гдз. физика 9кл перышкин гутник_2001

1. 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 ]

2. 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

3. 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

4. 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_ ........................... 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 MijZ`g_gb_ .......................... 44

5. 5 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 MijZ`g_gb_ .......................... 54

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

7. 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_lkh[hckhhdmighklvkbkl_fudhhj^bgZlijb[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_evgZb gZh[hjhl_keb_dlhjijhlbhiheh`ghgZijZe_g hkblh_]hijh_dpbygZg__[m^_lhljbpZl_evgZ 3. o1 = o0 + so. §4. 1. KdhjhklvxjZghf_jgh]hijyfhebg_cgh]h^b`_gby gZauZ_lky ihklhygguc_dlhj v 7 jZguchlghr_gbxi_j_f_s_gby s ; l_eZaZ ex[hcijhf_`mlhdj_f_gbt d agZq_gbxwlh]hijhf_`mldZ t s v ; 7 = .

8. 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 3. Mkdhj_gb_f jZghmkdhj_ggh]h ^b`_gby l_eZ a 7 gZauZ_lky _ebqbgZjZgZyhlghr_gbxbaf_g_gbykdhjhklb∆ v 7 d ijhf_`mldm j_f_gbtaZdhlhjucwlhbaf_g_gb_ijhbahreh t vv t v a 0 777 7 − = ∆ = . 4. b`_gb_k ihklhyggufmkdhj_gb_f 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_ 2 2 0 ta tvs x xx += . Ih^klZbf wlmnhjfmemujZ`_gb_^eyijh_dpbbmkdhj_gby t vv a xx x 0− = . Ihemqbf t vvt t vv tvs xxxx xx ⋅ + =⋅ − += 22 0 2 0 0 .

13. 9 LZddZdv0x = AO, vx = BC, t = OB kfjbkZ

14. mq_[gbdZ

15. lhfu ihemqZ_fqlhijh_dpby_dlhjZi_j_f_s_gby OB BCAO sx ⋅ + = 2 jZgZiehsZ^bnb]mjuOACB ²ijyfhm]hevghcljZi_pbbk hkghZgbyfbAO, BC b ukhlhcOB. 2. 2 2 0 ta tvs x xx += . §8. 1. Ihnhjfme_ 2 2 ta s x x = ²êyijh_dpbbi_j_f_s_gby 2 2 at s = — êyfh^mey_dlhjZi_j_f_s_gby 2. n2 jZaihkdhevdms ~ t2 3. 2 2 1 2 1 2/ 2/)( 1 n at nta s s t n == . 4. DZdjyîhke_^hZl_evguog_q_lguoqbk_e 5. eyhij_^_e_gbyjZghmkdhj_ggh]h^b`_gby §9. 1. jZaguokbkl_fZohlq_lZwlb_ebqbgubf_xljZagu_agZq_gbyb 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_kdZykbkl_fZkyaZgZk Khegp_f]_hp_gljbq_kdZy ²k A_fe_c 5. Kf_gZ^gyb ghqbh[tykgy_lkyjZs_gb_fA_febhdjm]kh_chkb §10. 1. JZghf_jghb ijyfhebg_cghbebihdhblky 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

17. 10 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[ZrZjbdZgZoh^ylky ihdh_hlghkbl_evghl_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_evgbpub dexqbfh[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_ 2 2 t s a = aZf_jb ijhc^_ggh_ l_e_`dhc jZkklhygb_ s b j_fy __ ^b`_gbyt?kebmf_gvrblvkbem^_cklmxsmxgZl_e_`dm ^Z 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

22. 11 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_ m F a 7 7 = . 5. HgbkhgZijZe_gu 6. G 2 k fd] 1 ⋅ . §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 §13. 1. b`_gb_ih^^_cklb_fkbeuly`_klb 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 §8). 3. K p_evxihdZaZlvqlhmkdhj_gb_kh[h^gh]hiZ^_gbyh^bgZdhh ^eyk_ol_e 4. Mkdhj_gb_uaZggh_^_cklb_fkbeuly`_klb 5. BaaZkbeukhijhlbe_gbyha^moZ

23. 12 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_lkyihaZdhgmv(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. ?kebgZijZblvhkv_jolhijh_dpby_dlhjZkdhjhklb gZwlm 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. 2 21 r mm GF = ]^_ F ² fh^mev ]jZblZpbhgghc kbeu m1, m2 — fZkkuaZbfh^_cklmxsbol_er ²jZkklhygb_f_`^mgbfbG — ]jZblZpbhggZyihklhyggZyjZgZy ⋅10-11 G⋅f2 d]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 §16. 1. _jgh 2. Mf_gvrZ_lky3. Fl = mg. 4. KbeZly`_klb[hevr_gZihexkZoldA_feyg_fgh]hkiexkgmlZ m ihexkh 5. Hghijb[ebabl_evgh jZaf_gvr_a_fgh]h

28. 13 §18. 1. RZjbd ^b`_lky hl lhqdb : d lhqd_ ih^ ^_cklb_f kbeu mijm]hklb F 7 WlZ kbeZ hagbdeZ j_amevlZl_ jZkly`_gby rgmjZ Kdhjhklv mkdhj_gb_ rZjbdZ b ^_cklmxsZy gZ g_]h kbeZ gZijZe_guhllhqdbA d lhqd_BRZjbd^b`_lkyijyfhebg_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 §19. 1. Hiulihuk_dZgbxbkdjubalhqbevgh]hdZfgy 2. Mkdhj_gb_ gZijZe_gh ih jZ^bmkm d p_gljm hdjm`ghklb b hgh gZauZ_lkyp_gljhklj_fbl_evguf 3. Ihnhjfme_Zp = r v2 . 4. Ih jZ^bmkm d p_gljm hdjm`ghklb ?_ fh^mev hij_^_ey_lky ih nhjfme_Fp = r mv2 . §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. ZldlZdh_^b`_gb_ijhbkoh^bllhevdhih^^_cklb_fkbeu ly`_klb 4. Khh[sblv_fmi_jmxdhkfbq_kdmxkdhjhklv 5. Zp = r v2 ; g = r v2 ; 2 v = gr grv =⇒ . IheZ]Zyr ≈ RAlhihemqZ_f qlh AgRv = ≈ dfk 6. Ihweebilbq_kdhchj[bl_hdjm]A_febihweebilbq_kdhchj[bl_ hdjm]KhegpZ

29. 14 §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`_gbym^Zjy_lkyh lhjhcb hklZgZebZ_lkyIjbwlhflhjhc 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 4. 22112211 vmvmvmvm 7777 +=′+′ ]^_m1, m2 ²fZkkul_e 1v 7 , 2v 7 ²bo kdhjhklb ^h aZbfh^_cklby 1v′ 7 , 2v′ 7 ² bo kdhjhklb ihke_ aZbfh^_cklby §23. 1. b`msbckyha^moh[eZ^Z_lg_dhlhjufbfimevkhfIhaZdhgm 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

31. 15 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 §24. 1. Dhe_[Zgb_fZylgbdZqZkhkljmgu]blZju 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 bebk`ZlZ

34. lhqd_O kbeZmijm]hklbgZrZjbd g_^_cklm_lld 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_gbxkhkdhjhklvx 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_fZfbgZauZxlkykbkl_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

35. 16 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_jhjhgdZk gZeblhcdjZkys_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^hcHlj_ahdOA khhl_lklm_lZfieblm^_dhe_[ZgbcZ hlj_ahdOB ²i_jbh^m 3. =Zjfhgbq_kdbfbdhe_[ZgbyfbgZauZxlkydhe_[Zgby dhlhjuo baf_g_gb_dZdhceb[hnbabq_kdhc_ebqbguijhbkoh^blihaZdhgm 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

42. 17 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. Hiulijhh^blkyk p_evx^_fhgkljZpbbye_gbyj_ahgZgkZey 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_ggZyqZklhlZkh[h^guo dhe_[Zgbckh[kl_ggZyqZklhlZ

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 hggZqg_lkh_jrZlvkh[h^gu_dhe_[ZgbyWlhuah_ldhe_[Zgby rgmjZ j_amevlZl_ q_]h gZ fZylgbd [m^_l ^_cklhZlv ugm`^ZxsZy kbeZ k qZklhlhc jZghc kh[kl_gghc qZklhl_

45. 18 fZylgbdZIh^^_cklb_fwlhckbeufZylgbdgZqg_lkh_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^_gbbqZklhlukh[kl_gguodhe_[Zgbckbkl_fuk 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 §31. 1. hafms_gbyjZkijhkljZgyxsb_ ijhkljZgkl_b m^Zeyxsb_ky 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 §32. 1. Ijh^hevgu_hegu²wlhlZdb_hegu dhlhjuodhe_[ZgbyqZklbp 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_gbyheggZijbf_jhegugZih_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]_

46. 19 §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 §34. 1. Wlb hiulu ^_fhgkljbjmxl dhe_[Zl_evguc oZjZdl_j 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. BgnjZamdhufbgZauZxlkydhe_[Zgbyk qZklhlhcgb`_=p mevljZamdhufb²k qZklhlhcur_=p §35. 1. Hiulijhh^blkyk p_evxuykgblvaZbkbfhklvukhluamdZhl 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`ghuyblvbkihevamyk_]hlhevdhh^bg^bkdey wlh]hgZ^hm_ebqbZlvkdhjhklv^bkdZQ_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

48. 20 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_lkyhkghguflhghfh[_jlhgubebukrb_]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 §36. 1. Hiulijhh^blkyk p_evxuykgblvaZbkbfhklv]jhfdhklbamdZ 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. Zfh`_lIjbf_jujZkijhkljZg_gbyamdZ l_jûol_eZo² jZkijhkljZg_gb_amdZih`_e_agh^hjh`gufj_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

50. 21 ^_j_vy ]Zau `b^dhklb d ihjbkluf ² hcehd ihjhehg i_ghieZkl 4. Iml_fhl^_edbihf_s_gbcamdhbaheypbhggufbfZl_jbZeZfb §38. 1. K qZklhlhckhhl_lklmxs_camdm 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_adbj_f_gbf_`^mkiurdhch]gyijbuklj_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 §39. 1. j_amevlZl_hljZ`_gbyamdZhljZaebqguoij_]jZ^ 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 §40. 1. DhjimkZ]blZju[ZeZeZcdb 2. eym_ebq_gby]jhfdhklb 3. BogZagZq_gb_²mkbe_gb_amdZb kha^Zgbyl_f[jZ 4. =hehkhu_kyadb 5. HlnhjfujZaf_jZfZl_jbZeZj_ahgZlhjZ §42. 1. Hiulihkeh`_gbxamdhuoheghl^mobklhqgbdhijhh^blky 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

51. 22 ]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`ûcbagboih^dexqZeky hl^_evghklbWlh]hhjblh lhfqlh 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. JZaghklvjZkklhygbcijhc^_gguo^mfyhegZfbhlbklhqgbdh ^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_hegijbdhlhjhfihemqZ_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_

56. 23 4. Khhl_lkl_gghijyfhebg_cghb djbhebg_cgh 5. AZgZijZe_gb_fZ]gblghcebgbb 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[ulvjZaebqghcb 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 §45. 1. GZ^haylvijhh^gbdb ijhimklblvihg_fmlhdkgZqZeZ h^ghf 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_flhhlklZe_ggucgZ°

57. 24 [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_ebgbcfZ]gblgh]hiheygmljb g_]hb gZh[hjhlagZy 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^bdmeyjghd 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_gufZ]gblgu_ebgbbb kbeZ^_cklmxsZygZijhh^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^

62. 25 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 oZjZdl_jbamxsZyfZ]gblgh_ihe_HgZh[hagZqZ_lkykbfhehf 7 . 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_ Il F B = . 3. kbkl_f_KBLeqblZ_lky©l_keZª

63. 4. EbgbyfbfZ]gblghcbg^mdpbbgZauZxlkyebgbbdZkZl_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 bg^mdpby 7 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

64. 26 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_lji_jbh^bq_kdb^b]ZlvfZ]gbl_job gbaIjbwlhf klj_edZ]ZevZghf_ljZ[m^_li_jbh^bq_kdbhldehgylvkyhlgme_h]h agZq_gby lh h^gm klhjhgm lh ^jm]mx Wlh [m^_l kb^_l_evklhZlvh lhfqlhb fh^mevkbeubg^mdpbhggh]hlhdZb _]hgZijZe_gb_i_jbh^bq_kdbf_gyxlkyhj_f_gbl_ 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

66. 27 §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]mWe_dljhfZ]gblgu_heguyeyxlky ihi_j_qgufb lZd dZd iehkdhklv dhlhjhc e_`Zl dhe_[exsb_ky _dlhju B 7 b E 7 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 2. _dlhj gZijy`_gghklb we_dljbq_kdh]h ihey E 7 b _dlhj fZ]gblghcbg^mdpbb B 7 . 3. λ = cT = k/ν. 4. eywlh]hg_h[oh^bfhqlh[uqZklhlZν dhe_[Zgbc_dlhjh B 7 b E 7 [ueZ^hklZlhqgh[hevrhc 5. We_dljhfZ]gblgu_hegui_ju_m^Zehkvh[gZjm`blv=_gjbom =_jpm ] 6. b^bfuck_lmevljZnbhe_ljZ^bhhegu 7. JZ^bhkyavjZ^bhehdZpbyjZ^bhZkljhghfbyj_gl]_gb ^j §53. 1. GZ kq_l k_lZ kms_klhZeb ^_ hkghguo l_hjbb dhjimkdmeyjgZyb heghZy hkgh_i_jhce_`Zehml_j`^_gb_h lhfqlhk_l²wlhihlhdqZklbp hkgh_lhjhcml_j`^_gb_h lhfqlhk_l²wlhhegZ

68. 28 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. GZijhhehqgh_dhevphk jmqdhcaZlygmlh_fuevghcie_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_lkyhlaZ^g_cih_joghklb lhqd_ihke_q_]huoh^blba 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 jZaguolhqdZojZaebqgZ?keb lhesbgZie_gdbhdZ`_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`guonZaZolhwlbheguijbkeh`_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

70. 29 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_evgucaZjy^gmljbwlh]hgZoh^ylkywe_dljhgudZ`^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[uehldZqZgha^mob ijhh^bekyhiul?kebgZimlbα- 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- qZklbplhgdmxnhev]mNlhijbaZbfh^_cklbbk _s_klhfhgb [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]euihjy^dZ 180°.

75. 30 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_ZlhfZgZoh^blkyiheh`bl_evghaZjy`_ggh_y^jhdhlhjh_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_evghaZjy`_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 dmehghkdhckbehcLdjZaf_juy^jZhq_gvfZeuihkjZg_gbxk 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. HeRnRd 4 2 222 86 226 88 +→ ]^_ He4 2 — αqZklbpZ Rd226 88 ² y^jh jZ^by Rn222 86 ²y^jhjZ^hgZ 5. _jog__qbkeh²fZkkhh_qbkehgb`g__²aZjy^hh_qbkeh 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. HeRnRd 4 2 222 86 226 88 +→ Ba^Zgghcj_Zdpbbb^ghqlhuihegyxlky aZdhgu khojZg_gby fZkkhh]h qbkeZ b aZjy^Z _cklbl_evgh 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

80. 31 §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_gbbRb j_amevlZl_wlh]hgZijy`_gb_f_`^mdZlh^hfb 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_ggufbl_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`_gbyqZklbpufufh`_fhij_^_eblv agZd aZjy^Z qZklbpu ih gZijZe_gbx ba]b[Z

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

85. 32 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 §59. 1. Hiul aZdexqZ_lky bkke_^hZgbb aZbfh^_cklby αqZklbp k y^jZfbZlhfhZahlZE_lysZyk [hevrhckdhjhklvxαqZklbpZijb 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 G1 1 bgZq_ gZauZ_lky ijhlhghf b h[hagZqZ_lkykbfhehf p1 1 bebp. 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 n1 0 bebn_]hfZkkZihqlbjZgZ g_fgh]h[hevr_

86. 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

87. 33 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. XA Z a^_kvO ²kbfheobfbq_kdh]hwe_f_glZ 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 G1 1

88. ^_cl_jbc G2 1 ), ljblbc G3 1 ). 5. IhlhfmqlhfZkkZZlhfhuqbkey_lkydZdkj_^g__agZq_gb_fZkk k_o_]hbahlhih §63. 1. FZkkZZlhfZmf_gvrZ_lkygZZ aZjy^_]hy^jZ²gZ 2. GZijbf_j HeRnRd 4 2 222 86 226 88 +→ . 3. Y^jhjZ^hgZkh^_j`blgZijhlhgZf_gvr_q_fy^jhjZ^by 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 HeYX 4 2 4 2 +→ − − A Z A Z . eyβjZkiZ^Z ~YX 0 0 0 11 ++→ −+ eA Z A Z . 9. αb βjZkiZ^qZklhkhijhh`^Z_lkyγbaemq_gb_f

89. 34 §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

90. M`_gZjZkklhygbbihjy^dZ-14 bo^_cklb_gbqlh`ghfZeh §65. 1. Wg_j]b_ckyaby^jZgZauZ_lkyfbgbfZevgZywg_j]by dhlhjmx g_h[oh^bfhaZljZlblvgZjZks_ie_gb_y^jZgZhl^_evgu_gmdehgu 2. ∆m = (Zmp + Nmn) – My]^_∆m ²^_n_dlfZkkZ b N ²qbkeh 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]bykyaby^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

91. 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

92. 35 §67. 1. JZkkfhljbff_oZgbafijhl_dZgbyp_ighcj_Zdpbb ^_e_gbyy^jZ gZijbf_j_bahlhiZ mjZgZ U235 92 jbk mq_[gbdZ

93. Ijb ^_e_gbb y^jZ ZlhfZ mjZgZ j_amevlZl_ aZoZlZ g_cljhgZ h[jZamxlky ljb 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

94. 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 §68. 1. Y^_jguc j_Zdlhj ² wlh mkljhcklh kihkh[gh_ hkms_kleylv 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

95. 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_cljhguh^Zkem`ZsZyaZf_^ebl_e_fg_cljhghb 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

96. 36 j_Zdpbbj_]mebjmxsb_kl_j`gbuh^ylbaZdlbghcahgu^hl_o ihjihdZg_gZqg_lkyp_igZyj_Zdpby 7. lhjZy nmgdpby h^u ihfbfh aZf_^e_gby g_cljhgh

97. 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^ylke_^mxsb_ ij_h[jZahZgbywg_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]byqZklbqghi_j_oh^blhgmlj_ggxxwg_j]bxh^uIjbwlhf 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]byh^ui_j_oh^blhgmlj_ggxxwg_j]bxiZjZZ 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

98. q_fLWK 3. :lhfgZywg_j]_lbdZlj_[m_lj_r_gbyke_^mxsbolj_ohkghguo ijh[e_f

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

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

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

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

103. 37 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_ m E D = ]^_ ? ² ih]ehs_ggZy _s_klhf wg_j]by m — fZkkZ_s_klZ?^bgbp_cbaf_j_gbyih]ehs_gghc^haubaemq_gby kbkl_f_KByey_lky]j_c=j

104. =j d]1 `1 . 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^bgZdhuoih]ehs_gguo^haZoDhwnnbpb_gldZq_klZbaemq_gby êyαbaemq_gbyjZ_gêyβ- γb j_gl]_ghkdh]hbaemq_gby² 1. 6. WdbZe_glgZy ^haZ baemq_gby [ueZ _^_gZ kyab k l_f qlh 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

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

106. 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^_jghcj_Zdpb_c gZauZ_lkyj_Zdpby kebygby e_]dbo y^_j ijbhq_gvukhdhcl_fi_jZlmj_ihjy^dZkhl_gfbeebhgh]jZ^mkh

107. 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_

108. 38 3. Kebygb_e_]dboy^_j 4. n1 0 4 2 3 1 2 1 HeHH +→+ . 5. HkghgZy ljm^ghklv ijb hkms_kle_gbb l_jfhy^_jghc j_Zdpbb 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_

109. 39 MijZ`g_gby MijZ`g_gb_ 1. Fh`gh h[hbokemqZyoldjZaf_jZfbZlhfh[beyijb^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

110. hlghkbl_evgh A_feb [

111. hlghkbl_evgh h^u

112. hlghkbl_evgh A_feb]

113. hlghkbl_evghhkbdhe_kZ^

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

115. o0 f[

116. sto = s1o + s2o f ±f

117. f

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

119. 40 MijZ`g_gb_ 1. I_juc Zlhfh[bev ^b]Zeky k [hevrbf mkdhj_gb_f ihkdhevdm _]hkdhjhklvaZh^bgZdhu_ijhf_`mldbj_f_gbhajZklZeZ[uklj__ 2. Zgh t = 30 c v1 fk v2 fk J_r_gb_ .fk5,1 k30 fk10fk55 212 = − = − = t vv a GZclbZ. Hl_la fk2 . 3. Zgh t = 12 c v2 – v1 fk J_r_gb_ .fk5,0 k12 fk6 212 == − = t vv a GZclbZ. Hl_la fk2 . MijZ`g_gb_ 1. Zgh v1 fk t = 4 c a = –20 fk2 J_r_gb_ t vv a 12 − = ⇒ v2 = v1 + at = fk ±fk2 ) ⋅ k fk GZclb v2. Hl_lv2 fk 2. Zgh a fk2 v1 = 0 v2 fk J_r_gb_ k10 fk0,2 fk2 2 2212 ===⇒= − = a v t t v t vv a GZclbt. Hl_lt k 3. Y[ W

120. 41 4. vx t5 10 5 -5 5. eyl_eZ,Z fk2 ^eyl_eZ,,Z fk2 . MijZ`g_gb_ 1. Zgh t = 5 c Zo fk2 v0o dfq fk J_r_gb_ sx = 2 2 0 ta tv x o + fk ⋅ k ( ) 2 k5fk0,5 22 ⋅ = f GZclbsx. Hl_lsx f 2. Zgh t = 20 c Zo fk2 v0o fk J_r_gb_ sx = 2 2 0 ta tv x o + ; ao = t v x0 − ⇒ sx = t tv tv x o 2 2 0 0 − = 2 0 tv x = fk ⋅ k f GZclbsx. Hl_lsx f MijZ`g_gb_ 1. Zgh s3 f t1 k J_r_gb_ s1 : s2 : s3 = 1 : 3 : 5; s1 : 2 f = 1 : 5 ⇒ s1 = 5f2 = 0,4 f; s1 = 2 2 1at ⇒ a = 2 1 12 t s = ( )2 k1 f0,42⋅ = 0,8 f/k2 . GZclb s1, a. Hl_ls1 fa fk2 . 2. Zgh s5 f t1 k t5 k J_r_gb_ s1 : s2 : s3 : s4 : s5 = 1 : 3 : 5 : 7 : 9; s1 : 6,3 f = 1 : 9 ⇒ ⇒ s1 = 5f6,3 = 0,7 f; s1 = 2 2 1at ⇒ a = 2 1 12 t s = ( )2 k1 f0,72⋅ = 1,4 f/k2 ; v5 = at5 fk2 ⋅ k fk GZclbv5. Hl_lv5 fk

121. 42 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 5*. Zgh v1 dfq fk v2 fk J_r_gb_ v = v1 + v2 fk fk 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_ 1. Zgh Z fk2 m d] J_r_gb_ IhhfmaZdhgmGvxlhgZ F = ma d]⋅ fk2 G GZclbF. Hl_lF G 2. Zgh t = 20 c v fk m l ⋅105 d] J_r_gb_ F = ma ²hcaZdhgGvxlhgZ a = t v ⇒ F = t mv = k20 fk4d]10841 5 ⋅⋅, = G dG GZclbF. Hl_lF dG 3. Zgh m1 = m2 a1 fk2 a2 fk2 F1 = 1,2 H J_r_gb_ IhhfmaZdhgmGvxlhgZ F1 = m1a1; F2 = m2a2. Ldm1 = m2lhihemqZ_f ==⇒= 1 12 2 2 2 1 1 a Fa F a F a F = ⋅ 2 2 fk0,08 G1,2fk0,64 9,6 H. GZclbF2. Hl_lF2 G

122. 43 4. Zgh m = 0,5 d] FA = 10 H FL = 5 H FC = 2 H J_r_gb_ IhhfmaZdhgmGvxlhgZF = ma. F = FA – FL – FC ⇒ FA – FL – FC = ma ⇒ ⇒a = d]0,5 H2H5H10 −− = −− m FFF CLA fk2 . GZclbF2. Hl_la fk2 . 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`_gguod l_emkbeKdhjhklvb i_j_f_s_gb_fh]ml[ulvdZd khgZijZe_guk jZgh^_cklmxs_cijbeh`_gguod l_emkbelZdb ijhlbhiheh`ghgZijZe_gu MijZ`g_gb_ 1. GZ l_eh ^_cklmxl kbeZ ly`_klb lF 7 b kbeZ j_Zdpbb hihju N 7 kfjbk

123. lF 7 N 7 2. G_ ij_ukbl ld jZgh^_cklmxsZy ijbeh`_gguo kbe gZ ^bgZfhf_ljjZgZ 3. Zgh m1 d] m2 d] a fk2 J_r_gb_

124. IhhfmaZdhgmGvxlhgZ F2x = m2ax d]⋅ fk2 G IhfmaZdhgmGvxlhgZF1x = –F2x ±G

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

126. i_jhfkemqZ_gblvf_`^m l_e_`dZfbgZlygmlZ kbevg__

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

128. ⋅ fk2 G GZclb F1x, F2x, Fx. Hl_l

129. F1x ±GF2x G

130. F1x GF2x = ±G

131. i_jhfkemqZ_

132. Fx G

133. 44 MijZ`g_gb_ 1. Zgh g ≈ fk2 t = 2 c J_r_gb_ h = 2 2 gt = ( ) 2 k2fk10 22 ⋅ f GZclbh. Hl_lh f 2. Zgh g ≈ fk2 h = 80 cf f J_r_gb_ h = 2 2 gt ⇒ t = 2 fk10 f0,822 ⋅ = g h = 0,4 k. GZclbt. Hl_lt k 3. Zgh g ≈ fk2 h = 45 f t1 = 1 c ∆t = 1 c J_r_gb_ h = 2 2 gt ⇒ t = 2 fk10 f4522 ⋅ = g h k s1 = 2 2 1gt = ( ) 2 k1fk10 22 ⋅ = 5 f; s2 = ( ) 2 û 2 22 ttggt − − = = ( ) ( ) 2 c1c3fk10 2 k3fk10 2222 −⋅ − ⋅ = 5 f GZclb t, s1, s2. Hl_lt ks1 fs2 f MijZ`g_gb_ Zgh v fk v1 = 0 g fk2 J_r_gb_ g = t v t vv = − 1 ⇒ t = 2 fk9,8 fk9,8 = g v =1 c; s = 2 2 gt vt − fk ⋅ k ± ( ) 2 1kfk9,8 22 ⋅ f GZclbt, s. Hl_lt ks f 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_

134. 45 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

135. ^_cklhZeZ[

136. ijbly`_gb_A_feb

137. baaZ^_cklbykbeuly`_klb 5. Zijbly]bZ_lkyghwlZkbeZ]hjZa^hf_gvr_kbeuly`_klbba aZjZkklhygbcEmgZlZd`_ijbly]bZ_lkyd wlhfmq_eh_dm MijZ`g_gb_ 1. Zgh g ≈ fk2 m1 d] m2 ] d] m3 l d] m4 l d] J_r_gb_ Fl = mg ⇒ Fl fk2 ⋅ d] G Fl fk2 ⋅ d] G Fl fk2 ⋅ d] G dG Fl fk2 ⋅ d] ⋅105 G dG GZclb Fl1, Fl2, Fl3, Fl4. Hl_lGGdGdG 2. Zgh g ≈ fk2 ; m d] J_r_gb_ Fl = mg d]⋅ fk2 G GZclbFl. Hl_lFl G 3. Zgh g ≈ fk2 ; Fl G J_r_gb_ Fl = mg ⇒ m = 2 l fk10 G819,3 = g F d] GZclbFl. Hl_lm d] 4. G_lihkdhevdmukhlZihe_lZkjZgbfZk jZaf_jZfbA_febKbem ly`_klb fh`gh jZkkqblZlv ih nhjfme_ Fl = 2 a ja )( hR mF G + ]^_ h — ukhlZgZ^A_fe_c 5. GZyklj_[Z^_cklm_lkbeZly`_klbb _kebhgkeh`bldjuevylh hgmiZ^_lgZA_fex 6. GZjZkklhygbbRa; 3Ra (Ra ²jZ^bmkA_feb

138. ihkdhevdmFl~ 2 a )( 1 hR + MijZ`g_gb_ 1. KbeZ F 7 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

139. 46 MijZ`g_gb_ 1. Zgh r kf f v fk J_r_gb_ Z = r v2 = ( ) f21,0 fk20 2 ≈ fk2 . GZclba. Hl_lZ ≈ fk2 . 2. Zgh R kf f T k J_r_gb_ Z = R v2 ; v = T R T l π = 2 ⇒ Z = RT R 2 22 4π = 2 2 4 T Rπ = = ( ) ( )2 2 k60 f02,014,34 ⋅⋅ ≈ 2⋅10-4 fk2 . GZclba. Hl_lZ ≈ 2⋅10-4 fk2 . 3. Z1 = r v2 ; Z2 = r v r v 22 2 2/ ⋅= = 2a1 ⇒ ml_j`^_gb__jgh 4. Zgh T1 k T2 k J_r_gb_ ( ) . 4 :gZeh]bqgh. 42 2 2 2 22 1 22 1 2 1 1 T R a T R R TR R v a π = π = π == .3600 c60 c3600 vghKe_^hZl_e 22 2 1 2 1 =      =      = T T a a GZclb 2 1 a a . Hl_l 2 1 a a = 3600. 5. Zgh Fa = 6⋅1024 d] Fe = 6⋅1022 d] G=6,67⋅10-11 2 2 d] fG⋅ r = df = 3,84⋅108 f J_r_gb_ Z

140. F]j = 2 ea r FF G = 6,67⋅10-11 2 2 d] fG ⋅ × 28 2224 f

141. 10(3,84 d]107d]106 ⋅ ⋅⋅⋅ × ≈ 1,9⋅1020 G [

142. Zp = a ]j F F = d]106 G109,1 24 20 ⋅ ⋅ ≈ 3,17⋅10-5 fk2 ;

143. v = rap = f1084,3fk1017,3 825 ⋅⋅⋅ − ≈fk GZclbF]j, Zp, v. Hl_lF]j ≈ 1,9⋅1020 Gv ≈ fk Zp = 3,17⋅10-5 fk2 .

144. 47 MijZ`g_gb_ 1. Zgh h df ⋅106 f Fa = 6⋅1024 d] Ra = 6,4⋅106 f G = 6,67⋅10-11 2 2 d] fG ⋅ J_r_gb_ = + ≈ hR M Gv a a = ⋅+⋅ ⋅ ⋅ ⋅ ⋅= − f

145. 106,4f10(2,6 d]106 d] fG 106,67 66 24 2 2 11 fk dfk GZclbv. Hl_lv dfk 2. Zgh v dfk ⋅103 fk ge ≈ fk2 J_r_gb_ ==⇒= e e g v r r v r 2 e 2 e ( ) 2 23 fk1,6 fk101,67⋅ = = 1,7⋅106 f ⋅103 df GZclb re. Hl_lre = 1,7⋅103 df MijZ`g_gb_ 1. Zgh v1x = –v2x fk m = 0,2 d] J_r_gb_ p1x = mv1x d]⋅ fk d]⋅fk p2x = – p1x ±d]⋅fk _dlhjubfimevkhfZrbgg_jZguldhgb ijhlbhiheh`gh gZijZe_gu Fh^meb _dlhjhbfimevkhjZgu GZclb p1x, p2x. Hl_lp1x d]⋅fkp2x ±d]⋅fk 2. Zgh v1 dfq fk v2 dfq fk m l d] J_r_gb_ ∆j = m∆v = m(v2 – v1) = d]⋅ fk ± fk

146. d]⋅fk 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

147. 48 2. Zgh m1 l m2 l v2 fk J_r_gb_ AZibr_faZdhgkhojZg_gbybfimevkZ m1v1 = (m1 + m2)v2 ⇒ v1 = 2 1 21 v m mm + = = fk0,5 35l l28l35 ⋅ + fk GZclb v1. Hl_lv1 fk MijZ`g_gb_ 1. Zgh ve fk m d] v fk me d] J_r_gb_ AZibr_faZdhgkhojZg_gbybfimevkZ (me + m)ve + mv = mev ⇒ v = e ee )( m vmvmm ++ = = ( ) d]200 fk8d]5fk2d]5d]200 ⋅+⋅+ fk GZclb v. Hl_lv fk 2. Zgh mj ] d] mi ] d] vi fk J_r_gb_ AZibr_faZdhgkhojZg_gbybfimevkZ mjvj=mivi⇒vj= j ii m vm = ≈ ⋅ d]0,3 fk100d]0,1 fk GZclb vj. Hl_lvj ≈ fk MijZ`g_gb_ 1. Dhe_[Zl_evgufb kbkl_fZfb yeyxlky [ ] _ G_ yeyxlky dhe_[Zl_evgufbZ^ 2. Z

148. Ih^^_cklb_fkbemijm]hklbrgmjh[

149. g_l

150. rgmju^bkd ]

151. ^Zyey_lky MijZ`g_gb_ 1. :fieblm^Z : qZklhlZ ν i_jbh^ L ² ihklhyggu_ F, v — i_j_f_ggu_ 2. Zgh ν = =p J_r_gb_ T = k5,0 =p2 11 == ν GZclb T. Hl_lT k

152. 49 3. Zgh T k J_r_gb_ ν = =p2 c5,0 11 == T GZclb ν. Hl_lν =p 4. Zgh n = 600 t fbg k J_r_gb_ ν = ; 1 T =p10 c60 600 ===ν⇒= t n n t T GZclb ν. Hl_lν =p 5. kfkfkfkf 6. Zgh A = 10 kf ν = 0,5 =p t k J_r_gb_ T = =p5,0 11 = ν = 2 c AZ k l_eh kh_jrZ_l ihegh_ dhe_[Zgb_b ijhc^_limlvS = 4: kf GZclb S. Hl_lS kf 7. Dhe_[exlky h^bgZdhuonZaZo kemqZyo[

153. ^

154. Dhe_[exlky ijhlbhiheh`guonZaZo kemqZyoZ

155. ]

156. _

157. MijZ`g_gb_ 1. ?iheGZijZ e_gb_ ^b`_gby fZylgbdZ Fmij v ?i ?d K lj_ gb_f ;_a lj_ gby Hl d H mf_gv m_e mf_gv m_e mf_gv g_ baf_g HlH d : m_e mf_gv . m_e mf_gv mf_gv g_ baf_g Hl: d H mf_gv m_e mf_gv m_e mf_gv g_ baf_g HlH d m_e mf_gv . m_e mf_gv mf_gv g_ baf_g 2. Z

158. ` ` [

159. ` ` `

160. ` h k_o kemqZyo MijZ`g_gb_ 1. Kihkh[gu kh_jrZlv kh[h^gu_ dhe_[Zgby l_eZ [

161. _

162. ugm`^_ggu_dhe_[Zgby²k_l_eZ 2. Z

163. ^ZgZijbf_jkljmgZfmaudZevgh]hbgkljmf_glZ[

164. g_l

165. 50 MijZ`g_gb_ 1. Z

166. ugm`^_ggu_[

167. [eZ]h^Zjydhe_[ZgbxfZylgbdZ

168. qZklhlZ fZylgbdZjZgZqZklhl_fZylgbdZ m fZylgbdZqZklhlZ [hevr_ q_fm fZylgbdZm fZylgbdZqZklhlZf_gvr_q_fm fZylgbdZ]

169. ldbo^ebgub khhl_lkl_gghkh[kl_ggu_qZklhlukhiZ^Zxl 2. FZevqbdb h^ZgZqbgZxldhe_[Zlvky ijhlbhnZa_ 3. Q_j_ak L = 1/ν k

170. MijZ`g_gb_ 1. Zgh λ f T k J_r_gb_ fk20 k13,5 f270 == λ = T v GZclb v. Hl_lv fk 2. Zgh ν =p v fk J_r_gb_ f7,1 =p200 fk340 == ν =λ v GZclb λ. Hl_lλ f 3. 2. Zgh v fk λ f J_r_gb_ k4 fk1,5 f6 == λ = T v GZclbT. Hl_lT = 4 c. MijZ`g_gb_ E_lysZyilbpZkha^Z_lbgnjZamdhu_hegu MijZ`g_gb_ 1. DhfZjAmdkha^ZZ_fucbfkZfucukhdbc 2. Mf_gvrblkyihkdhevdmqZklhlZ__ jZs_gbylZd`_mf_gvrblky 3. Ijb ihur_gbb l_fi_jZlmju kljmgZ jZkly]bZ_lky i_jbh^ __ dhe_[Zgbc m_ebqbZ_lky qZklhlZ b khhl_lkl_ggh ukhlZ amqZgbymf_gvrZ_lky MijZ`g_gb_ 1. G_lf_`^mA_fe_cb Emghcg_lmijm]hckj_^uihdhlhjhcfh`_l jZkijhkljZgylvkyamd 2. Amdhu_hegujZkijhkljZgyxlkyihgblb

171. 51 MijZ`g_gb_ 1. Zgh λ f T k J_r_gb_ fk1450 k0,002 f9,2 == λ = T v GZclb v. Hl_lv fk 2. Zgh v1 fk v2 fk v3 fk ν =p J_r_gb_ ;f47,0 =p725 fk3401 1 ≈= ν =λ v ;f05,2 =p725 fk14832 2 ≈= ν =λ v .f59,7 =p725 fk55003 3 ≈= ν =λ v GZclbλ1,λ2,λ3. Hl_lλ1 ≈ fλ2 ≈ fλ3 ≈ f 3. Amd [m^_l jZkijhkljZgylvky b ih f_lZeem b ih ha^mom b q_eh_dmkeurbl^Zm^ZjZ 4. Zgh ta k va fk tiZj k Sa = SiZj J_r_gb_ Sa = vata; SiZj = viZjtiZj; Sa = SiZj; vata = viZjtiZj ⇒ ⇒ fk20 k34 k2fk340 iZj aa iZj = ⋅ == t tv v GZclbviZj. Hl_lviZj fk 5. Dh]^Zb^bfu_b keurbfu_m^ZjugZqbgZxlkhiZ^ZlvkghZlh wlhagZqblqlhq_eh_dkeurblij_^u^msbci_j_^b^bfufm^Zj MijZ`g_gb_ 1. Kms_klm_l 2. FZ]gblgh_ ihe_ [m^_l ^_cklhZlv 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

172. ?klvwlhlhqdbD b K[

173. lhqd_:. 2. GZ iZju lhq_d P − Q, X − Y kh klhjhgu g_h^ghjh^gh]h fZ]gblgh]h ihey ^_cklmxl kbeu h^bgZdhu_ dZd ih fh^mex lZd b ih gZijZe_gbx ld PO = QO, XO = YO. , , ; 3 4 2

174. 52 MijZ`g_gb_ 1. 2. 3. K__jguc ihexk gZoh^blky kijZZ Z x`guc ke_Z Bo iheh`_gb_fh`ghbaf_gblvihf_gyiheyjghklvkhe_ghb^Z 4. Lhd[m^_ll_qvhllhqdbS d lhqd_N. 5. KijZZ²k__jgucihexkke_Z±x`gucihijZbem ijZhc jmdb

175. 6. i_jhf kemqZ_ aZbfh^_cklb_ h[mkehe_gh fZ]gblgufb kbeZfbhlhjhf±dmehghkdbfb MijZ`g_gb_ 1. IhijZbeme_hcjmdbhij_^_ey_fqlhijZh 2. IhijZbem e_hcjmdbhij_^_ey_fqlhlhdl_q_lhllhqdbB d lhqd_ A b ke_^hZl_evgh _jogbc ihexk bklhqgbdZ lhdZ ih^dexq_g d hljbpZl_evghfm ihexkm Z gb`gbc ² d iheh`bl_evghfm

176. 53 3. GZ e_hf jbkmgd_ e_uc ijhh^gbd ^b`_lky _jo ijZuc ijhh^gbd²gbaGZijZhfjbkmgd_e_ucijhh^gbd^b`_lky gbaijZucijhh^gbd²_jo 4. v 7 F 7 5. Ih ijZbem e_hc jmdb hij_^_ey_f qlh wlh iheh`bl_evgh aZjy`_ggZyqZklbpZ MijZ`g_gb_ 1. Zgh I = 4 A; F = 0,2 H l kf f J_r_gb_ Le5,0 :4f0,1 G2,0 = ⋅ == Il F B GZclbB. Hl_lB Le 2. FZ]gblgZy bg^mdpby g_ baf_gy_lky hgZ ihklhyggZy _ebqbgZ Baf_gy_lkylhevdhkbeZ^_cklmxsZygZijhh^gbd²hgZlZd`_ dZdb lhdmf_gvrZ_lky jZaZ MijZ`g_gb_ FZ]gblguc ihlhd ijhgbauZxsbc dZlmrdm D2 fh`gh f_gylv iml_fbaf_g_gbyaZbfghchjb_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^mdpbhgguclhdhagbdZ_l kemqZ_]

177. g_hagbdZ_l kemqZyo Z

178. [

179. ^

180. MijZ`g_gb_ 1. Zgh J_r_gb_

181. 54 ν =p T = k02,0 =p50 11 == ν GZclb T. Hl_lT k 2. Ih]jZnbdmgZoh^bfqlhT= k 60 1 , ν= ( )c601 11 = T =p : f: MijZ`g_gb_ Wlbiheygbq_fg_hlebqZxlkyb kms_klhZeb[u[_adZlmrdbK MijZ`g_gb_ 1. Zgh T = 10-7 c J_r_gb_ ν = =p10 c10 11 7 7 == − T GZclbν. Hl_lν = 107 =p 2. Zgh t = 8,3⋅10-7 c c = 3⋅108 fk J_r_gb_ S = ct = 3⋅108 fk ⋅ 8,3⋅10-7 k f GZclb S. Hl_lS = 249 f 3. Zgh λ f c = 3⋅108 fk J_r_gb_ ν = =p105 f600 fk103 5 8 ⋅= ⋅ = λ c GZclbν. Hl_lν = 5⋅105 =p 4. AgZy kdhjhklv jZkijhkljZg_gby kb]gZeZ k hgZ jZgZ kdhjhklb k_lZ

182. 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_^hZl_evghS = ct/2. 5. G_lamdhu_hegug_jZkijhkljZgy_lky Zdmmf_ MijZ`g_gb_ 1. K12 6 ²Z_f Li6 3 ²Z_f Ca40 20 ²Z_f 2. 6, 3, 20.

183. 55 3. n = Z_f1 Z_f6 jZa 4. Z

184. [

185. Z_f

186. jZa]

187. ^

188. _

189. `

190. 5. NOOK 14 7 14 7 0 1 014 16 14 6 =⇒+→ − − + _ ²Zahl MijZ`g_gb_ HOHeN 1 1 17 8 4 2 14 7 +→+ Bf__f Ke_^hZl_evgh aZdhgkhojZg_gbyaZjy^Zuihegy_lky MijZ`g_gb_ 1. y^j_ ZlhfZ [_jbeeby Be9 4 gmdehgh ² ijhlhgh ² g_cljhgh²N = A + Z = 9 – 4 = 5. 2. D39 19 Z

191. Z [

192. Np = Z

193. Q we_f_glZjguo we_dljbq_kdboaZjy^Zo

194. ]

195. Ne = Np ^

196. _

197. `

198. : a

199. N = A – Z = ± b

200. m Z_f 3. Qbkehijhlhghkhhl_lkl_gghwe_dljhgh

201. Zlhf_jZgh_]h ihjy^dhhfm ghf_jm lZ[ebp_ F_g^_e__Z ke_^hZl_evgh Z

202. eblbc[

203. nlhj MijZ`g_gb_ Wlb Zlhfu bf_xl h^bgZdhu_ fZkku gh bo obfbq_kdb_ khcklZ jZaebqguWlhh[tykgy_lkyl_fqlhm gbojZagu_aZjy^hu_qbkeZ ZagZqblb dhebq_klhwe_dljhgh MijZ`g_gb_ 1. HeThU 4 2 234 90 238 92 +→ . 2. ~UPa;~PaTh 0 0 0 1 234 92 234 91 0 0 0 1 234 91 234 90 ++→++→ −− ee Ke_^hZl_evgh j_amevlZl_^moβjZkiZ^h MijZ`g_gb_ Ld gmdehgu bf_xl fZkkm lh f_`^m gbfb ^_cklmxl kbeu ]jZblZpbhggh]hijbly`_gby

204. 56 AZ^Zqbij_^eZ]Z_fu_^eyihlhj_gby b ijbqZkZonbabdb g_^_ex 1. ey_dlhjZ a 7 bf__fZ

205. [

206. Zy ± ±

207. _Zy| = ]

208. 22 )52()5,05,0(|| −+−=a 7 = 3. ey_dlhjZ b 7 bf__fZ

209. [

210. by ±

211. _by_ ]

212. 22 )04()14(|| −+−=b 7 = 5. ey_dlhjZ c 7 bf__fZ

213. [

214. cy ±

215. _cy_ ]

216. 22 )11()46(|| −−−=c 7 = 2. ey_dlhjZ d 7 bf__fZ

217. ±

218. [

219. dy ±± ±

220. _dy_ ]

221. 22 )04()63(|| −−+−=d 7 = 5 ey_dlhjZ → e bf__fZ

222. ±

223. [

224. ey ±±±

225. |ey_ ]

226. 22 ))4(1()5,05,0(|| −−−+−=e 7 = 3. 2. ax = 0, bx = || b 7 , cx = 0, dx = || d 7 − . 3. Z

227. A (0;2), B ±

228. [

229. sx = 12 – 0 = 12, sy ±± ±

230. _sx| = 12, |sy| = 5; ]

231. 22 )23()012(|| −−+−=s 7 = 13. 4. x y B A sAB = 22 ))2(3())8(4( −−+−− LZddZdimlvg_fh`_lij_ukblv i_j_f_s_gbyfh^mevdhlhjh]h_klvgZbf_gvr__jZkklhygb_f_`^m gZqZevghcb dhg_qghclhqdZfbimlb

232. lhhgfh`_l[ulveb[hjZ_g eb[h[hevr_i_j_f_s_gbyghgb dh_fkemqZ_g_f_gvr__]h 5. Ijyfhebg_cguf jZghf_jguf ^b`_gb_f gZauZ_lky lZdh_ ^b`_gb_ ijb dhlhjhf aZ h^bgZdhu_ ijhf_`mldb j_f_gb l_eh kh_jrZ_lh^bgZdhu_i_j_f_s_gby ^hev g_dhlhjhchkblZd dZd ^b`_gb_ ijyfhebg_cgh_

233. Ihwlhfm sx = vxt ]^_ vx ² ihklhyggZy

234. 57 _ebqbgZ oZjZdl_jbamxsZy kdhjhklv i_j_f_s_gby Bkoh^y ba mjZg_gbyo = o0 + sxihemqbfx = x0 + vxt. 6. Zgh vx fkx0 f J_r_gb_ x(t) = x0 + vxt ⇒ x(t) = 3 + 5t. GZclbx(t). Hl_lx(t) = (3 + 5t

235. f 7. xixl x X hdaZe Zgh xi = 260 – 10t xl = –100 + 8t J_r_gb_ gZqZevgucfhf_glgZ[ex^_gby xi = 260 – 10 ⋅ 0 = 260; xl = –100 + 8 ⋅ 0 = –100. fhf_glklj_qbxi = xl beb±t = –100 + 8t. Hlkx^ZgZoh^bffhf_glj_f_gbklj_qbt = 20 c. x = 260 – 10 ⋅ 20 = –100 + 8 ⋅ f GZclb xi, xl, t, x. Hl_lxi = 260, xl = –100, t = 20 c, x f 8. Kh]eZkgh]jZnbdmiehl[uekims_ggb`_klhygdbgZf_ljh Ih]jZnbdmhij_^_ebfo0 = –10; vx fk fko = –10 + 2t. 9. Zgh t = 2 c v0 = 0 v fk v1 fk J_r_gb_ a = t v t vv = − 0 ; t1 = fk3 k2fk4,511 ⋅ == v tv a v = 3 c; s = ( ) fk32 k2fk4,5 222 22 1 2 22 1 2 1 ⋅ ⋅ === v tv tv tvvat = 6,75 f GZclbt1, s. Hl_l: t1 = 3 c, s = 6,75 f. 10. ( )( ) t vv tavv tta vt ta tvs 2222 0 000 2 0 77 777 7 7 7 77 + =++=      +=+= . 11. 2 2 0 ta tvs 7 77 += ; t vv a 0 77 7 − = ; t vv t tvv tvs 22 )( 0 2 0 0 7777 77 + = − += ; ( ) ( ) ( )( ) ⇒ − =−−+⋅=      +− = 2 ,, 2 1 2 ,, 2 0 2 0 2 0 2 0 00 vv vvvvvvt vv t vv sa 77 777777 7777 77 s vv a 7 77 7 2 2 0 2 − =⇒ . 12. Zgh tx = 0,3 k J_r_gb_

236. 58 s f vkj = fk43,1 k0,3 f,430 ≈= t s a = ; 2 2 t s v = at = k3,0 f43,022 ⋅ = t s ≈ 2,87 f/k. GZclbvkj, v. Hl_lvkj ≈ fkv ≈ fk 13. so[ = 2 2 o[ta ; sFd = 2 3 2 2 o[ 2 cd tata = = 3sh[. ⇒ jZaZ[hevr_ vkd = acdt = 3ah[t = 3vh[. ⇒ jZaZ[hevr_ 14. 0 vx t eyh[uqgh]h ebnlZ eykdhjhklgh]h ebnlZ 15. Zgh vx(t) = 10 + 0,5t J_r_gb_ v0x = vx(0) = 10 + 0,5 ⋅ fka fk2 . K l_q_gb_f j_f_gb fh^mev _dlhjZ kdhjhklb Zlhfh[beyhajZklZ_llZddZdZ!b v00). GZclbv0x. Hl_lv0x fk 16. Ihke_ m^ZjZ mkdhj_gb_ rZc[u gZijZe_gh ijhlb kdhjhklb Dh]^Z kdhjhklv h[jZsZ_lky gmev mkdhj_gb_ lh`_ klZghblky jZgufgmex    ≤≤− = .5fk0 ;50fk)5( |)(| t tt tvx vx t

237. 59 17. o = o0 + sx JZg__ [ueh ^hdZaZgh qlh ijb jZghmkdhj_gghf ^b`_gbbk mkdhj_gb_fZo b gZqZevghckdhjhklvxv0x i_j_f_s_gb_ jZghsx = v0xt + 2 tax ihwlhfmo = o0+ v0xt + 2 tax . 18. Zgh ax fk2 v0x = 0 x0 = 0 J_r_gb_ vx(t) = v0x + axt = 0,1t fk2 ). x(t) = x0 + v0xt + 2 2 tax = 2 1,0 2 t⋅ = 0,05t2 . GZclbvx(t), x(t). Hl_lv0x fk 19. Zgh |v_ dfq Z

238. |vhlg| = 0 [

239. |vhlg_ dfq

240. |vhlg_ dfq ]

241. |vhlg_ dfq J_r_gb_ |vf| = ||v| – |v|| ijb v ↑↑ vf beb |vf| = ||v| + |v|| ijb v ↑↓ vf. Z) v ↑↑ vf b v ↑↓ vf ⇒ |vf| = |40 df/q ± 0 df/q| = = 40 df/q. [) v ↑↑ vf ⇒ |vf| = |40 df/q – 10 df/q| = 30 df/q. v ↑↓ vf ⇒ |vf| = |40 df/q + 10 df/q| = 50 df/q.

242. v ↑↑ vf ⇒ |vf_ _dfq ±dfq_ v ↑↓ vf ⇒ |vf_ _dfq dfq_ dfq ]

243. v ↑↑ vf ⇒ |vf_ _dfq dfq_ dfq v ↑↓ vf ⇒ |vf_ _dfq ±dfq_ dfq GZclbvf. Hl_lZ

244. dfq [

245. dfq beb dfq

246. bebdfq[

247. dfq bebdfq 20. KdhjhklvdZl_jZhlghkbl_evgh[_j_]Zihl_q_gbxvd = = vd + vl = 6vl a^_kvvd ²kdhjhklvdZl_jZhlghkbl_evghh^uvl — kdhjhklv l_q_gby h^u hlghkbl_evgh [_j_]Z

248. kdhjhklv dZl_jZ hlghkbl_evgh [_j_]Z ijhlb l_q_gby vd = vd – vl = 4vl LZdbf h[jZahf 4 6 d d = − + v v = 1,5. 21. 33 3 f103 d]103,87 − − ⋅ ⋅ ==ρ V m d]f3 Fu b^bf qlh iehlghklv rZjbdZjZgZiehlghklbha^moZZke_^hZl_evghulZedbZxsZy kbeZ ^_cklmxsZy gZ rZjbd jZgZ _]h kbe_ ly`_klb AgZqbl ih i_jhfm aZdhgm GvxlhgZ rZjbd hklZg_lky khklhygbb ihdhy ld _]hhlimklbeb[_agZqZevghckdhjhklbbgZq_[uhgjZghf_jghb ijyfhebg_cghi_j_f_sZeky

249. 22. Kh]eZkghlj_lv_fmaZdhgmGvxlhgZkbeu^_cklmxsb_gZrZju jZguKh]eZkghlhjhfmaZdhgmGvxlhgZbomkdhj_gbyjZgu

250. 60 Zk = cm F , ZZ = am F Hlkx^Z c a a c m m a a = j_Zevguo nbabq_kdbo aZ^ZqZo dh]^Z fZkku rZjh g_ jZgu gmex

251. fh^mev mkdhj_gby klZevgh]h rZjZ g_ fh`_l jZgylvky gmex Hg fh`_l [ulv dZd [hevr_ lZd b f_gvr_ fh^mey mkdhj_gby Zexfbgb_h]h rZjZ qlh aZbkblebrvhlkhhlghr_gbyfZkkrZjh 23. Ba nhjfmeu êy g0 ihemqZ_f GM3 = 2 30Rg Ih^klZeyy nhjfmemêygihemqZ_fg = 2 3 2 30 )( hR Rg + . 24. r v a 2 1 = ; 1 2 1 2 1 2 a r v a == ; L1 = 1ma ; L2 = 112 2 1 2 1 Lmama == . DZdmkdhj_gb_lZdb kbeZ^_cklmxsZygZlhjhcrZjbd jZaZ f_gvr_ZgZeh]bqguo_ebqbgêylhjh]hrZjbdZ 25. GZ ukhl_ h hlghkbl_evgh a_feb r = R3 + h; mapk = mg; 2 3 2 30 3 2 )()( hR Rg hR v + = + ⇒ hR Rg v + = 3 2 30 26. Zgh R df ⋅ 106 f g0 fk2 h df ⋅ 106 f J_r_gb_ hkihevam_fkynhjfmehcihemq_gghc ij_û^ms_caZ^Zq_ ≈ ⋅+⋅ ⋅⋅ = + == f103,6f106,4 f

252. 10(6,4fk9,8 66 26 3 2 30 hR Rg vv ≈ fk GZclbv. Hl_lv ≈ fk 27. vx = gt. vx, fk t, c 28. Zgh l d] J_r_gb_ ∆p = m∆v = mg∆t.

253. 61 v0 = 0 t k ∆t = 1c Ld∆v1 = ∆v2 jZghmkdhj_ggh_^b`_gb_

254. lh ∆p1 = ∆p2 = ∆p d]⋅fk2 ⋅ 1 c d]⋅fk GZclbv. Hl_l∆p1 = ∆p2 = ∆p d]⋅fk 29. Ld m ² ihklhyggZy _ebqbgZ lh baf_g_gb_ bfimevkZ [m^_l hij_^_eylvkylhevdhbaf_g_gb_fkdhjhklbIh]jZnbdmkfaZ^Zqm

255. b^ghqlh_keb∆t1 = ∆t2lhb ∆v1 = ∆v2bagZqbl∆p1 = ∆p2. 30. mkehbyo kh[h^gh]h iZ^_gby kdhjhklb h[hbo rZjbdh ex[hc fhf_gl j_f_gb [m^ml h^bgZdhu b ke_^hZl_evgh hlghr_gb_ bo bfimevkh [m^_l aZbk_lv ebrv hl hlghr_gby bo fZkk LZd dZd ih mkehbx h[t_fu h^bgZdhu hgh [m^_l jZgh hlghr_gbxiehlghkl_cf_^bb Zexfbgby 33 33 Z f d]f102,7 d]f108,9 ⋅ ⋅ = ρ ρ ≈ 3,3. BlZd ex[hc fhf_gl j_f_gb f_^guc rZjbd bf__l bfimevk ijbf_jgh jZaZ[hevr_q_fZexfbgb_uc 31. 1 2 X2 ^hklhedgh_gby 1 ihke_klhedgh_gby X Zgh v1x fk v2x fk xv1′ fk J_r_gb_ Ih aZdhgm khojZg_gby bfimevkZ gZ hkv O): xxxx vmvmmvmv 2121 ′+′=+ ⇒ xxxx vvvv 1212 ′−+=′ = fk fk ±fk fk GZclbv. Hl_l xv2′ fk 32. 1 2 X2 ^hklhedgh_gby 1 ihke_klhedgh_gby X Zgh v1x fk v2x ±fk xv1′ = –fk J_r_gb_ Ih aZdhgm khojZg_gby bfimevkZ gZ hkv O): xxxx vmvmmvmv 2121 ′+′=+ ⇒ xxxx vvvv 1212 ′−+=′ = fk ±fk

256. ±±fk

257. fk GZclbv. Hl_l xv2′ fk 33. ( )2 2 2 1 2 2 2 1 222 xx xx vv mmvmv E +⋅=+= ; ( )2 2 2 1 2 2 2 1 222 xx xx vv mvmvm E ′+′⋅= ′ + ′ =′ ;

258. 62 2 2 2 1 xx vv + fk

259. 2 + ±fk

260. 2 = 0,05 f2 k2 ; 2 2 2 1 xx vv ′+′ ±fk

261. 2 + + fk

262. 2 = 0,05 f2 k2 ⇒ 2 2 2 1 xx vv + = 2 2 2 1 xx vv ′+′ ⇒ E = E′. 34. Ih ]jZnbdm hij_^_ey_f qlh L k b ν = c2 11 = T =p Ex[Zy^jm]ZylhqdZbaf_gy_lkdhjhklvk lhc`_kZfhcqZklhlhc 35. havf_f aZ t fhf_gl dh]^Z hldehg_gb_ kj_^g_c lhqdb kljmgujZghgmex =jZnbdg_]h^blky^ey^jm]bolhq_dkljmguldZfieblm^ZbohlebqgZ hlZfieblm^ukj_^g_clhqdbeykj_^gbolhq_dkljmg^jm]boZjnhg l_f[he__g_]h^blkylZddZdhgbbf_xlbgu_qZklhludhe_[Zgbc ;ff WfF 36. GZ^h ^Z h^bgZdhuo dZf_jlhgZ jZkiheh`blv gZ g_dhlhjhf jZkklhygbb^jm]hl^jm]ZlZdqlh[uboj_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]emrblvijbdhkgmrbkvjmdhcd g_fmlh fu mkeurbf amd hl lhjh]h dZf_jlhgZ hkgh_ ^Zggh]h hiulZ e_`blye_gb_amdhh]hj_ahgZgkZ 37. Ihevamykv ]jZnbdhf hij_^_ey_f Z

263. ijb =p Zfieblm^Z mklZghbrboky dhe_[Zgbc[m^_l [hevr_ q_f ijb =p [

264. qlh[u Zfieblm^Z mklZghbrbokydhe_[Zgbc[ueZ fZdkbfZevghc dZq_eb gZ^hih^lZedbZlvk qZklhlhc=p

265. kh[kl_ggZyqZklhlZdZq_e_c jZgZqZklhl_ugm`^Zxs_ckbeul_=p 38. Zgh: l kf f m ] d] B = 4 ⋅ 10-2 Le J_r_gb_ Fl = Ff; mg = BIl ⇒ I = f0,1Le104 fk9,8d]002,0 2 2 ⋅⋅ ⋅ = − Bl mg = = 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_ ^_cklm_l ^b`msbcky we_dljhg IhevamykvijZbehfe_hcjmdbhij_^_ey_fqlhwe_dljhge_l_e dZf_jm lhqd_.

гдз. физика 9кл перышкин гутник_2001

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гдз. физика 9кл перышкин гутник_2001