Meriam Kinematic Particles Dynamics 3

8/9/2019 Meriam Kinematic Particles Dynamics 3

1/22

4 S P E C I A L A P P L I C A T I O N S

4/1 !l'v1oxi"rnun7 dc/Y4nraye 0/ rh~ ~Q,.,th3rorar/or> I' "'Ch/'I/~d /or /Qu"ch ar r;'~t!!Y


2/22

4-/14Ir. =a(l-e)~R+H=6370+.s00z:6370k. ne:::O.7

Frt7'17 6.,.1/7 {"or~::: 7r/z ~::: I := IJ J r: Q fJ_eZ) (R+I{}(I+e):JO {"rom Et{-4/11)cr?~29R( I I-e )(1l+H){I+e) 2(R.+H)or crz:: gRZ I+e?:;: 9.8Z4(IO-~)(.~600r({'370r/-lO.7~

K+H I+e 6370+S"OO . 1+0.7= 65'1 (IO~) (k h)2.

er= 25 670 km/I,

4//5 I E9' f/g~with R '"6370 km, 9== 'I. .121 m/sa,T - 90(60) 3,

a~/z I90(60) = be 6370 Iq.8Z4(;0-~a3 :::2'14 (10) b"' J a.= i> &52 k'1.4/11, u.= Z f9.SZI)(IO-S;(.HOO)Z(('370j'/ ' --'-)(b70+. t . ro 2("nl

=: 808 (IO~) (krr/h)2-er::: 28 420 leh

4-/16 lFron-7 A.P,P" ..,y> ;,.8fo r- ;f-Ig "",,,00.72R .. . = /080 rn' I 3 z: So32. :ff/s~c.

50 FrY1C 7 E'l' 4-//2 ~-A/lax. vel' /s ?/p z: I< . IJ r;,V~ r: .r---:,---- ",,,"So V. =(/080)' /S.32 _1_/1260 =10404 .'/.p V SE~O 1200 1/40 . tnl/Sec..or z . . ; ; = /'0404(3600) = 3745 t??,/hr

4 / / g 1 1 1 far? A = ~ . F_~ ;; 4/7 r a.(I-e;)r: riJ I 7' , / .1 = /7'ec


3/22

4/70 I FOr ~'fuil. P.;5/!-/o""T f- rn q - ; r : . :0 (.) - - - - - - -.(1 )I ../ Z2;; z: rvl4y)' .,T;- ky r Yr>3 - ~ -ky :::my

Ce>r/J;;'c ...fl. (/) t .5el. r: ? : . ! ! . Y =0..)' rn

= .L; /?L.JOPo) = 3.90 Hx2T7 V : /0

J;-kyo -ZkJ =r.J = . = .L V /2r -J 2T1 2T7 r n

0"

4/7/ I Jvh~n .y= 0)/1 Y =.Y }

E=In!}2.,c = 2tn9 i- k ~F=rn;J,L-kX4-my -(rnJ t- k!):=rn,:;';/f-Ly=o4rYl

.,/:::. :::."'!-/k __I /kZrT 2TT V 4 rn - 4JT V;:n

..---,------------------------ ..- ---_ .._- - -4/73/~ I - ~ j ~! ] '- - (m!J ~8

8= C:;dc/~dbuoyancy c;/we 10 cleJ/ecr/ony bt=lolA/ etjw//. POSlitOY)8 = Vo!. )( den.$'fy 1 < '3

= 77d~?.'J = 7T(O.~2~ (I. 03X1(}) ('I. 81)4 4-= 2857y I\J

2 f = ; = - mQy; IrIJ-(rnfj ~8) = Y 7 1 J /.; f ~y =0!i'oo

P= - VZ8S7 = I K''i rod .:f = . . e _ I. ~9?00 . scC' 2TT - z - ; r - - = 0.30 Hz

4/74[ X ~ !rx = 0, . , . , ,But x : = - '; , 5';" pC UJh",..~So J _.l!. x : r;;CoSpt,. ,. , o /~ /

I~~I r;) J/~'" Ir .J=x = --X, . , . . ,p = v ; ; ; : . . ,J = jA:)-'/zx.o (;-,., 0

So q ,/ z fj; .: = - - - 2 c-o herc p z : :L ( ; ;.,/_ /W // eo =Zfli0,,-- er Y ;; '"

A = _ _ '_rn_4ft _w"Y>')

cc : Wc.,- tuh~,..,A -"> 00

per/De

_.----- .._--------


4/22

----------

4/80 1 D~;/~c"'/;;,n ~rS/>nhy /.1'1 eyQ;//6o'urnposH/on IS Fo l A - z: (ci:?)\YJ3/k

Add>i/;'no/ sprlYly .:I~.//~chOn /or d"uN7JoVCrCc:/!:/lecl"/cl7 Yo 0/ p/orforrn /. 5 ( . ..) 'YoL1~ :: ~ k [ { ( f ) 2 7T (f ;)l.y J 2 _ [ ( f ) 2 b 7 / 1 " ]

/ I~C ) 4 2= t'rI3Yc +-rr: -.yo 2 6 0 I ( _C)- ! - '"LJ'~ = - rn3 ';)0 .50 ..j V := Ll ~ +LJ ij' - = :2 k (b Y oI L J r t = - ~C?

50 /rna,,= 2.33,yo2pZThw5 t..-u;l'h ';;'1"):= ~~

, 2 1204/J=2,33 I 3bT~ = - e tuhere1 - 3.50 0.7S 3(1.2118)- - - - x : -= - e z: 47.{;6,3

b =... = 0,020 z: 3, f?6 l is",Un 2 (I ) /o z . Zt-J2)T:> I/f- = '/3 sec bJ= 3,'86/3) z - /,288x : . = 0.75 0.0157 In.3476(,------


5/22

x.=o.. .F = 2 ,.,tN.!" Z (1)(0012)(1600 ~)::: 853 No 0 pO4/8'sj = r:r ..v~- (r ..)Z8",t a t: ; . / .: t Xz , ;;= {= 0 SI"'.-c

Thw5 =v;-vz:ik(x.:!-X/}8wt" X /x; = c er

I z . ZfT/:.s: =.!...kx.l.(l_e-Zb7'-) .!.kX.2.(I_~ -n?J)2 , ~z / _",h~r~ J = / ! i :- . , .: ,~

Thus 3~o = - - - - -- - - =: 8. I:) In rY7/ _ .6327000~----,--------------------------------------------4/117 \au/YQ!eY7T .5,br';"'3 c"",,,,s7"aYlT k= P4:~ =4':;6./ 0.5 In

_ do where p2=k/rn" 4(1?J!!2,Z)=:S!5(r'''''tto - 1_ (eu/p)' ..3 .sccP z: vS7S = 22.7 rad/seccv = 2lT/2.) = /2--57 ra~h:,.~ k= ~ = 667 IV/mr- 0060.50

'-;/5'7 I M El, ""7j,j/"/~ damf;"7')(0:: I t I r 2 . = 1 < - 1 = ~..,., I < . ; N I . . . . , 1 / - (4)4)~1wh#lre.. "0. 030 "1S. = o. wO """"

AI := .2" I' '" 2>r(4) - = 8T' rad /5Fo,- )(o/S.:= ~ -c I, /-(w/p)% is "~'Jal/vt!rhus

/_ (8rr) 2- --2.--- - ,"'flJf

4/'10 Iror-c~ fr,,,,s"'ilfed;~ /ur I.,.be X::Xo si" wfWa.v~/ehJfh A'" t.rr" V ! J r So WO: 27T'


6/22

5/3 I S > { ~ r 1 k ' " 0/rv""55 - - G ;$'-~/"""y$, ;?->/q'u..-'v /;eru-~t!'>-7'60tJ ,/G i--- ---c : 5/,hc!y.:'"J So X-Compon~.,t0/ a cce r, 0/ J/,he,.1'5, /5 same as " 'G '

Fo r 7 Y -= ,Ic n -? 2F= n1a) GO = 2(3) a J- . 2Clx.= a = /0 n-1/S

S/t; I 0= L l ~ t- L 1 T.J L~f if = veloc ,ly oT c.enfer.5ph~re UPOH /;1'1/>,0&1. lv1/d.rk ...:fph~r~5 hu;/eve/ot:11,;; 01 Zr/2 up",,, ''".jJ>c-!..Jv : z:- 2 f" Y I o.l!.. - mJ Z b 0: - - Z Vz n-I9 bJ ..1;'2 VzL l T= -fmv'f z(}rn[Y]'l) = :';-Y]V' LThu5 0 = - zVi rnqo f ~mtf2.

v 7' -2/'2= 8J.Jb) -ir= 2 /Z ? y b

5/2 I The: /Jnrlc/~/e ""/ rh", -:;;~~ ~rr~.rnaJ.:J C~nkl'" ,3/Y(;$ F= rnQ .for I!'ac.h

c.a~c- .50 /he """"a~5 c~>7*r accQ/er;;/e>nSar~) /c/e" ~/C4'/. /n The fi:


7/22

I M o ! z:ov --------0,7 IV-m

5//31 LM = (~o = d1 - 1 0 fiM clt .: .dHo d t: ' J~ 0 "~t'"J ! 2 . m.-~' (!'~'G)= Lmt,,_2L1830:


8/22

Sjn I V~rl;cal thrust- : m'A'r, ~ 2(60+1)(600)= 73 200 '"= R r : f)(j f-Z)(~

13 '-1r .!y: f 7 = i:> YY1? = r f- rn 1- : ~So ZMo ::!! t-! q -

" 6/; ; T ~ ~ - ' ~ ; ~ / c - ' : " -: ; - ; , - ~ ~ ~ - ; ' - /rl/~--; ""'dSSCC'YJkr IS In //~4! 1 '< -- ; ; : ; , C F hlls rh' .5ql-rT~tA


9/22

~---.-------------------------------------;5/31 I tV=IOOO///SCCir '= nAr.f= ~ ~ /000----+- m. r: 32. Z /44I~ ~l,.--X :::2.0/.9 16-Jt-.!.5CCLJ Fl( ZF=nz.~f{ .~ X It v if i-F = 201. 'l(1000 -0) = - 2.02/0016 ~----~------------.---------------------------~5/371 --;;-'>+X 2:1{= rn'L1Z{

~

45 t -2.1-084 f- Tcos4So~~~~'/: T 14(006) =[306(600) -30(/20)](/0-1kAl -=O.84kIJ T=2s:0Io./A B C .

z r ; . = 0. .34.S-24 - 4('1.81) s/" ~ ""0Sin 0( = > O.2~.F" J M.'. I";. S3 .>S/3c) I~---. "'~;: 30/60 O.S J v ! J I sIr ; = 111 ~ trx. /F:O..s(IS/5.6-0)= 2.03 J c . N'; I,~F or m/A"" . R ::= 0.5 (12/5 -0) = 4.24 kN v' J ~ /

01 T=S,'l3 AI

.5/33 I 215 (ISO) = 1000 f! (0.030) o:"4-V= 56.4 ".,/s~'

= 22S0(13.2S) .: 29,foo JJm ,/

03S1

tJ"~IN'U. .Final Y'fdo,;,-tj of' di.lr-t.dw'a t..is . ! : ! " = E. ...!!'r.1

..,her. tTr.t = IT~'"".,':- ~A " Y - e . /= 1000 : (0.OZS)2(ZO+ 10):: 14. 73 kj/.s

; ! r : c :""'~~j r . : = /4.7.3 (10-[-20)). 44Z N-ZF" = m '.t1i>. ~/r.,J?1.' :.- ('Av

,!I=;;;rn.'Ll~ . -F ~ -04V[-(V_U)(I_c."'$~)1J D~ / 'Jp"U/~,... P = Ij;"" " = ~A v~ (V-UYI- cos &)d..P/dv " (lA (1-&OS~)(trZ_ 2",v) 0 for- ""''''x. pThv.$ ~"v/z 'P=;f pA v3(/_ coSI1)


10/22

)A-=-G 2.4 /b/fi'/'n'= /' Q '" bZ.4JC8.32,zn2:: /. 212. Ib-in.-'- 5~C.e c = 1.2. 9Z(8'O iz /8 CI?::>.30

-&'On2 [i4-(,15In30866 10

5/4/ I AC c: ~(o. It=: 0.00785 ,..., A.:: -lAc 0.03/4m'=/A.r . /,J.S(a.gJI4)(IS)

= '.36 Ic'j/s, . t c, '.36= /'217(o.0078S)~~ = , ~ " ,..Is~~8 CIOS'O . P__ .. 14 I<

IS4S--'b)m" :: .3/0 kgma.u q( . . , .f e , . " ', . . '; f' V = I(){)O[ (a2t(t.J

.:: I~e.s k9Q:: 0./25 ./sA'" !L(0.I)a::aoo7.fS"," A :.!r(o.2s)"=a04'7'4 J 4 . ","for=- a/A C0.125/0.00785= 192 "'/s~ :: QAo = 0.125/0.04"1I ::2. ss .s

R - (.:110+188.5)


11/22

5/4GI o: =: ..fL: o..os = = 4- ,.,/sI A, 0.012Su: ~ . . R . . _ 0.05 = 12.5' m/s

Z A " - z(o..OOZ}'" ':;;;.0.(15(103") = = SI.5 ",/s1i H ttT:t

" . , 1 I i E{ =m'.tI-:et..,44" ,S4cI;_s I ,2,L~'::I>7I'A~i m9=~rrr'tJ'(tr-0}

cr .L~r K~

.5/";;0 I ,~~8t) '"160tf.!/)~= 1570N

From ..stlll~/e.; ' 0 6 , , / . 5 "F= I'A (tr-u)'(!+CC$ 30")'"/OOO! ro..I5)'(/,6b)(1S0-u)'= 33.0 1180 _ u}7. N

EF =: mU.i 33.0(/80-u}% -IS70:= 1600 U

fu tor du = [ dt in t~1rate f 'Jet.o.OZ06(18o.-u)z-O.9!1 o JI /" 01422 (11'0-,,)+0.931/"_fd t :=-4

2.,10.0206[0.931) O.142Z(I.fO-U}-O.98f 0- "3.~'Z t;, /- o.ooS.35'u x: 4 I-O.oOS~u:= :!./Iq

1- 0o.Q578u ] 1-000578"u=

" 6 " 4.34 /s~" 210 ,.,,/5

c",,.t: VR '" ~ (nt!:J1"'};~/e r,.;CI;M), fi~ " = .3IS- 210.2: =: 133.4 ""/.5

IA"';./= 434 cDs.27--133.4- 253 m/s

I~IJ I.I'~ - 15 (.2.5'.3)-3100 N

Th~or. pow~" P < = ' F " a r: '((,.If}(;()~}A ~6.1)=1.340A{to' wAct ,./ powu-,. ,22/IO~) =: 0.90(0.85), A =0.0.215 '"&The"r. r=r ": /.340 A(109)7h~ rrd/4 =0.02/5', d= 0.1653 '" = 165.3 ~"."u= ~w, J)= 2u = ,2 (.: ", t) =.2_ SS tn /

. W 27o(2n/60}


12/22

2.50 = .300 a - 20 (2.4- cos 60)

a = 25"0 +24300a:::t 09/.3 ,..h2.

R~/Clt/~e //eloc';,y 0/


13/22

4/Z2 / I Ab sa/a t orhital vele ct'I'f'" ~370 /;.824){I03)

\ 6370+ 800I or- "., E 9. 4/11) Qt perig~~ P

~-R-- ~_Jp V'&~ 2('.8U.)(.s600)2(6370t~ _ I )I I 10' [ ino+ /$o Z(7I9S}

" IT= 29 +40 km/" = B.fa J


14/22

( LeSS f;..,o.-, Ra=o 0.1 P".,6 ~-;i5"'-' I'l-l, .l e


15/22

~S/6'11Eh/-i,., s1JI-,,,, /0$ c""JVlrvAf;ve Jo A~ sr--J'~xf -tr->' It 0) if"'./$X, a> ir;: 9/.1-For ell f;,.~s!lsi-,,,,Z~ : G)C,./,jL -R:: i t ~X:II').s: i t ~ x~n.)#ifJXThus R=1'9L -1:j79X/ R~f!l(L-fx)EJiI'II1l114{ion of Rz 0 /"or ) C . ZL/a:For Yertic. ..r,II:!""'" ZFx :m4x,i/,1X-P-/x!/P-1'9x/t. FM" "de,.!.'cH 1'1_ ;:' '''UI'. !'' r'~ ;;..'~t.,-~1~,J's9 /d~ ",rl . s In Irodue,d

Z'~ '" ~~ i /'!lxA r /la r=/,1/"6.,/9(L-Il}~. ~a. _/,V"&_",,/2 M ' 1 ' f. 9x) " ' f ' J " : /Zt l p I~X/LT - E .R. fo' .1 lore, I1x,rfe.:l - r"l'll+P.~..! Ily fJ/~I~,."., 1/j .;,.(uR ,,6h(L-IC)I r 7 .e.Il,-RI. z/fI El..-x) -1'1x/;2.1. R -0 ",.l. ~1(j -x) "'/9 " /!l. "" -" . :U/ .3


16/22

I=S r c/r-c,,,lur _r-o,-,b// if=RvglCl,r j 9.8'24

'" 637/ (I03)YI2 371 (103)::5677rn/5

!=OrellipTical Oy17,r at ap0,5c:= AV ; ; = R If. ; r ; : . : r.C lz V r ; . . , ,, , xwr;::crC r ; , , ! n = 637/+ 3000'" 9371 hl">1

r ; .. , o x = &371 ""6000 =12 371 h-n->50 Z1d=G371(/03)J '1.824 '137/YIOE!71(/03) 12.371

= S271 rn/5Thu5 L1V= 5G7/-527/=406rn/sSo 2..:;00 t '":900(406)

t:-= /62.5

i----2az-->-a: : R f-60001=6371-1-6000= IZ37/1r'YY7

2,Q z: 2a - 30002 '= 21742 kmc?'z:: 1087/ IT""

>4-/28 l;:Or PJ !/;",e 10 A /nnn E7 - 4/4', /.sa.3/z. [7195"'03] llz7/2 :: !T -- = IT _::. 303 7 s,RV} 6370(IO'>Vi8l4where a.=f(Z[6370] +1200f450)= 7/95"1r",

(-7570)J/ZPeriod for,5' /0",10 ce (3037)(2) 719S- s: 65"S6 57h{fS /vo": 3037 &::/3_


17/22

-I.oN'ndy-eloc./hes.fr"", steel I.brss 1'14tes) rt!:sl't:c'/vt!:lj'

I"'l'act yel"c,-11 = y!,z9h' =/1'l6Z(f7.1S} = I. 71. '"Is. er. !} /.OZ9-0.68~O . { . ' " - - 1 ~ = 1 _ OZCf S G.J =1.71.. ().~O().4 :: ~, " b = o . e e ",;$ = 0..572 rad/s CCW1.71i>

v--v::'=--~-F(I.;.-e)At: '" 3530-105'9 - 2470 J

4/ 1 Fina I ""toed:! 01' m is fo be ~eroso f'or L JG :=O~ m~ +0 c ..J()0.r +0

e D ~ So 0.3 = -..!!!.-, m:: 90 k1"i - 0 ' !JOO

Thus for U f =09.62(4) := s.s ./er = eV; : O.!1(I. 86) = 2.66 5

AE= m9h- -}m'v-2= qO(9.11){4)-i~OO(2.(,(,)"

4/.35' I

t . r= 12 r: -.!..L = :20S m/Sc.s S4.2 o.sss:

4/3'1\ Z{-0080h~/ore

Let"e::: coe//"c.I';HI

" 8 e V . 'd/kr

'1:>/ "'~.3h~ howI ,n-7 ~ .;.. 2 ,.., ~ :

1-{~- - ; ' = e (V;)"Get- 7.': ~tr v:~~vr;I 1../ ',j' I Z. 3 I

~/'neh(; ~r7I:r8Y /oJS I~LIT: ~;nV: [.l..-""1.(~eV'/f .!..2;n(~1F)L ].z, e 3 '2. .3'

_ ..!.-mtr"t(/~e")


18/22

4/4-? I 1/=VZ!jh ='/2(32.;)(6) :::1'1. 0GH/.x:cI _ ~ - - , - - - - - - - - - - - - - - - - - ~ - - - - - - - - - - - - - - ~ - - - - - - - - - t - - - - ~ " Jfj,V Ll6-=o' 2(19b6) f-O = (/1?.;.2)V V-=/.'16. 6-4/411 Lt!t a; '" ram veloc/ty at/er /""p4ct 2Ib~~) ~ .). S"'CBD /ni;-/al sprmy d.18~.;f~IeCT:'-'''''od G = O~400 ../19.62(;.2) .,.0 - 400 v ; . +250 v: /~ /b ~ T , :f = W/fZk) = ~ = . .3 I/?_ ~ 0 2(~4 e = (,/"- If,. ~111,62(1.2) 1/' -rhrr LIT f-Lllj f Ll~ = : 0

Co",b,ne' 'let "'r = (400-Z50t!)!i9.62(/.2) ::;a373(I-Se) L l'T= 0-i 3~2 (1.966)2.= -1.200 .:/1'-/6-100-1-2.5'0 .L l'/ ::: -20 5/ /2::: -/667! Jf-Ih t.uJtiV"'O IS 11'1mch~sMal(. transfer 01' ener.J~ occurs I'or v, '/1r !j I [ )2 2 ] ' _ /J + [f2._ 9u ; . Qn?/n;n1U'h wh,"cl, occurs Tor e = e",u =1 L lV e :: : 2(2)(3) (3+6 - 3 TZ - -'--;:r-.'- Jf-1b7h


19/22

I" I L"J:~.5I.o"" 8 = 7.16 ,"/5, 0 . . asyskl'n, .L1C7y0 So[m (6 cos30) - rn.]4;][ I ']- m(-if,'sln~) + m v . ; ' " 0

or V:z'-V-s/ne' s: /./'16I ,6011 Ll~=O6(-~) V,' = 0J u


20/22

(22 +-p )(IO~)75 z; i(3)(J03j [(240/3.6)2 - 0 J22t-P= e e . kN, P=66.9.1rA/

4/64 I Re/oh~e IVI"c:..ferenCI!' 0,/ 8)8overn~c/ by ,c-c :: rYi L lVF~ 5(~) (16/3.6) '"4.44 klv'G = 177 ~PI = :;-(16/3.(.):: 22.2 k/\/5rei ~ or Z2.2 (IO) * ,3 ./'n/s

I-he con.~ranr - vel07/ . . yI n - = - n-1or/on 0,/ A /6

r;'rn c /0I " I . ..: 5 ::-at2

VelocItyV= at

or0 .: 1 Cor

or t . . . . , . . .. =

4/571 In n-d/'r. 2'::-'='1'>14,., '-R+-2('1.!?I)C05 30n )= 2 ( 8 S i n .3O D )..:: 5'.99 III

L~= rnqt; 2(9.81 cos 30")'" Z(C?re/- 8


21/22

r+f)';'1 0

o .f,;etl. ,fF=rna .-rng S in ':; = 177 .1; ;"t t ) " 9., 10 '- B .>,.,..,,,11B + - r 9 = Q de;=I""~5 THello,",'" ' J l-.c: '[F=mq _rnqsin/e'+G):m(1.9-tic.ose)o a"~/erQTI".J' f :! ~./ 0,' 0Bufe'=e'-to 4 r()r.5n?ol/ ~fe',.5~n(O'-feo>::&'..,.~

cos 9""(5ub.5."!/lu;~ ~ = " '0 /: 5 '

.50Y>'1~ form t:l 5 < > 6 , , " ' 1 :.50 S,::..-wc .b~ r-roc/

4/61 I Z;:;= Y;''':?t-)' -my .51"" e = YY1 ( re ' - ~ CoS B); i=~[a C05e -35/; " & ], r 0e 19fide =.fB'clOo 0eZfl& . ]= ..L[a co!> G -.J . 511 ' 1 '& dB2 r 0i , 2 . = O.. . ! . . .[q 5 /1 '7 & -3(i- cos & ) ]2 r

,~ ,)~;:;'::mCln)' T-InJ cos 6 > z:rn (r& f' ~ SineT -= =m [3C05& 1- 2q ,.s;..,& -2.J(I-C.::>s8) -f~.5/~O]T - : : . YY/ [.3 (3 CbS e - Z) 1- 3ao SI'n e]

n J 1 ,21 0 ' reT , ..![ re{ ,'j Il':::-,~t I


22/22

RW2.:::. 0.0338'7 Y1'1ls~ (sap"-,,,h 4/65)-50for 0' = 30"h:Jn B:: 00:3387 0.866 = 0.001497 &= 5'

2(9.8>24) /_ 0.oJ3fl7 .L J _9. IiIZ4 4-_ ._ _ . _ _ . . - - - - Jk = ~ = ~ fbl/n.0~ .'fly = = , 4-(4reS:;) = dj .2 : ' zy + Sf3~ 2)(12.)Y = 0y + - 4g3y "0 y m /Ylch~5

- I - = - . ! : . . = 2 1 fT ' V4 il 3 = 3-50v 2TT CYC/

(6 )

For .:5n1C?/1 a",ylc56/ r.J.(;) =0,f/= 211 = 217a-p .J

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Meriam Kinematic Particles Dynamics 3