6 PLANE KINEMATICS OF RIGIDBODIES

6// I cc =- Z.O/bO :::: 'l'3

(.02-

u/'=2cX&)' A./=6l= 20<.. :::

r"<!V/..5 2 con5f.

\;: ) 2(/6'00/60 = /36-0 rev

2(1/3)

/ I '7,." 2 (V)l6 2 a=C1.=~· (V) =- -f17r) 'rA J 48

r = L =. 3 IrJ.4/3

6/3 I &=2t~1-3i212J w=e= 667.1-6t2. 2. t

2 ~. /2'= "t .;.6 -C, t:.;. - 2. = 0ft/h~1? W s: I raa/S, '" /I~/S (t,=-2S)

Wh~n eo= 72raa/5J

7Z=6t/.;.6t-, t1.ft -12.=0

t =3 s (t=--'ls)

when t=/s 6).= 2(/3) -1-3(/2)1-2. = 7rad,"fvh~n t = 35

Jr9::. 2(3J) f 3(3~-f 2. z- ?3 md

LlB =- [13 - 7= 76 r?7c;"So

f------.

6/4

4.9 radls Z

6/5' J 0<. = k 8 4 = k (16 x 217) k = c!- o: =. ~) 'olT ' e»:

CA.) 16 (2E7) 3217"

~ c/w = fc( dB wL._ 2 =f..£.. cif) = (3271) '2.:= 64J<- J } 2 rrr 2. r e») TT2. 0 0

U) :::2.0.2 rad/J

2-

~ = j(IZ-3ta)dt- :::[12t--t3J2= 16n:tct' (Cv)o 0

3 _ 3() -=J(12 -3t~dt = I!U - i3] z: - 7 raa' (aw)l 2

2

1J'JC -ivfClI nt-f~6t",.. o/Iuo.,.> /..$

N = (I b T 7) /2. rr ::' 3. b(, rev

.._- _..-_.-_.-.-_.-------------1~----- ..... fan e ::::re( = 0( ._ o. (;

rQ---~-,.., -r r: reo 1. eo 2 800 J.'

rJ~' 2,. uA-=rwW=---=f?raa/sI reo \ A A) /00'-,t,. 1,&3»\' 2) A rOdl--'''-- .~ thu 5 C{= o. G (6' =3S'.T5Z-'. a O,'{

\" (J //!{:; o. SO f'YI 15"-- __ .__ ..r

{3' /7 - Zr'Z ('20) L , '2./ <«: r ==-:;r- =-3600m./s~

a = V'q L f C? l' c:z = V et 7. _ Q 28 n t:) e 13 n

~ = V45002-3600 z.::: 2 700 in./J~c 2

, _ V1 (120)2. , zfOr A CC - - = -- =- 4(fOO In./s~c) n r ..3

,/ 2 , 1~---Z~~~-_~2~ = V On .;.~ : } 4fJoo -f 2700

= 5510 1~./.s~c2

6//0 I ArcCl Under co : t Curl//!' = de~ r,tIUd, "<, Thws from e-,» s)4 '- --:, - -~ t Cl{(2) = 0 - 4-, ~ = - 2 rQg/s

:..~ tu:: W = /0-1-(_2) s: -24 noaho 4 8 '0 ' 5 10 '1-4- 's

(V~,.a<t/5 : oy J/',.,.,Jar rriQn.:Jk5) I

I

I ? rb' ~- -t,s

tu10

6/14 '2 ut = r; CUB

'2eot3 z: r; (~P .50 rhaT

W'= (.0twC r;, A

51n?llarly 0( =(!j ) 20(C '2 I

8 CWA .: 01., t So the;! co:« (.r,) Zo( f

c 'i 1

For P a c- rz C<.~/-:=: I/(!!)~ tr) n Ilrz I J

y' 2 2 r ? I r 4 2 4a. = an f ~ .s. eX / i- (_') 0: tP I r: 1rz 2

C( = rz cc .: r: (!!) ~c C 2 r: 12

t = -1- !-Q n -1(Wo fk) 61/ S r = /:; r -o :=: Ct..J IrvKk V -:< t---- _ _I )------~==__=_~ , .....~= CFX!." :::cu~ x 6£ '" bc.o ~ k/hc:rc. & x~ = ~2 ,a = eo»: U.: cvk x bCUel =: - o a: r: "",here" !}X§; =-.!';-r? - - - _ _I

:?c = ~ X F :::eX.!5 X 6!'t ~ be<~)

w z: a>o f kG' = as/di-

o tI dB__ =f:t

J Co -Ikeo 0 0

eo

I ,'>l-kU-b ~"-' --I

I----a

n·lt.-r5 3 = - 1y , .Y s: - 3/4 rn

- 2 = 4 X- X. = -12. rn

3!' - 2i = 4!o »: (i'X. t-/y)

=4jX.-4lY

---1-6_/_/_7-..J!!"=o/X.!' =: 2!SX(-3j- f-4i)=-6i-6'!:' in./sec

a ::Cl..)X (cv x r) f C! X.F

- = ;1: x -(- 6~'-g/) -3~ x (-3; -I- 4'/)) '/ z= (12!:'-16/ -r- (9/ i- 12i) = 24i - ~. In scc.

c2 = /2 i -/6J' = 4(3 L.'- 4J') /n./.5Cc. 2-

f 2400/r I'i?oolf -17 .~ -, -, - ,) , 4

Cl = 9,/ -1-/2 to = 3(4t.. 1-3.; /rl,/.5Cc.rnm/s -~ _ - -_/r I - - 4OoC;,,'~o -

4l?

or U-:::- 4i f Z,4,/ 1-1.?!r n->/s 6/16'

a::: t}Jx (0) x.rJ=t;9x~=

k4-0 = -I:>-oi -160/- IZO!!-

1,!1 rn/52

J

-302.4

For

IT z: ~ _ o. S m/5L 8 -----

F"r L~ ~z:< 2tZL K

_z0.5

aL"'~

r: 0.0208 •••/51

6/i1 CU :: 3 raet' /sO[)

6/8'4

\\

\~WOD~ r .DOt-- ---

• 0,12 rn ,

~A J,/i

\\

0,03 m

//v::::: OD UJ :: 0.120):: 0, 3 6 rn/s.J) Ol)

VA= OA UJ = 0./5(4) =0,60m/sOA

CV= (l{ f ~)j AD = (0,60+0,36)/0.03:: .32 rad/s cw

6/5'2 cc' = ~O/80:: 240 rnrn60

OC':: !i?2./80 =300 mm60

If= oA eo =0.100(/0)A 0

= /0 rn/s

~B= ~c,:: ~~C'

A

ElEl0\ 01

eo L ~O -', CGO m",,"" I go mVYl.

"" I'" I

"" I"" I

'" I"'", I

""I\j ,( .. L-e. ors ra»,

18'0mM

- /,0- = z.s n;>o',<50./ ro. .3

ccw!/::: 6C'C() '=-5C',.\5 se "'-'AB

= (0.180-l-0.240)2.s-

:' /.05 rn/s

C~nfer)

c; = ,"nsronfanec:>ws cen/~r.5' 12

VD Si" f3:: s;;;;;:5o ,

6'/i3. -1/5' , )

A =- Sin (-;--_I" /2 Y2

',-.e "-..~ 0.08

-/~~'A./rn0.32 lIA~--'

w m 2~d~~ "

. -, 0.16 0 0&::sm 0,3'2=30

B

EC= 0(: - 0./6 =0.64-0.16-::.O.48m

AC: "O.A ern 30°:: 0.32V3z- 0.S!J4rn

~= OA UJOA::0.08(2) " 0,16 tn/s

if..:: ifC. tr:> oA·g 0.16to AC A 0.!J-S4

= (), J39 rn/s

cv;:: ~ - ~ = 0.2 S>9 raq6 AC - 0,554 s

CVV'

C:: /n~ranraneous c~nfe,...o/' xer»ve/oclfy for ABC

~:: 2. m/s So ~:: Zkos .300 :::t ""/5v3

A,II

130" 0.2"",I1

I v:I 8

C L~' ~':!'-...., 8........... O.lm<,

o ,lC:"30 -' <, ~ D

/'l{/

tu = CO t: V"D:: 4/('j _ 4c-AD CD CD 0.2 coS:30" - y:: /3.33

nut./:, CW

if:: AC CO = AC eoA AC CO

:: 0.Zcos30·(13,33)=Z.31 m/s

c

1),;= ~A 4

li: 2 Z t-;; ; Za ~A

W" s: -zr./~ =,!!:,cVQA = ~ (qo)4/2 = 360 r~,,:

1'17/"

cw- 3Q.

(h) ~= oc WD

:: yllO = /20 a.

~",OA waA ;:: 'lOa

~fifu::: ~-~ 'V:.=v+ZV:a.. a-' BD'"

= ~Ooa.Z%

'<I "'W =-=os: 8 a..12

cw

6/91 I Cl __ -laC a=rot=o.5(0.Z)6 T A I 2~__--[I =- O. / rn / s

C, ::;r-:c--::1::!:::--=====-::-====:::J1 ~ =r az z: 0.5(0. 5)6 .3 YY1 3 I"Yl. ;: O. 25" "'"Is 2

t.:28/A 0.25-0./ . 2FbI' h ~(J...., o{:co -=- ,; =- O.os r4J/s ccuAB 3

a = t( 1- a. = o. Z5 f 3/0.005') ': 0.4 rn/s 2.- C - 8 - c/p ('

,qp= 9 =- _~ +-.::z% = 0.1- 0(0.05)) b= 2 ~_._

Z.7 /Vz 0.150:

=-9nul3js'"a» = 3 raq'/s

1.{; =- r=a) = 0.2 (3) = 0.6 rn/s or y;; = - o.6i 1'>1/5

q z; Y'~ = O. 2 (9) z: /, 8n?j.) ~ Or ,:70 = -I. fit' rn/s 2o

6/771 ----"'" -/-J(,

• 14" ~ FroY>7 Sa~'pI,," P,-ob. 6//4

A B \ 0 u!3 =(CfeJ,.,= Iq 280 ,ft/.sce 2-

VA/B = ~ = 65; 4 ,/J'/SCC Z:;:: 6.5.45 .H/.uc

(aA/.!I)n=(65:45)/;~ = 3670 .:ft/5ec.z

4./3 ~ ~)11 a:: 13, 90S':; t' .f't/Si!Cz~ -;.q -

~

A~-VB 1:;;:;n~O1~~la8o ~= 10,280 ron 20.Q2

Cl.. = -3930i. .:H/.5i!cz-;4 -

fa)

(6 )

(3:=Sir1'~14

=20.92°q.A=go f-(gA/o)t f- (gAlo)n

(tZA/o)/ OAoIoA= 0./6 (0.832)= o. /33 YH/sz

(CiA1) r; OA eo. Z =O./G (2.50) 7= 0.'19"- ""'/~ .•\ IOJ'" OA

~=v'rO.b67T o. /33(1-(0.9%/

:: /. Z If >Y1 /5 2

oA .----===-13

~.:: 10,280 - 3670 ./f/jiXZ.

Cl = - 6610 I.' .ff/SCc.Z-A

6/9f 1

t3

0'- !Z13= -30.~.!: rn/s'1---.,.---_._---- --- --------- 1

6/991 %~2<'~ U~M Z{=O.3rn../.5

Vci,-::4= o. 3/rz.:: 0.2/2 •••.Ie:;, 1.

6/961 y,I

'A\ <" I

O' I

,et' G I

~.:}~-- - -.:

CLA=0, -.::18= -30.8j 1'>'1/52

~8= -77.01: rad/-!.Z

~t:} s: 11. .:ro-,-.:;//5

13

q&-'" ~A f-((?G/,4),.., +- (,gC;/A)t;

- '2. (2 2(ClG/""')n = GA ~6= o, j /J.55) = 13.33 r'Yl15

(CiGIA)t = GA O(AI3 =0. / (77.0):: 7, 70J?-1/~il

Fro rn dlClj re; H'1

(c2B/A)f= 4o/Vi '"28',2; rnrn/sZ

0(= (USIA)-tl_ ::. 2~.2f? :: 14./(/0-3) rad/.s1 cvv'I AB 2.000

qA =: q.g 1-(9AI8)" -I (C;ZAleJt ; ~e::- ~ho ,,~+-=-~--. A Z-;4 =0

O('OA(~)Y7=0)' (C2A)t: bcYO.<l

L (CZAja)n= L(VtJ/l!)2= ~/i:'

ra)= (UA/6)::<It n

.so he< A= 'V8?./.t(;) I· )

~ ---3q;.=o cw

6/10/ -s; = rea = 10 (4) = 40 /». /sec = Z1j

12" B q8 = -qA 1-[~8~)n r (qg/A)t

5" CUAI.3=O so (C<g/,A)n=O

60° ~ = 10 (4-):. 160 In/sec..2.

C (tZo) = v.;:>.j - = 4O/S:3ZO In.o 17 Co'18c sec.2

A

10"4ra~• 'S~c

60"

o

of.. I&'5 =- 15AO;A 8 ::. I 2. --~--'----

cvv

6/102V-o z "" 21%. S')

{/.z/(1 =- '" 0..30 ",/s~•• 2 (.2.4)

~ = 2So-lot1 / 3 ) - 0 13 no ~zA 2:>0 f Q. Q - _. __ /_'>

~8 '" Eo + (e8/0)" t- (g8/.,)t

fa ) =BoW2=0.2S(I.2)~S.7~l!!ll/o " Q.2S,.$'

,\ (0.8/")" ",/S1

\ ,. 5.1/'\

\all\

s 0.30 ••./s(o.~/jI)t

6/10)

B

2(0.~) =- ~ ract/s0.3 ,3

Cl' = Q,8-y.. ::. QAx.

I 0.3 0.3

2 (0. i?)_ 16 rod0.-:3' -"3 5Z

7.[=0.4 ""/5- -----*~=o.a

--"'---"'_ m /-52

gD = -00 r( g...p/c,)n r (~D/~) t

t7 = /00 C2 =..La ; .!.(z)(o.~):: ~ .:0.533 ""/-5 ~o 300 1.3)( 3 :.4,X'. .3 3

(tZ.///0)17= O. Z (/1/3/= /. 4-22 ""'/.$ 2 ,:.;(4Dt.~~o)~n:.-,,==a=o~/

(c<;ro ) t = O. 2(161.3) = 1.06 7 m /:' 1. /

/

Up

= V(1.4Z2 -0.533)"'+(1.067)2 (CZ]J/O)t / /~

= VI. 928 c; /.38'f?Y>'1/s2 'I

6/lol/- Cl-t4 $.6-t-4 11'1 2-o - __ Cl s: 2 v IS~----;0 - 1(, J 0

_ /tZ ) - _ 5.6 t- 4CC - t ' >4IS t /4B - ----

I(,/IZ

aA= -5:6 /f/.$c,'~/ p-r~t'O" W =0

_._--">-.....J.-.-:- - - - - !2pz: g.o f- [l%

ClP/o :(ClP/o); ;~{7.2).:: 6 /f/se-c2

6/105 W= 1.5t- Z.5'/611 Z

Pap" 90 .f-(q.PkJn t- (q.P/o \~

(IQ 2 Z<2plo)n = Tz 3 s: 7. 5" .H/su;.

(uP.0)" = ;c: 7.Z. = 6 JI/sCG ZB

/

z: 3 nUI/scc.Fro,.,., Proh 6/104Q = Z :If/sce. Z __o 2.

CC z: 7. 2 rad/S~c ")

(;/106 W=20 rad/s,--.....--... 0(= lOO

VB~dj;Z Z'c

~~~/6 ~4V-o 457C

at3 qc

q. =_4'c= !f8 f-(Qc/8)n f(t!!-c/e)t

(ucjj3)n:: CB u/= O. 3(202.):: 120 ;n/.sz

(tlc/a)f :::CB 0( = 0. 3 (/00) = 30 rnj,~s",,1.__ (~_CI.-,,8-,-).:..:h__

a=a z: 120/12 f- 30/'2G

c::: /5'0 = /06.1 rn/s ZVz

b/lo'i{J'{45" 'B

~

1~ 1J

!:{::: ?a f .f{18

V= t{= ifc;o/fi

= &. CO_ 0.3(20)fZ - -rz

.::4.24 rn/s

?!-D= {la f- rt].D/o)n + (q,D/o)t

~/i-O.2G,&,·-2i = O.733/-2i fl/..fcc2

~8 =gA 4- (ga/A)n 4- (58/.4)t

BA <= !? t

/) "82• (80/,/2).({l8 " = BO .! '" 10 ..!.

(E!fj),. = .f0 i rnm/s z.

(a ft/') = AB a'8 t' = 1500e "~"""'A t ~ - "'If-

({38)t = OB ~6l = 80 c(06 ir ) - a· )2Ig",/' :: AB ~A8J"'/50rO.377 Ju/A n _ _

S••b3f/luf~ '7~t- :::21.3:! "''''/052

40!·..;.80ot'08:!=21.3j+ISOo'Ae i Si •...,.,,!}

0( = 40 :: 0.26 7 ra.d/s ~ ccwA8 15'0

0( ==- 21.3,: 0.267 ro.dls& CW08 80a

8:: ';::'4-0--'-2-+-2-,.-3-2::-"7:: 45:3 ••.•m/s:Z

_~ z; -qo +-(!JC/o)n f ({le/o)t

z: IJ - Wro.4-li + 20(1.2)J- /2 - /2 -

= 3) - 0.267,/ .H/scc. 2.

V:=~4=2':/I/sa (~)= :'4:2 .H,,-A IZ ) Y rz Sec.

t/:13=2 6-= 3 /1/.5~c (~) =..§...Z:.j if12 I Y /2 .5~z.

CV: ~:: 0.4 rad/,jer:; CCW30/12

eX.:: ~ :: /. Z rad/.sec2(CIN

30/12

Fn>/'YI d/uc;ras-n a::: Ci: = /j .:I//.5"'GJ _ L _ 0 --=_:.....- __

6//09 a-(7 = (io 1-(9c,/0)" f- (q.c;/a)t

(12&/8)Y) = I~ (aA1B)n = I~ (/015) :c 290 H/sec'

(c?;'/8 )t = i$. (QA/e)t = ~ (1030) i: 2 :>80 ./r/.5cc. z/4

iZA tJ('j/a = Y(ZtJ8'O) 2..,. (Z'10) 2= 2S9(' ~f/st:C 2

H~rn #/Q,!j""W7~ = 7&' 70 .:Hkt:e.'\\

\ \\ \

\ \ -(a )\ ,,- ,11/13 t\

\ \, \ _- - - %/13 = 2srtG/\

\-<.-f

'rCZA/,q)n

:ff/scc 2

~13=-1. 309/fraa'/S

Y,!!S////

8(I"~ f

A-OO 'llf': o LUoe=4n./(l/s '!!-13=c:!0l3x(':!?oaxJ"o8)

----- ----X-. o. =4!:rX(4!:)([O.J2L-+O.lbj]

Fa/';= O.04(3.!'.1-41) m. I = -1.92j -2.56} rn/sz

!Ala::: -0.3{'7.!: -0./601 m ./. __ ---'v'------li ~ =. ~f

(~A/8)n= ~A8x(~uA8XJAI8)

z: I. 30 9!:: X (/.309 tr x [-0. 367i -0. 160j]):=0.6Z8j-f0.274j m/52 -

([J.R/I3Jt z: dAS Is x [-0. 367; - o./~il= -0. 3670(A6/ +0.160 dAsf

5",.b5r;-luI~J ~9W.:7~ Co~:f::!.of i e:/ k...•.s . :1

~~-/.92.+o.6Zf?rO./GOcl.At3 2 • ~=-2.2.9!:.WI/So = -2.5'6 «o. 2 74 -0- 3670(,11e j Sol. /5 SYAa= - 6. 23/: rod/!,"1

~ = Q = 313 -f- gAl" J' ~G= ~:: ~ =2.36 n.~b/IIZ yAC, o.3/1Z sec

(~/L3)n= O.3(Z.36)'l.::/.G'7 rn/.52.

aB aDI CA----tl

I "'0 I

I0 ,

:";>,I 450~'L -=----= - x.

f3

.fZJ)= _CZI3I-(q.P/B)r; r: (q,J)/a)&

u-ho-c (CiD/a)Y):: ~~(a.A/8Jn = 1-(/.661):: 2.22 m/.5

(aple ) t = :::: (C2-4!S)t::: Z. 2 Z YVI/52.

B q,Cl = _QA

!- q..841

~8 = !:!!13/(iYecX. '8k) +::!a eX lslc

= 5.'il3f! X(5. 83!! X o.llJi)

t-ot.I3C

JsxO.Jf?..j rn/52

z: - 6.I2Sj - O.l8ot{Jci rn/s Z

~60

A __ T" _

-060, 180o '80 80

I tUWo '0 8C.. -1- --- /I

C

100

DI,.,..,. In rrrrr:

~= 0Joxf'3{XCVo) = IO!:! X (10'[:)( [-0.06j +o.08iJ)= 6£.' - !? / In/s 7. (01 = 0)_ ~ -OA

(1ZtU4 )n z: CJJAI3 X (fYA J3x ..rBJA) = ;.sir .:< (2. 5!r X [0.24-; +o.I/J)= - /.5_1.. -0.625/ rn/S2

(UBA)-t = ~6~ X (O.Z~j +0.1:/)= -0./~13; +0.24~8j,5,,f):Jh'/ui-e Ih a cc a/', ~fwah;""" ?' C9vP/~ :' ~/c~.f5er -O./8d =: 6 -/.5'-O·/~B 150/. /5CC _ ~

-6./25' = -11-0.625 +0.240( :!-AB- IO.-1Zl! rad/~AB

(CX8C = - 19.2.1!r' /Odls

J;J.Q.." 0.467 ra.d/s.l. CCW-1-50

vc -0 ,.. ~~ ~ lJe w eo 0.15 /50(.tr)/' r « lJC ~o

"" 2 •.36 ",/5(.Vco"" "C-/o/co = 2.36/0.375

= 6.22 rAdls~ •. rbJ sx I"C/) = 2.3(, ",/s

tr'=2a .5, a = (Z.3(,)"" 0463/nls~•• e "2(6) -.-'--------'-

9.4 = Eo +- (gA/o)n + &~./o)-t I 30 =- o.-1-6 3.1 ••./s~(aAA,)" ::AO W~(-)) = -0.375(0.22<! = -14.80) I'>1/S"

fa.;,) == Ao etA i =- 00 t' ~ 0.463 i rn/s!Ln/O t 0- - -

EA:: 0.9ZS i -14.80 J ",,/s2.

iFor cons!-. Accel.

J

(120)(2".) /ere.;., So 60 r 200 ". cc 62fl "'''''/$

"8 pcrallel to ~ -so ~:: '8. "",0\,," 0

2/ (ZOOK)"EA:: ~B +EA/ai 1t8,"(aa)ne ~/r =-:;:0-

:: 7900 ••••/6 •.

(a....)"D (ZOO,.J'l!2S ""~/~O -Is"~ .• _~zr:~'ftit~< a<l \ Clp:= /997 "''''/6Z

~ ,-.~~-----I ,"e " 7'100 """'/5· '(~),,::.3I{'O •••",ls2.

X-:J a><e6 J."'V'e ""'I"far"'elo,,;', of

<v" ~ '" ~ 2 0./0 raJ/sriSe

~ := Y'A + f!,1x!: + Yr,/ i ~ xE :: 0./0(30).i. " 3,£ m/s

22.5) = ISi + 3J. + !f'rel J t7'r./ = -18i +- 22.5) mlsj No

!!',.el differs fro", -!!'A./~ b'j tu", ~.(!:.

'"'lA: :::;2-0./.2# ro,d. .

Zf4 s: 72 },-;-n/h.I

~\ (= : , __ !:O~OA

Z/:=- 7Zkm/h--/48 ,:: 2.0 rn/s :

x:Thus -20t' = 20c: + O,2!!x{-30i) f- Fre/

A r'l3u/a-r ve/oc:>6; <7/ Cl 'lt~;;

jj W= !2/3.6:0.2racl'/5lOO /e

60 0J=O,Zj:; rac/Is

i r = r: = -30'J' rri- _A18

Yr~/ = - 4O.!-' - 6i = - 46.i 1'>7/5

CUr'yaT£Ir'e 0./ road for A has 170 e:f/ec:1

on ~ / >j he",,""!'li'

b/1I9 \ x-'1 ax e s .rtt."ched' to a have. the.a n a u /ar V'e!oc;t4 w ~ IO.J:!:... ., 0.1745" raa/",;"

J J 180

tIT. = 12 k"ot, .A r= 2 n.rnt ~:; £"8 + !!lX!' to .!!'",..,(

A --x----"l3I I

o: ",10 knots-' ~B - ,

!I-10'/ -20.9+/:: -10,- 32.9""j knots

c 0.1745(.0)(21,i

= 20.94 j k"qts

V/",-12j-re1ir I" /rl-O....,~,.--+-.3~2,-.-'1=4~~= J4. 4 I<"0 t s-".1 y, ------

~ -I 10,.... --..32.94

.32.14I-10

0/122 r ~f P.oe~//-J, A.

E A 12tcJXVrel---~ -~?!re/rW ta =tcco <-

p

!2wx:V'" II~- - re:if. ! = .s: /2cvre 2

Mr R.=6378 .. 'km., c.v = 0.7292 (10 - ) TC7tf'/J.I

~/:::' ; ('378'f'to')(O.7292J</o·"'j = 233 rn/s

or V;el=Z33/S.b)=?37 kYY1/h~ 52.~~!/hr)

6/124/ o: = V. of- cax r- + V' I' w'=: "6 k '" -"o~';k~---~I--------------------------I-------~ -u - - -re, r--~-6;1Z1 For consfant tlCClJ1. 9. v;.:, ., 2<] h 'i ~/rl'f ••Is = 0.09.26 ~ ro.&/s

/ ( )(. u, !!!x!: :: O.0.,:Z6(150)(-J)= -/;1.I'I_i ••.•/3v;.e./ •• ,,2 '1.781 25) = 22.1 "'/5 >,,..,50,", Yre./ '" - 1.3.B'Ij -13.8'1,:' + 1.3.e'li :=-13.I'IJi

1

I a, -.4

~ -.~: 100 ••••••/~

s: <T,.~Ix. ,,0

=- 2 !11 J( !!'r~1 + ~rc(

= 2 (l2}(IOO)j + 0 "'''''/5''"

<u s: 12 raJ/"

.., ; (S r",J/~"

t4stw :~ -v:D- ---I~ _r~/__ x

AI R. ~

a a '" a +2l<JXIf +an -A -8 - -r_1 -reig re / e - ~o r.; +~.s: w" - 2 <J (2:J h)

R~/. ace" I. nc,-,..,al -tL> pipe /stln '" 2w~ w~st ""2(0. 7.z9)(/o"~)(2Zol)

take. ='s> 13 af particle

So !:: := 0

=>I 3.22 "''''/5 a west"

t:....iC.~""('> I/~rh"o / t2CCe.,;'2. -v.;: 2

12c.cJ X v;.el / co: /20 + rei/I<.2. '2. 2-

iJre/ - 2UJ R '..lie, + e. tu = 0

<(u;..el-rzw) =-0, u:;,.1= RUJ

rzcro a./;~olulC' ve/oc/6;)[v;.e/=G37/?(O.729Z)(IO·") = 0.465/ k,.,..j5

()Y 0.4b5/ (:3600)= /674 km.)h Ju •... /040 n-ti/ItY"

~A = ~lJ + i> x r + !:! x[!:'x.r) +.2!!'X!!;,,+qrca. ::: 0; a :k </8'2.) ",,(15.8q)~·=/'2¥~'.!!!

"4"13.S'l!J -A - -~ -;:-- -;;:0- ]s •.

~;g, !!')«(~)(£) r: -1.sO(0.O"2~)'".J° '" -1.28"'j ,"/s".2~ X Yrt:( '" 2 (0. O.,::lf,)i x (-13.$9 ol ) sr - 2.57 j ••./,,"

Thus ~., I. 2fll. j + 0 -/ ..zS6J' -2.S7Jo + a- _ - _ _ - r et s

~r~1 • 2. 57;:i •••/.s'j arcl = 2..57 m/sa from B t-oA

6//291 ~ = t;:yKj" .f ~X(~xF) +- 2~ x !:!;el f- firel

I~x..rl" 10(412) = 56 ..:r6 in./secz

y __ (_'" .~. l0?x (~x rJj = 4{2 (S:2) ::14/.4 In./seczt-- .....,r--------------------------I I "r = 4r2 In. -

6/126/ X-y a« .es attach~d 10 B U/;;th Q'7.,7"dQr W 14sQ'\. (. ) /2CUx V- 1- 2wx. - 2(S){G)I )i~X tpl<j:' - -r~1 - - . :2

.r #I'~/oc.,fy CV= 0./745 rud'/,..,;;" ('P~6.1J) ~ 2Wx1.7. :: 60 In,/sa~l ~ ~0A r=Zn.m' ~/:-/0.i-32.9~j knols (N ••) / Igrel/:: x, " W;n./secL

A -~-~:fw - . aq", = fl" l' ~)(.:+- ~ x (~x..!) t;y<r I ~:~I

OlJ I t {/I +2E:!xY~/f-g.rel -reiY a = 0 eo = 0 (aAJx.= S6.56/rz - /4/,4/'12 f- 20 z; 40 -lOOt- 20" -40 B

A ,-

f:!! X(q}X!") = CV!!)( (wfs )(rn =-2 (0. I 745 [60] t/ C2A&:: Sb·£J'/rz f-141.4/l2 -60=- 40 '1-/00 -Go = g>0/nk"'c2

:: -21'f.ZL n.l?1i/h2

2~)( !!;e/ z: Zwf!)( Yrel :: 2 (0 .1745)(60)5 x (-Ioj -32,'14:/)= _ 209. "./ -I- t"91. 5'1' n. In"Ih 2

g8 = z,;,Wl .: /o(an4.5')('{'O)/= 104.~· 17, ,-nt"/h2

.50 8re/:: 0 - /04. 'lJ f-2/?2! r 209.4./ - 65'9. If!

:: - 47/t r /05j n. n-11/h2

6//251 R~./'''''r I<>..hjwre .:#r1# Jo/u~~n forPn:;/b. 6///S' .:vh~re V- = - %,,' J?4/S

-~I -Cl) = 0. 2!r' n:rd/s ':on!5 f.

iZA

= !!-/3of ~X (~)(f) f- cjJ x.!' f 2~xYreI + q.r~1

ClA= (r//p)r-i) z: - U/ J s: - 4J m/52 (t?4) ,,0- ,.. I - /0 0 - - J t

~8=(V/"ay,../) =- t-4/ rn/52 (u'8)/':0

q!X(!;!/Xl')= O. 2Js;< (o.2!:r'x[-30.jJ)=/,Z) m/~2

c.Uxr=-o2l:!!)(~n.1= 2(O.Zj;)>«-46i)= -1?4/1'71/.5Z

.ro qrd= -1/-~' -/.Zj r Ill.4/ = 9,2i m/s 2.

6//271 B'j E'l.2.jf4j Let B ~ abso/ut-e anjular

"'~/oc,.tj Df OP

= 41+;:: 10+S ~/S

(J "" 0

ar .: r - rQ % =

aQ" 1"0 +2;'0o - 0./5(15)' = -33. 8,.,/3'

z: 0+ 0- 0~t.J = /0 ,...d/~

E?fo/l.3j X-'j "XIS attached tod/$K w;rh )( -cutis

"assin:1 throtlJh ?on'tion

"I A.o.A=i'xt: +tJx(4.J><r)+2wxLT .s a I

- - - - +r e! - ,.~wxr ::g, !:!J«(~1C!")= -o.ls(lO)j= -/S!.· m/sa

2!:!! x !!'r.' '" 2 (10 !)x(o,/s)(s)j '" -IS J In/s1• Z. ~ -

Erd:: - 0.15'1 !. = -3.75 i. ,.,/s"Thus a :: or = -1.5 -IS - 3,7.5 Q - 33. B ,.,/s a.

eon s i:

16/130 IL et A be th. p",,,t (I; 2, ~ or 4) i •• '1.,0('0"L ef refer •••c« c"Drd;"Qies b •• .{;'xed fo OM

•.•./fl. t>r,,"" eo;"",. d." t w/{J, e••,,/' p.,;"f ,." rc;r".Th.o i: ",g, i'xr -9, I- 51!)((~Jtr)=g· L,f l' 6.

I'"i"t fix.d t~ rotar,,,, r.{#r ••",,# fr","# , c.i"cid~nt..,its, A. Qp s: rwaj f!p s: 1.5(2)'.1 x: 6,i ,.,/s"

()

'i ~~ r:(o.'1!.-0.6j){Z)1_ls"

0,' 0.<' lJ ,: a ~ O."(2)t '" -'.2; "./s·o· '" \ ww • I - P,. - •l'-3 ,, J Qp = (0.-;. +a&j'){2) ,.,./s"

\.....- . - 4. -

(,J~z,;J 4-:r.J~ V"rd::re-0.6(3)=,.8 ""/s~s

~" '" 2~ x !!:,.~/J £le, • - 2(2)(I,IJi= - 7.2;' •••/s',a = 7.2j "'Is" Cl '" 7.2i ••/~' a =-72j~

.2 -C,a - -c, - J-'""4 _",

ar

••/ " r e j grel r o."O)'j =5.4J.') !'!rel = -s."'j, ~r.'~-SAi-I Z - •

0. "ap + 2t:.1)(..r I +~r~1 ar I -5.4J' ,..Is"-A - - -re. 'Lo - e.. _a " -+,2" mist a '" 3.61 - O.~j ••.•/s"_( - J -1 - _

~.I:: 3,0;' ",/s·,!!.., ::J,r.i+O.r.) "'/s-

6//3/ X= 2 Sin 4171: x= ?lTcoS4TTt- x..=-32lT2.sJ'n417t"I /

t9 =- o. 2..5,n ,j'TTi' 8 =/.6/7cos f?1Tt &=-12.8172-,,/;, ti'/7t) )

(tl) IVr FO !/ -;.r+))' t =0 1/ = 'it. = li'lT //J. !scc, rei 1-

~:: 2g; x Yr~1f .flr~/ are/" i =0

:: 2(1,6 /7)(f?TT);' +- 0 ?U=- B =- /, 677 rad/.5~c.x: 2S3J II7./';a:;.z tU :e.: 0

(6) ,cor x= r 2 1'n'1 SI'n 4i'7't -= ~ cos 477t =- 0.1 t::. //e se«<9=0 . "V;e/= X. :='0, .t.= -J2772;/?/sec.l

u.:'= ,~'" -/.6 rr radpC'c.eo =19 ==0

,BA =fPX.,!' r9jX(f:pXF) f Zg)xY'rel';- 8/"e'1

0-> 'iF.: ~ C!jX.(g?XF):: -2(/. 67T)~' z -5,'12171./. ;n/.s~cZ2~x?!"~/:: 0, grer ij = -32TT ~ I~./SC:C.;

~ = -..5;/2 17~' -321T}' = -.366} 1~./.sc:c2

6//32 /acce/. o/.6a//) <a=c a t-wx.(wxr)+-2wx .••...(' xy - -8 - - - - !'~J

O/JC~ 1:>a/1leaves A /is hor/z. t-!lrela.cc e/. I~ Z~ro .> a= 0

C1e=rw~'}'.:9x (~)(!:-"= 2r w'Z.

(j"" vecTor BA)2",)(.1-

r:';i~rCc.>'2.==rt.VZ

a.~/

12t!::'X !!-

~ )

£l" '!.jx re=r)

A

(AnCl(ySIS 1.$ .f/m,.ohfi~q' s//ghHy .6yq;IJ','uh/;'jIon!Jin 01' axes n:, A.)

6/133

~

Ll!:t pw I'0i"t o n d:5k Co;"cld~"t

,../tJ, A

Qp •• rw" = 0.1$3. (3)L",.!..:.J. ,../s"fl f'T

)C. 0,15 tan B, ,,= 0.1$ 6 S~C'(}

i = O.IS(Z)(h-t= 0.4 ..,/s.2!:!X Yr_t S Z (3 ~»/ (0." 1.). 2.4 j .../sa

a re l :. x = a.so e 1sec!O id" (J, ii" 0

j( '" 0,'0 (zJ"(!sr(~) c :; •••ls1

!3" •• fi r-1) + -W- (-j ~) ,.2.4 i + £# 1.- 0.:1.5 i +/.O$J· rn/sa

7T- -a~ -IO'()':2.5'+/~'" -/,0'0 ,../s"

t-----r------------------------------------------~6/135 Lel- P be a. jJo/nl on £80

!-V1'th A 0i = up r ~/p

t;= {,(2) s: /2 JI7.j.s-=c

~o;: eo e ?;:!.l- = 2. radA7 6 S~C

CCW16" Z:q~Z;50 .:z.::;/p

P;,./ { 6" C~ :c V"J1?/

A 2md/sce ~ = !}p -I z~x !!;..<::/ r ffrl!'l

t2A ~ (.:lA)nz: 6(2') =: 24 in/scc Z .: (t(,p){ n

12~ x0",i/" Z(z)(/zvz) = 48'rZ ~·z, -: LIi'X'!:l;/

rCZp)n= 6(22)= 241;'.jS~C2 /~---4~~~~~~/

~(t:2p)t = 48 11')/Jl:C 2

rad/st:c 2 cwFrc;;rn dlC?Jrorn

0( = 0<. = 48 = 8'Po {,

6/.c:"l/ - d6A

So

I O.Z ••

-dsc

Z;;;:= 0.4 =». t.;g = 0.2 rn/s

co » ?j;- ~ _ eJ.1-0.2 _ radAB - 0.400 = 0.:; 5

(1/1/

ds c £j ds :: j dsA o.~ c: c:I

~"7'A1t/ «c • :f «:A

V;: Z{, -r BOw=- 0.2 r- 0.200 (0.5) = 0.3 m/s

~ :: er: f- BC. CV_C _8

z: 0.2 r:o. /00(0,5) =: O.25' rr/s

v:: OC eo = ~ ~:: 0.(, O.F? ~/. 2 Yn/so AC 0.4

cw1---,------------- ..-- ,.

c/'-'0 400

I V= -=- ~ :: --4= Z rn/so 8.4 !?OO

u:» CB v: 1000 s: /c. 8A A = 800 4 = m 5

'if= z{'+Z{:: Z+SL Z 2

0\=.3 n1/5I I I1400 ./.200

"'I ImmII

I

C6/2/ ~ = 4 m/5) ~ '"3 n;/sV:;-l/. 4-3

W -z: ~:: --- :: 3.70 rac/Is c n/AB 0.270

3.5 rn/s

1{z: vg f- DSW = 3 f 0.0 'to (3.70)= 3 -I- D. 33 = 3. 33 l'Y1/s

,%=0

-z; = <t rn/s

CO = ~ ~,tj1 'I {-3AB = tiT =/~rad/s C/IV

Z6 =- ~ - Aa IV =: <{ - 0.4(15')== 3 177/5

Z{= Z;4+-Ac eo = 'J 1- 0.2(15)

== 12 1??/5

V= 1{;+l{_ 3+ 12. IL 2 - 2. : 7.5'n1S

/. 2 ~b 22 S = -:fq t t = Zs •.•...here Cl. = 2.4(Q. )-<. 0) <70 0 32 ;.q ~

~$ (Q re= = 6 (0.06) = 0.36 tn./scc2

A 0" At I I

a I~"x 2(/00)02):tl I<,~:;).('------I ~4-" Thtd t = Z4 (0. 36) = '14.3 sec

" \ JZ~ a -21- cX= -E'::: 21(0.36) / = /.125(10 Jra~ 2r: 32. /24 ~

CCw 1----,,..------- --,--- -.--.------~e/er 0= i.5/;' e -r , x.acas &

. &= _ ~ fona (-u) rX = -X- YX'2._rZ

r=- :<:.5//7 &

tcc e A 8

soo zoo -- J"'., ••••• fJoo

""'It sa

t "is --/2 (100)(100)' ,.. -f-OO ,..,.../sdSI _ dStJ _ ds<.300 - 200 - loo

aD.<:' 200a • .r:'~(IOC)= ~'.7 "''''/53 up~OO Q ~

V' ~ ZE9- er.. - .2(400) ~ 933 ",••/s "Pc soo ~ 3

6//36 k4~Y;; f- }A/p ,

A8~¥~Plorad/s

2$ ~_6~: 0 _ ~30' C__ 200 mm '"

AO=200YYlY>1

_~.= [lp r 2!!/ X !!re / r !Jrel

(a.p)n= up/Pc. dIOOOYi,)jfZ[200){3h) = 500013 """""/52

/2.0:'>< Yf"'el I =: 2.(5)(1000) -::10 000 mwt,,/.s2.

~ -=(QA)n; ~ JOA -::(2000)Jjoo z: 20000 ""•••../52

.5/nce cL2

(2{))~0 e'=d =0 t//O_It;=Odt2. , BC -"'PI

lZeso/ve COlon-pone" r$ p~rpe" a'/~ula".. ~

~ f/ 3dCZre/(O,5) =IOOOO!} -!>()oo'j ) Qf<>/"'8660"'''''/S2

~11 + !!A/8 c !lA'" ="Q + 2~J(ff,-.1 +!!,..,atJ • (a,,)n' O,25(S)a = '.2S" •••/ .•z

(aA

/,) • O,~S(O, 74'0)&" 0.$5{' ••.•/s"-v""/2 ~ x ir /'" Z (0. 740)(;.lf4) e: I. 707 •••;.,•.- - ••• rFro," diaj. (a"'//J)t C ,.2S(0.92,S1)-1. 707= 4.0' "'1.•_0( • (aA/e)f..::z 4.06 la ~. 2.5" rr..dlsZ Cif'

Aa AB o.e s:

rC(A)t ~" 0J/co5 30° = 3/0.!?6

C D ~(aA)n. =3.46.f-f/sec

p \~/~ (UA)hOrlZ.=O 5';"C~(1..f.\"Q

A1$ COrl.,n

Thu s a.a IS verf/e.d

raA)n= ~/AO =(2v5)/~ = 24 H/s~,,2.12-

(~)t = 24/18 -::/..J.f!G H/secz

0: = 0( = fa.A) t: /3.fIG = 27. 7 r-od/S(!r;OD 004 OA - 6/12 •

Vp::' %.:'l.(;; = 9(2/rj)r3.46)=6Jf/gcG

~=: gp +2~x Y~I i-3.rel V;el = 6/13 fI/.5,x

(Clp) = v,;IOp=62./~~ =Ur3 JI/XCZ

n 12 '3

(lZp) :. OPex' ::'.3..., ~ (27.7' = 24 H/sccZ.i OD I c: vi /

/20 x V(-"" I '" Z 2 q~ = 48'J'f/sc-c 2- - 6/12 .q . If

Fr??Y>1 a/C(!!. CZ = (24 + 4~yj. =- "3, / ;;;;. u-p

~6//j9

s-A -oJV:=3 if8 Jf!C

6"'10° ..:fo'

la,,) /~

/

From d/Q,;1"an-J

(a.) e- 3950 cos 17. 63<>f-3070Pt = 65'34 rnl'1"L/s'2

c( =: G'6'34 = 92./ rod/52 ccur74.2'-

are/

2wx'lJ'- -rei

'0 ~ !(QP)n

Q::' 90'- t>-30° = /7.63°

,. 6/140 Cp &;- 12S "f;so &- 2{t2S)(/so) cor~o·.I?.37S ,..•••2,

C7J ~ 1.:3'1.2 "'''' c _~=_~ f- ~~

~~ = y~ f- YBlc

~ !C -f- !Ble :;lA -r .!B~0

Yc of ~8/c = .?~ I Ye/A ._ X r = -2tfXO.3;' ~ o.G! rnls.Vc - ~o -c -.

v: = CV .>< rei = WeC!:!)( (-G.4-.!!) :; -o.4wec.j-Blc - BC - IC

J{ = /. 2..!: rn/s

J----..,------------------------, Ye/.A = t.!!8A)( '!8/A = ctJ13AIf J( (0. -1!' f 0.~)

G/14/ o: L rr- z: o.4wCA

_J - O.3cvBA

_i,;'A - -p -e- "'A/P ~,5u.b.:j;'-;hd:~ Q Je7'

0.6/ -O.4CUfX.j = 1.2j..' -r o.4cu8A'/ - 0, 3LUBAj.£q.uo/e n~specl;:e c.ocf.ficlenh of j fI;' lern?S $ evef

O. G =/.2 - O. 3CU8A J CVI3A= 2 nul/51

£,v8A= 21: n:~-0.4war= O.4Wd~ I., -_h' /.) __ 71 I?7tl

D"" ",r-. '-<-'f)C- '-<./8A ~8C-?~---S-

"'"" • !Ep + !!AlP I .!!,.~{= !!',../pu. :: /392 (2)= 27~ •.•••••/"P •

P is on CDA H ,. 130

../~1••••1ft" 1-EA ••.Ep -I-2!!,1t.!/nl + Er_t

(ap)" .: /s« 2 (2)2.. S57 ,.,../.r~(a., >f :: 139.2. r.) = 83 S y"",/s 1.

200tr,.., ,.8 r fl/2 3-= "93 ""p

"A =4'00_4

13 o.4m.

TfJ(..f5

~ I- Ys~z: K f Va/c

.st"o·

A CO =- 2 ;Od---?-- -- ~~ ~-

Zi=I. 2 m/sif; ra: =- 0.3(2) =0.6 r=/s- C .

O.3m

o

-, I

"FroJ?-7 vect'or pOYJon08'/ :. ~/V -~)::: !L 06 = 0 S'.!?2..re 3 (' A -3" s

,..d - z.;:; / - ::: 0.8';0.4""ee. - Sic s c

= 2 rad/s Cw

z.s:::OB W06

= </ ~,( 2f!", 25. / in.GO sec

F

6/146 j3 = absolu re an.jle fhrough U/h/chwheels ~rn5

Le f P b~ a. /X)/'n/ on BC c.o/ncI4IC'/J/

u--;'Ih A

50 1.{;=rW

i Cl = V- = reo Cl = r o:t: 0 ) _t __

<. if 2c2= 'l{_ 0

C r n-R._v'l.._P-__- o r(r+R)

-s r- 2-ac = __ (/-=0-__

7hu 5 c() =- AC IJ - rcos&

6/149

-2 __ 2 _ 1-U1 = 300 r lOO - 2(300)(100 )~S 120Q

CA = Jo2Yf3 =- 36/ YnI'Yt

/00 _ 36/ 13= /3_90°5/n(-> - s/nlZOt.> I

o :: 60 - /3 = %.1 0

u;,= V;; CoS r::300 CoS 4£_rl{=/OO(3)

;.300 Y>?"'1/s= 205' m»1/s

- u;..u: = CI3 p - 500 (208) = 288 m Y>t/s8 CA - 36/

61/5/ From Pro 6. 6/75' CUA8

= /.4/4 rod/sec <cvv'

z..;; = 2Z. 6 h/scc-u: = 32 /n./Jec

AIII If.D

&=90+(3 - '0-. / "7&'.3"

VA;,I {31/3II

<Z;5 = /0 in./xc

1/,4/8 10S/n 33.r .::s/,., 78'-:3-;-

5. 6(; in./..5cc.

S6(; z; 0.354/6 ----------------

n:lct/s Cw

~ /0 v: 0.927 47' IA::- ) A: /0 0.979 = <t. In. secS,n ('10·-/3) sin 7~3u

1.7= OC V;; :: - G (9,47) = 7.6'5' In./seco AC '14-2;-6'2.

6//531 ?:.; = ~ -;-!:A/a, 1/0 T ~/o = VB I-0/13

'0i;; = =t. 6 = 4 in.js<'!!cob

~/e (3 "'A/vVo--~~~-=~===========1 UB

VA/8= 4/cos 22.0·

= <f3/ In/scc:

Ib"

!3 BqS=gAr ~BMiZA = Po I- qA/o z: 0 t(9A!o)n(a,q/o)yt: 4 '14 = 4 /i-?/s~cz

(<<8/,4 ) nz: 4.37/;6 = I. /6 /n./s~cz.

{aB./A)t

\~~-

,c-rol'YJ c//c78ron;

cZ8.:::4- f- /,16/ws z z.o

.:;5.ZSlr7.lsec z

~~_5~J! t ~~ P ··fo/"t tJ" OC &o,'"c;,'d6'" w/flt p";"l.A.

u: =-400,..,,"/.1 (Prob.'/I'Ir)A/p

W'" 4.5"0 '" 1.5 raJ/s.$00

gA 0= EtJ +&:.•./lJ)n + (gA/~}t

\

a '" -yf.§8S)" + ({,75) z,A

IC ~7S17 = 8<13 "''''/5''

6/;'56 VAs: Ypf 2-';1 if '"2(0. zo f1)IO::: 3.46 m/s- lP, P Z

,--'0.0/ P ~AIP = Vt1!1=3.46 1-0" 30"A' ~ w"lOrctci /' =2.00 I'YI/s200\~5 V- <,mm. P Q ~= 4. 00 rn/szo ~60o.\ e=30o :30 t;;; UJ = l;:4 /.. " 4.00 =2.0 mcl cw

-- ~~ - - :40 1..•.•0 0.2 5o C )

{lA'" gp j-2~ux!:;e/ + _CZre/

- 2. 2) .-(tZA)n" AOc/')AO = o. 2(ZO 1::- 6'0 rn/s

a = (Q.,p) =:PCW~=2(O.Z{3)/02.=20{3p n PC Z

Iz~x 1&ed cc 2(10) 2." 40 ne/52

5/nce ;/=0 d2(Z8)-=-o i ci =0

J de z Aa

:)o(Cl.4) =-0t Qre/

Fr-CHtl C//'·"S' ,;'11/

~el= 20 v3 = 34.6 1YJ;5 ~ IoU/an:>" C

;l;-= 6 kM t9 ) ~ = X = b& .secztfJ

'l1;::: b41 seczs

. 2a6~ ~ = 2641 B sec G tu" t9

aB= 26w2sec:'as k" c9

6/35 / ,£)"''''''.9 /~fi;,/re.s/""6/ ~ rQ~o" dx ord'/,k 8 rh~ /nre-'1roror U/hee/ A Tu,-n.srnrou.3han an$/t!!' qz. E9VQr'/~.7 a.rc

/I!.nJr,l,s ,!!-''pes yd'x.;:" e/z .I'ro," ~h;Gh

L<= f hdJ(..

6/31 I LClt-V 0./ 5/~cs 2r = rS/n (77-&) 5/">(3

A~ ..2r 2 SIn (3 = 51n t9r .

8 j3__ ~ Zcosr (3 = cos e e7TT 77' __ •

o B tv/rh B=c.u ;3= wo )

d 2. . 2- ,~~ r : el' CoS iB := 1-51y) (3 / cos(3 = Y j- 45/Y] i9 ?vc s-r a i-:

6/32/ ~::: r: .5;1'76) X = rBc068) J

// .. = ~;; cos e - rB :.s/n t9<.-!x'" y 'v'2Jor B ~11/2 a:= 0 - r&) x Z, -' & =' 20( (i;r/:2) = 770{8u r Jor ex:' = & = consl,; I'

Thu 5 a = -vr-«)C

:: r .5//7 t9) .£:3 cc>s;9 = r <9 C05 6'..50

. r' COS e r COS t9C1.e=- j3 ::T & co~~ : t C<1, J

y /-(f5In&)2.

\ ',I.16/40 v: = z.-.r -f ~

-8 -A -8~

B ~ 2S/~ 6-00 = S/n 30°

Av: - 2 5/'1500

- . "306 or/s8 Sin 30° -'--'---

" .so"-u: z: z.e wS 30 f 2.:4' Cos 08,4< o /= 3.06 coS 30"'+ 2 COS So .::3.94 rr: 5

'-;= 2 rn/S

wAS= ~/A = 3.94 z: 7.88 rad/S CCWAB 0.5

I ??/Ol=-AO~D c- 0./60(S:5'5)

= O.81f7 vY7/:s

( z.;;;) y>< 4'/ 4. 444 + CJ. 8'5'7 = .s:.33 ,....,I~(1/:) . ~ 4-444 -0, U7 = -3. ""'1.5

;4 Yrll"1 ------

------.-.---------t6/45 Ve=~/~p

eo ~ 1.f8~

&4Z/cos 30"

0.200_Zi= YA .f ~4i = 1/ . .5'.s rl(tf/sVGM=GAW=ilF~ •

rOn? a'/;;Yr".<un Z{;:: 2/13 =- I. 16-::;- rn/ S

=

y: V;=zJ;.+-w)(r-u -.... - -81A

~ =- - z/ MIs I 1-8 = va i0J= cv}}, h/r4 = 0.200 (0.?66!-·-O.5j·

6/41 t;;.IB=- (?{is/ne f ves'-"";1) .

WAS':: v.4la/ c:

L =: cC>I?~-/a",l..7o rhal

0i co,6/ = ~ cosj1

L ~"jf/' of AB /sinV"riant, So Afnl-lJf h_ve corn-

8 p"ne"t of ve/oc/t'fQ/"" J 60. •.. of

~ ~ /0 •••/s 10 ~"J 45°. rl."'J(IIA)",," .: 10 ~"J 4So = 7.CJ7 ""/$

tVAI5 • "BA lAB c 1~~-vT ~ s: 8'1 r40.d/s COy

6/43 ~'~ r~I=I~/ol=rw=locoS4-5"t'= A _ = 7.0-7 rn/»0. ~v--rtu

32S , "45" 0 7. 0 7 ~.

~

,,'- • 0171«,.,.•.•• , I vv- -- =-21.fJ-,/ L 'v,;.=IOm/5 0.32:5 -'.' if. = reo GW;AA> ----

A,IIII

8- ---- ---

:Vgl = -Z/ + culs X O,200(O.gU./ -o,~')-2/ I- O,J732WJ' f O. /oo aij

- -u~, Z1J =-0, lOO a-:, 0 s: - 2 -I-O. /73 2.lV

W =- O.~7.32 =- 11.SS rad/s I !:..u:::1/. 5.s-Jr rad/s

?{ = ~ + 9->)( !'G/A = - 2/ + 11.SS!!, >( 0, /00(0. 866~'-O.5i

= -2/ + I.OOOJ· rO,577;- - -y& z: 0,577 ~. -1.0) h?/s

6/4f

------- -----------------------------J---:----r---------:::---------16/5"3 '''''AB B _~ = Ya {-~/~----:

Y; zJ>o JOO.v:; = ~ox FAoz: 10!! x (-0.06.i f- 0.08/)

= - O.Gi-O.~i rn/s

v = ..2.- v: z: !=.(3) = Z Jflsao 18 A .3

J.!;= -l{; f Ye;.,-1/:.eO ---.!! = .2 ./I/-st:c

(Jo

6/50

D

0./5m

~/B=AC3~8

= a. 25"(40) = /0 rn/5

/or;) = 6 1'1715

:::: '1 t'>'7 / s

0.075yY/

B

C7/ TT

O. / rn a.,' rn

'03 =- VA/t3 51Y;8 ;;::

-r r- :::: 0.15+0.0756vD

0./5

34.414/12

= 29.5 rOd/xccw

6/S2 Z-(,=rc();;:: /3(4) =- 5Z In.jsr:c

!:{ =Ye f Yc/8B

c-- -24"-- ~

V-= Z(.I )(:;-2) = 40 In/SeCc.. /3r,

:l)1f'Y1en_ In n?r>7

AO= CUo= 10 rod/:;~= ~8(XI8C

= ~3c!5 j( 0,/8'/= -o'/;~ci~ I = CV X r: rYI Is- 18 -AI3 -Ala

z: WAS!s X (- 0,24'/ -0./~)= -O.Z4C0.tJj + O./~tJ~· »r/eThus,

0, GJ-o.~!. = -O,lgc.ueci - 0,Z40A8j rO.ICUA8~·

.E'1~C7/c j /c:,...,...,.5 7/5cr c.u = 0.6 _ //- :A8 0,24 - 2.5' rOa'/5

ClJBc.: s: 113 ra <t. / S~A 8 = 2.S!:s. rod /s

.---------------------------1

~= ~ cos 0' = 24 cos 43,/'1D= 17.50 In./sec

/.1 -v::/- L DC=,142+12z-2(4)(/Z)COS30°:=8.771----.--,----------------------1 cuCB- :p DCwnere Y i,.,.= ~ = 2.00 raci/s!!c CW

8'.77

~~OA r0~:f!' ~,\!{=!:i f- '?;;/f38 rn /« OO_Y-- .4·.3./- V ,,"

B ::.--- /n~"\~--~OO

100 : ,;'-" //'1 2.4.0' if.Amm J '2>0: ,~ VA/a

!...- -- ' U,)X 0 OA

t=75mm -

if. v;,=o.4m/sA 0.4 CJI--~---~- = ~---

sin (reo - 'fI.t - 24.0) .sin 24.0

Z/. '" 0.4 5;" 114.80

z: o. fi'91 rrr/sA sin 24.00

r.' ?,.., 8'" / 3 c.g7 ma/s CCIIV'U/OA::: (/A/OA = o. 11/ O. =--''--'-- __ -=--__

6/5(; V= reo = O.3(2) = o. 6 rn/sA

.?;5 = ~ f- .?alA

<:v" V-C B/,4'(5"

___ 0_,_6___ ~ 24.0"51'n (1110 - 4/,/- 24,0) -;; \

s/nZ4.0 =o,2G9rn/s ~s/» 114.8°

si" Z4.00

if= 0.6B

-Z{::: 20 il7./s~c

FroYYl 5e.:7n-7~Tr'y 0/ ve/c>c/!y

poyson, ~/c=Z6;r7/5ec VC=ZOin/s=

~C::: C~I3C= Vel/BC= ~; = Z rod/sec CVV

o r: t q, 5' . 9' IvA' / = - (26) = 3 In;sec

le 13

(v) :::2.0-.2 (3'1) = S //?/sec ,k, I;,," I~/IA f- 13

~Lef

6 !7ld/S~cB

ec co/ne/denl iV/lh A

if= nu = +(6)J A . I= 24 In. sec

C ;;:;'ZFz,/A !~__

V:= 24!!2:.- if. ~ A sec 0' D

z: fan-I 4:,m 30 = /3.1'1° 0= 30 +(3 vt3 12- 4 CrOS 30" s: 43 j J q

D be po/nl on

Yn= ~ + ~41

,,\\

'"o /z,"

{;/60

"C .r .300 t:.4S 14.4r- ,",00 (0.91#4'2.) •• 2'10 """'/5

VCA .,. .300 .si n 14.4 q. ,. .300 (y.,. ).. 7S •••,./1Oi' •. too COS' 14.41- , 77S mm

lUllS""'9"..• /i'Aa 7S/77S-· 0.<>9'-8"...,d/$ ccs«~o •• UC/co •. 290/200' - 1.4-.:5".2 rAJ.h CW

f3

/t~~

/~1---.--------------------1 D ! 0,4 A if z: 0,6/""/62 '1r?r ,,- '1r- -r r: ,n. A0/·, C ~C = !-lA f ~C~ =.Y13 f ~C/8 -, L

',- 0 I W z, 2 ra.tfVg = 3 rn /s Z-A = 2 rn/s ",~30° ..30° C11/

0'bO° 60·-----. -- ~ ---

l;B"= 3 '"/5 -Z:;=2 ""/5

7{= 02,S f4n 30°)2 f- ~.52 : 1,52~ rn/5

li=CG W

= O. I (11, 55)

= /. /55 n?/.s

t-:4/AC,

2./0.1732. = 11.5'5 radhCvV

6/65 V':::6cu h=O,G=03rnA J 2 _. _

CD = 0.5 rY1

Z/" J)C tU =0.5(2)= /.0 n7/s.D

m/s

;:Or J/Y<::>? 1'&J6~ho..,clJ =CA 50

z-: = cB eo = c8 t3i = u:8 AG -A

6/6S'- _ 5/n 50" o,S

cB - 5/n /00'"

~+--::-J"7 ~ =' 2 111/5

2 4 h 0./--=--, eT""0,{-6 O./fh

VD ;: CD u;. ~ -I(O.I/Wt(o./f 2CA 0.1 - (0.1/3)

=/10 ~ J.I" ~/s

~----~-----------------------------------~

6/71I /

Clr----t1£::: 0.4 YYI/S

I /

/

C"-:V::f3= Z/:.A= AC'if = 2 (0, 4) = 0, 8 fY1 Is

ce" c: V -- 2 2U=CDCU = ci? Vg z: 0,/ +0.2 o.e = 0.596D BC' 0.3

6/7Z

6/73 co= 300x2TT=J1.42 rad60 sec.

2J=oc CV

.L: (31.42) '"2.62/2.

-if/.xc30 . Ior'V= 2,62 - = /. 7'1 h1//ht44

6/74

VB+---8

III

,,116 I

III /

""/C

m/5

p

-.f ~ 2- r;:;Cp= V(/x-!r::.) + (0,5) z: Vj7.1 t: 0.79/ rn

r2 Vi

v:- ; CP (L) s: 0, 79/ ( 2)P

::: /, SO' n-r/5

Z; = CAt{) -;:c;t Z =- 0.707 m/s

2.{= Ao e::: 6'(4) == 32 ;/7/sec

D WAt3= WAC = t:;::l/AC 3~ =VZ = /. 414 rad/6(2 Sec

weD v,;; CC"/6" VV

/6 " A

, 8=4 rad8' sec

o 19"-45"

//

//

/

'Zr.-gz: BCeo = BC u~:::.l£. (32.)se AC /6Vz

:::22, (; in./s~w - Vs 2.

BO- --= 62.6= 3. 77 rad'/sec CW80

6/'1'6 2-'B , AD = v'0.4 2._ 0./(/

~

'8 = 0,367 m.

ofl'-vI';, ~//1:/60 AO=O,3b7-0.rZ

v: ~ ~O LJ~mrY\. = 0.247 m;4 A C<..h13 3, - 5 - 5" )~ ----- O----·D OC=-AO::_ro.247::4 md/~ I20 :3.3

/ rv>"'" =0,411 m.- 4 - 4/ AC :: :3AO = 3(0.247)

/ == O. 32~ rn/

I / z.e = OB C<.be ~ 0.2,(4)== o.e YYI./S

,/ 00 ra.d.V U.J = CU = VB/,- :: . (J - 1 31

C AB BC 13c. 0.2 +0.411 -. 5CCW

6/771 C Met7.:5urc- or co""''p,.dr e{15mnccsf\t Aa e- v'14 z - (5sin 6cP) 2. f- S cos 60° = /5,?/ in.

~, AC~ Aa:f", 30°= /5.&'/0 s: 27.3'1 In. .,30 \ \ CI3= CO -5=Z(Ao)-5= .3/.63-5=- 26.63"1

\ \ 5' ()(- S· 0 0 "\ \ 117 - 14 SJn 60 :: 0,307 J d,=I8'.02.

\ \ W5CX" 0.95/\ \ - ';~--:2:--(----::2.\ C6=y 9.5"/ -f 27.38-3,0'1)

\ \l£ " 2(;.09 ;17.V B 1.{;:: 65.4- .fI /~t:c (So". of.!:

\0" 4" 5" Prvb!Q.,., 6/9)o; G eo"

oA ~if:: ACW:: AC V8 z: 273'1 ('5-4=- 67. 3 .H/sccA GB 26.63

2'-' ::: CG cu:= cZ ue /C-;' :: !:-ti:£.<f G5, 4 = 64, I fl!5tX(;r /( u 26,63 -... '_"

CV::: 'Z..;;/C-i3= G5.4/z;:3 ::_~9.5 roQ'/xc CCW

6/80 u:

6/79 ~ A ~= ;':: 0.4 rr-/»

(1""" -I 12S/z &,0300 (7:: cos 300:= 77. 9

8 ,f'f' c(= fon-' 4/3= 53,/3"v;.- /2.5"mm 0

'f3 \)It\,/ ~o (.3 = /?O-(d..-t-O) == /80 -/3/.11

~It '~ :: 4'i?1l't"I 75"';) e (3 _ _ _

DL--- -- -- DC - 75fun~-75(!.14-6)- [16.0I mm / 0 yY),.,: // OC:: 7S/C05(3 z: 7S/0, GS8 = /14./ mmV-

C V=CU AC.=- 1..If3 - 0,3+0,114/A Ac - AC" 0.4 -----

BC: 0./ +0. 0860

= o. 8'9 f 1'"YI/5

VA _ 0,8''11WOA= OA ():3':: 2,97 roct/s ccw