Mais conteúdo relacionado гдз. физика 9кл перышкин гутник_20012. 2
Kh^_j`Zgb_
hijhku ............................... 7
§1....................................... 7
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§27..................................... 16
3. 3
§28..................................... 17
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4. 4
§58..................................... 31
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§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 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 .
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 = ²^eyijh_dpbbi_j_f_s_gby
2
2
at
s = —
^eyfh^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. DZdjy^ihke_^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 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§ 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 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 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 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
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 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_gvrZlv^ebgmfZylgbdZ
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_
^ebg 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
Zfieblm^u mklZghbrboky ugm`^_gguo dhe_[Zgbc ijb
khiZ^_gbbqZklhlukh[kl_gguodhe_[Zgbckbkl_fuk qZklhlhc
ugm`^Zxs_ckbeu
3. ldbo^ebguZke_^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_^u kh_jrZxlky ^hev gZijZe_gby jZkijhkljZg_gby heg
gZijbf_jamdhu_heguIhi_j_qgu_hegu²wlhlZdb_heguijb
dhlhjuo dhe_[Zgby qZklbp kj_^u kh_jrZxlky i_ji_g^bdmeyjgh
gZijZe_gbxjZkijhkljZg_gbyheggZijbf_jhegugZih_joghklb
h^u
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]_
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 Zfieblm^u 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_ebqbguZfieblm^udhe_[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_j^uol_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_dmg^ihke_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
^ebgm hegu ijb[ebabl_evgh jZgmx kf =jhfdh]hhjbl_eb
mklZghbfgZjZkklhygbbf hlfbdjhnhgZ?kebl_i_jvdZ`^uc
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_ Zfieblm^u ?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`^ucbagboih^dexqZeky hl^_evghklbWlh]hhjblh lhfqlh
hegukdeZ^uZykvmkbebZxl^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 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 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
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 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 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 ^ey 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^ ^eblky 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 h^u 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 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 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
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
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 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_ b^u 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
^eyαbaemq_gbyjZ_g^eyβ- 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_ b^u
baemq_gbc uauZxl jZaebqgu_ [bheh]bq_kdb_ wnn_dlu
WdbZe_glgZy ^haZ baemq_gby H uqbkey_lky dZd ijhba_^_gb_
ih]ehs_gghc ^hau D gZ dhwnnbpb_gl dZq_klZ D: H = DK ?_
_^bgbp_cbaf_j_gbyyey_lkyab_jlA 106. 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 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_
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_
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 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
.
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 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[ 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 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_] 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.
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 193. Q we_f_glZjguo
we_dljbq_kdboaZjy^Zo 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
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 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 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 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 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 ^ey g0 ihemqZ_f GM3 = 2
30Rg Ih^klZeyy
nhjfmem^eygihemqZ_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_ebqbg^eylhjh]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_^u^ms_caZ^Zq_
≈
⋅+⋅
⋅⋅
=
+
==
f103,6f106,4
f 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 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 ′+′⋅=
′
+
′
=′ ;
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 [ 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_.