Фізика, збірник задач

7.4.Pbkl_jgZ aZih\g_gZ ^\hfZ j•agbfb j•^bgZfb <bkhlZ gb`gvh€

g_\_ebdbc hl\•j <\Z`Zxqb h[b^\• j•^bgb •^_Zevgbfb • g_klbkdm-

\Zgbfb \bagZqblb ihqZldh\m r\b^d•klv \bl•dZggy j•^bgb a hl\hjm f k

7.5.M i_\gbc fhf_gl \bkhlZ j•\gy \h^b \ ihkm^bg• \•^ghkgh ^gZ

Kd•evdb qZkm t [m^_ \bl•dZlb a ]hjbahglZevgh jhaf•r_gh]h rijbpZ fZklbeh ]mklbgZ ydh]h ρ

31

j•\ghf•jgbf kljmf_g_f \eb\Z}lvky \h^Z Ijbieb\ \h^b klZgh\blv

4d] k <bagZqblb \bkhlm G j•\gy \h^b ydbc [m^_ i•^ljb-

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11 FHE?DMEYJG: N1ABD: 1 L?JFH>BG:F1D:

J1<GYGGY KL:GM 1>?:EVGH=H =:AM JHAIH>1E FHE?DME =:AM A: R<B>DHKLYFB

Hkgh\g• nhjfmeb

J•\gyggy klZgm •^_Zevgh]h ]Zam j•\gyggy DeZi_cjhgZ – F_g^_e}}\Z

S9 = Pμ 57 ,

^_ P – fZkZ ]Zam μ – ch]h fheyjgZ fZkZ S – lbkd ' – h[¶}f 7 – l_fi_jZlmjZ ]Zam 5 – mg•\_jkZevgZ ]Zah\Z klZeZ

AZdhg ;hcey – FZj•hllZ

(7 = FRQVW , P = FRQVW )

S 9 = S 9 .

AZdhg =_c – ExkkZdZ

( S = FRQVW , P = FRQVW )

9 = 7 .

9 7

AZdhg RZjey

(9 = FRQVW , P = FRQVW )

S = 7 .

S 7

H[¶}^gZgbc ]Zah\bc aZdhg

( P = FRQVW )

p1V1 = p2V2 . T1 T2

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AZdhg >ZevlhgZ ^ey lbkdm kmf•r• •^_Zevgbo ]Za•\

S = S + S + + SQ ,

^_ S – lbkd kmf•r• ]Za•\ 5L – iZjp•Zevgbc lbkd •-€ dhfihg_glb kmf•r•

AZe_`g•klv lbkdm ]Zam \•^ dhgp_gljZp•€ fhe_dme • l_fi_jZlmjb

S = QN7 ,

^_ N – klZeZ ;hevpfZgZ

FheyjgZ fZkZ kmf•r• ]Za•\

μ= P + P + + PN ,

ν+ν + +νN

dhfihg_glb kmf•r• N – d•evd•klv dhfihg_gl kmf•r•

K_j_^gy d\Z^jZlbqgZ r\b^d•klv fhe_dme •^_Zevgh]h ]Zam

<υd\ >= 3RTμ ,

^_ 5 – mg•\_jkZevgZ ]Zah\Z klZeZ

Hkgh\g_ j•\gyggy fhe_dmeyjgh-d•g_lbqgh€ l_hj•€ •^_Zevgh]h ]Zam p = 31 ρ < υd\ >2 ,

^_ ρ – ]mklbgZ ]Zam

GZc•fh\•jg•rZ r\b^d•klv fhe_dme ]Zam

υ•f = 2RTμ .

K_j_^gy Zjbnf_lbqgZ r\b^d•klv

<υ >= 8πμRT .

AZdhg jhaih^•em fhe_dme aZ r\b^dhklyfb aZdhg FZdk\_eeZ Z d•evd•klv fhe_dme yd• fZxlv r\b^d•klv \ f_`Zo \•^ υ ^h

υ+ Gυ

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K_j_^gy _g_j]•y l_ieh\h]h jmom fhe_dmeb

<Æ >= 2i kT ,

^_ L – d•evd•klv klmi_g•\ k\h[h^b \•evghkl• fhe_dmeb

<gmlj•rgy _g_j]•y •^_Zevgh]h ]Zam

U = ν 2i RT .

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8.5.Kmo_ Zlfhkn_jg_ ih\•ljy f•klblv dbkgx Zahlm •

Zj]hgm \•^ aZ]Zevgh€ ch]h fZkb QZkldZ •grbo ]Za•\ fZeZ AgZclb fheyjgm fZkm kmoh]h Zlfhkn_jgh]h ih\•ljy d] fhev

<bagZqblb fZkm m2 \m]e_dbkeh]h ]Zam \ kmf•r• ]

8.7.>\• ihkm^bgb a ih\•ljyf h[¶}fb ydbo ^hj•\gxxlv V1 = 0,25 10-3 f3 •

V2 = 0,4 10-3 f3, a¶}^gZg• \mavdhx ljm[dhx a djZgbdhf L_fi_jZlmjb \ h[ho ihkm^bgZo \•^ih\•^gh ^hj•\gxxlv T1 • L2 D • i•^ qZk ^hke•^m i•^ljbfmxlvky klZebfb Ydsh djZg aZdjblbc lbkdb ih-

dIZ

8.8.I•^ qZk gZ]j•\Zggy ^\hZlhfgh]h ]Zam \ aZiZyg•c Zfime• \•^ l_fi_-

36

v1 f k ^h v2 f k \ \•^ v1 f k ^h v2 f k?

(1,38 %; 2,90 %; 2,76 %)

8.13.M kd•evdb jZa•\ d•evd•klv fhe_dme •a r\b^dhklyfb \ •gl_j\Ze• <vd\> ” v1 ” <vd\> + dv f_grZ \•^ d•evdhkl• fhe_dme r\b^dhkl• ydbo e_`Zlv \ •gl_j\Ze• vi ” v2 ” vi + dv, ^_ vi – gZc•fh\•jg•rZ r\b^d•klv fhe_dme ijb l•c kZf•c l_fi_jZlmj• ]Zam" (1,1)

8.14.M kd•evdb jZa•\ d•evd•klv fhe_dme •a r\b^dhklyfb \ •gl_j\Ze• <v> ” v1 ” v> + dv f_grZ \•^ d•evdhkl• fhe_dme r\b^dhkl• ydbo e_`Zlv \ •gl_j\Ze• vi ” v2 ” vi + dv ^_ vi – gZc•fh\•jg•rZ r\b^d•klv fhe_dme ijb l•c kZf•c l_fi_jZlmj• ]Zam" (1,03)

8.15.M kd•evdb jZa•\ d•evd•klv fhe_dme •a r\b^dhklyfb \ •gl_j\Ze• <vd\> ” v1 ” <vd\> + dv f_grZ \•^ d•evdhkl• fhe_dme r\b^dhkl• ydbo e_`Zlv \ •gl_j\Ze• <v> ” v2 ” v> + dv? (1,06)

8.16.Ydbc \•^khlhd fhe_dme ]Zam fZ} r\b^dhkl• sh \•^j•agyxlvky \•^ gZc•fh\•jg•rh€ g_ [•evr_ g•` gZ 1 %? (1,66 %)

8.17.L_fi_jZlmjZ ih\•ljy klZeZ • ^hj•\gx} t = 21 0K GZ yd•c \bkhl• h lbkd j ih\•ljy ^hj•\gx} \•^ lbkdm j0 gZ j•\g• fhjy" f

8.18.L_fi_jZlmjZ ih\•ljy ih \k•c \bkhl• k\_j^eh\bgb klZeZ • ^hj•\gx}

M kd•evdb jZa•\ lbkd j ih- \•ljy gZ ^g• k\_j^eh\bgb [•evrbc \•^ lbkdm j0 gZ ih\_jog• A_fe•" (2,1)

9. I?JRBC A:DHG L?JFH>BG:F1DB L?IEH/FG1KLV 1>?:EVGH=H =:AM :>1:;:LGBC IJHP?K

Hkgh\g• nhjfmeb

I_jrbc aZdhg l_jfh^bgZf•db

4 = 8 + $ ,

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^_ Q – l_iehlZ ydZ gZ^ZgZ kbkl_f• U – af•gZ \gmlj•rgvh€ _g_j]•€ kbkl_fb A – jh[hlZ ydZ \bdhgZgZ kbkl_fhx ijhlb ah\g•rg•o kbe

Jh[hlZ jharbj_ggy ]Zam Z ^ey •ah[Zjgh]h ijhp_km

Iblhf• l_ieh}fghkl• ]Zam ijb klZehfm h[’}f• lZ ijb klZehfm lbkdm

A\’yahd f•` fheyjghx & • iblhfhx k l_ieh}fghklyfb ]Zam

C = μc.

J•\gyggy FZc}jZ

&S − &9 = 5

J•\gyggy ImZkkhgZ

S9 γ = FRQVW

^_ γ = &S = L + – ihdZagbd Z^•Z[Zlb

&9 L

7 A\’yahd f•` ihqZldh\bfb • d•gp_\bfb agZq_ggyfb iZjZf_lj•\ klZg•\ ]Zam ijb Z^•Z[Zlghfm ijhp_k•

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a[•evrb\ky ^h j2 dIZ <bagZqblb l_fi_jZlmjm L2 dbkgx i•key gZ]j•\Zggy • d•evd•klv l_iehlb Q ydZ gZ^ZgZ ]Zam D d>`

f3 f•klblvky dbk_gv ijb l_fi_jZlmj•

L1 D • lbkdm j1 FIZ GZ]j•\Zxqbkv i•^ khgyqgbfb ijh- f_gyfb dbk_gv hljbfm} Q >` l_iehlb <bagZqblb l_fi_jZ-

lmjm L2 • lbkd j2 dbkgx i•key gZ]j•\Zggy D FIZ

9.5.:ahl fZkhx P d] jharbjy}lvky •ahl_jf•qgh ijb l_fi_jZ-

lmj• L1 D ijbqhfm h[¶}f Zahlm a[•evrm}lvky \ n = 3 jZab <bagZqblb af•gm \gmlj•rgvh€ _g_j]•€ U ]Zam \bdhgZgm i•^ qZk

jharbj_ggy ]Zam jh[hlm : d•evd•klv l_iehlb Q sh hljbfZ\ ]Za

>` >`

9.6. >_ydbc ]Za fZkhx P d] agZoh^blvky ijb l_fi_jZlmj• L D •

lbkdm j1 FIZ <gZke•^hd •ahl_jf•qgh]h klbkdZggy lbkd ]Zam a[•evrb\ky \ n = 2 jZab Jh[hlZ ydZ \bdhgZgZ i•^ qZk klbkdZggy ]Zam : – d>` JhajZom\Zlb fheyjgm fZkm μ ]Zam • ihqZldh- \bc iblhfbc h[¶}f V1/m ]Zam d] fhev f3 d]

9.7. I_\gZ d•evd•klv Zahlm ijb lbkdm j1 dIZ aZih\gx\ZeZ h[¶}f V1 e Z ijb lbkdm j2 dIZ – h[¶}f V2 e I_j_o•^ \•^ i_jrh]h klZgm ^h ^jm]h]h \•^[m\Z\ky \ ^\Z _lZib kihqZldm •ahohjgh Z ihl•f •ah[Zjgh H[qbkeblb af•gm \gmlj•rgvh€ _g_j]•€ U ]Zam d•evd•klv l_iehlb Q, • jh[hlm : \bdhgZgm ]Zahf m pvhfm

ijhp_k• >` >` – >`

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klZehfm h[¶}f• ^h lbkdm j2 dIZ <bagZqblb af•gm \gmlj•r- gvh€ _g_j]•€ U ]Zam \bdhgZgm gbf jh[hlm : • d•evd•klv l_iehlb Q, ydm i_j_^Zeb ]Zam F>` F>` F>`

9.9.Dbk_gv fZkZ ydh]h P d] agZoh^blvky ijb l_fi_jZlmj•

LD <gZke•^hd •ahohjgh]h hoheh^`_ggy lbkd ]Zam af_grb\ky

\ n = 4 jZab Z ihl•f \gZke•^hd •ah[Zjgh]h jharbj_ggy l_fi_jZlmjZ

dbkgx ^hj•\gx\ZeZ ihqZldh\•c L1 <bagZqblb jh[hlm : ydm \bdhgZ\ ]Za • af•gm \gmlj•rgvh€ _g_j]•€ U ]Zam >`

9.10. H[¶}f ν fhev •^_Zevgh]h ]Zam sh agZoh^b\ky ijb l_fi_jZlmj• L1 D ijb •ahl_jf•qghfm jharbj_gg• a[•evrb\ky \ n = 5,0 jZa•\

Ihl•f i•key •ahohjgh]h gZ]j•\Zggy lbkd ]Zam ^hj•\gx\Z\ ihqZldh\hfm AZ \_kv ijhp_k ]Za hljbfZ\ d•evd•klv l_iehlb Q d>` <bagZqblb

γ = Kj KV ^ey pvh]h ]Zam (1,4)

9.11.fhev •^_Zevgh]h ]Zam f•klblvky \ pbe•g^j• ijb l_fi_jZlmj• L1 =

D =Za •ah[Zjgh gZ]j•\Zxlv ^h l_fi_jZlmjb L2 D ihl•f

i_j_\h^ylv m ihqZldh\bc klZg H[qbkeblb ydm jh[hlm : \bdhgZ\ ]Za aZ pbde >`

9.12.J•agbpy iblhfbo l_ieh}fghkl_c kj – kV ^_ydh]h ^\hZlhfgh]h ]Zam ^hj•\gx} 296,8 >` d] D <bagZqblb fheyjgm fZkm ]Zam • ch]h iblhf• l_ieh}fghkl• kj • kV. >` d] D >` d] D

9.13.FheyjgZ fZkZ ^_ydh]h ]Zam μ d] fhev <•^ghr_ggy fheyj-

gbo l_ieh}fghkl_c Kj KV = 1,4 AgZclb iblhf• l_ieh}fghkl• kj • kV pvh]h ]Zam >` d] D >` d] D

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