>hfZrgyy jZ[hlZ ihnbabd_ aZ deZkk
d mq_[gbdm ©NbabdZ de Mq_[^eyh[s_h[jZah\Zlmq_[aZ\_^_gbcª :<I_jurdbg?F=mlgbd±_ ba^kl_j_hlbi± F ©>jhnZª ]
1
Kh^_j`Zgb_
11 11 12 12 12 13 13 13 14 14 14 15 15 16 16 2
§28. .................................... §29. .................................... §30. .................................... §31. .................................... §32. .................................... §33. .................................... §34. .................................... §35. .................................... §36. .................................... §37. .................................... §38. .................................... §39. .................................... §40. .................................... §42. .................................... §43. .................................... §44. .................................... §45. .................................... §46. .................................... §47. .................................... §48. .................................... §49. .................................... §50. .................................... §51. .................................... §52. .................................... §53. .................................... §54. .................................... §55. .................................... §56. .................................... §57. ....................................
17 17 17 18 18 19 19 19 20 20 21 21 21 21 22 23 23 24 25 25 25 26 27 27 27 28 28 29 30 3
§58. .................................... §59. .................................... §60. .................................... §61. .................................... §62. .................................... §63. .................................... §64. .................................... §65. .................................... §66. .................................... §67. .................................... §68. .................................... §69. .................................... §70. .................................... §72. ....................................
31 32 32 32 33 33 34 34 34 35 35 36 36 37
MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_
39 39 39 39 40 40 41 41 42 42 42 43 44 44
MijZ`g_gby ........................... 39 ........................... ........................... ........................... ........................... ........................... ........................... ........................... ........................... ........................... .......................... .......................... .......................... .......................... ..........................
4
MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_
.......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... ..........................
44 45 45 46 47 47 47 48 48 48 49 49 50 50 50 50 50 51 51 51 52 52 53 53 53 53 54 54 54 5
MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_ MijZ`g_gb_
.......................... .......................... .......................... .......................... ..........................
55 55 55 55 55
AZ^Zqbij_^eZ]Z_fu_ ^eyih\lhj_gby b ijb qZkZo nbabdb \g_^_ex .......... 56 EZ[hjZlhjgu_ jZ[hlu .................. 64 EZ[hjZlhjgZy EZ[hjZlhjgZy EZ[hjZlhjgZy EZ[hjZlhjgZy EZ[hjZlhjgZy EZ[hjZlhjgZy
jZ[hlZ ................. jZ[hlZ ................. jZ[hlZ ................. jZ[hlZ ................. jZ[hlZ ................. jZ[hlZ .................
64 67 67 68 69 70
6
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\ mkeh\bbaZ^ZqbjZaf_jZfbwlh]hl_eZfh`ghij_g_[j_qv 5. AZ fZl_jbZevgmx lhqdm fh`gh ijbgylv Z\lhfh[bev ijb hij_^_e_gbb _]h kdhjhklb gZ fZjrjml_ ] Ijhl\bgh ± ] Fhkd\Z Wlhl `_ Z\lhfh[bev g_evay kqblZlv fZl_jbZevghc lhqdhc ijb jZkq_l_^Z\e_gbyhdZau\Z_fh]hbfgZ^hjh]m 6. IjbihklmiZl_evghf^\b`_gbb 7. FZl_jbZevghc lhqdhc gZau\Z_lky l_eh jZaf_jZfb dhlhjh]h fh`ghij_g_[j_qv\ mkeh\byo^ZgghcaZ^Zqb 8. Ijbijyfhebg_cghf^\b`_gbbl_eZ 9. Kbkl_fZhlkq_lZhlghkbl_evghdhlhjhcjZkkfZljb\Zxl^\b`_gb_ ij_^klZ\ey_l kh[hc kh\hdmighklv kbkl_fu dhhj^bgZl ijb[hjZ ^ey baf_j_gby \j_f_gb b lhqdb hlkq_lZ k dhlhjhc k\yaZgZ kbkl_fZ dhhj^bgZl
§2.
1. G_l\k_aZ\bkblhlljZ_dlhjbb^\b`_gbyG_evaymagZlv]^_[m^_l Z\lhfh[bevq_j_a qZk_kebg_agZ_rvihdZdbf^hjh]Zfhgih_^_l 2. <_dlhjgZijZ\e_gguchllhqdbhlkq_lZgZqZeZ^\b`_gbyd lhqd_ hlkq_lZdhgpZ^\b`_gbyl_eZ 3. Fh`gh
§3.
1.
§4.
1. Kdhjhklvx jZ\ghf_jgh]h ijyfhebg_cgh]h ^\b`_gby gZau\Z_lky U Y ihklhygguc \_dlhj v jZ\guc hlghr_gbx i_j_f_s_gby s l_eZ aZ Y U s ex[hcijhf_`mlhd\j_f_gbt d agZq_gbxwlh]hijhf_`mldZ v = . t 7
2. Ihnhjfme_ sx = vxt. 3. Ijbijyfhebg_cghfjZ\ghf_jghf^\b`_gbb 4. Wlh\b^ghbajbkmq_[gbdZ 5. Hgb^\b`mlkyjZ\ghf_jgh\ jZaguogZijZ\e_gbyokhkdhjhklyfb jZ\gufbihfh^mex b dfq
§5.
1. D g_jZ\ghf_jghfm^\b`_gbx 2. Kdhjhklvl_eZ\ ^Zgghclhqd_\ ^Zggucfhf_gl\j_f_gb U 3. Mkdhj_gb_f jZ\ghmkdhj_ggh]h ^\b`_gby l_eZ a gZau\Z_lky U \_ebqbgZjZ\gZyhlghr_gbxbaf_g_gbykdhjhklb∆ v d ijhf_`mldm U U U U ∆v v − v 0 \j_f_gbtaZdhlhjucwlhbaf_g_gb_ijhbahreh a = = . t t 4. >\b`_gb_k ihklhyggufmkdhj_gb_f 5. HgihdZau\Z_l[ukljhlmbaf_g_gbyfh^mey\_dlhjZkdhjhklb 6. < kbkl_f_KB fk2. 7. M\_ebqb\Z_lky ijb iheh`bl_evghf mkdhj_gbb \ wlhf kemqZ_ \_dlhjkdhjhklbb \_dlhjmkdhj_gbykhgZijZ\e_gu mf_gvrZ_lky² ijb hljbpZl_evghf \ wlhf kemqZ_ \_dlhj kdhjhklb b \_dlhj mkdhj_gbyijhlb\hiheh`ghgZijZ\e_gu
§6.
1. Z vx = v0x + axt [ vx = axt. 2. < h[hbokemqZyoijyfZy\ kemqZ_ ©Zª²ijhoh^ysZyq_j_agZqZeh kbkl_fudhhj^bgZl 3. Wlb ^\b`_gby jZ\ghmkdhj_ggu_ h^gZdh \ i_j\hf kemqZ_ mkdhj_gb_iheh`bl_evghZ \h\lhjhf²hljbpZl_evgh
§7.
1. Ijh_dpby\_dlhjZi_j_f_s_gby\uqbkey_lkyihnhjfme_ axt 2 . 2 Ih^klZ\bf\ wlmnhjfmem\ujZ`_gb_^eyijh_dpbbmkdhj_gby v − v0 x ax = x . t Ihemqbf v − v0 x t 2 v0 x + v x s x = v0 x t + x ⋅ = ⋅t . t 2 2 s x = v0 x t +
8
LZddZdv0x = AO, vx = BC, t = OB kfjbkZ mq_[gbdZ lhfu AO + BC ⋅ OB ihemqZ_fqlhijh_dpby\_dlhjZi_j_f_s_gby s x = 2 jZ\gZiehsZ^bnb]mjuOACB ²ijyfhm]hevghcljZi_pbbk hkgh\ZgbyfbAO, BC b \ukhlhcOB. 2. s x = v0 x t +
axt 2 . 2
1. Ihnhjfme_ s x =
§8.
axt at 2 ²^eyijh_dpbbi_j_f_s_gby s = — 2 2 ^eyfh^mey\_dlhjZi_j_f_s_gby 2. < n2 jZaihkdhevdms ~ t2 3.
2
s n a (nt1 ) 2 / 2 = = n2 . 2 st1 at1 / 2
4. DZdjy^ihke_^h\Zl_evguog_q_lguoqbk_e 5. >eyhij_^_e_gbyjZ\ghmkdhj_ggh]h^\b`_gby 1. < jZaguokbkl_fZohlq_lZwlb\_ebqbgubf_xljZagu_agZq_gbyb ihjZaghfmhjb_glbjh\Zggu 2. RZjbd iZ^Zxsbc gZ ihe ^\b`ms_]hky Z\lhfh[bey g_ bf__l ]hjbahglZevghc kdhjhklb hlghkbl_evgh g_]h Hlghkbl_evgh A_feb hgbf__lkdhjhklvjZ\gmxkdhjhklbZ\lhfh[bey 3. Kdhjhklv imlv ljZ_dlhjby b l^ jZaebqgu \ jZaguo kbkl_fZo hlkq_lZ 4. =_ebhp_gljbq_kdZy kbkl_fZ k\yaZgZ k Khegp_f ]_hp_gljbq_kdZy ²k A_fe_c 5. Kf_gZ^gyb ghqbh[tykgy_lky\jZs_gb_fA_feb\hdjm]k\h_chkb
§9.
1. JZ\ghf_jghb ijyfhebg_cghbebihdhblky 2. G_l 3. L_hjby :jbklhl_ey aZdexqZxsZyky \ lhf qlh ijb hlkmlkl\bb \g_rg_]h\ha^_ckl\byl_ehfh`_llhevdhihdhblvky 4. L_f qlh ih =Zebe_x l_eZ fh]ml jZ\ghf_jgh ^\b]Zlvky \ hlkmlkl\bb\g_rgbokbe 5. Hiul bah[jZ`_gguc gZ jbk mq_[gbdZ ^hdZau\Z_l lh qlh ihfbfh bg_jpbZevguo kbkl_f hlkq_lZ \ dhlhjuo \uihegy_lky i_j\uc aZdhg GvxlhgZ kms_kl\mxl kbkl_fu bgh]h oZjZdl_jZ Hg
§10.
9
khklhbl \ ke_^mxs_f GZ l_e_`d_ h^bg rZjbd e_`bl gZ ]hjbahglZevghc ih\_joghklb Z \lhjhc ih^\_rb\Z_lky gZ gblb KgZqZeZ l_e_`dZ ^\b`_lky ijyfhebg_cgh b jZ\ghf_jgh b \ wlhf kemqZ_ h[Z rZjbdZ gZoh^ylky \ ihdh_ hlghkbl_evgh l_e_`db Klhbl lhevdh ijb^Zlv l_e_`d_ mkdhj_gb_ eb[h __ ijblhjfhablv eb[h ih^lhedgmlv dZd rZjbdb ijb^ml \ ^\b`_gb_ k mkdhj_gb_f hlghkbl_evghl_e_`dbLZdbfh[jZahfhlghkbl_evghl_e_`dbi_j\uc aZdhgGvxlhgZg_\uihegy_lky 6. Kms_kl\mxl kbkl_fu hlkq_lZ hlghkbl_evgh dhlhjuo l_eZ khojZgyxl k\hx kdhjhklv g_baf_gghc _keb gZ gbo g_ ^_ckl\mxl \g_rgb_ kbeu beb bo ^_ckl\b_ kdhfi_gkbjh\Zgh LZdb_ kbkl_fu gZau\Zxlkybg_jpbZevgufb 7. Bg_jpbZevgu_kbkl_fum^h\e_l\hjyxli_j\hfmaZdhgmGvxlhgZ g_bg_jpbZevgu_²g_l 8. Fh`gh 9. G_l
§11.
1. Ijbeh`_ggZyd l_emkbeZ 2. Q_f [hevr_ fhsghklv Z\lhfh[bey Z khhl\_lkl\_ggh _]h kbeZ ly]bl_f[uklj__hgm\_ebqb\Z_lk\hxkdhjhklv 3. Hiul bah[jZ`_gguc gZ jbk mq_[gbdZ ^hdZau\Z_l lh qlh ijbeh`_ggZy d l_em kbeZ y\ey_lky ijbqbghc mkdhj_gby >ey ijh\_^_gby^Zggh]hhiulZgZ^h\aylvl_e_`dmmklZgh\blvgZg_c^\Z h^bgZdh\hjZ[hlZxsbo\_glbeylhjZb dZi_evgbpm>eydhfi_gkZpbb kbeulj_gbyijbdj_ibfd l_e_`d_h^bgbadhgph\gblbi_j_dbgmlhc q_j_a [ehd Z d ^jm]hfm dhgpm gblb ih^\_kbf ]jma AZl_f hldjh_f djZg dZi_evgbpu b \dexqbf h[Z \_glbeylhjZ Ih^ ^_ckl\b_f kbeu \_glbeylhjh\ l_e_`dZ ijb^_l \ ^\b`_gb_ Ijb wlhf gZ klhe [m^ml iZ^Zlv dZieb q_j_a h^bgZdh\u_ ijhf_`mldb \j_f_gb L_i_jv _keb baf_jylvjZkklhygbyf_`^mkhk_^gbfbdZieyfblhfh`ghm[_^blvky qlh wlb jZkklhygby [m^ml hlghkblvky dZd jy^ ihke_^h\Zl_evguo g_q_lguo qbk_e LZdbf h[jZahf fh`gh aZdexqblv qlh l_e_`dZ ^\b]ZeZkvjZ\ghmkdhj_ggh kf§ IhkqblZ_fmkdhj_gb_ihnhjfme_ 2s a = 2 aZf_jb\ ijhc^_ggh_ l_e_`dhc jZkklhygb_ s b \j_fy __ t ^\b`_gby t ?keb mf_gvrblv kbem ^_ckl\mxsmx gZ l_e_`dm \ ^\Z jZaZ \udexq_gb_f h^gh]h ba \_glbeylhjh\ b kgh\Z ihkqblZlv mkdhj_gb_ lh hgh ihemqblky \ ^\Z jZaZ f_gvrbf q_f i_j\uc jZa ?keb l_i_jv m\_ebqblv fZkkm l_e_`db \ ^\Z jZaZ ^h[Z\e_gb_f d l_e_`d_ ]jmaZ fZkkhc jZ\ghc fZkk_ l_e_`db b kgh\Z ihkqblZlv 10
mkdhj_gb_ lh hgh ihemqblky \ ^\Z jZaZ f_gvrbf q_f i_j\uc jZa LZdbf h[jZahf aZdexqZ_f qlh mkdhj_gb_ l_e_`db ijyfh ijhihjpbhgZevgh ijbeh`_gghc d g_c kbe_ b h[jZlgh ijhihjpbhgZevgh__ fZkk_ 4. Mkdhj_gb_ l_eZ ijyfh ijhihjpbhgZevgh jZ\gh^_ckl\mxs_c ijbeh`_gguo d g_fm kbe b h[jZlgh ijhihjpbhgZevgh _]h fZkk_ U U F a= . m d] ⋅ f 5. HgbkhgZijZ\e_gu 6. G 1 2 . k
§12.
1. Hiulubah[jZ`_ggu_gZjbkmq_[gbdZih^l\_j`^Zxl lj_lbc aZdhg GvxlhgZ
\b`_gb_ih^^_ckl\b_fkbeuly`_klb 2. GZ^h baf_jblv jZkklhygby dhlhju_ rZjbd ijhoh^bl aZ ihke_^h\Zl_evgu_ h^bgZdh\u_ ijhf_`mldb \j_f_gb b m[_^blvky \ lhf qlh ^Zggu_ jZkklhygby hlghkylky dZd jy^ ihke_^h\Zl_evguo g_q_lguo qbk_e Wlh b [m^_l y\eylvky ^hdZaZl_evkl\hf lh]h qlh k\h[h^gh_iZ^_gb_l_eZy\ey_lkyjZ\ghmkdhj_gguf^\b`_gb_f kf §8). 3. K p_evx ihdZaZlv qlh mkdhj_gb_ k\h[h^gh]h iZ^_gby h^bgZdh\h ^ey\k_ol_e 4. Mkdhj_gb_\ua\Zggh_^_ckl\b_fkbeuly`_klb 5. BaaZkbeukhijhlb\e_gby\ha^moZ
§13.
11
6. =Zebe_c
§14.
1. >ZhgZij_iylkl\m_l_]hih^t_fm 2. K mkdhj_gb_f g Ijb ^\b`_gbb l_eZ \\_jo _]h kdhjhklv mf_gvrZ_lky ih aZdhgm v(t) = v0 – gt < \_jog_c lhqdb ljZ_dlhjbb kdhjhklv l_eZ jZ\gZ gmex b hgh gZqbgZ_l ^\b]Zlvky \gba m\_ebqb\ZykdhjhklvihaZdhgmv(t) = gt^hl_oihjihdZg_ miZ^_l gZa_fex 3. Hl\_ebqbgugZqZevghckdhjhklb 4. ?keb gZijZ\blv hkv \\_jo lh ijh_dpby \_dlhjZ kdhjhklb gZ wlm hkv iheh`bl_evgZ Z ijh_dpby mkdhj_gby k\h[h^gh]h iZ^_gby ² hljbpZl_evgZ
§15.
1. \Z l_eZ ijbly]b\Zxlky ^jm] d ^jm]m k kbehc ijyfh ijhihjpbhgZevghc ijhba\_^_gbx bo fZkk b h[jZlgh ijhihjpbhgZevghcd\Z^jZlmjZkklhygbyf_`^mgbfb mm 5. F = G 1 2 2 ]^_ F ² fh^mev ]jZ\blZpbhgghc kbeu m1, m2 — r fZkku \aZbfh^_ckl\mxsbo l_e r ² jZkklhygb_ f_`^m gbfb G — ]jZ\blZpbhggZyihklhyggZyjZ\gZy ⋅10-11 G⋅f2d]2. 6. AZdhg\k_fbjgh]hly]hl_gbykijZ\_^eb\\ ke_^mxsbokemqZyo ^ey^\mol_ejZaf_judhlhjuoij_g_[j_`bfhfZeuk jZkklhygb_fr f_`^mgbfb _kebh^ghbal_ebf__lnhjfmrZjZjZ^bmkb fZkkZ dhlhjh]h \h fgh]h jZa [hevr_ q_f m \lhjh]h l_eZ ijhba\hevghc nhjfu ^ey ^\mo h^ghjh^guo l_e rZjhh[jZaghc nhjfu ijb ex[uobojZaf_jZo 7. >Z 1. <_jgh 2. Mf_gvrZ_lky3. Fl = mg. 4. KbeZly`_klb[hevr_gZ ihexkZoldA_fey g_fgh]hkiexkgmlZ m ihexkh\ 5. Hghijb[ebabl_evgh\ jZaf_gvr_a_fgh]h
§16.
12
1. RZjbd ^\b`_lky hl lhqdb : d lhqd_ < ih^ ^_ckl\b_f kbeu U mijm]hklb F WlZ kbeZ \hagbdeZ \ j_amevlZl_ jZkly`_gby rgmjZ Kdhjhklv mkdhj_gb_ rZjbdZ b ^_ckl\mxsZy gZ g_]h kbeZ gZijZ\e_gu hl lhqdb A d lhqd_ B RZjbd ^\b`_lky ijyfhebg_cgh l__]hljZ_dlhjby²ijyfZyebgby 2. KbeZmijm]hklb\ rgmj_\hagbdeZ\ j_amevlZl__]hjZkly`_gbyb hgZgZijZ\e_gZd lhqd_OKdhjhklvrZjbdZb ^_ckl\mxsZygZg_]h kbeZ gZijZ\e_gu ih ijyfuf i_j_k_dZxsbfky ih^ m]ehf R . LjZ_dlhjby rZjbdZ ij_^klZ\ey_l kh[hc hdjm`ghklv l_ rZjbd ^\b`_lkydjb\hebg_cgh 3. ?keb kdhjhklv l_eZ b ^_ckl\mxsZy gZ g_]h kbeZ gZijZ\e_gu \^hev i_j_k_dZxsboky ijyfuo lh l_eh ^\b`_lky djb\hebg_cgh _keb\^hevh^ghcijyfhclhl_eh^\b`_lkyijyfhebg_cgh
§18.
1. Hiulih\uk_dZgbxbkdjubalhqbevgh]hdZfgy 2. Mkdhj_gb_ gZijZ\e_gh ih jZ^bmkm d p_gljm hdjm`ghklb b hgh gZau\Z_lkyp_gljhklj_fbl_evguf
§19.
3. Ihnhjfme_ Zp =
v2 . r 4. Ih jZ^bmkm d p_gljm hdjm`ghklb ?_ fh^mev hij_^_ey_lky ih nhjfme_ Fp =
mv 2 . r
§20.
1. H[jZs_gb_ieZg_l\hdjm]KhegpZb kimlgbdh\\hdjm]ieZg_l 2. Ld hg h[eZ^Z_l ^hklZlhqgh [hevrhc kdhjhklvx gZijZ\e_gghc ihdZkZl_evghcd ljZ_dlhjbb^\b`_gby 3. >Z ld lZdh_ ^\b`_gb_ ijhbkoh^bl lhevdh ih^ ^_ckl\b_f kbeu ly`_klb 4. Khh[sblv_fmi_j\mxdhkfbq_kdmxkdhjhklv 5. Zp =
v2 v2 ;g= ; v 2 = gr ⇒ v = gr . IheZ]Zyr ≈ RAlhihemqZ_f r r
qlh v = gRA ≈ dfk 6. Ihweebilbq_kdhchj[bl_\hdjm]A_feb ihweebilbq_kdhchj[bl_ \hdjm]KhegpZ
13
§21.
1. Bfimevkhf l_eZ gZau\Z_lky nbabq_kdZy \_ebqbgZ jZ\gZy ijhba\_^_gbxfZkkul_eZgZ_]hkdhjhklv 2. Bfimevkb kdhjhklv^\b`ms_]hkyl_eZ\k_]^ZkhgZijZ\e_gu 3. < kbkl_f_KB d]⋅fk
§22.
1. Hiul bah[jZ`_gguc gZ jbkmgd_ mq_[gbdZ ijh\h^blky ke_^mxsbfh[jZahf;_jmlky^\ZrZjbdZih^\_r_ggu_gZgblyolZd qlh[u hgb dZkZebkv ^jm] ^jm]Z H^bg ba rZjbdh\ hldehgyxl gZ g_dhlhjuc m]he b hlimkdZxl RZjbd ^hklb]gm\ k\h_]h ij_`g_]h iheh`_gby m^Zjy_lky h \lhjhc b hklZgZ\eb\Z_lky Ijb wlhf \lhjhc rZjbd hldehgy_lky gZ lhl `_ m]he LZdbf h[jZahf ijb \aZbfh^_ckl\bbbfimevki_j\h]hrZjbdZmf_gvrbekygZklhevdhgZ kdhevdhm\_ebqbekybfimevk\lhjh]hWlhlhiulih^l\_j`^Z_laZdhg khojZg_gbybfimevkZ 2. Kbkl_fZl_egZau\Z_lkyaZfdgmlhc_kebgZwlbl_eZg_^_ckl\mxl \g_rgb_kbeu 3. <_dlhjgZykmffZbfimevkh\l_eaZfdgmlhckbkl_fuihklhyggZ\h \j_f_gbijbex[uo^\b`_gbyob \aZbfh^_ckl\byowlbol_e U U U U U U 4. m1v1′ + m2 v ′2 = m1v1 + m2 v2 ]^_ m1, m2 ² fZkku l_e v1 , v 2 ² bo U U kdhjhklb ^h \aZbfh^_ckl\by v1′ , v 2′ ² bo kdhjhklb ihke_ \aZbfh^_ckl\by
§23.
1. >\b`msbcky \ha^mo h[eZ^Z_l g_dhlhjuf bfimevkhf Ih aZdhgm khojZg_gby bfimevkZ rZjbd h[eZ^Z_l lZdbf `_ ih fh^mex gh ijhlb\hiheh`guf ih gZijZ\e_gbx bfimevkhf < j_amevlZl_ hg ^\b`_lkyijhlb\hiheh`ghkljm_\uoh^ys_]hbarZjbdZ\ha^moZ 2. >\b`_gb_ \h^hf_lguo ]b^jhfhlhpbdeh\ j_Zdlb\guo kZfhe_lh\ b jZd_l 3.
ijhkljZgkl\_]ZaubadZf_juk]hjZgby\ulZedb\ZxlkygZjm`mq_j_a khieh k h]jhfghc kdhjhklvx < kbem aZdhgZ khojZg_gby bfimevkZ jZd_lZ ihemqZ_l bfimevk jZ\guc ih fh^mex b ijhlb\hiheh`gh gZijZ\e_ggucbfimevkm\ue_l_\r_ckljmb]ZaZ 6. Hlkdhjhklbbkl_q_gby]ZaZfZkkulhieb\ZlbiZlhieb\Zb l^ 7. Kihkh[ghklvjZa\b\Zlv[hevrmxkdhjhklv 8. Khiehf\gbald\ lZdhfkemqZ_j_Zdlb\gZykljmy]Zkblkdhjhklv jZd_lu 1. Dhe_[Zgb_fZylgbdZqZkh\kljmgu]blZju 2. >\b`_gb_ih\lhjy_lkyq_j_ahij_^_e_ggucijhf_`mlhd\j_f_gb 3. I_jbh^hf dhe_[Zgbc gZau\Z_lky ijhf_`mlhd \j_f_gb q_j_a dhlhjuc ^\b`_gb_ ih\lhjy_lky \j_fy kh\_jr_gby h^gh]h dhe_[Zgby 4. AZ\j_fyjZ\gh_i_jbh^mdhe_[ZgbcdZ`^h_babah[jZ`_gguogZ jbkmgd_ mq_[gbdZ l_e ^\Z`^u ijhoh^bl q_j_a iheh`_gb_ jZ\gh\_kby ^\b]Zykv\ ijhlb\hiheh`guogZijZ\e_gbyo
§24.
§25.
1. KbeZmijm]hklb^_ckl\m_lgZrZjbd\ lhqdZo<, K, D, :lddh]^Z rZjbdgZoh^blky\ wlbolhqdZoijm`bgZ^_nhjfbjh\ZgZ jZklygmlZ beb k`ZlZ < lhqd_ O kbeZ mijm]hklb gZ rZjbd g_ ^_ckl\m_l ld dh]^Z rZjbd gZoh^blky \ wlhc lhqd_ ijm`bgZ g_ ^_nhjfbjh\ZgZ LhqdZO gZau\Z_lkyiheh`_gb_fjZ\gh\_kbyrZjbdZ 2. Ih f_j_ ijb[eb`_gby rZjbdZ d lhqd_ O kdhjhklv l_eZ m\_ebqb\Z_lky ld kbeZ mijm]hklb b mkdhj_gb_ kh\iZ^Zxl ih gZijZ\e_gbx kh kdhjhklvx Ih f_j_ m^Ze_gby rZjbdZ hl lhqdb O kdhjhklv l_eZ mf_gvrZ_lky ld kbeZ mijm]hklb b mkdhj_gb_ ijhlb\hiheh`ghgZijZ\e_gukdhjhklb 3. Ld ex[h_ l_eh h[eZ^Z_l k\hckl\hf khojZgylv k\hx kdhjhklv _kebgZg_]hg_^_ckl\mxlkbeubeb^_ckl\b_kbekdhfi_gkbjh\Zgh Ijb ijhoh`^_gbb iheh`_gby jZ\gh\_kby gZ rZjbd g_ ^_ckl\m_l kbeZ mijm]hklb Z _]h kdhjhklv g_ jZ\gZ gmex b khojZgy_l k\h_ agZq_gb_b gZijZ\e_gb_ 4. Dhe_[ZgbygZau\Zxlkyk\h[h^gufb_kebhgbijhbkoh^yllhevdh aZkq_lgZqZevgh]haZiZkZwg_j]bbkbkl_fu 5. Dhe_[Zl_evgufbkbkl_fZfb gZau\Zxlkykbkl_ful_ekihkh[guo kh\_jrZlvk\h[h^gu_dhe_[Zgby 6. FZylgbdhf gZau\Z_lky l\_j^h_ l_eh kh\_jrZxs__ ih^ ^_ckl\b_f ijbeh`_gguo kbe dhe_[Zgby hdheh g_ih^\b`ghc lhqdb beb\hdjm]hkb 15
7. Ijm`bggucfZylgbdkhklhblbal_eZaZdj_ie_ggh]hgZijm`bg_ GblyghcfZylgbdkhklhblbal_eZih^\_r_ggh]hgZgblb
§26.
1. :fieblm^Z ² fZdkbfZevgh_ kf_s_gb_ dhe_[exs_]hky l_eZ hl iheh`_gbyjZ\gh\_kby:fieblm^Zh[hagZqZ_lky[md\hc©:ªb \KB baf_jy_lky\ f_ljZo f I_jbh^ ² \j_fy kh\_jr_gby h^gh]h dhe_[Zgby I_jbh^ h[hagZqZ_lky[md\hc©Tªb \KBbaf_jy_lky\ k_dmg^Zo k QZklhlZ ² dhebq_kl\h dhe_[Zgbc \ _^bgbpm \j_f_gb QZklhlZ h[hagZqZ_lky[md\hc©νªb \KBbaf_jy_lky\ ]_jpZo =p 2. H^ghihegh_dhe_[Zgb__klvdhe_[Zgb_aZi_jbh^ 3. K\yavf_`^mi_jbh^hfb qZklhlhc\ujZ`Z_lkynhjfmehcL = 1/ν bebν = 1/L. 4. Z Q_f[hevr_^ebgZgblbfZylgbdZl_ff_gvr_qZklhlZ [ q_f [hevr_^ebgZgblbfZylgbdZl_f[hevr_i_jbh^ 5. Kh[kl\_gghcqZklhlhcdhe_[Zl_evghckbkl_fugZau\Z_lkyqZklhlZ k\h[h^guodhe_[Zgbckbkl_fu 6. ?keb fZylgbdb dhe_[exlky \ ijhlb\hiheh`guo nZaZo lh bo kdhjhklb ijhlb\hiheh`gh gZijZ\e_gu _keb \ h^bgZdh\uo lh bo kdhjhklbkhgZijZ\e_gu
§27.
1. Hiul klZ\beky k p_evx ihdZaZlv qlh dhe_[Zgby ijm`bggh]h fZylgbdZy\eyxlky]Zjfhgbq_kdbfbHgaZdexqZ_lky\ lhfqlh]jma gZijbf_j \hjhgdZ k gZeblhc djZkys_c `b^dhklvx mdj_ie_gguc gZ ijm`bg_ ijb k\h_f dhe_[Zl_evghf ^\b`_gbb hklZ\ey_l ke_^ ljZ_dlhjbb gZ ^\b`ms_cky k ihklhygghc kdhjhklvx [mfZ`ghc e_gl_ Ihemq_ggZy lZdbf kihkh[hf ljZ_dlhjby y\ey_lky kbgmkhb^hc 2. Kbgmkhb^hc Hlj_ahd OA khhl\_lkl\m_l Zfieblm^_ dhe_[Zgbc Z hlj_ahdOB ²i_jbh^m 3. =Zjfhgbq_kdbfb dhe_[Zgbyfb gZau\Zxlky dhe_[Zgby \ dhlhjuo baf_g_gb_dZdhceb[h nbabq_kdhc \_ebqbgu ijhbkoh^bl ih aZdhgm kbgmkZbebdhkbgmkZ 4. Qlhdhe_[Zgbygbl_\h]hfZylgbdZy\eyxlky]Zjfhgbq_kdbfb 5. FZl_jbZevgZy lhqdZ h[eZ^ZxsZy fZkkhc b dhe_[exsZyky gZ ihklhygghf jZkklhygbb hl lhqdb ih^\_kZ gZau\Z_lky fZl_fZlbq_kdbffZylgbdhf
16
6. Dhe_[Zgby gblygh]h fZylgbdZ fh`gh kqblZlv ]Zjfhgbq_kdbfb _keb^ebgZgblbfgh]h[hevr_jZaf_jh\ih^\_r_ggh]hgZg_cl_eZ gZijbf_j rZjbdZ gblv hq_gv e_]dZy b fZehjZkly`bfZy kbeu lj_gby\ kbkl_f_hlkmlkl\mxlZfieblm^Zdhe_[ZgbcfZeZ 7. F_gyxlkyihaZdhgmkbgmkZbebdhkbgmkZ
§28.
1. Ijbmkeh\bbhlkmlkl\byihl_jvwg_j]bb 2. KmffZ dbg_lbq_kdhc b ihl_gpbZevghc wg_j]bc ihklhyggZ kh]eZkgh aZdhgm khojZg_gby wg_j]bb b jZ\gZ i_j\hgZqZevghfm aZiZkmihl_gpbZevghcwg_j]bbdhe_[Zl_evghckbkl_fu 3. G_l 4. Mf_gvrZ_lky 5. < \h^_ ld \ g_c gZ fZylgbd ^_ckl\m_l [hevrZy kbeZ khijhlb\e_gbyq_f\ \ha^mo_
§29.
1. G_lbaaZkhijhlb\e_gbykj_^u 2. Ijbeh`blvd dhe_[exs_fml_emi_jbh^bq_kdmx\g_rgxxkbem 3. Dhe_[ZgbygZau\Zxlky\ugm`^_ggufb_kebhgbijhbkoh^ylih^ ^_ckl\b_fi_jbh^bq_kdbbaf_gyxs_cky\g_rg_ckbeu 4. hl_oihjihdZ^_ckl\m_l\ugm`^ZxsZykbeZ
§30.
1. Hiul ijh\h^blky k p_evx ^_fhgkljZpbb y\e_gby j_ahgZgkZ >ey wlh]h [_jml ^\Z fZylgbdZ \bkysb_ gZ h[s_f rgmj_ >ebgZ fZylgbdZ g_baf_ggZ b ke_^h\Zl_evgh _fm khhl\_lkl\m_l hij_^_e_ggZy qZklhlZ k\h[h^guo dhe_[Zgbc kh[kl\_ggZy qZklhlZ >ebgm fZylgbdZ fh`gh f_gylv ijb ihfhsb k\h[h^guo dhgph\ gbl_cIjbwlhff_gy_lky_]hkh[kl\_ggZyqZklhlZ?kebhldehgblv fZylgbdhliheh`_gbyjZ\gh\_kbyb ij_^hklZ\blvkZfhfmk_[_lh hg gZqg_l kh\_jrZlv k\h[h^gu_ dhe_[Zgby Wlh \uah\_l dhe_[Zgby rgmjZ \ j_amevlZl_ q_]h gZ fZylgbd [m^_l ^_ckl\h\Zlv \ugm`^ZxsZy kbeZ k qZklhlhc jZ\ghc kh[kl\_gghc qZklhl_ 17
fZylgbdZ Ih^ ^_ckl\b_f wlhc kbeu fZylgbd gZqg_l kh\_jrZlv \ugm`^_ggu_dhe_[Zgby?kebl_i_jvmf_gvrZlv^ebgmfZylgbdZ lh _]h qZklhlZ b qZklhlZ \ugm`^Zxs_c kbeu ^_ckl\mxs_c gZ fZylgbd [m^ml m\_ebqb\Zlvky Ijb wlhf Zfieblm^Z mklZgh\b\rboky \ugm`^_gguo dhe_[Zgbc fZylgbdZ [m^_l \hajZklZlv HgZ ^hklb]g_l fZdkbfZevgh]h agZq_gby ijb jZ\_gkl\_ ^ebg fZylgbdh\ Z khhl\_lkl\_ggh ijb jZ\_gkl\_ qZklhlu \ugm`^Zxs_c kbeu b kh[kl\_gghc qZklhlu fZylgbdZ < wlhf b khklhblkmlvy\e_gbyj_ahgZgkZ 2. Y\e_gb_ j_ahgZgkZ aZdexqZ_lky \ j_adhf m\_ebq_gbb Zfieblm^u mklZgh\b\rboky \ugm`^_gguo dhe_[Zgbc ijb kh\iZ^_gbb qZklhlu kh[kl\_gguo dhe_[Zgbc kbkl_fu k qZklhlhc \ugm`^Zxs_ckbeu 3. ldbo^ebguZke_^h\Zl_evghb qZklhlujZ\gu 4. Lhevdhd \ugm`^_gguf 5. Ihe_agh_ y\e_gb_ \ fmaudZevguo bgkljmf_glZo <j_^gh_ y\e_gb_ ijb ijhoh`^_gbb khe^Zl ih fhklm \ gh]m \ j_amevlZl_ j_ahgZgkZfhklfh`_ljZajmrblvky 1.
§31.
1. Ijh^hevgu_\hegu²wlhlZdb_\hegu\ dhlhjuodhe_[ZgbyqZklbp kj_^u kh\_jrZxlky \^hev gZijZ\e_gby jZkijhkljZg_gby \heg gZijbf_ja\mdh\u_\heguIhi_j_qgu_\hegu²wlhlZdb_\heguijb dhlhjuo dhe_[Zgby qZklbp kj_^u kh\_jrZxlky i_ji_g^bdmeyjgh gZijZ\e_gbxjZkijhkljZg_gby \heg gZijbf_j\hegu gZ ih\_joghklb \h^u 2.
§32.
18
§33.
1. >ebghc\hegugZau\Z_lkyjZkklhygb_f_`^m^\mfy[eb`Zcrbfb lhqdZfb\hegudhe_[exsbfky\ h^bgZdh\uonZaZo 2. ;md\hc©λª qblZ_lky©eZf[^Zª 3. AZi_jbh^L h^gh]hihegh]hdhe_[Zgby 4. IhnhjfmeZf λ = vL b v = λ/L = λν. 5. F_`^mlhqdZfbb b 1. Wlb hiulu ^_fhgkljbjmxl dhe_[Zl_evguc oZjZdl_j \hagbdgh\_gby a\mdZ < i_j\hf hiul_ \ dZq_kl\_ bklhqgbdZ a\mdZ [_j_lky h[uqgZy ebg_cdZ aZ`ZlZy \ lbkdZo \h \lhjhf ² kljmgZ dhgpudhlhjhcaZdj_ie_gu\ lj_lv_f²dZf_jlhg?kebdZ`^mxba \ur_ i_j_qbke_gguo kbkl_f \u\_klb ba iheh`_gby jZ\gh\_kby b ^Zlv _c kh\_jrZlv k\h[h^gu_ dhe_[Zgby lh fu mkeurbf a\md LZdbf h[jZahf bklhqgbdZfb a\mdZ y\eyxlky dhe_[Zl_evgu_ kbkl_fu 2. Ex[hcbklhqgbda\mdZy\ey_lkydhe_[Zl_evghckbkl_fhc 3. Dhe_[Zgby k qZklhlhc hl =p ^h =p gZau\Zxlky a\mdh\ufbihkdhevdm\hkijbgbfZxlkyq_eh\_dhf 4. BgnjZa\mdh\ufb gZau\Zxlky dhe_[Zgby k qZklhlhc gb`_ =p mevljZa\mdh\ufb²k qZklhlhc\ur_=p
§34.
1. Hiul ijh\h^blky k p_evx \uykgblv aZ\bkbfhklv \ukhlu a\mdZ hl qZklhlu dhe_[Zgbc >ey ijh\_^_gby ^Zggh]h hiulZ [_jml ijb[hj khklhysbcbag_kdhevdboam[qZluof_lZeebq_kdbo^bkdh\bf_xsbo jZaebqgh_ qbkeh am[v_\ b aZdj_ie_gguo gZ h^ghc hkb AZl_f \k_ ^bkdb ijb\h^yl \h \jZs_gb_ b lhgdhc dZjlhgghc ieZklbgdhc ihhq_j_^gh dZkZxlky am[v_\ dZ`^h]h ba ^bkdZ Ijb wlhf fu mkeurbfjZagu_ih\ukhl_a\mdbFh`ghaZf_lblvqlhq_f [hevr_ qbkeh am[v_\ gZ ^bkd_ b khhl\_lkl\_ggh [hevr_ qZklhlZ dhe_[Zgbc dZjlhgghcieZklbgdbl_f [hevr_ [m^_l\ukhlZa\mdZ :gZeh]bqgmx aZ\bkbfhklvfh`gh \uy\blv bkihevamy \k_]h lhevdh h^bg ^bkd >ey wlh]hgZ^h m\_ebqb\Zlvkdhjhklv ^bkdZ Q_f [hevr_ kdhjhklv ^bkdZ l_f [hevr_ qZklhlZ dhe_[Zgbc dZjlhgghc ieZklbgdb b l_f \ur_ [m^_lba^Z\Z_fuca\md 2. Hiulijh\h^blkyk p_evx\uykgblvaZ\bkbfhklv\ukhlua\mdZhl qZklhlu dhe_[Zgbc >ey ijh\_^_gby ^Zggh]h hiulZ [_jml ^\Z dZf_jlhgZ ba^Zxsbo a\mdb jZaghc \ukhlu H[Z dZf_jlhgZ ijb\h^yl \ dhe_[Zl_evgh_ ^\b`_gb_ Ijb wlhf hkljby
§35.
19
aZdj_ie_ggu_ gZ gbo hklZ\eyxl gZ ^\b`ms_cky kl_deygghc ieZklbgd_ke_^u?kebkjZ\gblvwlbke_^ulhfh`ghm[_^blvkyqlh qZklhlZdhe_[Zgbc[hevr_m dZf_jlhgZk [he__\ukhdbfa\mdhf 3. HlqZklhludhe_[Zgby 4. Qbkluf lhghf gZau\Z_lky a\md bklhqgbdZ kh\_jrZxs_]h ]Zjfhgbq_kdb_dhe_[Zgbykljh]hhij_^_e_gghcqZklhlu 5. A\md hij_^_e_gghc \ukhlu khhl\_lkl\mxsbc kZfhc gbadhc qZklhl_ keh`gh]h a\mdZ kh\hdmighklb g_kdhevdbo qbkluo lhgh\ gZau\Z_lky hkgh\guf lhghf h[_jlhgu beb \ukrb_ ]Zjfhgbq_kdb_ lhgu²\k_hklZevgu_lhgukeh`gh]ha\mdZ 6. DZq_kl\h a\mdZ hij_^_ey_fh_ kh\hdmighklvx h[_jlhgh\ keh`gh]ha\mdZgZau\Z_lkyl_f[jhf 7. ey ijh\_^_gby ^Zggh]h hiulZ [_jml dZf_jlhg AZl_f _]h ijb ihfhsb fhehlhqdZ ijb\h^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^hca\mqbl]jhfq_ 2. =jhfdhklvlZd`_mf_gvrblky 3. A\mdqZklhlu=p]jhfq_ 4. Hl\_ebqbguZfieblm^udhe_[Zgbc 5. < kbkl_f_KB ^; 6. Kemoq_eh\_dZmom^rZ_lky
§36.
§37.
1. Hiul ijh\h^blky k p_evx ihdZaZlv qlh \ \Zdmmf_ a\md g_ jZkijhkljZgy_lky >ey wlh]h a\hghd ihf_sZxl ih^ dhehdhe \ha^mrgh]h gZkhkZ b \dexqZxl _]h AZl_f baih^ dhehdheZ gZqbgZxl hldZqb\Zlv \ha^mo Ih f_j_ jZaj_`_gby \ha^moZ a\md keur_g\k_lbr_b lbr_bgZdhg_pij_djZsZ_lkykh\k_f?keb`_ \ha^mo gZqZlv \gh\v \imkdZlv lh a\md klZgh\blky keur_g \k_ ]jhfq_b ]jhfq_LZdbfh[jZahfa\md\ [_a\ha^mrghfijhkljZgkl\_ g_jZkijhkljZgy_lky 2. >Z fh`_l Ijbf_ju jZkijhkljZg_gby a\mdZ \ l\_j^uo l_eZo ² jZkijhkljZg_gb_ a\mdZ ih `_e_agh^hjh`guf j_evkZf \ `b^dhklyo ²[jhr_ggucih^\h^mdZf_gv\ ]ZaZo²]jhf 3. Mijm]b_ l_eZ y\eyxlky emqrbfb ijh\h^gbdZfb a\mdZ q_f ihjbklu_ D mijm]bf l_eZf hlghkylky [hevrbgkl\h f_lZeeh\ 20
^_j_\vy ]Zau `b^dhklb d ihjbkluf ² \hcehd ihjhehg i_ghieZkl 4. Iml_fhl^_edbihf_s_gbca\mdhbaheypbhggufbfZl_jbZeZfb 1. K qZklhlhckhhl\_lkl\mxs_ca\mdm 2. Ijh^hevgmx\hegm\ h[hbokemqZyo 3. Q_j_ag_kdhevdhk_dmg^ihke_\kiurdbfhegbbfukeurbf]jhf 4. < f \_d_ njZgpmakdbfb mq_gufb [ueZ baf_j_gZ kdhjhklv a\mdZ< ^\moimgdlZojZkklhygb_f_`^mdhlhjufb[uehba\_klgh ijhba\h^beb \uklj_eu ba imr_d < h[hbo imgdlZo baf_jyeb hlj_adb \j_f_gb f_`^m \kiurdhc h]gy ijb \uklj_e_ b fhf_glhf dh]^Z [ue keurZg a\md \uklj_eZ Kdhjhklv a\mdZ hij_^_eyeb dZd hlghr_gb_ jZkklhygby f_`^m imgdlZfb d baf_j_gghfm hlj_adm \j_f_gb 5. v fk 6. >ZaZ\bkbl
§38.
1. < j_amevlZl_hljZ`_gbya\mdZhljZaebqguoij_]jZ^ 2. < fZe_gvdhc dhfgZl_ hljZ`_gguc a\md \hi_j\uo keb\Z_lky k hkgh\gufb\h\lhjuoohjhrhih]ehsZ_lkyf_[_evx 3. Kl_guaZeZke_^m_lhl^_eZlva\mdhih]ehsZxsbffZl_jbZehf 4. Lda\mdh\u_\hegu\ jmihj_h[jZamxlmadhgZijZ\e_ggucimqhd
§39.
1. DhjimkZ]blZju[ZeZeZcdb 2. >eym\_ebq_gby]jhfdhklb 3. BogZagZq_gb_²mkbe_gb_a\mdZb kha^Zgbyl_f[jZ 4. =hehkh\u_k\yadb 5. HlnhjfujZaf_jZfZl_jbZeZj_ahgZlhjZ
§40.
1. Hiulihkeh`_gbxa\mdh\uo\heghl^\mobklhqgbdh\ijh\h^blky ke_^mxsbf h[jZahf < dZq_kl\_ bklhqgbdh\ a\mdZ [_jml ^\Z ]jhfdh]h\hjbl_ey=jb =jih^dexq_ggu_d a\mdh\hfm]_g_jZlhjm A= BaemqZ_fuc bfb a\md ihiZ^Z_l \ fbdjhnhg F ]^_ ihke_ ij_h[jZam_lky \ we_dljbq_kdb_ dhe_[Zgby Wlb dhe_[Zgby mkbeb\Zxlky mkbebl_e_f gbadhc qZklhlu MGQ b j_]bkljbjmxlky ]Zev\Zghf_ljhf = GZkljhbf ]_g_jZlhj gZ qZklhlm =p l_ gZ ^ebgm \hegu ijb[ebabl_evgh jZ\gmx kf =jhfdh]h\hjbl_eb mklZgh\bfgZjZkklhygbbf hlfbdjhnhgZ?kebl_i_jvdZ`^uc
§42.
21
]jhfdh]h\hjbl_ev ihhq_j_^gh ih^dexqblv d ]_g_jZlhjm lh fh`gh aZf_lblv qlh ihdZaZgby ]Zev\Zghf_ljZ = \ h[hbo kemqZyo [m^ml h^bgZdh\u LZdbf h[jZahf a\mdh\u_ \hegu h^bgZdh\hc qZklhlu [m^ml bf_lv h^bgZdh\u_ Zfieblm^u ?keb l_i_jv ih^dexqblv ^\Z ]jhfdh]h\hjbl_ey h^gh\j_f_ggh lh ihdZaZgby ]Zev\Zghf_ljZ m\_ebqZlky ijbf_jgh \ ^\Z jZaZ ih kjZ\g_gbx kh kemqZyfb dh]^Z dZ`^uc ba gbo ih^dexqZeky \ hl^_evghklb Wlh ]h\hjbl h lhf qlh \hegukdeZ^u\Zykvmkbeb\Zxl^jm]^jm]Zl_Zfieblm^Zdhe_[Zgbc \ kmffZjghca\mdh\hc\heg_[hevr_q_f\ h^ghc?kebl_i_jvh^bg ba ]jhfdh]h\hjbl_e_c ihkl_i_ggh ijb[eb`Zlv d fbdjhnhgm lh fh`gh gZclb lZdb_ _]h iheh`_gby dh]^Z ihdZaZgby ]Zev\Zghf_ljZ [m^ml jZ\gu gmex \hegu ]Zkyl ^jm] ^jm]Z b dh]^Z hgb [m^ml fZdkbfZevgu \hegu mkbeb\Zxl ^jm] ^jm]Z < i_j\hf kemqZ_ wlb iheh`_gby [m^ml khhl\_lkl\h\Zlv jZkklhygbyf f_`^m i_j_^\b]Z_fuf ]jhfdh]h\hjbl_e_f b fbdjhnhghf ijhihjpbhgZevgufkf iheh\bg_^ebgu\hegu \h\lhjhfkemqZ_ wlhjZkklhygb_ijhihjpbhgZevghkf ^ebg_\hegu 2. JZaghklv jZkklhygbc ijhc^_gguo ^\mfy \hegZfb hl bklhqgbdh\ ^hdhgdj_lghclhqdbgZau\Z_lkyjZaghklvxoh^Z^\mo\heg 3. < aZ\bkbfhklbhljZaghklboh^Z\hegj_amevlbjmxsb_dhe_[Zgby eb[hmkbeb\Zxlkyeb[hhkeZ[_\Zxl 4. ey\k_o\b^h\\heg
§43.
1. >\b`msbfbkywe_dljbq_kdbfbaZjy^Zfb 2.
4. Khhl\_lkl\_gghijyfhebg_cghb djb\hebg_cgh 5. AZgZijZ\e_gb_fZ]gblghc ebgbb\ dZdhceb[hlhqd_ijbgbfZxl gZijZ\e_gb_ k_\_jgh]h ihexkZ fZ]gblghc klj_edb ihf_s_gghc \ wlmlhqdm 6. Q_fkbevg__ihe_l_f]ms_jZkiheh`_gu\ g_ffZ]gblgu_ebgbb 7. H gZijZ\e_gbbb \_ebqbg_fZ]gblgh]hihey
§44.
1. FZ]gblgu_ ebgbb ihehkh\h]h fZ]gblZ \uoh^yl ba k_\_jgh]h ihexkZ \oh^yl \ x`guc
§45.
23
[hevrhc iZe_p [m^_l mdZau\Zlv gZijZ\e_gb_ ebgbc fZ]gblgh]h ihey\gmljbkhe_ghb^Z 5. AgZy gZijZ\e_gb_ lhdZ \ khe_ghb^_ fh`gh hij_^_eblv gZijZ\e_gb_ ebgbc fZ]gblgh]h ihey \gmljb g_]h b gZh[hjhl agZy gZijZ\e_gb_ fZ]gblguo ebgbc \gmljb khe_ghb^Z fh`gh hij_^_eblvgZijZ\e_gb_lhdZ
§46.
1. ;_j_lkyijh\h^gbdb ih^\_rb\Z_lkygZ]b[dboijh\h^Zodhlhju_ q_j_aj_hklZlih^dexq_gud bklhqgbdmlhdZIjh\h^gbdihf_sZxl \ fZ]gblgh_ ihe_ ih^dh\hh[jZagh]h fZ]gblZ ?keb aZfdgmlv p_iv lhijh\h^gbdk lhdhfijb^_l\ ^\b`_gb_?keb`_fZ]gblm[jZlvb aZfdgmlv p_iv lh k ijh\h^gbdhf ijhbkoh^blv gbq_]h g_ [m^_l LZdbf h[jZahf gZ ijh\h^gbd k lhdhf ihf_s_gguf \ fZ]gblgh_ ihe_^_ckl\m_lkbeZ 2. FZ]gblgh_ihe_h[gZjm`b\Z_lkyk\hbf^_ckl\b_fgZijh\h^gbdk lhdhf 3. GZijZ\e_gb_ wlhc kbeu aZ\bkbl hl gZijZ\e_gby lhdZ \ ijh\h^gbd_b gZijZ\e_gbyfZ]gblguoebgbc 4. >eyijh\h^gbdZ _kebe_\ZyjmdZjZkiheh`_gZlZdqlh__ q_luj_ iZevpZgZijZ\e_guihgZijZ\e_gbxlhdZZ fZ]gblgu_ebgbb\oh^yl \ eZ^hgv i_ji_g^bdmeyjgh d g_c lh hlklZ\e_gguc [hevrhc iZe_p mdZ`_lgZijZ\e_gb_^_ckl\mxs_cgZijh\h^gbdkbeu >ey^\b`ms_ckyaZjy`_gghcqZklbpu _kebe_\ZyjmdZjZkiheh`_gZ lZd qlh __ q_luj_ iZevpZ jZkiheh`_gu ijhlb\ gZijZ\e_gby ^\b`_gby hljbpZl_evghc qZklbpu ih gZijZ\e_gbx ^\b`_gby iheh`bl_evghc Z fZ]gblgu_ ebgbb \oh^yl \ eZ^hgv i_ji_g^bdmeyjgh d g_c lh hlklZ\e_gguc [hevrhc iZe_p mdZ`_l gZijZ\e_gb_^_ckl\mxs_cgZwlmqZklbpmkbeu 5. AZ gZijZ\e_gb_ lhdZ \h \g_rg_c qZklb p_ib ijbgbfZxl gZijZ\e_gb_^\b`_gbyhliheh`bl_evgh]hihexkZbklhqgbdZlhdZd hljbpZl_evghfm 6. Ih ijZ\bem e_\hc jmdb fh`gh hij_^_eblv gZijZ\e_gb_ kbeu ^_ckl\mxs_c gZ ijh\h^gbd k lhdhf \ fZ]gblghf ihe_ beb gZijZ\e_gb_ kbeu ^_ckl\mxs_c gZ aZjy`_ggmx qZklbpm ^\b`msmxky \ fZ]gblghf ihe_ LZd`_ ihevamykv wlbf ijZ\behf fh`ghhij_^_eblvgZijZ\e_gb_lhdZ\ ijh\h^gbd_ _kebagZ_fdZd gZijZ\e_gu fZ]gblgu_ ebgbb b kbeZ ^_ckl\mxsZy gZ ijh\h^gbd gZijZ\e_gb_ fZ]gblguo ebgbc _keb agZ_f dZd gZijZ\e_g lhd \ ijh\h^gbd_b kbeZ^_ckl\mxsZygZg_]h agZdaZjy^Z^\b`ms_cky qZklbpu _keb agZ_f dZd gZijZ\e_gu fZ]gblgu_ ebgbb kdhjhklv ^\b`_gbyqZklbpub kbeZ^_ckl\mxsZygZg__ b l^ 24
7. < kemqZ_dh]^ZgZijZ\e_gb_lhdZ\ ijh\h^gbd_eb[hgZijZ\e_gb_ kdhjhklbqZklbpukh\iZ^Zxlk gZijZ\e_gb_ffZ]gblghcebgbbbeb iZjZee_evgu_c
§47.
1. FZ]gblgZy bg^mdpby ² wlh \_dlhjgZy nbabq_kdZy \_ebqbgZ U oZjZdl_jbamxsZyfZ]gblgh_ihe_HgZh[hagZqZ_lkykbf\hehf < . 2. Fh^mev \_dlhjZ fZ]gblghc bg^mdpbb hij_^_ey_lky dZd hlghr_gb_ fh^mey kbeu ^_ckl\mxs_c gZ jZkiheh`_gguc i_ji_g^bdmeyjghfZ]gblgufebgbyfijh\h^gbdk lhdhfd kbe_lhdZ F b _]h^ebg_ B = . Il 3. < kbkl_f_KB Le qblZ_lky©l_keZª 4. EbgbyfbfZ]gblghcbg^mdpbbgZau\Zxlkyebgbb dZkZl_evgu_ d dhlhjuf \ dZ`^hc lhqd_ ihey kh\iZ^Zxl k gZijZ\e_gb_f \_dlhjZ fZ]gblghcbg^mdpbb 5. FZ]gblgh_ ihe_ h^ghjh^gh _keb \h \k_o _]h lhqdZo fZ]gblgZy U bg^mdpby < ihklhyggZ < ijhlb\ghf kemqZ_ fZ]gblgh_ ihe_ g_h^ghjh^gh 6. KbeZ^_ckl\mxsZygZfZ]gblgmxklj_edmbeb^\b`msbckyaZjy^ \ fZ]gblghf ihe_ [m^_l l_f [hevr_ q_f [hevr_ fh^mev \_dlhjZ fZ]gblghcbg^mdpbb\ ^Zgghclhqd_ihey
§48.
1. FZ]gblgucihlhdijhgbau\Zxsbciehkdbcdhglmj\ fZ]gblghf ihe_ aZ\bkbl hl fh^mey \_dlhjZ fZ]gblghc bg^mdpbb iehsZ^b dhglmjZ b hjb_glZpbb dhglmjZ ih hlghr_gbx d gZijZ\e_gbx fZ]gblguoebgbc 2. M\_ebqb\Z_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 gZijZ\e_gbx fZ]gblguo ebgbc b jZ\_g gmex _kebiehkdhklvdhglmjZiZjZee_evgZfZ]gblgufebgbyf 4. >Zf_gy_lky
§49.
1.
ijh\h^gbdhf iehsZ^v < i_j\hf hiul_ ]Zev\Zghf_lj j_]bkljbjm_l ihy\e_gb_ lhdZ \ aZfdgmlhc gZ g_]h dZlmrd_ ijb \klZ\e_gbb \ g__ fZ]gblZ
§50.
1. We_dljbq_kdbc lhd i_jbh^bq_kdb f_gyxsbcky \h \j_f_gb ih fh^mex b ih gZijZ\e_gbx gZau\Z_lky i_j_f_gguf lhdhf I_j_f_gguc lhd fh`gh ihemqblv _keb \ dZlmrd_ aZfdgmlhc gZ ]Zev\Zghf_lj i_jbh^bq_kdb ^\b]Zlv fZ]gbl \\_jo b \gba Ijb wlhf klj_edZ ]Zev\Zghf_ljZ [m^_l i_jbh^bq_kdb hldehgylvky hl gme_\h]h agZq_gby lh \ h^gm klhjhgm lh \ ^jm]mx Wlh [m^_l k\b^_l_evkl\h\Zlv h lhf qlh b fh^mev kbeu bg^mdpbhggh]h lhdZ b _]h gZijZ\e_gb_ i_jbh^bq_kdb f_gyxlky \h \j_f_gb l_ \ dZlmrd_ h[jZam_lkyi_j_f_gguclhd 2. < we_dljhk_lyo 3. GZy\e_gb_we_dljhfZ]gblghcbg^mdpbb 4. =_g_jZlhj khklhbl ba klZlhjZ ² g_ih^\b`ghc qZklb \uihegyxs_cnmgdpbxaZfdgmlh]hdhglmjZjhlhjZ²\jZsZxs_cky qZklb \uihegyxsbc nmgdpbx fZ]gblZ \ ijhfure_gguo ]_g_jZlhjZo bkihevamxlky h[uqgh we_dljhfZ]gblu Ijbgpbi ^_ckl\by ]_g_jZlhjZ hkgh\Zg gZ y\e_gbb we_dljhfZ]gblghc bg^mdpbbIjb\jZs_gbbjhlhjZ\g_rg_ckbehcf_gy_lkyfZ]gblguc ihlhdijhgbau\ZxsbcklZlhj\ j_amevlZl_q_]h\ g_fbg^mpbjm_lky i_j_f_gguclhd 5. GZ l_ieh\hc we_dljhklZgpbb jhlhj ]_g_jZlhjZ ijb\h^blky \h \jZs_gb_ iZjh\hc lmj[bghc gZ ]b^jhwe_dljhklZgpbb ² \h^yghc lmj[bghc 6. LZd dZd kdhjhklv \jZs_gby \h^yguo lmj[bg hlghkbl_evgh g_\ukhdZ lh ^ey kha^Zgby lhdZ klZg^Zjlghc qZklhlu ijbf_gyxl fgh]hihexkgu_jhlhju 7. =p 26
§51.
1. :g]ebckdbfmq_guf>DFZdk\_eehf \ ]WlZ l_hjby \djZlp_ k\h^blky d lhfm qlh f_gyxs__ky \h \j_f_gb we_dljbq_kdh_ ihe_ ihjh`^Z_l i_j_f_ggh_ fZ]gblgh_ ihe_ b gZh[hjhl f_gyxs__ky \h \j_f_gb fZ]gblgh_ ihe_ ihjh`^Z_l i_j_f_ggh_we_dljbq_kdh_ihe_ 2. Bklhqgbdhfwe_dljhfZ]gblgh]hiheykem`ZlaZjy^u^\b`msb_ky k mkdhj_gb_f 3. Kbeh\u_ ebgbb \boj_\h]h we_dljbq_kdh]h ihey aZfdgmlu Z kbeh\u_ ebgbb we_dljhklZlbq_kdh]h ihey gZqbgZxlky gZ iheh`bl_evguoaZjy^Zob aZdZgqb\ZxlkygZhljbpZl_evguo
§52.
1. We_dljhfZ]gblgZy \hegZ ij_^klZ\ey_l kh[hc kbkl_fm ihjh`^Zxsbo ^jm] ^jm]Z b jZkijhkljZgyxsboky \ ijhkljZgkl\_ i_j_f_gguo we_dljbq_kdh]h b fZ]gblgh]h ihe_c i_ji_g^bdmeyjguo ^jm] ^jm]m We_dljhfZ]gblgu_ \hegu y\eyxlky ihi_j_qgufb lZd dZd iehkdhklv \ dhlhjhc e_`Zl dhe_[exsb_ky U U \_dlhju B b E i_ji_g^bdmeyjgZ gZijZ\e_gbx jZkijhkljZg_gby \hegu Bklhqgbdhf we_dljhfZ]gblguo \heg y\eyxlky mkdhj_ggh ^\b`msb_ky we_dljbq_kdb_ aZjy^u Kdhjhklv jZkijhkljZg_gby we_dljhfZ]gblguo\heg\ \Zdmmf_jZ\gZkdhjhklbk\_lZl_ dfk U 2. <_dlhj gZijy`_gghklb we_dljbq_kdh]h ihey E b \_dlhj U fZ]gblghcbg^mdpbb B . 3. λ = cT = k/ν. U 4. >eywlh]hg_h[oh^bfhqlh[uqZklhlZν dhe_[Zgbc\_dlhjh\ B b U E [ueZ^hklZlhqgh[hevrhc 5. We_dljhfZ]gblgu_ \hegu \i_j\u_ m^Zehkv h[gZjm`blv =_gjbom =_jpm\ ] 6.
§53.
27
2. < ] Zg]ebckdbc mq_guc LhfZk Xg] ihdZaZe qlh k\_lm ijbkms_ k\hckl\h bgl_jn_j_gpbb Wlh ^hdZau\Zeh lh qlh k\_l h[eZ^Z_l\hegh\ufbk\hckl\Zfb 3. GZ ijh\hehqgh_ dhevph k jmqdhc aZlygmlh_ fuevghc ie_gdhc \ aZl_fg_gghc dhfgZl_ gZijZ\eyeky k\_l gZijbf_j `_elh]h p\_lZ Ijb wlhf gZ ie_gd_ h[jZah\u\Zebkv q_j_^mxsb_ky `_elu_ b l_fgu_ihehku 4. K\_l iZ^Zy gZ ie_gdm qZklbqgh hljZ`Z_lky hl i_j_^g_c ih\_joghklb \ lhqd_ : Z qZklbqgh ijhoh^bl \gmljv ie_gdb b hljZ`Z_lky hl aZ^g_c ih\_joghklb \ lhqd_ < ihke_ q_]h \uoh^bl ba ie_gdb \ lhqd_ K
§54.
1. < \b^_mijm]bo\hegih^h[gha\mdh\uf 2. L_fqlhk\_ljZkijhkljZgy_lkyb \\Zdmmf_ 3. FZdk\_ee ij_^iheh`be qlh k\_l ² wlh qZklguc kemqZc we_dljhfZ]gblguo \heg Hkgh\Zgb_f ^ey wlh]h ihkem`beh lh qlh k\_lh\u_ b we_dljhfZ]gblgu_ \hegu y\eyxlky ihi_j_qgufb b h[eZ^Zxlh^bgZdh\hckdhjhklvxjZkijhkljZg_gby 4. QZklbpZwe_dljhfZ]gblgh]hbaemq_gbygZau\Z_lkynhlhghf
§55.
1. Hldjulb_ ;_dd_j_ey khklhyeh \ lhf qlh g_dhlhju_ \_s_kl\Z kZfhijhba\hevgh baemqZxl g_\b^bfu_ emqb gZa\Zggu_ \ihke_^kl\bbjZ^bhZdlb\gufbaemq_gb_f 2. JZ^bhZdlb\ghklvx 3. < ] Wjg_kl J_a_jnhj^ hiulguf iml_f h[gZjm`be qlh jZ^bhZdlb\gh_ baemq_gb_ jZ^by g_h^ghjh^gh b bf__l keh`guc khklZ\ < lheklhkl_gguc k\bgph\uc khkm^ hg ihf_sZe djmibgdm 28
jZ^by Imqhd jZ^bhZdlb\gh]h baemq_gby jZ^by ijhoh^be kd\hav madh_ hl\_jklb_ b ihiZ^Ze gZ nhlhieZklbgdm Ihke_ ijhy\e_gby nhlhieZklbgdb gZ g_c h[gZjm`behkv h^gh iylgh AZl_f hiul \b^hbaf_gyeb L_i_jv imqhd baemq_gby ijhoh^be q_j_a h[eZklv fZ]gblgh]h ihey ij_`^_ q_f ihiZklv gZ nhlhieZklbgdm < j_amevlZl_ fZ]gblgh_ ihe_ jZa^_eyeh wlhl imqhd gZ ljb b gZ nhlhieZklbgd_ ihke_ ijhy\e_gby h[gZjm`b\Zehkv ljb iylgZ ² h^gh ih p_gljm ^\Z k[hdm hl g_]h Wlh ]h\hjbl h lhf qlh imqhd baemq_gby khklZ\eyeb iheh`bl_evgh aZjy`_ggu_ αqZklbpu hljbpZl_evgh aZjy`_ggu_ βqZklbpu b g_cljZevgu_ γqZklbpu qZklbpu 4. αqZklbpZ ij_^klZ\ey_l kh[hc iheghklvx bhgbabjh\Zgguc Zlhf ]_eby k aZjy^hf jZ\guf fh^mex m^\h_ggh]h aZjy^Z we_dljhgZ βqZklbpZ ² we_dljhg γqZklbpZ ² h^bg ba ^bZiZahgh\ we_dljhfZ]gblgh]hbaemq_gby 5. H keh`ghfkljh_gbbZlhfZ
§56.
1. Kh]eZkgh fh^_eb ij_^eh`_gghc Lhfkhghf Zlhf ij_^klZ\eye rZj ih \k_fm h[t_fm dhlhjh]h jZ\ghf_jgh jZkij_^_e_g iheh`bl_evguc aZjy^
3. J_a_jnhj^ ijbr_e d \u\h^m qlh klhev kbevgh_ hldehg_gb_ αqZklbp \hafh`gh lhevdh lh]^Z dh]^Z \gmljb ZlhfZ bf__lky hq_gv kbevgh_we_dljbq_kdh_ihe_LZdh_kbevgh_ihe_lhevdhfh]eh[ulv kha^Zgh aZjy^hf kdhgp_gljbjh\Zgguf \ hq_gv fZehf h[t_f_ ih kjZ\g_gbx k h[t_fhf ZlhfZ Bkoh^y ba \k_]h wlh]h J_a_jnhj^ ij_^eh`be ieZg_lZjgmx fh^_ev ZlhfZ Kh]eZkgh wlhc fh^_eb \ p_glj_ ZlhfZ gZoh^blky iheh`bl_evgh aZjy`_ggh_ y^jh dhlhjh_ b [ueh ijbqbghc kbevgh]h hldehg_gby αqZklbp
§57.
1. JZ^bcij_\jZsZ_lky\ jZ^hg 2. Ijhbkoh^blij_\jZs_gb_h^gh]hobfbq_kdh]hwe_f_glZ\ ^jm]hc 3. Y^jh 222 4 4 226 4. 226 88 Rd → 86 Rn + 2 He ]^_ 2 He — αqZklbpZ 88 Rd ² y^jh
jZ^by 222 86 Rn ²y^jhjZ^hgZ 5. <_jog__qbkeh²fZkkh\h_qbkeh gb`g__²aZjy^h\h_qbkeh 6. FZkkh\h_qbkehy^jZZlhfZ^Zggh]hobfbq_kdh]hwe_f_glZjZ\gh k lhqghklvx^hp_euoqbkemZlhfguo_^bgbpfZkkukh^_j`Zsboky \ fZkk_ wlh]h y^jZ AZjy^h\h_ qbkeh y^jZ ZlhfZ ^Zggh]h obfbq_kdh]h we_f_glZ jZ\gh aZjy^m y^jZ \ujZ`_gghfm \ we_f_glZjguowe_dljbq_kdboaZjy^Zo 222 4 7. 226 88 Rd → 86 Rn + 2 He Ba^Zgghcj_Zdpbb\b^ghqlh\uihegyxlky aZdhgu khojZg_gby fZkkh\h]h qbkeZ b aZjy^Z >_ckl\bl_evgh fZkkh\h_qbkeh b aZjy^ jZkiZ^Zxs_]hkyy^jZZlhfZjZ^by jZ\gu khhl\_lkl\_ggh kmff_ fZkkh\uo qbk_e b kmff_ aZjy^h\ h[jZah\Z\rboky \ j_amevlZl_ jZkiZ^Z Zlhfh\jZ^hgZb ]_eby 8. Y^jZZlhfh\bf__lkeh`gh_kljh_gb_ 9. JZ^bhZdlb\ghklvxgZau\Zxlkihkh[ghklvy^_jZlhfh\g_dhlhjuo obfbq_kdbo we_f_glh\ kZfhijhba\hevgh ij_\jZsZlvky \ ^jm]b_ y^jZk bkimkdZgb_fqZklbp 30
§58.
1. Kq_lqbd =_c]_jZ khklhbl ba ]_jf_lbqghc kl_deygghc ljm[db aZiheg_gghc jZaj_`_gguf ]Zahf gZijbf_j Zj]hghf < g__ \iZygu we_dljh^u dZlh^ b Zgh^ ih^dexq_ggu_ q_j_a khijhlb\e_gb_ R d bklhqgbdm \ukhdh]h gZijy`_gby Ijbgpbi kq_lqbdZ =_c]_jZ ke_^mxsbc Ijb ijhe_l_ \gmljb ljm[db dZdhcgb[m^v [ukljhc qZklbpu kihkh[ghc bhgbabjh\Zlv Zlhfu ]ZaZ h[jZam_lky g_dhlhjh_ qbkehwe_dljhgbhgguoiZjWe_dljhgugZqbgZxl^\b]Zlvkyd Zgh^mZ iheh`bl_evgu_ bhgu ² d dZlh^m ?keb gZijy`_gghklv ihey ^hklZlhqgh\_ebdZlhwe_dljhgmkdhjyykvfh`_lijbh[j_klbwg_j]bx ^hklZlhqgmx ^ey bhgbaZpbb Zlhfh\ ]ZaZ eyj_]bkljZpbbwe_dljhgh\b γd\Zglh\ 3. DZf_jZ
31
5. Imaujvdh\Zy dZf_jZ h[eZ^Z_l [hevrbf [ukljh^_ckl\b_f \ hlebqb_ hl dZf_ju
§59.
h[hagZqZ_lkykbf\hehf 11 p bebp. 4. Ij_^iheh`_gb_h lhfqlhijhlhgu\oh^yl\ khklZ\y^jZex[h]h ZlhfZ
§60.
1. Y^jZZlhfh\bf_xl[hevrmxfZkkmq_fkmfZfZkkkhklZ\eyxsbo boijhlhgh\Wlh[uehmklZgh\e_ghhiulgufiml_fb ^Z_liheZ]Zlv qlhihfbfhijhlhgh\\ khklZ\y^jZ\oh^yldZdb_lh^jm]b_qZklbpu 2. Wlhij_^iheh`_gb_[ueh\ukdZaZghWjg_klhfJ_a_jnhj^hf\ ] 3. >`_cfkQ_^\bd\ ] 4. M g_cljhgh\ hlkmlkl\m_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^_ckl\by g_cljhgZ k ^jm]bfb qZklbpZfb 5. G_cljhgh[hagZqZ_lkykbf\hehf 01 n bebn _]hfZkkZihqlbjZ\gZ g_fgh]h[hevr_ fZkk_ijhlhgZ
§61.
1. Gmdehgu 2. FZkkh\uf qbkehf gZau\Z_lky qbkeh gmdehgh\ \ y^j_ ZlhfZ FZkkh\h_qbkehh[hagZqZ_lky[md\hc:. 3. FZkkh\h_ qbkeh jZ\gh k lhqghklvx ^h p_euo qbkem Zlhfguo _^bgbpfZkkukh^_j`Zsboky\ fZkk_ZlhfZ 4. Qbkeh ijhlhgh\ \ Zlhf_ h[hagZqZ_lky [md\hc Z b gZau\Z_lky aZjy^h\ufqbkehf 5. I_j_^kbf\hehfkgbam 32
6. AZjy^h\h_qbkehjZ\ghaZjy^my^jZ\ujZ`_gghfm\ we_f_glZjguo we_dljbq_kdbo aZjy^Zo AZjy^h\h_ qbkeh ZlhfZ jZ\gh _]h ihjy^dh\hfmghf_jm\ lZ[ebp_F_g^_e__\Z 7. ZA X a^_kvO ²kbf\heobfbq_kdh]hwe_f_glZ 8. Qbkehg_cljhgh\\ y^j_h[hagZqZxl[md\hcN. 9. A = Z + N.
§62.
1. Bahlhiu ² we_f_glu k h^bgZdh\ufb aZjy^Zfb y^_j gh jZaebqgufbfZkkZfb 2. Y^jZbahlhih\h^gh]hwe_f_glZbf_xlh^bgZdh\ucaZjy^ 3. JZagu_ bahlhiu h^gh]h we_f_glZ kh^_j`Zl jZagh_ dhebq_kl\h g_cljhgh\ 4. M \h^hjh^Z _klv ljb bahlhiZ ijhlbc 11 G ^_cl_jbc 21 G ), ljblbc 31 G ). 5. IhlhfmqlhfZkkZZlhfh\\uqbkey_lkydZdkj_^g__agZq_gb_fZkk \k_o_]hbahlhih\
1. FZkkZZlhfZmf_gvrZ_lkygZZ aZjy^_]hy^jZ²gZ 222 4 2. GZijbf_j 226 88 Rd → 86 Rn + 2 He . 3. Y^jhjZ^hgZkh^_j`blgZijhlhgZf_gvr_q_fy^jhjZ^by 4. Ijb αjZkiZ^_ h[jZam_lky gh\uc obfbq_kdbc we_f_gl ihjy^dh\uc 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 gh\uc obfbq_kdbc we_f_gl ihjy^dh\uc ghf_j dhlhjh]h \ lZ[ebp_ F_g^_e__\Z [hevr_ bkoh^gh]hgZ 7. G_l ihlhfm qlh fZkkh\h_ qbkeh jZ\gh qbkem gmdehgh\ Z wlh qbkehijbβjZkiZ^_g_f_gy_lky 8. >eyαjZkiZ^Z ZA X → AZ−−42Y + 42 He . >eyβjZkiZ^Z A X → A Y + 0 e+ 0 ~ .
§63.
Z
Z +1
−1
0
9. αb βjZkiZ^qZklhkhijh\h`^Z_lkyγbaemq_gb_f
33
§64.
1.
§65.
1. Wg_j]b_c k\yab y^jZ gZau\Z_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]byk\yab y^jZ∆m ²^_n_dlfZkkk ²kdhjhklvk\_lZ\ \Zdmmf_
§66.
1. >_e_gb_ y^_j mjZgZ ijb [hf[Zj^bjh\d_ 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^_ckl\mxsb_lhgZgmdehgu\ \ulygmlhfy^j_bo^_ckl\b_ hkeZ[_\Z_l b gmdehgu jZae_lZxlky ih^ ^_ckl\b_f we_dljhklZlbq_kdbo kbe LZdbf h[jZahf ^_e_gb_ y^jZ fh`_l gZqZlvky lhevdh lh]^Z dh]^Z hgh ^_nhjfbjm_lky ih^ ^_ckl\b_f ih]ehs_ggh]hnhlhgZ 3. < j_amevlZl_ ^_e_gby y^jZ h[jZamxlky ^\Z hkdhedZ jZgg__ khklZ\eyxsb_y^jh 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[jZah\Z\rbokyhkdhedh\b g_cljhgh\ 5. Dbg_lbq_kdZy wg_j]by hkdhedh\ ijb bo lhjfh`_gbb ij_h[jZam_lky\h\gmlj_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
§67.
1. JZkkfhljbf f_oZgbaf ijhl_dZgby p_ighc j_Zdpbb ^_e_gby y^jZ gZ ijbf_j_ bahlhiZ mjZgZ 235 92 U jbk mq_[gbdZ Ijb ^_e_gbb y^jZ ZlhfZ mjZgZ \ j_amevlZl_ aZo\ZlZ g_cljhgZ h[jZamxlky ljb g_cljhgZ >\Z ba gbo \ua\Zeb j_Zdpbx ^_e_gby _s_ ^\mo y^_j mjZgZijbwlhfh[jZah\Zehkvq_luj_g_cljhgZey 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 \ Zdlb\ghc ahg_ ih]ehsZxlg_cljhgub p_igZyj_Zdpbyb^lbg_fh`_l>eyaZimkdZ
§68.
35
j_Zdpbb j_]mebjmxsb_ kl_j`gb \u\h^yl ba Zdlb\ghc ahgu ^h l_o ihjihdZg_gZqg_lkyp_igZyj_Zdpby 7.
§69.
1. < k\yabk [hevrbfjhklhfihlj_[e_gbywe_dljhwg_j]bb 2.
§70.
36
2. Ih]ehs_gghc ^hahc baemq_gby gZau\Z_lky ih]ehs_ggZy \_s_kl\hf wg_j]by bhgbabjmxs_]h baemq_gby jZkkqblZggZy gZ _^bgbpm fZkku Ih]ehs_ggZy ^haZ baemq_gby D hij_^_ey_lky ih E nhjfme_ D = ]^_ ? ² ih]ehs_ggZy \_s_kl\hf wg_j]by m — m fZkkZ\_s_kl\Z?^bgbp_cbaf_j_gbyih]ehs_gghc^haubaemq_gby 1 >` \ kbkl_f_KBy\ey_lky]j_c =j =j . 1 d] 3. Ijb[hevr_c^ha_baemq_gby 4. JZagu_ \b^u bhgbabjmxsbo baemq_gbc ijb h^bgZdh\hc ih]ehs_gghc ^ha_ h[emq_gby hdZau\Zxl jZaebqgu_ ih \_ebqbg_ [bheh]bq_kdb_ wnn_dlu \ `b\hf hj]Zgbaf_ GZijbf_j ijb h^bgZdh\hc ih]ehs_gghc ^ha_ [bheh]bq_kdbc wnn_dl hl αbaemq_gbyijbf_jgh\ jZa[hevr_q_fhlγbaemq_gby 5. Dhwnnbpb_gl dZq_kl\Z baemq_gby ihdZau\Z_l \h kdhevdh jZa [hevr_jZ^bZpbhggZyhiZkghklvhl\ha^_ckl\bygZ`b\hchj]Zgbaf ^Zggh]h \b^Z baemq_gby ih kjZ\g_gbx k γbaemq_gb_f ijb h^bgZdh\uo ih]ehs_gguo ^haZo Dhwnnbpb_gl dZq_kl\Z baemq_gby ^ey αbaemq_gbyjZ\_g^eyβ- γb j_gl]_gh\kdh]h baemq_gby ² 1. 6. Wd\b\Ze_glgZy ^haZ baemq_gby [ueZ \\_^_gZ \ k\yab k l_f qlh ijb h^bgZdh\hc ih]ehs_gghc ^ha_ baemq_gby jZaebqgu_ \b^u baemq_gbc \uau\Zxl jZaebqgu_ [bheh]bq_kdb_ wnn_dlu Wd\b\Ze_glgZy ^haZ baemq_gby H \uqbkey_lky dZd ijhba\_^_gb_ ih]ehs_gghc ^hau D gZ dhwnnbpb_gl dZq_kl\Z D: H = DK ?_ _^bgbp_cbaf_j_gbyy\ey_lkyab\_jl A\ 7. Qm\kl\bl_evghklv jZaebqguo ldZg_c `b\h]h hj]ZgbafZ hij_^_ey_lky dhwnnbpb_glhf jZ^bZpbhggh]h jbkdZ \j_fy h[emq_gby 8. Hl \ha^_ckl\by gZ `b\hc hj]Zgbaf jZ^bhZdlb\guo baemq_gbc ijbf_gyxlky ki_pbZevgZy h^_`^Z jZaebqgu_ aZsblgu_ m[_`bsZ JZ^bhZdlb\gu_ ij_iZjZlu ke_^m_l ojZgblv \ ki_pbZevguo aZsblguodhgl_cg_jZoh[uqghk\bgph\uo
§72.
1. L_jfhy^_jghc j_Zdpb_c gZau\Z_lky j_Zdpby kebygby e_]dbo y^_j ijbhq_gv\ukhdhcl_fi_jZlmj_ ihjy^dZkhl_gfbeebhgh\]jZ^mkh\ 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_ jZkklhygbyijbdhlhjuo\hafh`ghbokebygb_ 37
3. Kebygb_e_]dboy^_j 4. 21 H + 31 H → 42 He+ 01n . 5. Hkgh\gZy ljm^ghklv ijb hkms_kl\e_gbb l_jfhy^_jghc j_Zdpbb aZdexqZ_lky \ lhf qlh[u m^_j`Zlv \ukhdhl_fi_jZlmjgmx ieZafm \gmljb mklZgh\db ?keb ieZafZ dhkg_lky kl_ghd mklZgh\db \ dhlhjhchgZgZoh^blkylhhgbjZkieZ\ylkyb 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
MijZ`g_gby MijZ`g_gb_
1. Fh`gh \ h[hbo kemqZyo ld jZaf_jZfb Z\lhfh[bey ijb ^Zgguo gZqZevguomkeh\byofh`ghij_g_[j_qv 2.
MijZ`g_gb_
1. Ijhc^_ggucimlv2. Ijyfhebg_cgh
MijZ`g_gb_ U s\
1.
x\
U sf xf
x\ = xk + s\o = 10 df + (–2 df) = 8 df; xf = xk + sfo dfdf df 2. Z o0 f [ sto = s1o + s2o f ±f f \ xt = o0 + sto f f f O
xc
MijZ`g_gb_
1. =jZnbd fh^mey \_dlhjZ kdhjhklb g_ fh`_l gZoh^blvky ih^ hkvx Otihkdhevdmfh^mev\_dlhjZkdhjhklb\k_]^Ziheh`bl_e_g=jZnbd ijh_dpbb \_dlhjZ kdhjhklb fh`_l gZoh^blvky ih^ hkvx Ot, ihkdhevdm agZd aZ\bkbl ijh_dpbb \_dlhjZ kdhjhklb hl \u[hjZ kbkl_fudhhj^bgZl 2. vx, dfq 80 60
tq –90
39
MijZ`g_gb_
1. I_j\uc Z\lhfh[bev ^\b]Zeky k [hevrbf mkdhj_gb_f ihkdhevdm _]hkdhjhklvaZh^bgZdh\u_ijhf_`mldb\j_f_gb\hajZklZeZ[uklj__ 2. >Zgh J_r_gb_ t = 30 c v −v 55 fk − 10 fk a= 2 1 = = 1,5 fk 2 . v1 fk t 30 k v2 fk GZclbZ. Hl\_l a fk2. 3. >Zgh J_r_gb_ t = 12 c v −v 6 fk a= 2 1 = = 0,5 fk 2 . v2 – v1 fk t 12 k GZclbZ. Hl\_l a fk2.
MijZ`g_gb_
1. >Zgh v1 fk t=4c a = –20 fk2 GZclb v2. 2. >Zgh a fk2 v1 = 0 v2 fk GZclbt. 3.
J_r_gb_ v −v a = 2 1 ⇒ v2 = v1 + at = t fk ±fk2) ⋅ k fk Hl\_l v2 fk
J_r_gb_ v −v v v 2 fk a= 2 1 = 2 ⇒t = 2 = = 10 k t t a 0,2 fk 2
Y[
Hl\_l t k
W 40
4. vx 5 10
5
-5
t
5. >eyl_eZ, Z fk2^eyl_eZ,, Z fk2. 1. >Zgh t=5c Zo fk2 v0o dfq fk GZclbsx. 2. >Zgh t = 20 c Zo fk2 v0o fk GZclbsx. 1. >Zgh s3 f t1 k GZclb s1, a. 2. >Zgh s5 f t1 k t5 k
MijZ`g_gb_
J_r_gb_ sx = v0 o t +
axt 2 2
fk ⋅ k
f Hl\_l sx f
0,5 fk 2 ⋅ (5 k ) = 2 2
J_r_gb_
axt 2 v v t2 v t ; ao = − 0 x ⇒ sx = v0 o t − 0 x = 0 x = 2 t 2t 2 fk ⋅ k f Hl\_l sx f sx = v0 o t +
MijZ`g_gb_
J_r_gb_ s1 : s2 : s3 = 1 : 3 : 5; s1 : 2 f = 1 : 5 ⇒ s1 = 2 f 5 = 0,4 f; at12 2s 2 ⋅ 0,4 f = 0,8 f/k2. ⇒ a = 21 = 2 2 t1 (1 k) Hl\_l s1 fa fk2. s1 =
J_r_gb_ s1 : s2 : s3 : s4 : s5 = 1 : 3 : 5 : 7 : 9; s1 : 6,3 f = 1 : 9 ⇒ ⇒ s1 = 6,3 f 5 = 0,7 f; at12 2s 2 ⋅ 0,7 f = 1,4 f/k2; ⇒ a = 21 = 2 t1 (1 k)2 v5 = at5 fk2 ⋅ k fk Hl\_l v5 fk s1 =
GZclbv5.
41
MijZ`g_gb_
1. fk 2. G_l ihkdhevdm b ^_j_\h b \hdaZe `_kldh k\yaZgu k ^jm]hc kbkl_fhchlkq_lZ²A_fe_c 3. Ijbmkeh\bbg_ih^\b`ghklbwlbol_ehlghkbl_evgh^jm]^jm]Z 4. dfq fk 5*. >Zgh J_r_gb_ v1 dfq fk v\ = v1 + v2 fk fk fk v2 fk va = v2 – v1 fk ±fk fk GZclbv\, va. Hl\_l v\ fk va fk
MijZ`g_gb_
AZdhgbg_jpbb\uihegy_lky\ kbkl_f_hlkq_lZk\yaZgghck A_fe_cb \ kbkl_f_ hlkq_lZ k\yaZgghc k ih_a^hf \h \j_fy _]h ijyfhebg_cgh]h b jZ\ghf_jgh]h ^\b`_gby g_ \uihegy_lky \ kbkl_f_ hlkq_lZ k\yaZgghc k ih_a^hf \h \j_fy _]h lhjfh`_gby Bg_jpbZevghckbkl_fhcfh`ghkqblZlva_fexZ ih_a^²g_evay
MijZ`g_gb_
1. >Zgh J_r_gb_ Z fk2 IhhfmaZdhgmGvxlhgZ m d] F = ma d]⋅ fk2 G GZclbF. Hl\_l F G 2. >Zgh J_r_gb_ t = 20 c F = ma ²hcaZdhgGvxlhgZ v fk v mv 1,84 ⋅ 10 5 d] ⋅ 4 fk 5 = = = = a ⇒ F m l ⋅10 d] 20 k t t G dG GZclbF. Hl\_l F dG 3. >Zgh J_r_gb_ IhhfmaZdhgmGvxlhgZ m1 = m2 a1 fk2 F1 = m1a1; F2 = m2a2. Ldm1 = m2lhihemqZ_f a2 fk2 F1 F2 a F 0,64 fk 2 ⋅ 1,2 G = ⇒ F2 = 2 1 = = 9,6 H. F1 = 1,2 H a1 a 2 a1 0,08 fk 2 GZclbF2.
Hl\_l F2 G
42
4. >Zgh m = 0,5 d] FA = 10 H FL = 5 H FC = 2 H
J_r_gb_ IhhfmaZdhgmGvxlhgZ F = ma. F = FA – FL – FC ⇒ FA – FL – FC = ma ⇒ F − FL − FC 10 H − 5 H − 2 H fk2. ⇒a = A = m 0,5 d] GZclbF2. Hl\_l a fk2. 5. Ijb ^\b`_gbb \\_jo kdhjhklv b i_j_f_s_gb_ ijhlb\hiheh`gh gZijZ\e_gu k kbehc ly`_klb mkdhj_gb_ ² khgZijZ\e_gh Ijb ^\b`_gbb\gbakdhjhklvi_j_f_s_gb_b mkdhj_gb_khgZijZ\e_guk kbehcly`_klb 6. Mkdhj_gb_ \k_]^Z khgZijZ\e_gh k jZ\gh^_ckl\mxs_c ijbeh`_gguo d l_em kbe Kdhjhklv b i_j_f_s_gb_ fh]ml [ulv dZd khgZijZ\e_gu k jZ\gh^_ckl\mxs_c ijbeh`_gguo d l_em kbe lZd b ijhlb\hiheh`ghgZijZ\e_gu
MijZ`g_gb_
U U 1. GZ l_eh ^_ckl\mxl kbeZ ly`_klb Fl b kbeZ j_Zdpbb hihju N kfjbk U N
U Fl
2. G_ ij_\ukbl ld jZ\gh^_ckl\mxsZy ijbeh`_gguo kbe gZ ^bgZfhf_ljjZ\gZ 3. >Zgh J_r_gb_ IhhfmaZdhgmGvxlhgZ m1 d] m2 d] F2x = m2ax d]⋅ fk2 G a fk2 IhfmaZdhgmGvxlhgZ F1x = –F2x ±G IhhfmaZdhgmGvxlhgZ F1x = m1ax d]⋅ fk2 G IhfmaZdhgmGvxlhgZ F2x = –F1x ±G < i_j\hf kemqZ_ gblv f_`^m l_e_`dZfb gZlygmlZ kbevg__ IhhfmaZdhgmGvxlhgZ Fx = (m1 + m2)ax d]d] ⋅ fk2 G GZclb F1x, Hl\_l F1x ±GF2x G F1x GF2x = ±G \ i_j\hfkemqZ_ Fx G F2x, Fx. 43
1. >Zgh g ≈ fk2 t=2c
J_r_gb_
gt 2 10 fk 2 ⋅ (2 k ) = 2 2 Hl\_l h f
2
h=
GZclbh. 2. >Zgh g ≈ fk2 h = 80 cf f GZclbt. 3. >Zgh g ≈ fk2 h = 45 f t1 = 1 c ∆t = 1 c
GZclb t, s1, s2. >Zgh v fk v1 = 0 g fk2 GZclbt, s.
MijZ`g_gb_ f
J_r_gb_
gt 2 2h 2 ⋅ 0,8 f ⇒t= = = 0,4 k. 2 g 10 fk 2 Hl\_l t k h=
J_r_gb_ h=
gt 2 2h 2 ⋅ 45 f ⇒t= = 2 g 10 fk 2
k
gt12 10 fk 2 ⋅ (1 k )2 = = 5 f; 2 2 2 gt 2 g (t − ût ) s2 = − = 2 2 2 2 10 fk 2 ⋅ (3 k ) 10 fk 2 ⋅ (3 c − 1 c ) = − =5f 2 2 Hl\_l t ks1 fs2 f s1 =
MijZ`g_gb_
J_r_gb_ v − v1 v v 9,8 fk g= = ⇒t= = =1 c; t t g 9,8 fk 2
gt 2 9,8 fk 2 ⋅ (1k ) fk ⋅ k ± 2 2 Hl\_l t ks f
2
s = vt −
f
MijZ`g_gb_
1.
m\_ebqb\Z_lky Dh]^Z klZgpby gZoh^blky gZ k_j_^bg_ hgZ kbevg__ ijbly]b\Z_lkyd A_fe_ldfZkkZA_feb[hevr_fZkkuEmgu 3. G_l 4. Z ^_ckl\h\ZeZ [ ijbly`_gb_A_feb \ baaZ^_ckl\bykbeuly`_klb 5. >Zijbly]b\Z_lky ghwlZkbeZ]hjZa^hf_gvr_kbeuly`_klb ba aZjZkklhygbcEmgZlZd`_ijbly]b\Z_lkyd wlhfmq_eh\_dm 1. >Zgh g ≈ fk2 m1 d] m2 ] d] m3 l d] m4 l d]
GZclb Fl1, Fl2, Fl3, Fl4. 2. >Zgh g ≈ fk2; m d] GZclbFl. 3. >Zgh g ≈ fk2; Fl G
MijZ`g_gb_
J_r_gb_ Fl = mg ⇒ Fl fk2 ⋅ d] G Fl fk2 ⋅ d] G Fl fk2 ⋅ d] G dG Fl fk2 ⋅ d] ⋅105 G dG Hl\_l G G dG dG J_r_gb_ Fl = mg d]⋅ fk2 G Hl\_l Fl G J_r_gb_
Fl 819,3 G d] = g 10 fk 2 GZclbFl. Hl\_l m d] 4. G_lihkdhevdm\ukhlZihe_lZkjZ\gbfZk 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^_ckl\m_lkbeZly`_klbb _kebhgkeh`bldjuevylh hgmiZ^_lgZA_fex 1 6. GZjZkklhygbbRa; 3Ra (Ra ²jZ^bmkA_feb ihkdhevdmFl~ (Ra + h)2 Fl = mg ⇒ m =
MijZ`g_gb_
U 1. KbeZ F fh]eZ^_ckl\h\Zlvlhevdh\ gZijZ\e_gbb 2. KbeZ ^_ckl\h\ZeZ gZ rZjbd gZ mqZkldZo RZjbdih\hjZqb\Zekyih^^_ckl\b_f\g_rgbokbe 3. KbeZ^_ckl\h\ZeZgZl_ehgZ\_jgydZgZmqZkldZo:<&'GZl_eh fh]eZ^_ckl\h\ZlvkbeZb gZhklZevguomqZkldZo 45
MijZ`g_gb_
1. >Zgh r kf f v fk GZclba. 2. >Zgh R kf f T k
GZclba. 3. Z1 =
J_r_gb_
v 2 (20 fk )2 = ≈ fk2. r 0,21 f Hl\_l Z ≈ fk2. Z=
J_r_gb_ Z=
v2 l 2πR 4π 2 R 2 4π 2 R ;v= = ⇒Z= 2 = 2 = R T T T R T 2 4 ⋅ (3,14 ) ⋅ 0,02 f = ≈ 2⋅10-4 fk2. (60 k )2 Hl\_l Z ≈ 2⋅10-4 fk2.
v2 v2 v2 ; Z2 = = 2a1 ⇒ ml\_j`^_gb_\_jgh = 2⋅ r r/2 r
4. >Zgh T1 k T2 k
J_r_gb_ v 2 (2πR T1 )2 4π 2 R 4π 2 R a1 = 1 = . :gZeh]bqgh a 2 = . = 2 R R T1 T22 Ke_^h\Zl_evgh
GZclb
a1 . a2
Hl\_l
5. >Zgh Fa = 6⋅1024 d] Fe = 6⋅1022 d]
G ⋅ f2
d] 2 r = df = 3,84⋅108 f G=6,67⋅10-11
GZclbF]j, Zp, v.
2
a1 T1 3600 c = = = 3600. a 2 T2 60 c 2
a1 = 3600. a2
J_r_gb_ Z F]j = G ×
F aF e 2
= 6,67⋅10-11
r 6 ⋅ 10 24 d] ⋅ 7 ⋅10 22 d] (3,84 ⋅ 10 8 f 2
[ Zp =
F]j
Fa
=
G ⋅ f2 d] 2
×
≈ 1,9⋅1020 G
1,9 ⋅ 10 20 G 6 ⋅ 10 24 d]
≈ 3,17⋅10-5 fk2;
\ v = ap r = 3,17 ⋅10−5 fk2 ⋅ 3,84⋅108 f ≈fk Hl\_l F]j ≈ 1,9⋅1020 Gv ≈ fk Zp = 3,17⋅10-5 fk2.
46
MijZ`g_gb_ 1. >Zgh h df ⋅106 f Fa = 6⋅1024 d] Ra = 6,4⋅106 f G = 6,67⋅10-11
G ⋅ f2 d] 2
J_r_gb_ Ma v≈ G = Ra + h = 6,67 ⋅ 10−11
G ⋅ f2 d] 2
⋅
6 ⋅ 1024 d]
(2,6 ⋅ 106 f + 6,4 ⋅ 106 f
fk dfk GZclbv. Hl\_l v dfk 2. >Zgh J_r_gb_ v dfk ⋅103 fk v2 v2 1,67 ⋅10 3 fk re = ⇒ re = = ge ≈ fk2 re ge 1,6 fk 2 = 1,7⋅106 f ⋅103 df GZclb re. Hl\_l re = 1,7⋅103 df
(
)
=
2
=
MijZ`g_gb_ 1. >Zgh v1x = –v2x fk m = 0,2 d] GZclb p1x, p2x. 2. >Zgh v1 dfq fk v2 dfq fk m l d] GZclb ∆p.
J_r_gb_ p1x = mv1x d]⋅ fk d]⋅fk p2x = – p1x ±d]⋅fk <_dlhjubfimevkh\fZrbgg_jZ\guldhgb ijhlb\hiheh`gh gZijZ\e_gu Fh^meb \_dlhjh\bfimevkh\jZ\gu Hl\_l p1x d]⋅fk p2x ±d]⋅fk J_r_gb_ ∆j = m∆v = m(v2 – v1) = d]⋅ fk ± fk d]⋅fk Hl\_l ∆p d]⋅fk
MijZ`g_gb_
1. Ih aZdhgm khojZg_gby bfimevkZ eh^dZ gZqg_l ^\b]Zlvky \ klhjhgmijhlb\hiheh`gmx^\b`_gbxq_eh\_dZ 47
2. >Zgh m1 l m2 l v2 fk GZclb v1. 1. >Zgh ve fk m\ d] v\ fk me d]
J_r_gb_ AZibr_faZdhgkhojZg_gbybfimevkZ m + m2 v2 = m1v1 = (m1 + m2)v2 ⇒ v1 = 1 m1 35 l + 28 l = ⋅ 0,5 fk fk 35l Hl\_l v1 fk J_r_gb_ AZibr_faZdhgkhojZg_gbybfimevkZ ( m + m\ ) v e + m\ v \ (me + m\)ve + m\v\ = mev ⇒ v = e = me (200 d] + 5 d] )⋅ 2 fk + 5 d] ⋅ 8 fk fk = 200 d] Hl\_l v fk
GZclb v. 2. >Zgh mj ] d] mi ] d] vi fk GZclb vj.
MijZ`g_gb_
J_r_gb_ AZibr_faZdhgkhojZg_gbybfimevkZ m v 0,1 d] ⋅ 100 fk mjvj=mivi⇒vj= i i = ≈ fk mj 0,3 d] Hl\_l vj ≈ fk
MijZ`g_gb_
1. Dhe_[Zl_evgufb kbkl_fZfb y\eyxlky [ ] _ G_ y\eyxlky dhe_[Zl_evgufbZ\^ 2. Z Ih^^_ckl\b_fkbemijm]hklbrgmjh\ [ g_l \ rgmju^bkd ] ^Zy\ey_lky
MijZ`g_gb_
1. :fieblm^Z : qZklhlZ ν i_jbh^ L ² ihklhyggu_ F, v — i_j_f_ggu_ 2. >Zgh J_r_gb_ 1 1 ν = =p T= = = 0,5 k ν 2 =p GZclb T. Hl\_l T k 48
3. >Zgh T k GZclb ν. 4. >Zgh n = 600 t fbg k
J_r_gb_ 1 1 ν= = = 2 =p T 0,5 c Hl\_l ν =p
J_r_gb_ 1 t n 600 ν= ; T = ⇒ν= = = 10 =p T n t 60 c GZclb ν. Hl\_l ν =p 5. kf kf kf kf 6. >Zgh J_r_gb_ A = 10 kf 1 1 T = = = 2 c AZ k l_eh kh\_jrZ_l ihegh_ ν = 0,5 =p ν 0,5 =p t k dhe_[Zgb_b ijhc^_limlvS = 4: kf GZclb S. Hl\_l S kf 7. Dhe_[exlky \ h^bgZdh\uo nZaZo \ kemqZyo [ ^ Dhe_[exlky \ ijhlb\hiheh`guonZaZo\ kemqZyoZ \ ] _
MijZ`g_gb_
GZijZ\ e_gb_ ^\b`_gby fZylgbdZ Hl< d H
mf_gv
Hl: d H
mf_gv
1.
HlH d : HlH d <
Fmij
m\_e m\_e
v m\_e
mf_gv . m\_e mf_gv .
?i
?d
mf_gv
m\_e
mf_gv
m\_e
m\_e m\_e
mf_gv mf_gv
?ihe K lj_ ;_a lj_ gb_f gby mf_gv mf_gv mf_gv mf_gv
g_ baf_g g_ baf_g g_ baf_g g_ baf_g
2. Z >` >` [ >` >` >` \ >` \h \k_o kemqZyo
MijZ`g_gb_
1. Kihkh[gu kh\_jrZlv k\h[h^gu_ dhe_[Zgby l_eZ [ _ \ugm`^_ggu_dhe_[Zgby²\k_l_eZ 2. Z ^ZgZijbf_jkljmgZfmaudZevgh]hbgkljmf_glZ [ g_l 49
MijZ`g_gb_
1. Z Zgh λ f T k
GZclb v. 2. >Zgh ν =p v fk GZclb λ. 3. 2. >Zgh v fk λ f GZclbT.
MijZ`g_gb_
J_r_gb_ λ 270 f v= = = 20 fk T 13,5 k Hl\_l v fk
J_r_gb_ v 340 fk λ= = = 1,7 f ν 200 =p Hl\_l λ f J_r_gb_ λ 6f v= = = 4 k T 1,5 fk Hl\_l T = 4 c.
MijZ`g_gb_
E_lysZyilbpZkha^Z_lbgnjZa\mdh\u_\hegu
MijZ`g_gb_
1. DhfZjA\mdkha^Z\Z_fucbfkZfuc\ukhdbc 2. Mf_gvrblkyihkdhevdmqZklhlZ__ \jZs_gbylZd`_mf_gvrblky 3. Ijb ih\ur_gbb l_fi_jZlmju kljmgZ jZkly]b\Z_lky i_jbh^ __ dhe_[Zgbc m\_ebqb\Z_lky qZklhlZ b khhl\_lkl\_ggh \ukhlZ a\mqZgbymf_gvrZ_lky
MijZ`g_gb_
1. G_lf_`^mA_fe_cb Emghcg_lmijm]hckj_^uihdhlhjhcfh`_l jZkijhkljZgylvkya\md 2. A\mdh\u_\hegujZkijhkljZgyxlkyihgblb 50
1. >Zgh λ f T k
GZclb v. 2. >Zgh v1 fk v2 fk v3 fk ν =p
MijZ`g_gb_
J_r_gb_ λ 2,9 f v= = = 1450 fk T 0,002 k Hl\_l v fk
J_r_gb_ v 340 fk v 1483fk λ1 = 1 = ≈ 0,47 f; λ 2 = 2 = ≈ 2,05 f; 725 =p ν 725 =p ν v 5500 fk λ3 = 3 = ≈ 7,59 f. 725 =p ν GZclbλ1, λ2, λ3. Hl\_l λ1 ≈ fλ2 ≈ fλ3 ≈ f 3. A\md [m^_l jZkijhkljZgylvky b ih f_lZeem b ih \ha^mom b q_eh\_dmkeurbl^\Zm^ZjZ 4. >Zgh J_r_gb_ ta\ k Sa\ = va\ta\; SiZj = viZjtiZj; Sa\ = SiZj; va\ta\ = viZjtiZj ⇒ va\ fk v t 340 fk ⋅ 2 k ⇒ viZj = a\ a\ = = 20 fk tiZj k t iZj 34 k Sa\ = SiZj GZclbviZj. Hl\_l viZj fk 5. Dh]^Z\b^bfu_b keurbfu_m^ZjugZqbgZxlkh\iZ^Zlvkgh\Zlh wlhagZqblqlhq_eh\_dkeurblij_^u^msbci_j_^\b^bfufm^Zj
MijZ`g_gb_
1. Kms_kl\m_l 2. FZ]gblgh_ ihe_ [m^_l ^_ckl\h\Zlv gZ klj_edm k gZb[hevr_c kbehc \ lhqd_ N k gZbf_gvr_c ² \ lhqd_ F K jZkklhygb_f fZ]gblgh_ihe_hkeZ[_\Z_l
MijZ`g_gb_
1. Z ?klvwlhlhqdbD b K [ \ lhqd_:. 2. GZ iZju lhq_d P − Q, X − Y kh klhjhgu g_h^ghjh^gh]h fZ]gblgh]h ihey ^_ckl\mxl kbeu h^bgZdh\u_ , dZd ih fh^mex lZd b ih gZijZ\e_gbx ld PO = QO, XO = , YO.
3 2 ;
<
4
51
MijZ`g_gb_ 1.
2.
3. K_\_jguc ihexk gZoh^blky kijZ\Z Z x`guc ke_\Z Bo iheh`_gb_fh`ghbaf_gblvihf_gy\iheyjghklvkhe_ghb^Z 4. Lhd[m^_ll_qvhllhqdbS d lhqd_N. 5. KijZ\Z ² k_\_jguc ihexk ke_\Z ± x`guc ih ijZ\bem ijZ\hc jmdb 6. < i_j\hf kemqZ_ \aZbfh^_ckl\b_ h[mkeh\e_gh fZ]gblgufb kbeZfb\h\lhjhf±dmehgh\kdbfb
MijZ`g_gb_
1. IhijZ\beme_\hcjmdbhij_^_ey_fqlh\ijZ\h 2. Ih ijZ\bem e_\hc jmdb hij_^_ey_f qlh lhd l_q_l hl lhqdb B d lhqd_ A b ke_^h\Zl_evgh \_jogbc ihexk bklhqgbdZ lhdZ ih^dexq_g d hljbpZl_evghfm ihexkm Z gb`gbc ² d iheh`bl_evghfm
52
3. GZ e_\hf jbkmgd_ e_\uc ijh\h^gbd ^\b`_lky \\_jo ijZ\uc ijh\h^gbd²\gbaGZijZ\hfjbkmgd_ e_\ucijh\h^gbd^\b`_lky \gba ijZ\ucijh\h^gbd²\\_jo 4.
U v
U F
5. Ih ijZ\bem e_\hc jmdb hij_^_ey_f qlh wlh iheh`bl_evgh aZjy`_ggZyqZklbpZ 1. >Zgh I = 4 A; F = 0,2 H l kf f
MijZ`g_gb_
J_r_gb_ F 0,2 G B= = = 0,5 Le Il 0,1 f ⋅ 4 : GZclbB. Hl\_l B Le 2. FZ]gblgZy bg^mdpby g_ baf_gy_lky hgZ ihklhyggZy \_ebqbgZ Baf_gy_lkylhevdhkbeZ^_ckl\mxsZygZijh\h^gbd²hgZlZd `_ dZdb lhdmf_gvrZ_lky\ jZaZ
MijZ`g_gb_
FZ]gblguc ihlhd ijhgbau\Zxsbc dZlmrdm D2 fh`gh f_gylv iml_fbaf_g_gby\aZbfghchjb_glZpbbdZlmr_db baf_g_gb_fkbeu lhdZj_hklZlhfR bebaZfudZgb_fjZafudZgb_fdexqZD
MijZ`g_gb_
1. Baf_gblvfZ]gblgucihlhdq_j_adZlmrdmD2 iml_fhibkZgguf\ mijZ`g_gbb 2. Bg^mdpbhgguclhd\hagbdZ_l\ kemqZ_] g_\hagbdZ_l\ kemqZyo Z [ \ ^ 1. >Zgh
J_r_gb_
MijZ`g_gb_
53
ν =p
1 1 = = 0,02 k ν 50 =p GZclb T. Hl\_l T k 1 1 1 =p 2. Ih]jZnbdmgZoh^bfqlhT= k , ν= = 60 T (1 60 )c : f: T=
MijZ`g_gb_
Wlbiheygbq_fg_hlebqZxlkyb kms_kl\h\Zeb[u[_adZlmrdbK
MijZ`g_gb_ 1. >Zgh T = 10-7 c GZclbν. 2. >Zgh t = 8,3⋅10-7 c c = 3⋅108 fk GZclb S. 3. >Zgh λ f c = 3⋅108 fk
J_r_gb_ 1 1 ν = = −7 = 10 7 =p T 10 c Hl\_l ν = 107 =p
J_r_gb_ S = ct = 3⋅108 fk ⋅ 8,3⋅10-7 k f Hl\_l S = 249 f
J_r_gb_ c 3 ⋅ 108 fk ν= = = 5 ⋅ 105 =p 600 f λ GZclbν. Hl\_l ν = 5⋅105 =p 4. AgZy kdhjhklv jZkijhkljZg_gby kb]gZeZ k hgZ jZ\gZ kdhjhklb k\_lZ b \j_fy _]h jZkijhkljZg_gby t g_ljm^gh jZkkqblZlv ijhc^_ggh_ jZkklhygb_ S AZ \j_fy t kb]gZe ijhc^_l jZkklhygb_ S lm^Zb h[jZlghbke_^h\Zl_evgh S = ct/2. 5. G_la\mdh\u_\hegug_jZkijhkljZgy_lky\ \Zdmmf_
MijZ`g_gb_
1. 126 K ²Z_f 63 Li ²Z_f 40 20 Ca ²Z_f 2. 6, 3, 20.
54
6 Z_f jZa 1 Z_f 4. Z [ Z_f \ \ jZa ] ^ _ ` 5. 146 K → 146−+01O + −01 _ ⇒147 O =147 N ²Zahl 3. < n =
MijZ`g_gb_
14 4 17 1 7 N + 2 He → 8 O +1 H Bf__f
Ke_^h\Zl_evgh aZdhgkhojZg_gbyaZjy^Z\uihegy_lky
MijZ`g_gb_
1. < y^j_ ZlhfZ [_jbeeby 94 Be gmdehgh\ ² ijhlhgh\ ² g_cljhgh\²N = A + Z = 9 – 4 = 5. [ Np = Z \ Q \ we_f_glZjguo 2. 39 19 D Z Z we_dljbq_kdboaZjy^Zo ] Ne = Np ^ _ ` : a N = A–Z= ± b m Z_f 3. Qbkeh ijhlhgh\ khhl\_lkl\_ggh we_dljhgh\ \ Zlhf_ jZ\gh _]h ihjy^dh\hfm ghf_jm \ lZ[ebp_ F_g^_e__\Z ke_^h\Zl_evgh Z eblbc [ nlhj
MijZ`g_gb_
Wlb Zlhfu bf_xl h^bgZdh\u_ fZkku gh bo obfbq_kdb_ k\hckl\Z jZaebqguWlhh[tykgy_lkyl_fqlh m gbojZagu_aZjy^h\u_ qbkeZ ZagZqblb dhebq_kl\hwe_dljhgh\
MijZ`g_gb_
1.
238 234 4 92 U → 90Th + 2 He . 234 234 0 0 ~ 234 234 0 0~ 90Th → 91Pa + −1 e+ 0 ; 91Pa → 92 U + −1 e+ 0
2. j_amevlZl_^\moβjZkiZ^h\
Ke_^h\Zl_evgh \
MijZ`g_gb_
Ld gmdehgu bf_xl fZkkm lh f_`^m gbfb ^_ckl\mxl kbeu ]jZ\blZpbhggh]hijbly`_gby
55
AZ^Zqbij_^eZ]Z_fu_^eyih\lhj_gby b ijbqZkZonbabdb\ g_^_ex
U 1. >ey\_dlhjZ a bf__f Z [ Zy ± ± \ _Zy| = U ] | a | = (0,5 − 0,5) 2 + (2 − 5) 2 = 3. U >ey\_dlhjZ b bf__f Z [ by ± \ _by_ ] U | b | = (4 − 1) 2 + (4 − 0) 2 = 5. U >ey\_dlhjZ c bf__f Z [ cy ± \ _cy_ ] U | c | = (6 − 4) 2 − (1 − 1) 2 = 2. U >ey\_dlhjZ d bf__f Z ± [ dy ±± ± \ _dy_ ] U | d | = (3 − 6) 2 + (−4 − 0) 2 = 5 >ey\_dlhjZ e bf__f Z ± [ ey ±± ± \ U |ey_ ] | e | = (0,5 − 0,5) 2 + (−1 − (−4)) 2 = 3. U U 2. ax = 0, bx = | b | , cx = 0, dx = − | d | . 3. Z A (0;2), B ± [ sx = 12 – 0 = 12, sy ±± ± \ _sx| = 12, U |sy| = 5; ] | s | = (12 − 0) 2 + (−3 − 2) 2 = 13. →
4. y
B
sAB = ( 4 − ( −8)) + (3 − ( −2))
x
A 2
2
LZd dZd imlv g_ fh`_l ij_\ukblv
i_j_f_s_gby fh^mevdhlhjh]h_klvgZbf_gvr__jZkklhygb_f_`^m gZqZevghcb dhg_qghclhqdZfbimlb lhhgfh`_l[ulveb[hjZ\_g eb[h[hevr_i_j_f_s_gbyghgb \dh_fkemqZ_g_f_gvr__]h 5. Ijyfhebg_cguf jZ\ghf_jguf ^\b`_gb_f gZau\Z_lky lZdh_ ^\b`_gb_ ijb dhlhjhf aZ h^bgZdh\u_ ijhf_`mldb \j_f_gb l_eh kh\_jrZ_l h^bgZdh\u_ i_j_f_s_gby \^hev g_dhlhjhc hkb lZd dZd ^\b`_gb_ ijyfhebg_cgh_ Ihwlhfm sx = vxt ]^_ vx ² ihklhyggZy 56
\_ebqbgZ oZjZdl_jbamxsZy kdhjhklv i_j_f_s_gby Bkoh^y ba mjZ\g_gbyo = o0 + sxihemqbfx = x0 + vxt. 6. >Zgh J_r_gb_ vx fk x0 f x(t) = x0 + vxt ⇒ x(t) = 3 + 5t. GZclbx(t). Hl\_l x(t) = (3 + 5t f 7. xl xi Zgh J_r_gb_ xi = 260 – 10t < gZqZevgucfhf_glgZ[ex^_gby xl = –100 + 8t xi = 260 – 10 ⋅ 0 = 260; xl = –100 + 8 ⋅ 0 = –100. < fhf_gl\klj_qb xi = xl beb±t = –100 + 8t. Hlkx^ZgZoh^bffhf_gl\j_f_gb\klj_qb t = 20 c. x\ = 260 – 10 ⋅ 20 = –100 + 8 ⋅ f GZclb xi, Hl\_l xi = 260, xl = –100, t = 20 c, x\ f xl, t, x\. 8. Kh]eZkgh]jZnbdm iehl[uekims_ggb`_klhygdbgZf_ljh\ Ih]jZnbdmhij_^_ebfo0 = –10; vx fk fk o = –10 + 2t. 9. >Zgh J_r_gb_ t=2c v − v0 v v v t 4,5 fk ⋅ 2 k = ; t1 = 1 = 1 = = 3 c; a= v0 = 0 3 fk t t a v v fk at 2 vv 2 t 2 v 2 t (4,5 fk )2 ⋅ 2 k v1 fk = 6,75 f s= 1 = 1 2 = 1 = 2 2v 2 ⋅ 3 fk 2tv GZclbt1, s. Hl\_l: t1 = 3 c, s = 6,75 f. U U U U U U U U v +v at 2 U at t U 10. s = v0 t + = t v0 + = (v0 + (v0 + at )) = 0 t. 2 2 2 2 U U U U U U U U U (v − v 0 )t 2 v 0 + v a t 2 U v − v0 U U t; 11. s = v0 t + = ; a= ; s = v0 t + 2 2t 2 t U U U U U2 U2 (aU, sU) = v − v0 , v0 + v t = 1 ⋅ (vU, vU0 ) + vU2 − vU02 − (vU0 , vU) = v − v0 ⇒ 2 2 t 2 U2 U2 U v − v0 ⇒a= U . 2s
(
12. >Zgh tx = 0,3 k
)
J_r_gb_ 57
s f
s 0,43 f = ≈ 1,43 fk t 0,3 k 2s 2 s 2 ⋅ 0,43 f a = 2 ; v = at = ≈ 2,87 f/k. = t 0,3 k t GZclbvkj, v. Hl\_l vkj ≈ fkv ≈ fk 2 a t a t 2 3a t 2 13. so[ = o[ ; sFd = cd = o[ = 3sh[. ⇒ < jZaZ[hevr_ 2 2 2 vkd = acdt = 3ah[t = 3vh[. ⇒ < jZaZ[hevr_ 14. vkj =
>eykdhjhklgh]h ebnlZ
vx
>eyh[uqgh]h ebnlZ
0
t
15. >Zgh vx(t) = 10 + 0,5t
J_r_gb_ v0x = vx(0) = 10 + 0,5 ⋅ fk a fk2. K l_q_gb_f \j_f_gb fh^mev \_dlhjZ kdhjhklb Z\lhfh[bey\hajZklZ_l lZddZdZ!b v0>0). Hl\_l v0x fk
GZclbv0x.
16. Ihke_ m^ZjZ mkdhj_gb_ rZc[u gZijZ\e_gh ijhlb\ kdhjhklb Dh]^Z kdhjhklv h[jZsZ_lky \ gmev mkdhj_gb_ lh`_ klZgh\blky (5 − t ) fk 0 ≤ t ≤ 5; jZ\gufgmex | v x (t ) |= t > 5. 0 fk
vx
t
58
17. o = o0 + sx JZg__ [ueh ^hdZaZgh qlh ijb jZ\ghmkdhj_gghf ^\b`_gbbk mkdhj_gb_fZo b gZqZevghckdhjhklvx v0x i_j_f_s_gb_ a t a t jZ\gh sx = v0xt + x ihwlhfmo = o0+ v0xt + x . 2 2 18. >Zgh J_r_gb_ ax fk2 vx(t) = v0x + axt = 0,1t \ fk2). v0x = 0 a t2 0,1 ⋅ t 2 x(t) = x0 + v0xt + x = = 0,05t2. x0 = 0 2 2 GZclbvx(t), x(t). Hl\_l v0x fk 19. >Zgh J_r_gb_ |v\_ dfq |vf| = ||v\| – |v\|| ijb v\ ↑↑ vf beb |vf| = ||v\| + |v\|| Z |vhlg| = 0 ijb v\ ↑↓ vf. [ |vhlg_ dfq Z) v\ ↑↑ vf b v\ ↑↓ vf ⇒ |vf| = |40 df/q ± 0 df/q| = \ |vhlg_ dfq = 40 df/q. ] |vhlg_ dfq [) v\ ↑↑ vf ⇒ |vf| = |40 df/q – 10 df/q| = 30 df/q. v\ ↑↓ vf ⇒ |vf| = |40 df/q + 10 df/q| = 50 df/q. \ v\ ↑↑ vf ⇒ |vf_ _dfq ±dfq_ v\ ↑↓ vf ⇒ |vf_ _dfq dfq_ dfq ] v\ ↑↑ vf ⇒ |vf_ _dfq dfq_ dfq v\ ↑↓ vf ⇒ |vf_ _dfq ±dfq_ dfq GZclbvf. Hl\_l Z dfq [ dfq beb dfq \ bebdfq [ dfq bebdfq 20. KdhjhklvdZl_jZhlghkbl_evgh[_j_]Zihl_q_gbx vd = = vd + vl = 6vl a^_kvvd ²kdhjhklvdZl_jZhlghkbl_evgh\h^uvl — kdhjhklv l_q_gby \h^u hlghkbl_evgh [_j_]Z kdhjhklv dZl_jZ hlghkbl_evgh [_j_]Z ijhlb\ l_q_gby vd = vd – vl = 4vl LZdbf v 6 h[jZahf d + = = 1,5. vd − 4 m 3,87 ⋅ 10 −3 d] d]f3 Fu \b^bf qlh iehlghklv = V 3 ⋅ 10 −3 f 3 rZjbdZjZ\gZiehlghklb\ha^moZZke_^h\Zl_evgh\ulZedb\ZxsZy kbeZ ^_ckl\mxsZy gZ rZjbd jZ\gZ _]h kbe_ ly`_klb AgZqbl ih i_j\hfm aZdhgm GvxlhgZ rZjbd hklZg_lky \ khklhygbb ihdhy ld _]h hlimklbeb [_a gZqZevghc kdhjhklb bgZq_ [u hg jZ\ghf_jgh b ijyfhebg_cghi_j_f_sZeky 22. Kh]eZkghlj_lv_fmaZdhgmGvxlhgZkbeu^_ckl\mxsb_gZrZju jZ\guKh]eZkgh\lhjhfmaZdhgmGvxlhgZbomkdhj_gbyjZ\gu 21. ρ =
59
a m F F Hlkx^Z c = a < j_Zevguo nbabq_kdbo , ZZ = mc ma a a mc aZ^ZqZo dh]^Z fZkku rZjh\ g_ jZ\gu gmex fh^mev mkdhj_gby klZevgh]h rZjZ g_ fh`_l jZ\gylvky gmex Hg fh`_l [ulv dZd [hevr_ lZd b f_gvr_ fh^mey mkdhj_gby Zexfbgb_\h]h rZjZ qlh aZ\bkblebrvhlkhhlghr_gbyfZkkrZjh\ 23. Ba nhjfmeu ^ey g0 ihemqZ_f GM3 = g 0 R32 Ih^klZ\eyy \ Zk =
nhjfmem^eygihemqZ_f g =
g 0 R32 ( R3 + h) 2
.
v2 v2 1 1 1 ; a1 = = a1 ; L1 = ma1 ; L2 = ma 2 = ma1 = L 1 . r 2r 2 2 2 DZd mkdhj_gb_lZd b kbeZ^_ckl\mxsZy gZ \lhjhc rZjbd \ jZaZ f_gvr_ZgZeh]bqguo\_ebqbg^ey\lhjh]hrZjbdZ 25. GZ \ukhl_ h hlghkbl_evgh a_feb r = R3 + h; mapk = mg; 24. a1 =
g 0 R32 g 0 R32 v2 = ⇒ v = ( R3 + h) ( R3 + h) 2 R3 + h 26. >Zgh J_r_gb_
GZclbv. 27. vx = gt.
vx, fk
28. >Zgh l d]
t, c
J_r_gb_ ∆p = m∆v = mg∆t. 60
v0 = 0 Ld∆v1 = ∆v2 jZ\ghmkdhj_ggh_^\b`_gb_ lh t k ∆p1 = ∆p2 = ∆p d]⋅ fk2 ⋅ 1 c d]⋅fk ∆t = 1c GZclbv. Hl\_l ∆p1 = ∆p2 = ∆p d]⋅fk 29. Ld m ² ihklhyggZy \_ebqbgZ lh baf_g_gb_ bfimevkZ [m^_l hij_^_eylvky lhevdh baf_g_gb_f kdhjhklb Ih ]jZnbdm kf aZ^Zqm \b^ghqlh_keb∆t1 = ∆t2lhb ∆v1 = ∆v2bagZqbl∆p1 = ∆p2. 30. < mkeh\byo k\h[h^gh]h iZ^_gby kdhjhklb h[hbo rZjbdh\ \ ex[hc fhf_gl \j_f_gb [m^ml h^bgZdh\u b ke_^h\Zl_evgh hlghr_gb_ bo bfimevkh\ [m^_l aZ\bk_lv ebrv hl hlghr_gby bo fZkk LZd dZd ih mkeh\bx h[t_fu h^bgZdh\u hgh [m^_l jZ\gh ρ f 8,9 ⋅ 10 3 d]f 3 = ≈ 3,3. ρ Z 2,7 ⋅10 3 d]f 3 BlZd \ ex[hc fhf_gl \j_f_gb f_^guc rZjbd bf__l bfimevk ijbf_jgh\ jZaZ[hevr_q_fZexfbgb_\uc 31. ^hklhedgh\_gby X 1 2 hlghr_gbxiehlghkl_cf_^bb Zexfbgby
ihke_klhedgh\_gby 1
2
X
^hklhedgh\_gby 1
2
X
2
X
>Zgh v1x fk v2x fk v1′ x fk GZclbv. 32.
J_r_gb_ Ih aZdhgm khojZg_gby bfimevkZ gZ hkv O): mv1x + mv2 x = mv1′ x + mv′2 x ⇒ v ′2 x = v1x + v 2 x − v1′ x = fk fk ±fk fk Hl\_l v ′2 x fk
ihke_klhedgh\_gby 1
>Zgh v1x fk v2x ±fk v1′ x = –fk GZclbv.
J_r_gb_ Ih aZdhgm khojZg_gby bfimevkZ gZ hkv O): mv1x + mv2 x = mv1′ x + mv′2 x ⇒ v ′2 x = v1x + v 2 x − v1′ x = fk ±fk ± ±fk fk Hl\_l v ′2 x fk
33. E=
(
)
(
)
mv12x mv22x m 2 mv ′ 2 mv ′22x m + = ⋅ v1x + v 22x ; E ′ = 1x + = ⋅ v1′ x2 + v ′22x ; 2 2 2 2 2 2 61
v12x + v22x fk 2 + ±fk 2 = 0,05 f2k2; v1′x2 + v′22x ±fk 2 +
+ fk = 0,05 f k ⇒ v1x + v2 x = v1′ x + v′2 x ⇒ E = E′. 2
2
2
2
2
2
34. Ih ]jZnbdm hij_^_ey_f qlh L
2
k b ν =
1 1 =p = T 2c Ex[Zy^jm]ZylhqdZbaf_gy_lkdhjhklvk lhc`_kZfhcqZklhlhc 35. eykj_^gbolhq_dkljmg ^jm]bo Zjnhg l_f[he__g_]h^blkylZddZdhgbbf_xlbgu_qZklhludhe_[Zgbc ;ff
WfF
36. GZ^h ^\Z h^bgZdh\uo dZf_jlhgZ jZkiheh`blv gZ g_dhlhjhf jZkklhygbb ^jm] hl ^jm]Z lZd qlh[u bo j_ahgZlhjgu_ ysbdb [ueb h[jZs_gu ^jm] d ^jm]m ?keb l_i_jv m^Zjblv ih h^ghfm ba gbo b q_j_ag_dhlhjh_\j_fyaZ]emrblvijbdhkgm\rbkvjmdhcd g_fmlh fu mkeurbf a\md hl \lhjh]h dZf_jlhgZ < hkgh\_ ^Zggh]h hiulZ e_`bly\e_gb_a\mdh\h]hj_ahgZgkZ 37. Ihevamykv ]jZnbdhf hij_^_ey_f Z ijb =p Zfieblm^Z mklZgh\b\rboky dhe_[Zgbc [m^_l [hevr_ q_f ijb =p [ qlh[u Zfieblm^Z mklZgh\b\rboky dhe_[Zgbc [ueZ fZdkbfZevghc dZq_eb gZ^hih^lZedb\Zlvk qZklhlhc=p \ kh[kl\_ggZy qZklhlZ dZq_e_c jZ\gZqZklhl_\ugm`^Zxs_ckbeul_=p 38. >Zgh: J_r_gb_ l kf f mg 0,002 d] ⋅ 9,8 fk 2 = = m ] d] Fl = Ff; mg = BIl ⇒ I = Bl 4 ⋅10 −2 Le ⋅ 0,1 f B = 4 ⋅ 10-2 Le = 4,9 A. GZclbI. Hl\_l: I = 4,9 A. 39. < ^Zgghf kemqZ_ jhev p_gljhklj_fbl_evghc kbeu \uihegy_l kbeZ k dhlhjhc fZ]gblgh_ ihe_ ^_ckl\m_l ^\b`msbcky we_dljhg IhevamykvijZ\behfe_\hcjmdbhij_^_ey_fqlhwe_dljhg\e_l_e\ dZf_jm\ lhqd_<. 62
40. >Zgh v = 3 ⋅ 107 fk |_| = 1,6 ⋅ 10-19 De m = 9,1 ⋅ 10-31 d] B = 8,5 ⋅ 10-3 Le
J_r_gb_ Fpk = Ff;
mv 2 mv = B|_|v ⇒ r = = r B|e|
9,1 ⋅ 10 −31 d] ⋅ 3 ⋅10 7 fk
8,5 ⋅ 10 −3 Le ⋅ 1,6 ⋅10 -19 De GZclbr. Hl\_l r = 2 ⋅ 10-2 f 41. < j_amevlZl_βjZkiZ^Z 146 C → 147 N + -01 e . 42. 43.
=
27 1 24 4 13 Al+ 0 n → 11 N + 2 He . 10 7+ 4−10 7 4 5 Al+ 3+ 2−5 X → 3 N + 2 He
⇒
7 + 4−10 3+ 2−5 X
= 2 ⋅ 10-2 f
= 01 n ²g_cljhg
63
EZ[hjZlhjgu_jZ[hlu EZ[hjZlhjgZyjZ[hlZ
Bkke_^h\Zgb_jZ\ghmkdhj_ggh]h^\b`_gby[_agZqZevghckdhjhklb
at 2 a (3t1 ) at12 at 2 a (2t1 ) 22 32 s1 , s3 = 3 = s3 ,…, , s 2 = 2 == = = 2 2 2 2 2 2 2 at 2 a (nt1 )2 n 2 sn = n = s1 , = 2 2 2 lhfh`ghaZf_lblvke_^mxsmxaZdhghf_jghklv s1 : s2 : s3 : … : sn = 12 : 22 : 32 :…: n2 = 1 : 4 : 9 :…: n2. ?keb wlZ aZdhghf_jghklv \uihegy_lky ^ey baf_j_gguo \ jZ[hl_ fh^me_c \_dlhjh\ i_j_f_s_gbclh wlhb [m^_l ^hdZaZl_evkl\hf lh]h qlh ^\b`_gb_ [jmkdZ ih gZdehgghc iehkdhklb y\ey_lky jZ\ghmkdhj_gguf Ijbf_j\uiheg_gbyjZ[hlu. AZ^Zgb_ Bkke_^h\Zgb_ oZjZdl_jZ ^\b`_gby [jmkdZ ih gZdehgghc iehkdhklb 2
2
t, c
0
0,02
0,04
0,06
0,08
0,10
0,12
0,14
0,16
0,18
0,20
0,22
0,24
0,26
0,28
0,30
sff
0
1
3
7
15
24
36
50
65
82
102
126
146
170
198
227
s1 =
s 6 36 ff s s s 50 ff 65 ff 82 ff = = 36, 7 = = 50, 8 = = 65, 9 = =82, s1 1 ff s1 1 ff s1 1 ff s1 1 ff s 11 126 ff s10 102 ff s s 146 ff = = 102, = = 126, 12 = = 146, 13 = ff ff s1 1 ff 1 s 1 s1 s1 1
s s 170 ff 198 ff 227 ff = 170, 14 = = 198, 15 = = 227. 1 ff s1 1 ff s1 1 ff Hlkx^ZgZoh^bf s1 : s2 : s3 : s4 : s5 : s6 : s7 : s8 : s9 : s10 : s11 : s12 : s13 : s14 : s15 = = 1 : 3 : 7 : 15 : 24 : 36 : 50 : 65 : 82 : 102 : 126 : 146 : 170 : 198 : 227. WlZ aZdhghf_jghklv g_ hq_gv kbevgh hlebqZ_lky hl l_hj_lbq_kdhc aZdhghf_jghklb ^ey jZ\ghmkdhj_ggh]h ^\b`_gby LZdbf h[jZahf fh`gh kqblZlv qlh ^\b`_gb_ [jmkdZ ih gZdehgghc iehkdhklb y\ey_lkyjZ\ghmkdhj_gguf AZ^Zgb_ Hij_^_e_gb_mkdhj_gby^\b`_gby[jmkdZ 2s Mkdhj_gb_[m^_f\uqbkeylvihnhjfme_ a = 2 . t 2 ⋅ 0,102 f t10 = 0,2 c; s10 = 102 ff = 0,102 f; a1 = = 5,1 f/k2. 2 (0,2 k) 2 ⋅ 0,227 f t15 = 0,3 c; s15 = 227 ff = 0,227 f; a1 = ≈ 5,04 f/k2. (0,3 k)2 =
a1 + a 2 5,1 fk 2 + 5,04 fk 2 fk2. = 2 2 AZ^Zgb_ Hij_^_e_gb_ f]gh\_gghc kdhjhklb [jmkdZ \ jZagu_ fhf_glu \j_f_gb b ihkljh_gb_ ]jZnbdZ aZ\bkbfhklb f]gh\_gghc kdhjhklbv hl\j_f_gbt. AgZq_gb_f]gh\_gghckdhjhklb[m^_f\uqbkeylvihnhjfme_ v = at. t = 0,1 c; v fk2 ⋅ k fk t = 0,2 c; v fk2 ⋅ k fk t = 0,3 c; v fk2 ⋅ k fk =jZnbdaZ\bkbfhklbf]gh\_gghckdhjhklbv hl\j_f_gbt. akj =
65
v, fc
t, c
>hihegbl_evgh_ aZ^Zgb_ Ihkljh_gb_ ]jZnbdZ aZ\bkbfhklb dhhj^bgZlu x [jmkdZ hl \j_f_gb t. x0 = 0, t0 = 0, xi(ti) = si, i = 1,2,3,…,15. x, ff
\b`_gb_ rZjbdZ ih gZdehgghfm `_eh[m y\ey_lky jZ\ghmkdhj_gguf ?keb fu hlimklbf [_a gZqZevghc kdhjhklb rZjbd b baf_jbf ijhc^_ggh_ bf jZkklhygb_ s ^h klhedgh\_gby k pbebg^jhf b \j_fy t hl gZqZeZ ^\b`_gby ^h klhedgh\_gby lh fu 2s fh`_fjZkkqblZlv_]hmkdhj_gb_ihnhjfme_ a = 2 . t AgZymkdhj_gb_afufh`_fhij_^_eblvf]gh\_ggmxkdhjhklvv ih nhjfme_ v = at. Ijbf_j\uiheg_gbyjZ[hlu. Qbkeh m^Zjh\ f_ljhghfZ n 3
JZkklhygb_ sf
<j_fy ^\b`_gby t, c
0,9
1,5
t, c
Mkdhj_gb_
a=
2s t2
fk
0,8
2
F]gh\_ggZy kdhjhklv v = atfk 1,2
66
2 ⋅ 0,9 f
(1,5 k )2
fk2; v fk2 ⋅ k fk
EZ[hjZlhjgZyjZ[hlZ
Baf_j_gb_mkdhj_gbyk\h[h^gh]hiZ^_gby P_ev jZ[hlu baf_jblv mkdhj_gb_ k\h[h^gh]h iZ^_gby k ihfhsvxijb[hjZ^eybamq_gby^\b`_gbyl_e K\h[h^gh_ iZ^_gb_ l_eZ y\ey_lky jZ\ghmkdhj_gguf ^\b`_gb_f ?keb fu hlimklbf [_a gZqZevghc kdhjhklb dZdhcgb[m^v ]jma gZ mklZgh\d_hk\h[h`^Z_faZ`bf b baf_jbfijhc^_ggh_bfjZkklhygb_ s b \j_fy taZdhlhjh_ [ueh ijhc^_gh wlh jZkklhygb_ lh fu fh`_f 2s jZkkqblZlvmkdhj_gb_k\h[h^gh]hiZ^_gbyihnhjfme_ g = 2 . t Ijbf_j\uiheg_gbyjZ[hlu. <j_fy ^\b`_gbyt = nT, c 0,28
Imlvsff
Imlvsf
400
0,4
n = 14; t = 14 ⋅ 0,02 c = 0,28 c; gwdki =
2 ⋅ 0,4 f
(0,28 k )2
Mkdhj_gb_k\h[h^gh]h iZ^_gbyg = 2s/t2fk2
≈fk2.
∆g = |gwdki – gl_hj _ _fk2 ± fk2_ fk2. ∆g 0,4 fk 2 ⋅ 100% = ⋅100% ≈ 4,1 %. g 9,8 fk 2
EZ[hjZlhjgZyjZ[hlZ
Bkke_^h\Zgb_aZ\bkbfhklbi_jbh^Zb qZklhluk\h[h^guo dhe_[Zgbcgblygh]hfZylgbdZhl_]h^ebgu P_evjZ[hlu \uykgblvdZdaZ\bkyli_jbh^b qZklhlZk\h[h^guo dhe_[Zgbcgblygh]hfZylgbdZhl_]h^ebgu Ijbbaf_g_gbb^ebgugblygh]hfZylgbdZf_gy_lky_]hqZklhlZb i_jbh^ < ^Zgghc jZ[hl_ fu ^he`gu hij_^_eblv wlm aZ\bkbfhklv I_jbh^ b qZklhlm hij_^_ey_f ke_^mxsbf h[jZahf Hldehgbf rZjbdfZylgbdZhliheh`_gbyjZ\gh\_kbygZg_[hevrmxZfieblm^m b aZk_q_f \j_fy t \ l_q_gb_ dhlhjh]h fZylgbd kh\_jrbl N . dhe_[Zgbc Lh]^Z i_jbh^ b Zfieblm^m fh`gh ihkqblZlv ih nhjfmeZf
67
t 1 N , ν= = . N T t Baf_jyy i_jbh^ b qZklhlm ijb jZaguo agZq_gbyo ^ebgu fZylgbdZ ful_fkZfufihemqZ_faZ\bkbfhklvi_jbh^Zb qZklhluhl^ebgu Ijbf_j\uiheg_gbyjZ[hlu. T=
hiulZ Nba\_e
lkf N t, c T, c ν, =p
1
2
3
4
5
5 30 13 0,43 2,31
20 30 27 0,9 1,11
45 30 40 1,33 0,75
80 30 53 1,77 0,57
125 30 67 2,23 0,45
Ba ^Zgguo \ lZ[ebp_ fh`gh aZf_lblv lZdmx aZdhghf_jghklv q_f [hevr_ ^ebgZ fZylgbdZ l_f [hevr_ i_jbh^ b f_gvr_ qZklhlZ b gZh[hjhl >hihegbl_evgh_aZ^Zgb_. P_ev aZ^Zgby \uykgblv dZdZy fZl_fZlbq_kdZy aZ\bkbfhklv kms_kl\m_lf_`^m^ebghcfZylgbdZb i_jbh^hf_]hdhe_[Zgbc T2 ≈2 T1
T3 ≈3 T1
T4 ≈ 4 T1
T5 ≈5 T1
l2 =4 l1
l3 =9 l1
l4 = 16 l1
l 2 = 25 l1
Ba ^Zgguo \ lZ[ebp_ ohjhrh ijhkfZljb\Z_lky k\yav f_`^m i_jbh^hf dhe_[ZgbcfZylgbdZb _]h^ebghc b
Tk = T1
lk l1
]^_k fh`_lijbgbfZlv
EZ[hjZlhjgZyjZ[hlZ
Bamq_gb_y\e_gbywe_dljhfZ]gblghcbg^mdpbb P_evjZ[hlu bamqblvy\e_gb_we_dljhfZ]gblghcbg^mdpbb DZd ba\_klgh y\e_gb_ we_dljhfZ]gblghc bg^mdpbb aZdexqZ_lky \ \hagbdgh\_gbb we_dljbq_kdh]h lhdZ \ aZfdgmlhf ijh\h^gbd_ ijb baf_g_gbb fZ]gblgh]h ihlhdZ ijhgbau\Zxs_]h ho\Zq_ggmx ijh\h^gbdhfiehsZ^v Ijbf_j\uiheg_gbyjZ[hlu. 1. K[hjdZmklZgh\db jbkmq_[gbdZ 2. < i_j\hfhiul_bg^mdpbhgguclhd\hagbdZe\ dZlmrd_ \ kemqZ_ dh]^Z fZ]gbl ^\b]Zeky hlghkbl_evgh dZlmrdb Ijb lhjfh`_gbb fZ]gblZ kbeZ bg^mdpbhggh]h lhdZ j_adh \hajZklZeZ b iZ^ZeZ ^h gmeydh]^ZfZ]gblhklZgZ\eb\Zeky ihdhbeky 68
3. Baf_g_gb_ fZ]gblgh]h ihlhdZ y\ey_lky ijbqbghc \hagbdgh\_gby bg^mdpbhggh]hlhdZL_fZ]gblgucihlhdΦijhgbau\ZxsbcdZlmrdm f_gyeky\f_kl_k bg^mdpbhgguflhdhfl_\h\j_fy^\b`_gbyfZ]gblZ 4. Bg^mdpbhgguc lhd \hagbdZe \ dZlmrd_ ijb baf_g_gbb fZ]gblgh]hihlhdZijhgbau\Zxs_]hwlmdZlmrdm 5. Ijbijb[eb`_gbbfZ]gblZd dZlmrd_ fZ]gblguc ihlhd f_gyeky ld fZ]gblguc ihlhd aZ\bkbl hl fh^mey \_dlhjZ fZ]gblghc U bg^mdpbb B fh^mev wlh]h \_dlhjZ g_ ihklhyg_g ld fZ]gblgh_ ihe_ihklhyggh]hfZ]gblZg_h^ghjh^gh 6. GZijZ\e_gb_ bg^mdpbhggh]h lhdZ [m^_l jZaebqguf ijb ijb[eb`_gbbfZ]gblZd dZlmrd_b m^Ze_gbb_]hhlg__ 7. Q_f [hevr_ kdhjhklv ^\b`_gby fZ]gblZ hlghkbl_evgh dZlmrdb l_f [hevr_ fZ]gblguc ihlhd Φ Z ke_^h\Zl_evgh b agZq_gb_ bg^mdpbhggh]hlhdZ 8. K[hjdZmklZgh\db jbkmq_[gbdZ 9. Bg^mdpbhgguclhd\hagbdZ_l\ kemqZyoZ b \ 10. FZ]gblgucihlhdf_gy_lky\ kemqZyoZ b \ 11.
EZ[hjZlhjgZyjZ[hlZ
Bamq_gb_^_e_gbyy^_jmjZgZihnhlh]jZnbyflj_dh\ P_ev jZ[hlu m[_^blvky \ kijZ\_^eb\hklb aZdhgZ khojZg_gby bfimevkZgZijbf_j_^_e_gbyy^_jmjZgZ Ijbf_j\uiheg_gbyjZ[hlu. AZ^Zgb_Y^jhmjZgZijbaZo\Zl_g_cljhgZjZa^_ey_lkyijbf_jghgZ ^\_jZ\gu_qZklbdhlhju_gZau\ZxlkyhkdhedZfb^_e_gbyIjbwlhf hkdhedb jZae_lZxlky \ ijhlb\hiheh`gu_ klhjhgu Wlh fh`gh h[tykgblv gZ hkgh\_ aZdhgZ khojZg_gby bfimevkZ Bfimevk y^jZ mjZgZ ^h aZo\ZlZ g_cljhgZ ijZdlbq_kdb jZ\_g gmex Ijb aZo\Zl_ g_cljhgZy^jhihemqZyhlg_]hg_dhlhjucbfimevkjZkdZeu\Z_lkygZ ^\_ jZae_lZxsboky qZklb fZkkZfb m1 b m2 ?keb aZibkZlv aZdhg U U khojZg_gby bfimevkZ 0 = m1v1′ + m2 v ′2 lh kjZam \b^gh qlh kdhjhklb h[jZah\Z\rbokyhkdhedh\ijhlb\hiheh`ghgZijZ\e_gu^jm]^jm]mb ke_^h\Zl_evghqZklbpujZae_lZxlky\ ijhlb\hiheh`gu_klhjhgu AZ^Zgb_ . 92 U + 0 n → 56 Ba + Z X + 2 0 n < kbem aZdhgZ khojZg_gby aZjy^ZaZibr_f Z + 2 ⋅ Hlkx^ZihemqZ_fZ Ih lZ[ebp_>BF_g^_e__\Zhij_^_ey_fqlhwlhy^jhdjbilhgZ
69
EZ[hjZlhjgZyjZ[hlZ
Bamq_gb_lj_dh\aZjy`_gguoqZklbpih ]hlh\ufnhlh]jZnbyf P_evjZ[hlu h[tykgbloZjZdl_j^\b`_gbyaZjy`_gguoqZklbp Ijbf_j\uiheg_gbyjZ[hlu. AZ^Zgb_ Lj_db qZklbp ^\b`msboky \ fZ]gblghf ihe_ bah[jZ`_gugZjbkmq_[gbdZldgZwlbonhlh]jZnbyobo ljZ_dlhjbbdjb\hebg_cgu AZ^Zgb_ Z αqZklbpu ^\b]Zebkv ke_\Z gZijZ\h [ H^bgZdh\Zy ^ebgZ lj_dh\ αqZklbp ]h\hjbl h lhf qlh hgb bf_eb h^bgZdh\mx wg_j]bx \ LhesbgZ lj_dZ mlhesZ_lky aZ kq_l lh]h qlh mf_gvrZeZkvkdhjhklvbaaZklhedgh\_gbck qZklbpZfbkj_^u AZ^Zgb_ Z JZ^bmk djb\bagu f_gyeky aZ kq_l lh]h qlh mf_gvrZeZkv kdhjhklv baaZ klhedgh\_gbc k fhe_dmeZfb \h^u [ QZklbpu ^\b]Zebkv kijZ\Z gZe_\h baaZ lh]h qlh lhesbgZ lj_dh\ kijZ\ZgZe_\hm\_ebqb\Z_lky AZ^Zgb_ Z We_dljhg ihklhyggh l_jye k\hx kdhjhklv aZ kq_l khm^Zj_gbc k qZklbpZfb kj_^u b ihwlhfm lj_d bf__l nhjfm kibjZeb[ We_dljhg^\b]Zeky\ gZijZ\e_gbbk]ms_gbykibjZebih mdZaZgghc \ur_ ijbqbg_ \ Lj_d gZ jbk ^ebgg__ ihlhfm qlh hg\ f_gvr_ckl_i_gb\aZbfh^_ckl\m_lk kj_^hc
70
