly^jZb g_bkiuluZ_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 4. 226 Rd → 222 Rn + 4 He ]^_ 4 He — αqZklbpZ 226 Rd ² y^jh jZ^by 222 Rn ²y^jhjZ^hgZ 88 86 2 2 88 5. _jog__qbkeh²fZkkhh_qbkehgb`g__²aZjy^hh_qbkeh 86 6. FZkkhh_qbkehy^jZZlhfZ^Zggh]hobfbq_kdh]hwe_f_glZjZgh k lhqghklvx^hp_euoqbkemZlhfguo_^bgbpfZkkukh^_j`Zsboky fZkk_ wlh]h y^jZ AZjy^hh_ qbkeh y^jZ ZlhfZ ^Zggh]h obfbq_kdh]h we_f_glZ jZgh aZjy^m y^jZ ujZ`_gghfm we_f_glZjguowe_dljbq_kdboaZjy^Zo 7. 226 Rd → 222 Rn + 4 He Ba^Zgghcj_Zdpbbb^ghqlhuihegyxlky aZdhgu khojZg_gby fZkkhh]h qbkeZ b aZjy^Z _cklbl_evgh 88 86 2 fZkkhh_qbkeh

76. b aZjy^

77. jZkiZ^Zxs_]hkyy^jZZlhfZjZ^by jZgu khhl_lkl_ggh kmff_ fZkkhuo qbk_e

78. b kmff_ aZjy^h

79. h[jZahZrboky j_amevlZl_ jZkiZ^Z ZlhfhjZ^hgZb ]_eby 8. Y^jZZlhfhbf__lkeh`gh_kljh_gb_ 9. JZ^bhZdlbghklvxgZauZxlkihkh[ghklvy^_jZlhfhg_dhlhjuo obfbq_kdbo we_f_glh kZfhijhbahevgh ij_jZsZlvky ^jm]b_ y^jZk bkimkdZgb_fqZklbp 30

80. §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^

81. ih^dexq_ggu_ q_j_a khijhlbe_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 bhgbabjhZlv 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 êy bhgbaZpbb Zlhfh ]ZaZ ghv h[jZahZrb_ we_dljhgumkdhjyxlkyihe_fb khxhq_j_^vijhbah^ylbhgbaZpbx ^ZZy gZqZeZ ghuf we_dljhgZf b bhgZf ljm[d_ h[jZam_lky lZd gZauZ_fZy we_dljhgghbhggZy eZbgZ j_amevlZl_ wlh]h ljm[d_ hagbdZ_l jZajy^ b p_ib kq_lqbdZ ijhbkoh^bl djZldhj_f_ggh_ b j_adh_ hajZklZgb_ kbeu lhdZ dhlhjh_ j_]bkljbjm_lky ki_pbZevguf mkljhcklhf JZajy^ êblky ijbf_jgh fbdjhk_dmg^m b aZl_f ij_djZsZ_lky ld hkghgZy qZklv gZijy`_gby iZ^Z_l gZ khijhlbe_gbb R b j_amevlZl_ wlh]h gZijy`_gb_ f_`^m dZlh^hf b Zgh^hfj_adhmf_gvrZ_lky 2. eyj_]bkljZpbbwe_dljhghb γdZglh 3. DZf_jZ bevkhgZ khklhbl ba pbebg^jZ KK kh kl_deygghc djurdhcLLgmljbpbebg^jZfh`_li_j_f_sZlvkyihjr_gvPGZ ^g_ dZf_ju e_`bl q_jgZy ijhiblZggZy kf_kvx hû kh kibjlhf ldZgv FF [eZ]h^Zjy dhlhjhc dZf_j_ ha^mo gZkus_g dZf_j_ hlkmlklmxl y^jZ dhg^_gkZpbb Ijbgpbi ^_cklby dZf_ju bevkhgZke_^mxsbc j_amevlZl_j_adh]h^b`_gbyihjrgygba l_fi_jZlmjZ g_c iZ^Z_l b iZju gmljb klZghylky i_j_kus_ggufb l_ hgb l_i_jv fh]ml e_]dh dhg^_gkbjhZlvky 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 kh_f imlb bhgu y^jZ dhg^_gkZpbb

82. 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

83. LZdbf h[jZahf k ihfhsvx dZf_ju bevkhgZ fu fh`_f magZlv ljZ_dlhjbx^b`_gbyqZklbpu 4. ?kebdZf_jmbevkhgZihf_klblv fZ]gblgh_ihe_lhhij_^_eb ljZ_dlhjbx ^b`_gby qZklbpu fu fh`_f hij_^_eblv agZd aZjy^Z qZklbpu ih gZijZe_gbx ba]b[Z

84. __ fZkkm wg_j]bx aZjy^ ih jZ^bmkmdjbbaguljZ_dlhjbb

85. 31

86. 5. ImaujvdhZy dZf_jZ h[eZ^Z_l [hevrbf [ukljh^_cklb_f hlebqb_ hl dZf_ju bevkhgZ ImaujvdhZy 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_lZyur_lhqdbdbi_gby`b^dhklv 1. Hiul aZdexqZ_lky bkke_^hZgbb aZbfh^_cklby αqZklbp k §59. y^jZfbZlhfhZahlZE_lysZyk [hevrhckdhjhklvxαqZklbpZ ijb ihiZ^Zgbb y^jh ZlhfZ ZahlZ u[bZeZ ba g_]h y^jh ZlhfZ h^hjh^Zdhlhjh_J_a_jnhj^gZaZeijhlhghf 2. H lhfqlh j_amevlZl_aZbfh^_cklbyαqZklbpk y^jZfbZlhfh ZahlZh[jZahZebkvy^jZdbkehjh^Zb h^hjh^Z 3. Y^jh ZlhfZ h^hjh^Z 1 G bgZq_ gZauZ_lky ijhlhghf b h[hagZqZ_lkykbfhehf 1 p bebp. 1 1 4. Ij_^iheh`_gb_h lhfqlhijhlhguoh^yl khklZy^jZex[h]h ZlhfZ §60. 1. Y^jZZlhfhbf_xl[hevrmxfZkkmq_fkmfZfZkkkhklZeyxsbo boijhlhghWlh[uehmklZghe_ghhiulgufiml_fb ^Z_liheZ]Zlv qlhihfbfhijhlhgh khklZy^jZoh^yldZdb_lh^jm]b_qZklbpu 2. Wlhij_^iheh`_gb_[uehukdZaZghWjg_klhfJ_a_jnhj^hf ] 3. `_cfkQ_^bd ] 4. M g_cljhgh hlkmlklm_l aZjy^ ihkdhevdm hg g_ hldehgy_lky we_dljbq_kdbf b fZ]gblguf ihe_f FZkkm hij_^_ebeb ba dhebq_kl_gguo oZjZdl_jbklbd aZbfh^_cklby g_cljhgZ k ^jm]bfb qZklbpZfb 5. G_cljhgh[hagZqZ_lkykbfhehf 0 n bebn_]hfZkkZihqlbjZgZ 1 g_fgh]h[hevr_

87. fZkk_ijhlhgZ §61. 1. Gmdehgu 2. FZkkhuf qbkehf gZauZ_lky qbkeh gmdehgh y^j_ ZlhfZ FZkkhh_qbkehh[hagZqZ_lky[mdhc:. 3. FZkkhh_ qbkeh jZgh k lhqghklvx ^h p_euo qbkem Zlhfguo _^bgbpfZkkukh^_j`Zsboky fZkk_ZlhfZ 4. Qbkeh ijhlhgh Zlhf_ h[hagZqZ_lky [mdhc Z b gZauZ_lky aZjy^hufqbkehf 5. I_j_^kbfhehfkgbam 32

88. 6. AZjy^hh_qbkehjZghaZjy^my^jZujZ`_gghfm we_f_glZjguo we_dljbq_kdbo aZjy^Zo AZjy^hh_ qbkeh ZlhfZ jZgh _]h ihjy^dhhfmghf_jm lZ[ebp_F_g^_e__Z 7. Z X a^_kvO ²kbfheobfbq_kdh]hwe_f_glZ A 8. Qbkehg_cljhgh y^j_h[hagZqZxl[mdhcN. 9. A = Z + N. §62. 1. Bahlhiu ² we_f_glu k h^bgZdhufb aZjy^Zfb y^_j gh jZaebqgufbfZkkZfb 2. Y^jZbahlhihh^gh]hwe_f_glZbf_xlh^bgZdhucaZjy^ 3. JZagu_ bahlhiu h^gh]h we_f_glZ kh^_j`Zl jZagh_ dhebq_klh g_cljhgh 4. M h^hjh^Z _klv ljb bahlhiZ ijhlbc 1 G

89. ^_cl_jbc 2 G ), ljblbc 3 G ). 1 1 5. IhlhfmqlhfZkkZZlhfhuqbkey_lkydZdkj_^g__agZq_gb_fZkk 1 k_o_]hbahlhih 1. FZkkZZlhfZmf_gvrZ_lkygZZ aZjy^_]hy^jZ²gZ §63. 2. GZijbf_j 226 Rd → 222 Rn + 4 He . 3. Y^jhjZ^hgZkh^_j`blgZijhlhgZf_gvr_q_fy^jhjZ^by 88 86 2 4. Ijb αjZkiZ^_ h[jZam_lky ghuc obfbq_kdbc we_f_gl ihjy^dhuc ghf_j dhlhjh]h lZ[ebp_ F_g^_e__Z f_gvr_ bkoh^gh]hgZ 5. Ijb βjZkiZ^_ baemqZ_lky we_dljhg b Zglbg_cljbgh H^bg g_cljhg y^j_ijblZdhfjZkiZ^_ij_jZsZ_lky ijhlhgwe_dljhg b Zglbg_cljbgh 6. Ijb βjZkiZ^_ h[jZam_lky ghuc obfbq_kdbc we_f_gl ihjy^dhuc ghf_j dhlhjh]h lZ[ebp_ F_g^_e__Z [hevr_ bkoh^gh]hgZ 7. G_l ihlhfm qlh fZkkhh_ qbkeh jZgh qbkem gmdehgh Z wlh qbkehijbβjZkiZ^_g_f_gy_lky 8. eyαjZkiZ^Z Z X → A−4 Y + 4 He . A eyβjZkiZ^Z X → Y + e+ 0 ~ . Z −2 2 A A 0 Z Z +1 −1 0 9. αb βjZkiZ^qZklhkhijhh`^Z_lkyγbaemq_gb_f 33

90. §64. 1. hagbdZehijhkh lhfihq_fmy^jZg_jZkiZ^ZxlkygZhl^_evgu_ gmdehgu ih^ ^_cklb_f we_dljhklZlbq_kdbo kbe hllZedbZgby f_`^m iheh`bl_evgh aZjy`_ggufb gmdehgZfb Bkoh^y ba wlh]h mq_gu_ ijbreb d aZdexq_gbx qlh f_`^m gmdehgZfb y^jZ ^_cklmxlkbeuijbly`_gby^jm]hcijbjh^u 2. Kbeuijbly`_gbyf_`^mgmdehgZfb y^j_gZauZxlkyy^_jgufb Bo hkh[_gghklv khklhbl lhf qlh bo ^_cklb_ agZqbl_evgh ijhyey_lky gZ jZkklhygbyo kjZgbfuo k jZaf_jZfb y^jZ ihjy^dZ 10-15 f

91. M`_gZjZkklhygbbihjy^dZ-14 bo^_cklb_gbqlh`ghfZeh §65. 1. Wg_j]b_c kyab y^jZ gZauZ_lky fbgbfZevgZy wg_j]by dhlhjmx g_h[oh^bfhaZljZlblvgZjZks_ie_gb_y^jZgZhl^_evgu_gmdehgu 2. ∆m = (Zmp + Nmn) – My ]^_ ∆m ² ^_n_dl fZkk Z b N ² qbkeh ijhlhgh b g_cljhgh y^j_ khhl_lkl_ggh mn b mp ² fZkku ihdhyg_cljhgZb ijhlhgZkhhl_lkl_gghMy ²fZkkZy^jZ 3. ∆E0 = ∆mc2]^_∆E0 ²wg_j]bykyab y^jZ∆m ²^_n_dlfZkkk ²kdhjhklvk_lZ Zdmmf_ §66. 1. _e_gb_ y^_j mjZgZ ijb [hf[Zj^bjhd_ bo g_cljhgZfb [ueh hldjulh ]Hllh=Zghfb Njbp_fRljZkkfZghf 2. Ijb ih]ehs_gbb y^jhf g_cljhgZ hgh ^_nhjfbjm_lky b ijbh[j_lZ_l ulygmlmx nhjfm Ld y^_jgu_ kbeu ² dhjhldh^_cklmxsb_lhgZgmdehgu ulygmlhfy^j_bo^_cklb_ hkeZ[_Z_l b gmdehgu jZae_lZxlky ih^ ^_cklb_f we_dljhklZlbq_kdbo kbe LZdbf h[jZahf ^_e_gb_ y^jZ fh`_l gZqZlvky lhevdh lh]^Z dh]^Z hgh ^_nhjfbjm_lky ih^ ^_cklb_f ih]ehs_ggh]hnhlhgZ 3. j_amevlZl_ ^_e_gby y^jZ h[jZamxlky ^Z hkdhedZ jZgg__ khklZeyxsb_y^jh

92. b g_cljhgZ 4. QZklv gmlj_gg_c wg_j]bb y^jZ ijb _]h ^_e_gbb i_j_oh^bl dbg_lbq_kdmxwg_j]bxh[jZahZrbokyhkdhedhb g_cljhgh 5. Dbg_lbq_kdZy wg_j]by hkdhedh ijb bo lhjfh`_gbb ij_h[jZam_lkyhgmlj_ggxxwg_j]bxhdjm`Zxs_ckj_^u 6. J_Zdpby ^_e_gb_ y^_j mjZgZ b^_l k u^_e_gb_f wg_j]bb hdjm`Zxsmxkj_^m 34

93. §67. 1. JZkkfhljbf f_oZgbaf ijhl_dZgby p_ighc j_Zdpbb ^_e_gby y^jZ gZ ijbf_j_ bahlhiZ mjZgZ 235 U jbk mq_[gbdZ

94. Ijb ^_e_gbb y^jZ ZlhfZ mjZgZ j_amevlZl_ aZoZlZ g_cljhgZ h[jZamxlky ljb 92 g_cljhgZ Z ba gbo uaZeb j_Zdpbx ^_e_gby _s_ ^mo y^_j mjZgZijbwlhfh[jZahZehkvq_luj_g_cljhgZghvh[jZahZrb_ g_cljhgu uaZeb ^_e_gb_ q_luj_o y^_j mjZgZ ijb wlhf h[jZahZehkv ^_ylv g_cljhgh b l^ LZdbf h[jZahf qbkeh g_cljhgh dmkd_mjZgZeZbghh[jZaghjZkl_lk l_q_gb_fj_f_gb Z ke_^hZl_evgh j_adh hajZklZ_l qbkeh ^_e_gbc y^_j mjZgZ b wg_j]byu^_eyxsZyky _^bgbpmj_f_gb 2. Djblbq_kdhc fZkkhc mjZgZ gZauZ_lky gZbf_gvrZy fZkkZ ijb dhlhjhc g_cljhgh ihybrboky ijb ^_e_gbb y^_j jZgh qbkem ihl_jygguo g_cljhgh aZoZq_gguo y^jZfb [_a ^_e_gby b ue_l_rboaZij_^_eudmkdZmjZgZ

95. 3. ?keb fZkkZ mjZgZ f_gvr_ djblbq_kdhc lh j_Zdpby ^_e_gby g_ ijhl_dZ_lbaaZg_^hklZldZg_cljhgh 4. ?keb fZkkZ mjZgZ [hevr_ djblbq_kdhc lh p_igZy j_Zdpby ijbh^bl d ajum baaZ j_adh]h m_ebq_gby qbkeZ kh[h^guo g_cljhgh 5. FZkkZmjZgZgZebqb_hljZ`Zxs_ch[hehqdbgZebqb_ ijbf_k_c aZf_^ebl_evg_cljhgh 1. Y^_jguc j_Zdlhj ² wlh mkljhcklh kihkh[gh_ hkms_kleylv §68. mijZey_fmxy^_jgmxj_Zdpbx 2. MijZe_gb_ y^_jghc j_Zdpb_c aZdexqZ_lky j_]mebjhZgbb kdhjhklb h[jZahZgby g_cljhgh lZdbf h[jZahf qlh[u bo qbkeh hklZZehkvg_baf_gguf 3. Hkghgu_qZklbj_ZdlhjZ^_eys__ky_s_klhy^_jgh_lhiebh

96. aZsblgZy h[hehqdZ ZdlbgZy ahgZ hljZ`Zl_ev j_]mebjmxsb_ kl_j`gbl_iehh[f_ggbd 4. Zdlbghc ahg_ j_ZdlhjZ gZoh^ylky mjZghu_ kl_j`gb yeyxsb_ky y^_jguf lhiebhf j_]mebjmxsb_ kl_j`gb ih]ehsZxsb_ g_cljhgu h^Z kem`ZsZy aZf_^ebl_e_f g_cljhgh b l_iehghkbl_e_f 5. ey lh]h qlh[u h^ghf kl_j`g_ p_ighc j_Zdpbb g_ ijhbkoh^behWlh^_eZ_lkyjZ^b[_ahiZkghklb 6. J_]mebjmxsb_ kl_j`gb gZoh^ykv iheghklvx Zdlbghc ahg_ ih]ehsZxlg_cljhgub p_igZyj_Zdpbyb^lbg_fh`_leyaZimkdZ 35

97. j_Zdpbb j_]mebjmxsb_ kl_j`gb uh^yl ba Zdlbghc ahgu ^h l_o ihjihdZg_gZqg_lkyp_igZyj_Zdpby 7. lhjZy nmgdpby h^u ihfbfh aZf_^e_gby g_cljhgh

98. ² l_iehghkbl_evhlh^ysbcl_ieh 8. h lhjhf dhglmj_ iZj h[jZahZrbc af__bd_ jZsZ_l lmj[bgm dhlhjZy ijbh^bl d jZs_gbx jhlhjZ ]_g_jZlhjZ we_dljbq_kdh]h lhdZ AZl_f hljZ[hlZgguc iZj ihklmiZ_l dhg^_gkZlhj ]^_ ij_jZsZ_lky h^m AZl_f pbde ihlhjy_lky LZdbfh[jZahfg_ij_jughujZ[ZluZ_lkywe_dljbq_kdbclhd 9. Ijb ihemq_gbb we_dljbq_kdh]h lhdZ gZ Zlhfguo we_dljhklZgpbyo ijhbkoh^yl ke_^mxsb_ ij_h[jZahZgby wg_j]bb gmlj_ggyy wg_j]by Zlhfguoy^_jmjZgZijb^_e_gbbqZklbqghi_j_oh^bl dbg_lbq_kdmx wg_j]bx g_cljhgh b hkdhedh G_cljhgu b hkdhedb jZae_lZykv k [hevrhc kdhjhklvx ihiZ^Zxl h^m Ijb wlhf bo dbg_lbq_kdZy wg_j]byqZklbqgh i_j_oh^bl h gmlj_ggxx wg_j]bx h^u Ijb wlhf h^Z gZ]j_Z_lky b ijhoh^y q_j_a l_iehh[f_ggbd i_j_^Z_l wg_j]bx h^_ gZoh^ys_cky af__bd_ ij_jZsZy __ iZj l_ gmlj_ggyy wg_j]by h^u i_j_oh^bl h gmlj_ggxx wg_j]bx iZjZ Z aZl_f _]h dbg_lbq_kdmx AZl_f iZj jZsZ_l lmj[bgm dhlhjZy ijbh^bl d jZs_gbx jhlhjZ ]_g_jZlhjZ we_dljbq_kdh]h lhdZ l_ dbg_lbq_kdZy wg_j]by iZjZ i_j_oh^bl dbg_lbq_kdmx wg_j]bx jhlhjZ lmj[bgu b jhlhjZ ]_g_jZlhjZ dhlhjZy khx hq_j_^v i_j_oh^bl we_dljbq_kdmx §69. 1. kyabk [hevrbfjhklhfihlj_[e_gbywe_dljhwg_j]bb 2. hi_juo:WKlj_[m_lkygZfgh]hf_gvr__dhebq_klhlhiebZ q_f LWK hlhjuo :WK f_gvr_c kl_i_gb aZ]jyagyxl hdjm`Zxsmxkj_^mijbijZbevghcwdkiemZlZpbb

99. q_fLWK 3. :lhfgZywg_j]_lbdZ lj_[m_l j_r_gby ke_^mxsbo lj_o hkghguo ijh[e_f

100. kh_jr_gklhZgb_ l_ogheh]bc k p_evx mf_gvr_gby h[jZahZgby hloh^h

101. i_j_jZ[hldZ hloh^h b mf_gvr_gb_ hiZkghklb hl jZkijhkljZg_gby hdjm`Zxs_c kj_^_

102. gZ^_`gZy baheypbyhloh^hhlhdjm`Zxs_ckj_^u 4. Hl_j`^_gb_`b^dbohloh^hhkl_dehZgb_hloh^h 1. lhf qlh ha^_cklb_ α- β b γemq_c gZ `bmx ldZgv §70. ijhbkoh^bl __ bhgbaZpby

103. gZjmrZ_l `bag_^_yl_evghklv de_lhd ^Zgghc ldZgb qlh hljbpZl_evgh kdZauZ_lky gZ a^hjhv_ `bh]h hj]ZgbafZ 36

104. 2. Ih]ehs_gghc ^hahc baemq_gby gZauZ_lky ih]ehs_ggZy _s_klhf wg_j]by bhgbabjmxs_]h baemq_gby jZkkqblZggZy gZ _^bgbpm fZkku Ih]ehs_ggZy ^haZ baemq_gby D hij_^_ey_lky ih nhjfme_ D = ]^_ ? ² ih]ehs_ggZy _s_klhf wg_j]by m — E fZkkZ_s_klZ?^bgbp_cbaf_j_gbyih]ehs_gghc^haubaemq_gby m 1 ` kbkl_f_KByey_lky]j_c=j

105. =j 1 d] . 3. Ijb[hevr_c^ha_baemq_gby 4. JZagu_ bû bhgbabjmxsbo baemq_gbc ijb h^bgZdhhc ih]ehs_gghc ^ha_ h[emq_gby hdZauZxl jZaebqgu_ ih _ebqbg_ [bheh]bq_kdb_ wnn_dlu `bhf hj]Zgbaf_ GZijbf_j ijb h^bgZdhhc ih]ehs_gghc ^ha_ [bheh]bq_kdbc wnn_dl hl α- baemq_gbyijbf_jgh jZa[hevr_q_fhlγbaemq_gby 5. Dhwnnbpb_gl dZq_klZ baemq_gby ihdZauZ_l h kdhevdh jZa [hevr_jZ^bZpbhggZyhiZkghklvhlha^_cklbygZ`bhchj]Zgbaf ^Zggh]h b^Z baemq_gby ih kjZg_gbx k γbaemq_gb_f ijb h^bgZdhuo ih]ehs_gguo ^haZo Dhwnnbpb_gl dZq_klZ baemq_gby êy αbaemq_gbyjZ_gêyβ- γb j_gl]_ghkdh]h baemq_gby ² 6. WdbZe_glgZy ^haZ baemq_gby [ueZ _^_gZ kyab k l_f qlh 1. ijb h^bgZdhhc ih]ehs_gghc ^ha_ baemq_gby jZaebqgu_ bû baemq_gbc uauZxl jZaebqgu_ [bheh]bq_kdb_ wnn_dlu WdbZe_glgZy ^haZ baemq_gby H uqbkey_lky dZd ijhba_^_gb_ ih]ehs_gghc ^hau D gZ dhwnnbpb_gl dZq_klZ D: H = DK ?_ _^bgbp_cbaf_j_gbyyey_lkyab_jlA

106. 7. Qmklbl_evghklv jZaebqguo ldZg_c `bh]h hj]ZgbafZ hij_^_ey_lky dhwnnbpb_glhf jZ^bZpbhggh]h jbkdZ

107. j_fy h[emq_gby 8. Hl ha^_cklby gZ `bhc hj]Zgbaf jZ^bhZdlbguo baemq_gbc ijbf_gyxlky ki_pbZevgZy h^_`^Z jZaebqgu_ aZsblgu_ m[_`bsZ JZ^bhZdlbgu_ ij_iZjZlu ke_^m_l ojZgblv ki_pbZevguo aZsblguodhgl_cg_jZoh[uqghkbgphuo §72. 1. L_jfhy^_jghc j_Zdpb_c gZauZ_lky j_Zdpby kebygby e_]dbo y^_j ijbhq_gvukhdhcl_fi_jZlmj_ihjy^dZkhl_gfbeebhgh]jZ^mkh

108. 2. Ijhl_dZgb_ l_jfhy^_jguo j_Zdpbc hafh`gh lhevdh ijb hq_gv ukhdbo l_fi_jZlmjZo ld g_h[oh^bfh ijb^Zlv y^jZf ^hklZlhqgh [hevrmxdbg_lbq_kdmxwg_j]bx^eybok[eb`_gbygZhq_gvfZeu_ jZkklhygbyijbdhlhjuohafh`ghbokebygb_ 37

109. 3. Kebygb_e_]dboy^_j 4. 2 H + 3 H → 4 He+ 0 n . 1 5. HkghgZy ljm^ghklv ijb hkms_kle_gbb l_jfhy^_jghc j_Zdpbb 1 1 2 aZdexqZ_lky lhf qlh[u m^_j`Zlv ukhdhl_fi_jZlmjgmx ieZafm gmljb mklZghdb ?keb ieZafZ dhkg_lky kl_ghd mklZghdb dhlhjhchgZgZoh^blkylhhgbjZkieZylkyb ij_jZlylky iZj 6. j_amevlZl_ l_jfhy^_jguo j_Zdpbc ijhl_dZxsbo gZ Khegp_ u^_ey_lkywg_j]byg_h[oh^bfZy^ey`bagbgZA_fe_ 38

110. MijZ`g_gby MijZ`g_gb_ 1. Fh`gh h[hbo kemqZyo ld jZaf_jZfb Zlhfh[bey ijb ^Zgguo gZqZevguomkehbyofh`ghij_g_[j_qv 2. k_aZbkblhlmkehbcaZ^Zqdhlhju_gm`ghj_rblv^bki_lq_jm b iZkkZ`bjm 3. Ih_joghklvA_feb 4. IjZ b fZevqbd b ^_hqdZ FZevqbd u[jZe kbkl_fm hlkq_lZ kyaZggmxk a_fe_c^_hqdZ²k dj_kehfdZjmk_eb 5. Z

111. hlghkbl_evgh A_feb [

112. hlghkbl_evgh h^u

113. hlghkbl_evgh A_feb]

114. hlghkbl_evghhkbdhe_kZ^

115. hlghkbl_evghA_feb MijZ`g_gb_ 1. Ijhc^_ggucimlv2. Ijyfhebg_cgh MijZ`g_gb_ 7 7 1. s sf x xf x = xk + so = 10 df + (–2 df) = 8 df; O xc xf = xk + sfo dfdf df 2. Z

116. o0 f[

117. sto = s1o + s2o f ±f

118. f

119. xt = o0 + sto f f f MijZ`g_gb_ 1. =jZnbd fh^mey _dlhjZ kdhjhklb g_ fh`_l gZoh^blvky ih^ hkvx ijh_dpbb _dlhjZ kdhjhklb fh`_l gZoh^blvky ih^ hkvx Ot, Otihkdhevdmfh^mev_dlhjZkdhjhklbk_]^Ziheh`bl_e_g=jZnbd ihkdhevdm agZd aZbkbl ijh_dpbb _dlhjZ kdhjhklb hl u[hjZ kbkl_fudhhj^bgZl vx, dfq 2. 80 60 tq –90 39

120. MijZ`g_gb_ 1. I_juc Zlhfh[bev ^b]Zeky k [hevrbf mkdhj_gb_f ihkdhevdm _]hkdhjhklvaZh^bgZdhu_ijhf_`mldbj_f_gbhajZklZeZ[uklj__ Zgh J_r_gb_ 2. 55 fk − 10 fk v1 fk = 1,5 fk 2 . t = 30 c v −v 30 k a= 2 1 = v2 fk t GZclbZ. Hl_la fk2. Zgh J_r_gb_ 3. 6 fk v2 – v1 fk = 0,5 fk 2 . t = 12 c v −v 12 k a= 2 1 = GZclbZ. Hl_la fk2. t MijZ`g_gb_ Zgh J_r_gb_ 1. v1 fk v −v a = 2 1 ⇒ v2 = v1 + at = a = –20 fk2 t=4c fk ±fk2) ⋅ k fk t GZclb v2. Hl_lv2 fk Zgh J_r_gb_ 2. a fk2 2 fk = 10 k v −v v v a 0,2 fk 2 a= 2 1 = 2 ⇒t = 2 = v2 fk v1 = 0 t t GZclbt. Hl_lt k Y[ 3. W 40

121. 4. vx 5 -5 5 10 t 5. eyl_eZ,Z fk2^eyl_eZ,,Z fk2. MijZ`g_gb_ Zgh J_r_gb_ 1. 0,5 fk 2 ⋅ (5 k ) Zo fk2 fk ⋅ k t=5c axt 2 2 sx = v0 o t + v0o dfq fk = f 2 2 GZclbsx. Hl_lsx f Zgh J_r_gb_ 2. Zo fk2 t = 20 c axt 2 v v t2 v t sx = v0 o t + ; ao = − 0 x ⇒ sx = v0 o t − 0 x = 0 x = v0o fk fk ⋅ k f 2 t 2t 2 GZclbsx. Hl_lsx f MijZ`g_gb_ Zgh J_r_gb_ 1. s3 f s1 : s2 : s3 = 1 : 3 : 5; s1 : 2 f = 1 : 5 ⇒ s1 = 2 f 5 = 0,4 f; t1 k 2 ⋅ 0,4 f = 0,8 f/k2. 2 at1 2s (1 k) s1 = ⇒ a = 21 = 2 2 GZclb s1, a. Hl_ls1 fa fk2. t1 Zgh J_r_gb_ 2. s5 f s1 : s2 : s3 : s4 : s5 = 1 : 3 : 5 : 7 : 9; s1 : 6,3 f = 1 : 9 ⇒ t1 k ⇒ s1 = 6,3 f 5 = 0,7 f; t5 k 2 ⋅ 0,7 f = 1,4 f/k2; 2 at1 2s (1 k)2 s1 = ⇒ a = 21 = 2 v5 = at5 fk2 ⋅ k fk t1 GZclbv5. Hl_lv5 fk 41

122. MijZ`g_gb_ 1. fk 2. G_l ihkdhevdm b ^_j_h b hdaZe `_kldh kyaZgu k ^jm]hc kbkl_fhchlkq_lZ²A_fe_c 3. Ijbmkehbbg_ih^b`ghklbwlbol_ehlghkbl_evgh^jm]^jm]Z 4. dfq fk Zgh J_r_gb_ 5*. v1 dfq fk v = v1 + v2 fk fk fk v2 fk va = v2 – v1 fk ±fk fk GZclbv, va. Hl_lv fkva fk MijZ`g_gb_ AZdhgbg_jpbbuihegy_lky kbkl_f_hlkq_lZkyaZgghck A_fe_cb kbkl_f_ hlkq_lZ kyaZgghc k ih_a^hf h j_fy _]h ijyfhebg_cgh]h b jZghf_jgh]h ^b`_gby g_ uihegy_lky kbkl_f_ hlkq_lZ kyaZgghc k ih_a^hf h j_fy _]h lhjfh`_gby Bg_jpbZevghckbkl_fhcfh`ghkqblZlva_fexZ ih_a^²g_evay MijZ`g_gb_ Zgh J_r_gb_ 1. Z fk2 IhhfmaZdhgmGvxlhgZ m d] F = ma d]⋅ fk2 G GZclbF. Hl_lF G Zgh J_r_gb_ 2. F = ma ²hcaZdhgGvxlhgZ v fk t = 20 c mv 1,84 ⋅ 10 5 d] ⋅ 4 fk m l ⋅10 d] 20 k v 5 a= ⇒F= = = G dG t t GZclbF. Hl_lF dG Zgh J_r_gb_ 3. IhhfmaZdhgmGvxlhgZ a1 fk2 F1 = m1a1; F2 = m2a2. Ldm1 = m2lhihemqZ_f m1 = m2 a2 fk2 F1 F2 a F 0,64 fk 2 ⋅ 1,2 G 0,08 fk 2 F1 = 1,2 H = ⇒ F2 = 2 1 = = 9,6 H. a1 a 2 a1 GZclbF2. Hl_lF2 G 42

123. Zgh J_r_gb_ 4. m = 0,5 d] IhhfmaZdhgmGvxlhgZF = ma. FA = 10 H F = FA – FL – FC ⇒ FA – FL – FC = ma ⇒ fk2. FL = 5 H F − FL − FC 10 H − 5 H − 2 H 0,5 d] FC = 2 H ⇒a = A = GZclbF2. Hl_la fk2. m 5. Ijb ^b`_gbb _jo kdhjhklv b i_j_f_s_gb_ ijhlbhiheh`gh gZijZe_gu k kbehc ly`_klb mkdhj_gb_ ² khgZijZe_gh Ijb ^b`_gbbgbakdhjhklvi_j_f_s_gb_b mkdhj_gb_khgZijZe_guk kbehcly`_klb 6. Mkdhj_gb_ k_]^Z khgZijZe_gh k jZgh^_cklmxs_c ijbeh`_gguo d l_em kbe Kdhjhklv b i_j_f_s_gb_ fh]ml [ulv dZd khgZijZe_gu k jZgh^_cklmxs_c ijbeh`_gguo d l_em kbe lZd b ijhlbhiheh`ghgZijZe_gu MijZ`g_gb_ 7 7 1. GZ l_eh ^_cklmxl kbeZ ly`_klb Fl b kbeZ j_Zdpbb hihju N kfjbk

124. 7 N 7 Fl 2. G_ ij_ukbl ld jZgh^_cklmxsZy ijbeh`_gguo kbe gZ ^bgZfhf_ljjZgZ Zgh J_r_gb_ 3. m1 d]

125. IhhfmaZdhgmGvxlhgZ m2 d] F2x = m2ax d]⋅ fk2 G a fk2 IhfmaZdhgmGvxlhgZF1x = –F2x ±G

126. IhhfmaZdhgmGvxlhgZ F1x = m1ax d]⋅ fk2 G IhfmaZdhgmGvxlhgZF2x = –F1x ±G

127. i_jhf kemqZ_ gblv f_`^m l_e_`dZfb gZlygmlZ kbevg__

128. IhhfmaZdhgmGvxlhgZ Fx = (m1 + m2)ax d]d]

129. ⋅ fk2 G GZclb F1x, Hl_l

130. F1x ±GF2x G

131. F1x GF2x = F2x, Fx. ±G

132. i_jhfkemqZ_

133. Fx G 43

134. MijZ`g_gb_ Zgh J_r_gb_ 1. g ≈ fk2 gt 2 10 fk 2 ⋅ (2 k ) f 2 t=2c h= = GZclbh. Hl_lh f 2 2 Zgh J_r_gb_ 2. g ≈ fk2 2 ⋅ 0,8 f h = 80 cf f = 0,4 k. gt 2 10 fk 2 2h h= ⇒t= = GZclbt. Hl_lt k 2 g Zgh J_r_gb_ 3. g ≈ fk2 2 ⋅ 45 f h = 45 f k gt 2 10 fk 2 2h h= ⇒t= = 2 g gt1 10 fk 2 ⋅ (1 k )2 t1 = 1 c = 5 f; ∆t = 1 c 2 s1 = = gt 2 g (t − ût ) 2 2 2 s2 = − = 10 fk 2 ⋅ (3 k ) 10 fk 2 ⋅ (3 c − 1 c ) 2 2 =5f 2 2 = − GZclb t, s1, s2. Hl_lt ks1 fs2 f 2 2 MijZ`g_gb_ Zgh J_r_gb_ v fk v − v1 v 9,8 fk g 9,8 fk 2 v = ⇒t= = g fk2 v1 = 0 g= =1 c; t t 9,8 fk 2 ⋅ (1k ) fk ⋅ k ± f 2 gt 2 s = vt − GZclbt, s. Hl_lt ks f 2 2 MijZ`g_gb_ 1. k_l_eZiZ^ZxlgZa_fexih^^_cklb_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

135. m_ebqbZ_lky Dh]^Z klZgpby gZoh^blky gZ k_j_^bg_ hgZ kbevg__ ijbly]bZ_lkyd A_fe_ldfZkkZA_feb[hevr_fZkkuEmgu 3. G_l 4. Z

136. ^_cklhZeZ[

137. ijbly`_gb_A_feb

138. baaZ^_cklbykbeuly`_klb 5. Zijbly]bZ_lky ghwlZkbeZ]hjZa^hf_gvr_kbeuly`_klb ba aZjZkklhygbcEmgZlZd`_ijbly]bZ_lkyd wlhfmq_eh_dm MijZ`g_gb_ Zgh J_r_gb_ 1. g ≈ fk2 Fl = mg ⇒ m1 d] Fl fk2 ⋅ d] G m2 ] d] Fl fk2 ⋅ d] G m3 l d] Fl fk2 ⋅ d] G dG m4 l d] Fl fk2 ⋅ d] ⋅105 G dG GZclb Fl1, Fl2, Fl3, Fl4. Hl_lGGdGdG Zgh J_r_gb_ 2. g ≈ fk2; m d] Fl = mg d]⋅ fk2 G GZclbFl. Hl_lFl G Zgh J_r_gb_ 3. g ≈ fk2; Fl 819,3 G Fl G d] g 10 fk 2 Fl = mg ⇒ m = = GZclbFl. Hl_lm d] 4. G_lihkdhevdmukhlZihe_lZkjZgbfZk jZaf_jZfbA_febKbem F a mj ly`_klb fh`gh jZkkqblZlv ih nhjfme_ Fl = G ]^_ h — ( Ra + h) 2 ukhlZgZ^A_fe_c 5. GZyklj_[Z^_cklm_lkbeZly`_klbb _kebhgkeh`bldjuevylh hgmiZ^_lgZA_fex 6. GZjZkklhygbbRa; 3Ra (Ra ²jZ^bmkA_feb

139. ihkdhevdmFl~ 1 (Ra + h)2 MijZ`g_gb_ 7 1. KbeZ F fh]eZ^_cklhZlvlhevdh gZijZe_gbb 2. KbeZ ^_cklhZeZ gZ rZjbd gZ mqZkldZo RZjbdihhjZqbZekyih^^_cklb_fg_rgbokbe 3. KbeZ^_cklhZeZgZl_ehgZ_jgydZgZmqZkldZo:'GZl_eh fh]eZ^_cklhZlvkbeZb gZhklZevguomqZkldZo 45

140. MijZ`g_gb_ Zgh J_r_gb_ 1. r kf f v 2 (20 fk )2 v fk Z= ≈ fk2. 0,21 f = GZclba. Hl_lZ ≈ fk2. r Zgh J_r_gb_ 2. R kf f T k Z= ⇒Z= 2 = 2 = v2 l 2πR 4π 2 R 2 4π 2 R ;v= = R T T 4 ⋅ (3,14 ) ⋅ 0,02 f T R T ≈ 2⋅10-4 fk2. 2 (60 k )2 = GZclba. Hl_lZ ≈ 2⋅10-4 fk2. 3. Z1 = ; Z2 = = 2a1 ⇒ ml_j`^_gb__jgh v2 v2 v2 = 2⋅ r r/2 r Zgh J_r_gb_ 4. T1 k T2 k . :gZeh]bqgh a 2 = v 2 (2πR T1 )2 4π 2 R 4π 2 R a1 = 1 = = 2 . R R T1 T22 Ke_^hZl_evgh 2 a1  T1  2  3600 c  =  = T   = 3600. a2  2   60 c  GZclb Hl_l a1 a1 . = 3600. a2 a2 Zgh J_r_gb_ 5. Fa = 6⋅1024 d] F aF e G ⋅ f2 Fe = 6⋅1022 d] Z

141. F]j = G d] 2 = 6,67⋅10-11 × G ⋅ f2 2 6 ⋅ 10 24 d] ⋅ 7 ⋅10 22 d] r d] 2 ≈ 1,9⋅1020 G G=6,67⋅10-11 (3,84 ⋅ 10 8 f

142. 2 × r = df = 3,84⋅108 f 1,9 ⋅ 10 20 G [

143. Zp = ≈ 3,17⋅10-5 fk2; F]j Fa 6 ⋅ 10 24 d] =

144. v = ap r = 3,17 ⋅10−5 fk2 ⋅ 3,84⋅108 f ≈fk GZclbF]j, Zp, v. Hl_lF]j ≈ 1,9⋅1020 Gv ≈ fk Zp = 3,17⋅10-5 fk2. 46

145. MijZ`g_gb_ Zgh J_r_gb_ 1. h df ⋅106 f Ma Fa = 6⋅1024 d] v≈ G = Ra = 6,4⋅106 f Ra + h G ⋅ f2 G ⋅ f2 6 ⋅ 1024 d] d] 2 (2,6 ⋅ 106 f + 6,4 ⋅ 106 f

146. = 6,67 ⋅ 10−11 d] 2 G = 6,67⋅10-11 ⋅ = fk dfk GZclbv. Hl_lv dfk Zgh J_r_gb_ 2. v dfk ⋅103 fk 1,67 ⋅10 3 fk ( ) ge ≈ fk2 2 v2 v2 1,6 fk 2 re = ⇒ re = = = re ge = 1,7⋅106 f ⋅103 df GZclb re. Hl_lre = 1,7⋅103 df MijZ`g_gb_ Zgh J_r_gb_ 1. v1x = –v2x fk p1x = mv1x d]⋅ fk d]⋅fk m = 0,2 d] p2x = – p1x ±d]⋅fk _dlhjubfimevkhfZrbgg_jZguldhgb ijhlbhiheh`gh gZijZe_gu Fh^meb _dlhjhbfimevkhjZgu GZclb p1x, p2x. Hl_lp1x d]⋅fkp2x ±d]⋅fk Zgh J_r_gb_ 2. v1 dfq fk v2 dfq fk ∆j = m∆v = m(v2 – v1) = d]⋅ fk ± fk

147. d]⋅fk m l d] GZclb ∆p. Hl_l∆p d]⋅fk MijZ`g_gb_ 1. Ih aZdhgm khojZg_gby bfimevkZ eh^dZ gZqg_l ^b]Zlvky klhjhgmijhlbhiheh`gmx^b`_gbxq_eh_dZ 47

физика 9кл перышкин гутник_2001_ответы и решения

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (20)

More from vova123367

More from vova123367 (20)

физика 9кл перышкин гутник_2001_ответы и решения