Фізика, збірник задач

15.20. Ih h[fhlp• lhjh€^Z [_a hk_j^y sh fZ} N = 1500 \bld•\ ijhoh^blv

kljmf kbehx 1 : Ah\g•rg•c ^•Zf_lj lhjh€^Z d1 \gmlj•rg•c d2 f AgZclb fZ]g•lgm •g^mdp•x < ihey gZ hk• lhjh€^Z fLe

15.22. Khe_gh€^ ^h\`bghx • f fZ} N = 2000 \bld•\ Hi•j h[fhldb

ijhl•dZ} kljmf kbehx 1 : <bldb s•evgh ijbey]Zxlv h^bg ^h h^gh]h >•Zf_lj khe_gh€^Z d<<• ^_ • – ch]h ^h\`bgZ. <bagZqblb

fZ]g•lgm •g^mdp•x < ihey \ p_glj• khe_gh€^Z fdLe

KBE: :FI?J: KBE: EHJ?GP:

Hkgh\g• nhjfmeb

KbeZ :fi_jZ – kbeZ a ydhx fZ]g•lg_ ihe_ •g^mdp•y ydh]h B ,

^•} gZ _e_f_gl ijh\•^gbdZ d ih ydhfm l_q_ kljmf 1

H[_jlZevgbc fhf_gl iZjb kbe yd• ^•xlv gZ jZfdm a• kljmfhf \ h^ghj•^ghfm fZ]g•lghfm ihe•

M = PmB sin

71

gh]h \ h^gZdh\bo gZijyfdZo ijhl•dZxlv kljmfb kbeZfb 11 = 20 : •

16.3.Ih ljvho iZjZe_evgbo ijyfhe•g•cgbo ijh\•^gbdZo sh jhaf•s_g• gZ h^gZdh\•c \•^klZg• G f h^bg \•^ h^gh]h l_qmlv h^gZdh\•

kljmfb kbehx 1 : M ^\ho ijh\•^gbdZo gZijyfdb kljmf•\ a[•]Zxlvky AgZclb kbem F sh ^•} gZ \•^j•ahd aZ\^h\`db • f

dh`gh]h ijh\•^gbdZ (F1 = F2 fG )3 ≈ fG

16.4. < h^g•c iehsbg• a g_kd•gq_ggh ^h\]bf ijyfhe•g•cgbf ijh\•^gb-

12 : >h\r• klhjhgb jZfdb iZjZe_evg• ^h ijyfh]h ijh\•^gbdZ ijbqhfm [eb`qZ agZoh^blvky \•^ gvh]h gZ \•^klZg• Z1 f, Z

gZijyf kljmfm \ g•c a[•]Z}lvky •a gZijyfhf kljmfm 11 <bagZqblb

72

kbeb \aZ}fh^•€ ijyfhe•g•cgh]h kljmfm a dh`ghx klhjhghx jZfdb

(F1 fdG )2 = F4 ≈ fdG )3 fdG

16.5.D\Z^jZlgZ ^jhlygZ jZfdZ jhaf•s_gZ \ h^g•c iehsbg• a ^h\]bf

ijyfhe•g•cgbf ijh\•^gbdhf lZd sh ^\• €€ klhjhgb iZjZe_evg• ^h ijh\•^gbdZ Ih jZfp• • ijh\•^gbdm ijhl•dZxlv h^gZdh\• kljmfb kbehx 1 : GZc[eb`qZ ^h ijh\•^gbdZ klhjhgZ jZfdb jhaf•- s_gZ gZ \•^klZg• sh ^hj•\gx} klhjhg• jZfdb <bagZqblb kbem F, sh ^•} gZ jZfdm fdG

Gf <bagZqblb kbem F ydZ ^•} gZ kljb`_gv a [hdm fZ]g•lgh]h

ihey sh kl\hjx}lvky kljmfhf m ijh\•^gbdm fdG

16.7. < h^ghj•^ghfm fZ]g•lghfm ihe• a •g^mdp•}x < fLe m ieh-

sbg• sh i_ji_g^bdmeyjgZ ^h e•g•c •g^mdp•€ jhaf•s_gbc ^j•l m \b]ey^• lhgdh]h i•\d•evpy ^h\`bghx • f ih ydhfm l_q_ kljmf kbehx 1 : AgZclb j_amevlmxqm kbem F sh ^•} gZ

i•\d•evp_ fG

i_ji_g^bdmeyjg• ^h e•g•c •g^mdp•€ ihey Z ghjfZev ^h iehsbgb jZfdb ml\hjx} a gZijyfdhf fZ]g•lgh]h ihey dml . = 300 Ih jZfp•

ijhl•dZ} kljmf 1 : <bagZqblb fhf_gl kbeb F sh ^•} gZ jZfdm fG f

16.9.?e_dljhg ihqZldh\Z r\b^d•klv ydh]h ^hj•\gx} gmex ijhcrh\ \ h^ghj•^ghfm _e_dljbqghfm ihe• ijbkdhjx\Zevgm j•agbpx ih- l_gp•Ze•\ U < I•key pvh]h _e_dljhg \e•lZ} \ h^ghj•^g_

fZ]g•lg_ ihe_ a •g^mdp•}x < fLe \_dlhj ydh€ kijyfh\Zgbc i_ji_g^bdmeyjgh ^h \_dlhjZ gZijm`_ghkl• _e_dljbqgh]h ihey <bagZqblb jZ^•mk R dheZ ih ydhfm jmoZ}lvky _e_dljhg f

16.10.?e_dljhg a ihqZldh\hx r\b^d•klx v0 = 0 ijbkdhj_gbc j•agbp_x ihl_gp•Ze•\ U < jmoZ}lvky iZjZe_evgh ^h ijyfhe•g•cgh]h

73

ijh\•^gbdZ gZ \•^klZg• R ff \•^ gvh]h YdZ kbeZ [m^_ ^•ylb gZ _e_dljhg ydsh ih ijh\•^gbdm ihl_q_ kljmf 1 :? (2,7Â-16 G

16.11.?e_dljhg • ijhlhg sh ijbkdhj_g• h^gZdh\hx j•agbp_x ihl_g-

p•Ze•\ \e•lZxlv \ h^ghj•^g_ fZ]g•lg_ ihe_ i_ji_g^bdmeyjgh ^h e•g•c •g^mdp•€ M kd•evdb jZa•\ jZ^•mk Rj dheZ ih ydhfm jmoZlb-

f_lvky ijhlhg [•evrbc \•^ jZ^•mkZ Re dheZ yd_ hibkm} _e_dljhg"

jZaZ

16.12. .-qZklbgdZ a ihqZldh\hx r\b^d•klx v0 = 0 ijbkdhjx}lvky _e_d- ljbqgbf ihe_f Q_j_a qZk t k \hgZ \e•lZ} \ fZ]g•lg_ ihe_ a

•g^mdp•}x < fLe ydZ kijyfh\ZgZ i_ji_g^bdmeyjgh ^h \_dlhjZ gZijm`_ghkl• _e_dljbqgh]h ihey <bagZqblb m kd•evdb jZa•\ ghjfZevg_ ijbkdhj_ggy .-qZklbgdb m p_c fhf_gl [•evr_ \•^

€€ lZg]_gp•Zevgh]h ijbkdhj_ggy (8000)

16.13. Ijhlhg \e•lZ} i_ji_g^bdmeyjgh ^h e•g•c •g^mdp•€ h^ghj•^gh]h fZ]g•lgh]h ihey < fLe Kd•evdb h[_jl•\ ajh[blv ijhlhg \

< fLe jmoZ}lvky ih dhem jZ^•mkhf R kf AgZclb fhf_gl •fimevkm L ydbc fZ} _e_dljhg i•^ qZk jmom \ fZ]g•lghfm ihe•

(4Â-26 d]Âf2 k

16.15.Ijhlhg fhf_gl •fimevkm ydh]h L = 2Â-23 d]Âf2 k \e•lZ} \ h^ghj•^g_ fZ]g•lg_ ihe_ i_ji_g^bdmeyjgh ^h e•g•c •g^mdp•c ihey FZ]g•lgZ

•g^mdp•y ihey < fLe <bagZqblb d•g_lbqgm _g_j]•x ?d ijhlhgZ (1,99Â-18 >`

16.16.?e_dljhg sh fZ} ihqZldh\m r\b^d•klv v0 = 0, ijhcrh\rb

ijbkdhjxxqm j•agbpx ihl_gp•Ze•\ U < \e•lZ} \ h^ghj•^g_ fZ]g•lg_ ihe_ i•^ dmlhf . = 600 ^h e•g•c •g^mdp•€ ihey 1g^mdp•y

fZ]g•lgh]h ihey < fdLe <bagZqblb jZ^•mk R lZ djhd h ]\bglh\h€ e•g•€ ih yd•c jmoZlbf_lvky _e_dljhg f f

16.17. Ijhlhg jmoZ}lvky ih ]\bglh\•c e•g•€ a jZ^•mkhf R f • djhdhf h f \ h^ghj•^ghfm fZ]g•lghfm ihe• a •g^mdp•}x < Le. H[qbkeblb d•g_lbqgm _g_j]•x ?d ijhlhgZ (0,08 n>`

74

JH;HL: IJB I?J?F1S?GG1 IJH<1>GBD: 1 DHGLMJM A1 KLJMFHF M F:=G1LGHFM IHE1

Hkgh\g• nhjfmeb

FZ]g•lgbc ihl•d q_j_a ih\_jogx iehs_x S, hohie_gm iehkdbf dhglmjhf \ h^ghj•^ghfm fZ]g•lghfm ihe•

N = BS cos = Bn S, Bn = B cos

17.1.Ijh\•^gbd ^h\`bghx • f ih ydhfm ijhoh^blv kljmf kbehx 1 : j•\ghf•jgh jmoZ}lvky \ h^ghj•^ghfm fZ]g•lghfm ihe• a •g-

^mdp•}x < Le R\b^d•klv jmom ijh\•^gbdZ v f k • gZijyf-

e_gZ i_ji_g^bdmeyjgh ^h e•g•c •g^mdp•€ fZ]g•lgh]h ihey <bagZqblb jh[hlm : ijb i_j_f•s_gg• ijh\•^gbdZ aZ qZk W k. >`

17.2. >\Z ijyfhe•g•cg• ^h\]• iZjZe_evg• ijh\•^gbdb jhalZrh\Zg• gZ \•^klZg• d1 f h^bg \•^ h^gh]h Ih ijh\•^gbdZo \ h^ghfm

gZijyfdm l_qmlv kljmfb 11 : • 12 : Ydm jh[hlm : gZ h^bgbpx ^h\`bgb ijh\•^gbd•\ lj_[Z \bdhgZlb sh[ jhakmgmlb p• ijh\•^gbdb gZ \•^klZgv d2

17.3.Dheh\bc dhglmj jZ^•mkhf 5 f ih ydhfm ijhoh^blv kljmf kbehx 1 : ihf•s_gbc \ h^ghj•^g_ fZ]g•lg_ ihe_ a •g^mdp•}x

<fLe lZd sh iehsbgZ dhglmjm i_ji_g^bdmeyjgZ ^h gZijyfdm

e•g•c •g^mdp•€ ihey Ydm jh[hlm : lj_[Z \bdhgZlb sh[ ih\_jgmlb

75

dhglmj gZ dml 3 0 gZ\dheh hk• sh a[•]Z}lvky a ^•Zf_ljhf dhglmjm" f>`

17.4. D\Z^jZlgZ jZfdZ a ^h\`bghx klhjhgb Z f • kljmfhf kbehx

1: \•evgh i•^\•r_gZ \ h^ghj•^ghfm fZ]g•lghfm ihe• a •g^md-

p•}x < Le <bagZqblb jh[hlm : ydm lj_[Z \bdhgZlb sh[ ih\_jgmlb jZfdm gZ dml . = 1800 gZ\dheh hk• sh i_ji_g^bdmeyjgZ

^h gZijyfdm e•g•c •g^mdp•€ fZ]g•lgh]h ihey >`

17.5.IjyfhdmlgZ jZfdZ a• kljmfhf jhaf•s_gZ \ h^ghj•^ghfm fZ]g•l- ghfm ihe• iZjZe_evgh ^h e•g•c fZ]g•lgh€ •g^mdp•€. GZ jZfdm ^•} h[_jlZevgbc fhf_gl F G f <bagZqblb jh[hlm kbe ihey ijb ih\hjhl• jZfdb gZ dml . = 300. >`

17.6. IjyfhdmlgZ jZfdZ a• klhjhgZfb Z f • b f ih yd•c ijhl•dZ} kljmf kbehx 11 : jhaf•s_gZ \ h^g•c iehsbg• a g_kd•g- q_ggh ^h\]bf ijyfhe•g•cgbf ijh\•^gbdhf ih ydhfm l_q_ kljmf

kbehx 12 : >h\r• klhjhgb jZfdb iZjZe_evg• ^h ijh\•^gbdZ Z [eb`qZ klhjhgZ jZfdb jhalZrh\ZgZ \•^ gvh]h gZ \•^klZg• b0 f Z

gZijyf kljmfm \ g•c a[•]Z}lvky •a gZijyfhf kljmfm 12. AgZclb jh[hlm : ydm lj_[Z \bdhgZlb sh[ ih\_jgmlb jZfdm gZ dml 3 π gZ\dheh

^Zevgvh€ ^h\rh€ klhjhgb fd>`

76

?E?DLJHF:=G1LG: 1G>MDP1Y

Hkgh\g• nhjfmeb

AZdhg NZjZ^_y

h[f_`_gm dhglmjhf

?JK m ijh\•^gbdm ^h\`bghx • ydbc jmoZ}lvky \ h^ghj•^ghfm fZ]g•lghfm ihe• a• r\b^d•klx v εi = B υsin  ,

^_ Â – dml f•` \_dlhjZfb B i υ .?JK kZfh•g^mdp•€

εi = −L dIdt ,

^_ L – •g^mdlb\g•klv dhglmjm dI – r\b^d•klv af•gb kljmfm \ dhglmj• dt

18.1. Ijyfbc ijh\•^gbd ^h\`bghx • f jmoZxqbkv j•\ghijbkdhj_gh \

h^ghj•^ghfm fZ]g•lghfm ihe• a ihqZldh\hx r\b^d•klx v0 f k • ijbkdhj_ggyf D f k2 i_j_f•klb\ky gZ \•^klZgv G f FZ]g•lgZ

•g^mdp•y ihey < Le • gZijyfe_gZ i_ji_g^bdmeyjgh ^h r\b^dhkl•

jmom ijh\•^gbdZ <bagZqblb k_j_^gx ?JK •g^mdp•€ \ ijh\•^gbdm • fbll}\_ agZq_ggy ?JK •g^mdp•€ \ ijh\•^gbdm \ d•gp• i_j_f•s_ggy

< <

18.2. < h^ghj•^ghfm fZ]g•lghfm ihe• a •g^mdp•}x < Le j•\ghf•jgh a qZklhlhx n k-1 h[_jlZ}lvky jZfdZ ydZ fZ} N = 500 \bld•\ M fhf_gl qZkm t = 0 iehsbgZ jZfdb jhalZrh\ZgZ i_ji_g^bdmeyjgh

77

^h gZijyfdm fZ]g•lgh]h ihey AgZclb fbll}\_ agZq_ggy ?JK •g^mdp•€ ijb h[_jlZgg• jZfdb gZ dml Â

fZ]g•lghfm ihe• fZ]g•lgZ •g^mdp•y < ydh]h af•gx}lvky aZ aZdhghf

<<0Âcos ω t, ^_ <0 Le Z e•g•€ •g^mdp•€ ihey i_ji_g^bdmeyjg• ^h

hk• h[_jlZggy jZfdb M ihqZldh\bc fhf_gl iehsbgZ jZfdb i_ji_g-

^bdmeyjgZ ^h e•g•c •g^mdp•€ ihey H[qbkeblb fZdkbfZevg_ agZq_ggy ?JK •g^mdp•€ sh \bgbdZ} \ jZfp• f<

18.7. M iehsbg• sh i_ji_g^bdmeyjgZ ^h gZijyfdm fZ]g•lgh]h ihey a

•g^mdp•}x < fLe gZ\dheh lhqdb H j•\ghf•jgh h[_jlZ}lvky f_lZe_\bc kljb`_gv H: aZ\^h\`db • f Dmlh\Z r\b^d•klv h[_jlZggy kljb`gy ω jZ^ k AgZclb ?JK •g^mdp•€ ydZ \bgbdZ}

\ kljb`g• f•` lhqdZfb H • :. f<

18.8. D\Z^jZlgZ ^jhlygZ jZfdZ a ^h\`bghx klhjhgb D f \•^^Zey}lvky a• klZehx r\b^d•klx v f k \ gZijyfdm i_ji_g^bdmeyjghfm ^h

78

g_kd•gq_ggh ^h\]h]h ijyfh]h ijh\•^gbdZ ydbc e_`blv \ iehsbg• jZfdb • iZjZe_evgbc ^h ^\ho €€ ijhlbe_`gbo klhj•g Ih ijh\•^gb-

dm ijhoh^blv kljmf 1 : YdZ ?JK •g^mdm}lvky \ jZfp• \ fhf_gl qZkm dheb \•^klZgv \•^ ijh\•^gbdZ ^h [eb`qh€ klhjhgb jZfdb

18.10. :exf•g•}\_ d•evp_ ^•Zf_ljhf ' f jhaf•s_g_ \ h^ghj•^ghfm fZ]g•lghfm ihe• lZd sh ch]h iehsbgZ i_ji_g^bdmeyjgZ ^h \_dlhjZ

^jm]•c dhlmrp• aZ qZk t fk af_grm}lvky ^h gmey Ydh€ kbeb kljmf 11 ihl_q_ m p_c qZk m i_jr•c dhlmrp•" :

79

F:=G1LG? IHE? < J?QH<BG1 ?G?J=1Y F:=G1LGH=H IHEY

Hkgh\g• nhjfmeb

GZfZ]g•q_g•klv j_qh\bgb

^_ Pm – fZ]g•lgbc fhf_gl fhe_dmeb j_qh\bgb V – h[¶}f j_qh\bgb

A\¶yahd f•` gZfZ]g•q_g•klx J • gZijm`_g•klx fZ]g•lgh]h ihey

H \ j_qh\bg•

^_ χ – fZ]g•lgZ kijbcgyleb\•klv j_qh\bgb

A\¶yahd f•` fZ]g•lghx •g^mdp•}x B • gZijm`_g•klx fZ]g•lgh]h

ihey H \ j_qh\bg•

B = μμo H ,

^_ μ – fZ]g•lgZ ijhgbdg•klv j_qh\bgb

A\¶yahd fZ]g•lgh€ •g^mdp•€ ihey < • gZijm`_ghkl• fZ]g•lgh]h ihey G ^ey aZe•aZ aZ j_amevlZlZfb _dki_jbf_glZevgbo ^hke•^`_gv

< Le

1,4

1,2

1,0

0,8

0,6

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