1611143555-22ae02dc410aecb2fd3cbdc2740b0b9d (825017), страница 5

Просмтор этого файла доступен только зарегистрированным пользователям. Но у нас супер быстрая регистрация: достаточно только электронной почты!

Текст из файла (страница 5)

" + ) +  % # % "  ! /*) *M " %"# #" + # #" ,$ $ "$# $ $/ $2 "42 95 48 8:5 72% 5 877 2%7 6!:5 89( 6:2 42 45( *2 5 189( ;9 17 81 : *4 92 89 42 5 65 87 12 "917 8 4 8 7 5 "3 9 % 45 2%   1 17 ; 8 5%27 955 !6: "8! %7 " 67 6:7 18 897 23 952/ 5 8! 15 48 89 #%2 8:523 :2 4:55 85 52 :57 "92 % ;4527 (27% +523 8( 9 8182427 48; 2 927 "9 8! 5) 4: 7 :2 1452 89 72 897 4#2 6595 92 :92 5% ;9 8:95 5 .+8 5 89 53 4 .482  8;2 2%8 8( 5( 5 5 4 4 #7 87  2:,5.51:,7827 *5 457 "4 95% "4 49 57 ; ;5 + 45 5 + 6;6 "4 "4% %7 #2 953 482 ;57 15 #2% ;:57 +17 17% 8#9 45 "9(:57 ; # "7 4 7 :57 69 4 57 8 8 ( 87 48 8:: 8;2 : ! "! 84 " 2 8 4 :8+" 2( ;" ;6: 92 :2 687 645 53 45 +53 452 46 6:7 !5 45 :55 89( 89(4 2 : 482 82 ,8# 46:2 ,2 2 :5 :57 4523 4492 7 5 52""98 5 5 287 23 2 *89 :2 ;:57 422 ;:57 8( 97 4482 8#5 85( 485 897% 89%75$ 45 5$ 5$ 5$ 5 $2 $ 5$ $2 ;$ 4 S (& # "  ("% * "   #% ! # / % (  - "# )"" !#)  ( *  M , * " ' +  !%. + .

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mmv(t) = v0 e−kt/mαmgFkr0dv= −kv + mgdtmg −kt/m,+1−ek= −kvv0(8.6)v(t)r(t)(8.7);:57 8!57 :84 492 472 8 5+*.2 465:27$ 98,2 927 89 88 29(27 :545 841( :74822 12:( 62 2 15 4 87 462 18457 :2 9 ;2 ;5 ;:2 ::2 7255 8 "9 445) (  +3 5 : 5 %82 42 % 2 72 !8( 45% :28 5 6: ; ;52 "# 8( ( ,22 16:5 ;2 62 85 :( 85 1 48289( *5 5 6:2 823 8 18 8 )54 5 2 482 2  8;7 55 4"29 4% 1 8 4( ,:2 5) 4:2 ::9 88# 5 8;:72 "92 4822 :5 85% 4492442 6:5 8 4 7 4 5(3 8 88# 89(- "27 4 2 ; 6:254  52 9: :5 6:2 ; 6&' 8# "62 ;82 "14 " ;52( 85 :955 5;45 95 2 ; :9 :92 2142 :22 4;! 4; *5% (2 42 :23 (8" 4 8 ! 88 8 88 $% :5 2 42r0 = (0, 0)mUi, Vimi+1vx = U, vy = VdVdU= −kU , m= −kV − mg .dtdtτ = T /NUUi+1 − UiVi+1 − Vi= −kUi , m= −kVi − mg .ττ(8.8)NTiVdUUi+1 − Ui dVVi+1 − Vi≈,≈.dtτdtττ(8.9)2 8B 457 15 5 ) : ; 6:5 ,2 2 5 45% =& 72 7 4 *4 72 5' % 424, : 4 8 *8 8245(1" 595 27 % :5 ; 6:2 92 ; 5"% 8*952 :4" #72 " 57 49 442 , "4# 53 4492 8: 187 84 82 ,59:5 4 " ) 15 2( #7 5 4 .2 955 ;2 7 ;7 22 557 ;45 7 4( 8:5 ( ;:5 :55 8 "*  5 45  4575 9( ":93 7 5>& 4 4423"142 12 8;2 +47 8897 857 87 8678+92 445 12 27' 187 4:952 527 6:2 6:5 695 : 57 9957 5(;52 %7 95 8 42 2 8 8: ,2 :57 ; #2 2187 #2 :5 , 455 7 , .2 457 5 :55 57 ( 415 ": 5 72 :7 6 72 48 87 1455 84 8 ,89 8:2 1;52 17/ 427 ;8 1/ :57 ;8 5 9( 87 #7 17 "4272 95 5% "93 152 "44 65 8 15 6/ 4(;8 4( 189 4: *52 45 4 4: 27 12 5 ;# 5 14257 42 7 42 53 7 ( 445 :9 : :5 8 "915 2 8: 57 8 7 , 42 5 22 45(  ;573 5 $ 45 5% 7 5% :$2 48 2 $7 :5$" % $( gxyv0 = (v0 cos α, v0 sin α)v0Ui+1 = Ui −U0 = v0 cos αg, mk2".$,2;:5757846:2553 1 9  ;55 5341( 68 "4 *842 8 8: 27482 ,2 8 827 57 49 *45:9 44 4:- 41 "#7442 "8 65 2 18 3 :92 : #9 62 8; ;2 "82*248 8:5 8 88:5 :223 8 #57 9 5 4:7 8 657 7 41;54597 668992 57 92 :9 ;28 :5 ;57 ;5 6:5 8 :95 65 95%7758./ :44 47 8 85( 2"2 $ 4$ "y452 189 15 ( 49 :7 :2 "#  8 457 82 12 42,4822 853,:22 #9 6 45 1872 ,5,7 152 48 .5 ":92 "6:92 27 4;5 ,728;3"4 ;8 82 ,+ , 85 :9 ;5% #7 #( 9 .

2 1:2 86:5 #2 :9 + 452 2 8 "6:5 16: 442 7 #53 452 57 92!,845 7 8 82 ;5 8 42 8( 81855 + , : 92 2: #445% 45 % 4 4822 * 6:2 66:5 55 "4( 15 , ! 145595% ;87 :#5 2 457 M 772 8: ,85 ;5 15 62 187642 2 # 47 88 42 :2 286 5 57 4 / :  445$ 1$ $% " $2 "$ 5;:2 89( 72 48 242 "45 ;8 8 66"88& 42 :2 ; ;:578# ( 88PF66: :2J ;85: 5 42 2 ;87 6: 18 44 "2 ( 5(' 8!2::9 4( 489 8 495442 857 89 2 "282 #57 5 8#142 8" 465 "# 42%18 :9 12 "4 4 822;82 48# ,42 68:3 68$7 :5$ , *8$2x2iτkτkUi , Vi+1 = Vi − Vi − τ g .mmU (t) = dx/dtτk 1.m(8.10)V0 = v0 sin αV (t) = dy/dtx yN(8.11) :85( ;45 8:7< ;7 482% ; 8572 45 5 4:52 27 8%3 444/ 8 4 845 523 (2 557 8% 9527 87 ;5&"4# 75 , 7 44 ;57 453" 8:7 +8 ;57 4:2 55 :2 <<' 8:52 + " 89 ,% 82 6 49 :2 45(52 3M 6: 2 42 " % 2 4 7 57% 85 7 8 8 52 45:92 " /*42 872 ; ;:57 65 7482 2 ;55 65 " 4822 ,92 4527 2 452 #* 3 4 8(53 ;  4 5.

5 6: ;:41 +4 6:2 492 *2 8 84 48 7 48 44 * 8 922  :3+ 52$% ;5 12 488 4% ; 482 1:22( 2Fmmt0 = 0%J%.:KC?#%2:m1 = 1m2 = 22g = 105 4 67 :92 4 45 482 ;:57 57:;:57 857 :22 8;657 , 9 8 8: ;5 2,:8; ; :55% 42(3 87 1 ;:57 57 45482 6:5 ;%786 % 892 :557:5% 8 48 8244 89( 6:5 49255 87 6:5 ;56$ 57 !85$ :55%79536 ;57 7 6557 95:57 5 44 876:5 8:244 3 45 6: 8979 8:7 9252 < 482 553 4 5 :92; :5 7 25 9 8 8 486559752 7 9 ;54 5 :2 45779 2 2- ' ' ( %,( % "" & %. ,%' ) %%)%" 2"( /  O %J%.;KC?#%2.τ2%J%..KC?#%2187 8:3"19 482 - 6:57 49 ;5 8( ;72 ,85 5& :2( 6:9 4(4 87 452 '. : 8 +6 + 8 ;3 =' 8#( 9 "92"8#7 8 82 9573 27 4442 812 :2 .8# 47 66: ! 412 +1 745%*5 65 " ;57% # ,:2 5 ;57 #72 48 7 8B43 88 2 42 .2 8 4 #72 8:" 82# 42( ;75 + 2 7 45( 9 :5 55 82 :9 !8 8 6: " ":45 #72 2 + 2 ":2 2 2 86 2 "2 42 7 27 8 7 6:5 9 5 :"4 ' 8;8:7 8& 5 - 85 ( 81 .27 !:5 :55 .2 8: 6571/ #5 42 15 '& 45 ;8# ;27 9 85 6%, 5 ;5 53 8 ( 7 "3 #5 #) -&.72 6; 8#( 2 44 :55 52 6:2 ;4"7  85 2 >- 972 952 1 *452 ;6 1892 422 $2 645 55 87( ;849 --& + 462 957-;9 6;:5 482 8 41(8 1 4 652 > 853 :2 :57 6; : 87 5 8 482482 "53 57 8: -& 2 ,42 4 952 !8 81 #92 9 4592/ "$ " 4$22 >- :$7 882 "4# :$2 , 82/ 27 1$2 85Ui+1 = Ui −  , %m2 4PB:H::PI9FFx: ?:2 :5 9 ; 5 7 +;6 #2 8:2 5 : :95 ; 15 72 45 #FP:9@F@@ττ k Ui + Ui+1τ k Vi + Vi+1, Vi+1 = Vi −−τ g (8.12)m2m2i+1Ui+1 Vi+1F = βt= −kvβαm3 = 3F = 0.5;:575798*482!4:271 XF=(Fik + Fki)2iR6:226:5 889 :5845 97877 ;:52217855745 84822 412Fik .k6=ii,k; i6=kdP=Fdt pi = mivi;45%8442/2$%(;5 722!  2 iiimiv̇i =P=XFR=PMV = Ṙ ==ii mi r iXFi972 7492 8877, 4 287 178!42927 Fi =Xddti, M=miviiXV!mi ,XPpi ., P=MiX5X 48PF2! ! F@84sP@@'  ( $%"4 8P! FF &,;45%(2 818 4 5255745,48225*456:2682799827 &&''*!98 4:92 84: 8*482 7 ,2 85 7 9 : 7 41 8; 95 892 :52 38  :5#4 ,42 6: 8;5 6565 :53+ 4 2"1;5 9%2 " :97 42577 8;: .2(% 4482 6:2;:5  + 257 45 18 #7 "492 :7 : 27+ 9;2 1 :#% 577 :5 4: 889 ;:55 2 "9 ;5:2 7 ;5 :2 92 + % 42 :25 9$ 2 v272 795 88772245 1;:57 87574:2 ;47 52655:7 "4%#4 8+7 677 88877 4(2 " 9"+17 @8! 565 6:4" $8% 1%76 877 "!:4#5 ;52 *27 15v1  !( ! /i=11565$17 87 s8!2 ! 45 m`5 *2 87 3  "9" 2 : %7 *42 +9 1:2 .

2( 4 87 ( " 9( ;4 85 2%7 +877 89 2 6: 1$ i/Fi =XX4%&:268279)9"5:*4822978:81245892F=NX'4 8887 657:9 95(4 94 :2+2 8%;45(+45tτ = m/k= 0,mivi = const .(9.1),,(9.2a)(9.3a)(9.3b)PS 45458 7495 .927"26 4452:22 6:442 857"2- 2: 7 887 9929;$2 87:!5 9274:2 6522 :7 4$2"#*:4492898*482r1R=r = r1 − r2 .F12 = −F21 = F(r1 − r2) .m1r̈1 = F(r1 − r2) , m2r̈2 = −F(r1 − r2)r2m1 r 1 + m2 r 2m1 + m2(9.4)mm ≈ m186 68: 4(: ; 92 "958 85 4/ + 442% :3 @P45 5( 7 B4I (" 8A8*9 1 6185 8:"482 9 957 F:+ 6# "!4:2 27 2 7 2 95 8 7 87 57 1877 ; %/ 52 : ;5 68: 9" 452 1%4:5 8!7"V.27 8;892 *8987 +482" 54 5%178!"68:792/445%5%765i mi%P28184(9.2b)% 45 87 s 4( 4# 6: 15 87 25: 7 7 5( 8;2 " 9 "! 45 557 8 5 m ;45 : 7 4:22 7 92 ,45:485 89 8( 8 44892 927 89 57%*842 482 87 82 <& 85 28;2 27 4 495 ( ;7 877 '&* % 5'+7; %29255+8845 8 2 " 65(17 874 97 462 1 48# 8 17 958! ;55 7257 8: + 5 ;2 ;7 8 +:"5 5) 67 :55 !; :8& #( 2244792 "8 9 :92 +7 ; 7;4 897 577:29 882:58(8*;; 8 42 ! 9 !*42 8:9"92 ,8 .+97 82 5 82 388 5( 45 65 5 (729;9J 95% 2 41 5% 7( F6#I5F 8 1;$ $2 7 2 1$ 6$7$ $FBI !4 5'2  (M =.5m27 ;57 68: :992 184 ,62 17 :53 ,6 7 982 4:2 *52 # + ;5 6 44 $( ;8 " 82 44 842 65 9( 8 ( :5 65 : 657 5 957 5% 4% 48 ( 5 : 5) 7 6 854 : 453 ;;5 6 ;5 462 53 5 87 95 8:245% 55 4! 5 2/ 4!2 8: 57 :5 92 462 "758: "7 62 488 457 6577 48 27 +45 42 :#5 8:2 :754( 4 48 5 48 45 86( ;55 462 52 :53 ;7 22:9 "97 8 45% 5  : 2 4 8% 8 1845% 42 45 "5 ;57 ;57 :2 8 5 +M4  6(78 89 65 8% :57 ;5 2 !2 #( :2 ,;84 9( + ;3 6: :5 8 42 " 5% 887 6 4 8/ 4 18 7 "9 ;7&8:7 6:9 17 57 952 7 7 8% ; 22 153< ' 95 84 7 8: 52 6:5 ; 657 55 ,92 "( 65 88 "8 ;8 4$ 8% +; ; :55 8( :58:879;$2:554578245:574852M V̇ = F)8#6:22244"#:94428&':(2+724:2 877217 78( 8!422 492 7 257 7(457& ;4<' 5%5;:57578*9482!R̈ = 0, mr̈ = F(r) .m=(9.5)m1 m2m1 + m2(9.6)m 2 m1R = R0 + VtmF(r)mvρm0gF 553 442  *23 8 49 54822 86  8565 7 4:2 85Q 554 849 6:2 65: "% 2 #5844 5 65 442 ;6:2 #5 "62 ;5(8149 4557 8:2 49 .2 844187 "4% 97 8;27 4( *5 8;72 ;45 62 :5527 :2 "%5 7 8(# :2 $ 9$ 5$Ximivi = const.:9 "4 8 7 17 2427 8 9 8! 81895 8 1:2 42 "7 42;1 4(2 55 7 5 ;5 ":% 8!2 *555 5 % 455 :8( 92 2 7 6:;45( :2 4:9 ;5 822 )7#5 8 422 :55% 8:4 *27 8;7 72482 ;:55 :557 68: 8 87 81 4 89(6 ;5 7 ( 57 8( 8!: ) 2%772 7 49 45 892 :9 " +4 $2v0vi0miFiv00 $FiFi =defdpi.dtm0i"2 G47178$%!"265(95+.26:5282%J%.9KC?#%8;%mi%' 5;; 656:5 5289 874565 27:92 94825 48 $6 +17 8717 !8! P:4I54 ) #( %+.R/2 *!!;55 8 95 ;5% :8 7 27 6 :4 4 82 7 584 :29" :7!4:2 45 :5 "9 ;55  8 2 :;8:7 82 :245 5 : ;7 :5:;2 ;: 87 : 93 8"45 7 6452;:2 !42 ;9 48(8:7& ;:5 :555 455<N' :55 9 :5% 45 ":2( 45%8 #5$ 45 45$RR/25998(7 27 :28 7 2 8, +2 "45 .2 9;55 553*:2.

84: 423 4822 82&5 68 "6 :53 4 "" ;# 5625 :*2 44 2 " ;:57 #2 44257 4; +72 !8 87 F:6:. 5I  PJ 4FI4 59 4" 8 8 8": #"9: @ 8 )4F" 8 #2 9 F7F > I:@ 8 "" F 7J FBF4 @ 4 : F 8: :>" P+@.F G9 @%J%.3KC?#%8:482 ;: 4652;:57 865 *8957 57 4588 44 53;:57 8: 4;:2482 49 446 ; 92/ 7"5: "67 % 2" 896 ( 67:!5 897 52727 8 ;652 57 ;:55:( 95 7;8 :$2 65$ (µivimivi + m0v0 = mivi0 + m0v00 ,i| v00 − v0 |mi = m0 0.| vi − vi |(10.1) 92818478"4688(1;8591;54("927 F:: "FlA12 =Z1FdldA = Fdl .2Fdl =Z12Fl dl .(11.1)!21Fdl =Z1mv22 mv12−= A12 .22!845:8:25)75545,48226512;;;9( :5 8:(952 452 49  4@ ; 5%84 55 @ ; 4;!87545:9: 8"8 484PH 52 :53@4 117" ;8 8! 4 (" 5 992 85 887 818 89 94 5536 .28 5$F(r)A12 =Zdll2F(r)dp2dp1= F12 = −= −F21,dtdt!" 2 72 8 1 87 899 9 272 17 7 42 45 42 < 57 5278 8:5 4 2 4 ;; 5 : 1482 84 48 95 : 145 4;42 ;4 ;5 1 89 :5 492 8787 :5 45 42 482 45: 7 84 27 87 ;45 89 7442 872 87 557 872 42 42 6:578 ;:5 482 5 8 455 58 8 57 87 1 4 5 456 9 2 72 87 45 65 57 9 17 5 4 52 95 985 8 17 7 87 48 2 :227 8 1455 22 :7 48229 42 4 1 < : 95;8%J%.0#=E?)D+@C#)#+.

Характеристики

Список файлов книги