meriam kinematic particles dynamics 2
DESCRIPTION
Dynamics of Machines, Mechanical Engineering, Ingenieria Mecanica, Dynamica de Particulas, Kinematics, KinematicaTRANSCRIPT
3/~ I Le!- rrr = r1'74'o!'o!' of crare
zF=rnCt . -o.3rnQ=rnC1xx. X.J J
Cjx= -0.3.9 =-o.3(9.~/)=-2.941'¥1/$2
052
1----,-----------------------1 JV-dlr =Jtix. d)t)' -:!!: z: t?xoS
$/3 2!3' 250 Ih 6016 tr:= rri V- 0 2_ L. X. Q)C
~ IZO If:, 60 f-120 _ 250 s/» /5° S =- _(_",,_0,-:::v':--3=-.6-:-)-<2./,---2_ = 64. 3 rn-2.94_---t.. == ~ a.
k. 32.2.
- -;;-0 \ AI a. = 32.2 (1'/ Ei'O- 64.7) =14. liS .:1'11 __3- -- 25'0 /~t-_::_:_:_I---:-----------------I
3/9 I
3 K1NETICS OF PARTICLES
T-/oo ==- ..!E.£. a32.2
/50 - T:: ..!2Qa.32.2
-.-;-0.:= 25-0 a32.2
3/7 I0.3/6
t c2Hk<(i t: 5j ~~o . .3 r:o. 2. k
zF=I"Y7a.· 0.3 ro.2k -0. 3= ~!SQ) J J
O. z. k = 1.5'150 -100 =!.!!..q a a= 32.2= 16. I /13Z.2 ) 2 s~C.z
3/2 I For e,.-;rlre tn?!1 £F= rrr aTrac;h've J0,.-ee eo 000 = 30000 Q) Q=O.67,..,/sZ
For rra;/er £F= YHa.) T= ZO000 (0.67) = /3 300 '"
or T= 1.3.3 Ir-N
SI/? e z; o.099.5'" co.:; Cl = 0.99.5'0
:5=.JO-dt = 7ft-Qv
== 6./6 years
= G5f-40 103(z 2SI)rZ4)2.
z: 2. 114 (10 jJ km
3/15 [ u~ ..5c>/~h';n (0 Pr-o~. ,3/1+
v:.2_V2.Z , .-=--- = s>'? e -~ Cos e.29)(
0·272or
<9 .5,;" 6; 0.:5 cose Sin $-0. 3(,05 e30° 0.5 0.260 0.240.31° 0051.5 0.257 0.25''8'32° 0.5.30 0.254 0.276 0,29
33" OS4S 0.Z$2 0.293 0.21;'
0.270.272
Fo: -204.'l7+29~,51, F=73,516
t-----f- -- ---~~
--/ ---
/:0.26j---V----I-j---j
/ 31. I? e»o. 25t--l/--r---+-------'=--=---~~--- ----
0.24~--~--L--~.30° 3/° .3z-
e
An~. o e sr.e "
33
="!?J6] ;;;-= T e 1-'-;3=T.h-LH!~/2~/S'
SO(9.91) rAI
O. Z (17'+7r)re = -3.5/ T
ZF= rrra. ..I
So (9. fll) f- T- 3.$1 T = So (/.2)
T= 17/.3 "-l
12003(430) -120"= --- e<3Z.i!
0-= 2.4/ ..:H/.sec.2
311817"~ ~
~5 1?N,M-AI100
S/"ce .s = ..!...at'Z .50 for sQrne t2
a.. = .!.l:. a. = o. e J:!...Z = O.e (40/3. (, )/5 fruc.k ZS 2.(/5)Cos B= 0.9988
Sin B = 0.0499
AI = 7.:)0(9. I?1)( o. 99? r):: 7350 AI
LF=l'na; ,;U(7350)-7S0(9.Nj(o.0499)= 7So (3.2.9)
/A':: 0.35'&
--------------- --------
3/5'0 r Fe K "",m. B ut Km .: g'€% fo F = ? R."'m,L:1. ~ LJ.
whe" 'I = 9,...yif ••t'tH'(4( ace,l.
At ~<lrfJ.,'s S.,,~faCfls: . 9ml
--\ ,~ ,
m~~ea•..th
Per/od T = 2 rr l = .3!!...!:. IJ:"tr /? 7-;
L= 3/4 39f (101) mR. = b 3 70 (/01) ".,
r. 2" (34'4 J'lf) /3.1'4 39t (/0.1/ ='J7o -.;' f,F2"1
A,.. .•..__ 23.7.2 (10.1) S d~ • = 27. ays(J.OO)(2~. 9J)
== 27 147 k,.,,/h {)I'" v'" 7S41 ••.•/s(~370-f-('4-0)J/z'r1 2" .!..=.::..:.:~==:::==-= Sf-l-2 S 0.,. r ~ I J, 37 M;n 22 s6J70-l9. 1'2-1.(10 '9
t\T = pr (~ & - 3 sm e)
when G=7T/Z I T= 0, So 0 =jJr(~f -.3),
..50 ~ = Z3/Jr f/ T= fJ.1r( f!-SI'n &)
T .1,,, {} = ".,x) T si •• it = I>TX
ZF ;:; 1>1 !j. T c:« s 8 - ""'J :: m 'I"'j )
~. 1r :; cos Id - <] j 'i - ,.,:, si~kt -9i + C.
a :: CoL S <> ~ = ,.,:, .1 i" k f - ') f .,.<f
·3/8'6 [ ; Fro •.••Prob. 2//3'1
r."_if;C#'9 C Q".:.: (2e CI~IJ _6)",2. = (O.IS[OS]-o.l}(ZO/0 <, F.....~ = -I().DO ""/$4
1/ P a.1I" 2cw-:' $;" I} .O.IS(20)J.-(y/Zr «:....F,. = 4"2.(J •.••/s •.
/ b:: 100 "'", C:::: kAr = 5".4([100-75(1)]-[100-7S(I)))/ c- 7S".", =- 202, Np.w= 20 ra.c/Is ~F;.r m4,.; ;;: -202 = 0.5(-10)
-)0=60° r;. :< -$+202 ;: /97 N
S;"c. F is nO r:",4/ to SMD"ili Co.", s« r:ra.ce.Fr/F,. = Jrj,.d 8 I r;, '" r~ f!,.
Thus F., • ~J"" (}(F ) '" 75 ( .yT (197)= 205" N~". r ,,, ••-7$' Y>.) :l-
IFt} ="'Qei P-..!O.5"= 0•.5"('>2.0)
3/91 I U=-LJ~' 64.4(10) + L1. ==-1 ;:::(i07._4-~(/ = 31?4 -644 = - 260 ./t-/6'cl-
I L. Z_m,3X- =s>» -0
}( = 2rng = 2.(10)(9, ?/) = 0.436 mk 450
h = / i- X- = /.43{; m
3/95" I U:: LJT,' 0. ?rn3 (20) = irn [V"~- (40/3. G)2}
V~O.fi(9.?I)(2)(zo) +(40/3.6/"=437.4 (""'/J)2
v=- 20. CJ rn/.5 Or V = 20.9' (3.')::: 75.3<;r0 ./r"""'/hA 1 Jrly~r U/'W.5 /"It> 1- s,oeec//~/y.
~Q'
~-----r---------------------------- ---
3/105"ly~m!J -:, /1, // I
'" 1
-: O.3A! 1/.8rn'1-' I
~--'----------------'---------I ~'" ~;£- -- ':!- __ :3/'1'1 1 poU/er r'e9ul'r~cI == rak ",;I Incr,,-asc
0.7 por-<!"1-"1 rl'a/ enC:"-9 Y
p z: 36 )( I fO x. 30 /3 3,0 Cl0 :::- 4.!J 8 hp
e= 4.58 _ 0,'12.5
1---'I---------------~-----t~3~VI,I-:::0-:GI f5=Oj-R = 20('1.fj'I)c:o~GOo= 9~.1 N3/100 ."_ F . .: r ) /' . ). O( ,1
. r - ,"" 160,:'- 2~' - 40! . (I.Z.i +1.3t.l-I.Kt'5) 80 tJ U = LJ T [50 (16) - 20 ('7. 5'1 ,sIn 60 4/
j, r 20/°_8/)" j-O.4(98"I)(4)O'~21 (20) (v '1:. 0),., le/' 'for t -= 4 s b"comlts (7. '"
/ 2. 8 - G 8.0 - 15. 70 z: U 2.
V2= 44,3 V= 6.66 »r/s)
3/96 [mq (9= -Ion-IO. / s: S. 7/"
-~cose= O.Cf950 N=rhJ =-58-'_ _ 0In8=-0.0995 =0.Q950(9,&'I)m
I ~ f -:::::::~ 5'013.6 = /3.89 = 9.76 mN O.7N .r: m/5
U=.LJT; -0. 7 (9.76 m) 5 -f 9. gin--? (0. 099.5)5= -;pr13.89/,
.s: 86.s = 9G.!J) 5= 16-1-7trI
----------- --- - ---------------1--:;;;=r P=- Wj U/herc j = Vs/nB&= lon-Io.os == 2,8'6°, s/n s= 0.0499
p= zoo (2044) 0,04-99 '" 2 93.0 .H-16/s~c3001' p= .3:.,93.0 = 0.533 hp
5'6-0
== 100 (9. 8'1) (a. 5 +- /.0) =
/,4715= 0.921.6
1471,5' W
p ••.(60,i -25j - 40!)·(1.2J + 7.2) - 23.S~)
= 72 -180 + /152 = /044 W
or p", /.044 kw
3//0/ I For Xo= 7S mm, 1.1=- AT (
I I ( 2'20.075 R"., = 'I 0.25 6(0) , R•••=: 1.2 MN
FoY' x= 2$ "''''') 1<.=-:11.2(10')= O.4(la~) N
U=.1TJ• -£(0.025)0.4(/06) =' -j-O.2S(600"-v-Z)
(/"2. '" 320000 ("'/s/, 1/'= 5'66 m/s
3/1021 U=LJTj' rngy=fmV2
f-0
VL:- 29.1 :: 2(9.8'1)(0,9/12) = /Z.4~ 1.,.-~ == 3,53 tn/s
3'/. r 8 b" C103 o.e rs , ~ _ SysleYYl "S/I'd~"J cortt;¥ ,b"'I/~y of C
U= -o.s t :~)+/'2:~- Iq = /.583 ft-Ib
12
1I
"I101,A., :-t ~ - - - - - -;:'4-;; - - - - -
AC ::2(;" 'AC-Bc =20")
U=,tjT' /583=...!... 0.5(7/":0).J' Z 32.2 )
\/.2 11>
ffV~ 2.03, q V= 14.3-'-
) Sec
3/1041 U=LlT' 250 (.jZ.42-f-/,gZ -0,6)-10(9.8'1)(2.4)) =---2: 10VZ
600 - Z3S-=5V'~ VL= 72.9 {rn/~)2., 1./== 5>.54 rn/s
v; = O. 4s rri /s~ = O.15rn/s
,[F=o' N - trIg cos e ::0.Y .J
U=.tJ~·
(moS/nB -O.3/?7oCose) 1.,8./ J Sln&
I /-2 -'2)= '2 rr: ( O. / S - O. 4-5
( )( 0.3) - 0.180I. g 9.8'/ /- -/a •..•t} = 2
/an & = O. 298~ &= 16.6 "
~---,-----.------.--------------- -
3/1071 U=L!T / mjh =- j-rnv;, 2 ,,./If/; no "/r;cr/on
So ~ = 'Z13' = J25'hf1/'1!1, ./r;'c /;';n pr~.s en t, rhe .:frJ~t/D" force ?VIII oe,JreClfer In C(2JC: (a) rh c;-n 1'1 ",a.Je (6) 6ecCLU6C!:
.the nor,..,~a/ reac/?on 6~/iV~e/'} /h~ beac/ q,,4"/A/lre /S .3rea/~r In (a) ~h~n In 11,) 7hu.>rnor~ ne.:; ah",,,, t-Uor/r- fA/;I/ be done {I Irl'n~hi:;
eneryy ?V'III 6e /e s s or /3 ~"'han 8,'.$0 ~~<:~,
1---0-,------=--.-----.------.--13/1// my= 'ih'liJ AB:o re" 'Jot = 47.1 rrr 7(9.8'1) N
1_ U=LlT:: 0 :front A fo C:\ ~: '- ZJrA! 2000(47.1)-9/i'/(12.06rf)=0
:30·\ C, 'Xl ,5=2(94 Z.4fl - /IF~/)/'i8110ml '- S s/Z: \8 30' = /61?0 III
y---~------- -,A ----- .'
'10 (1- cos 30·) =12. ~6 /'YI
3/loe [(j= LlT .for "",Tire: S:;.$7'<'·'·'
) )' (..2\, /2,
/4(9.1714- - IoN. 8'1 4 = 2" 14-(2/ -0) -f. ZIO(V --0)'2. ( . ( )( , . 2/ 2?/ s: '1.ill) 4 4,'/12 z: 13.0?? I">t/5 J if::: 3.62 rn./S
3/109 , Ler .s = a'/ST.::I'r}ce .r:;I'DbUM /;"'c.h;'C' 6~fo,.-er~ver--.5.Q1' c,J/ d;r~cr/on
(/= IIO(Z)(IOrS-S) - 300 (IO-l-5-5)'? -/04/- .[J-_'~13 - c~, L- '''''
LJT= ; f;.~(V2._[r92]) = 4.66 V2_ 377.3 ft-I/;
1046 = 4.66 V..2-_ 377.3) V"= 305.6 J if= /7. 5 dl/sec
In;'!';"/ k;·n~flc. energy / s ,b<P5.·..i-/;,e ,,-c.J0,.-u/t!!ss.0../ d/r~c r'-io/7 0./ ve/oc,·,y.
3///0 \ ';-0(9.81) N-~)b;-.J~.-4N
.(.10 N
{'",.. 1.2-m d.-sl'- of block, P "'oV~ 1.2",
d"w" in c:/,i-!e. T doer no ••.",..1..
L~ = 0;, ;J ~ sor'1 . .1I)-./T = 425 N2
0.4 N= 16'1.9 N
U~LJT.I
4-,fO (1.2) - /69.9 ri, 2) - 4 90r}Jfi.2)::: i So o: 2.
1Ft.;: 77.8 = .3./1 (".,/s)2-ZS
er::: I. 764 m/S
3/1/3\ Lel X = do"ao·'Y/or-..on
j-/ia>L. force occurs tuherC?r: \ I 2-U z: /.5, .' &> -f- x.-! - 72 8'0 X. "0
40 x. 2 - /5 X- - 2 70 = 0, x: =
c.f ':;'prlYI,3 'n I;"e:he~
x. IS ynay. ("jT::.o)
3z:Y3~4(5'){S4)16
x= 2.79 m (X=-2.42 m.)5/.JrIYJ.3 force /5 kx;; 80(2.79): 223 16
,£2'may:. 1~".5/on /n roe! at 8/5 T= 2.23 r6 " 229 16
;;;/5 r-Fo ;.-~~~ le rY7 . ~,-;--:;;;-;;;- ~-;-:'6;c:
1.>1. t U= AT~pJ~~'!1?" U~ 200[1(0.450) 7.+ (0.22Sf -0. 2ZS]
i: 200 t.J - 7(9. ~/)(O.450) - fk(o.075/
~I~'? '= SS. G - 30. 9 - O.Oo2f?/k vLIT =-0 50
a.oo z s r i« =..5-5.6-30.9
If- =- 8790 N/....., 01' A-"? 7'1 kM/,...
!~ U==~~· _)1(43 --. _ / 4? / ')x2.f-60x)dx -2...32.2(0-V 12
o,1(.3 +30x}l4 z: ~ v,z VI;' ./1/.5cc.
~o 32.2 )
V- 2= ..32. 2 164 + 480) " 6'0.&'2 (H/Jec / tJ = ;: &'0 ./I')se<:.ZffS- \' ) ---' ---'--
3/1/2\ U;:::-Ll~' U=JrE +mg) .d.r
=Io: c/x; f -5 dy f {d Z - Yn!J dz )
==jr-15dIC +IOdy f-15dz -ZN.~/)dil)
::: -15(0-0.6) +-10(0.8-0) t: (15-19.62)(0-0.5)
;; 9 + i + 2.:1; = 1'j.31 J
So /9.31 == ; 2 (v;/ - (_2)2), 213 2= 23.3/(rn/:,/·
'2-8;; 4. Ei'3 rn/s
3///71 ~tnJ = 6000(9.81) = .5'8.86 kA/
R - - =...t-F = ..d:..6000 ('1. il) z; 2354 AIl' /00
N, AlzV 2= l{, 2 f- z» 5) a.. = (';'02._ 3(/-);37;2._
I. 96' rn/s'l2.(/40) -
,Q - 2354 '" 6000 (1.98').1 R. = /4259 AI
P z: 14 2!J9 (~) = 2.3 7. 7 (IOV W.)'.6Q'- P=238 kW
LF==tna. .)
P=RV;
3/118]
3/124T hV-= h V V 7T z/- )/-: r'/ I " p= P, ~:: 350(103) r (0.050
V 77r' X
- 17.5{/0:; Po- C(.
Ll/.::::O 50 (../=0 fA' _f PG 'J JP O.IC J,ooA<lx - ,c.:JX== 0
10.40 o4-Ct
/7,5(/03) IT /02)2 -J' ""'/ 2
t---:--,----------------------I ---- t o, c/x: 5 1/ I O. 2)
'
X ----- "- - 10 - d,Jt- -,cr. 4- )3/lz/ U = L1Tout- LlT:: 0 .so {/= 0 0.05 4- "1- O. 0.05
~
(9'8/) N f x.z 5 0" 0.40 0.05 = 06(9. ~/)(O.IOO + cS) _ 4000x dx = 0 41.0 In;;:;;-; - 3.11 (O.4-u.oS)(I03) - O.~S-~:o
)Cl F::O.~5(')-49. 8.2.079-1 - 3./4~O,35003) ::43.?8wl,~re ~=O.OSOY>'1- X=0.o50+J' rn: 0.3S
kx.=:40ooX. I / 2 F= 124.8 A!
/hw,:, S:F~6 f-.:J~.?6 J' = Zoo 0[(0.05+ 03)2_ {0.05)2J
or Zooo EL+- 141.16 -5: 85'6 = 0
6 = -/41./ r:"; /99.zo T 47088 = -/4/. /:to 258.1
t(/or-k :::/O>?e' by vv~tjh; /,$ rnq /r: - 0)J 17/2
.= 0.5(9.81)(O.3''f).= 2.3/ Jdo rl e. by r 1.5 rt-: _r )'::IO/O.3fT- O.3!T\
1)- rr/z ( c 2. )
I 2. = 4.71J2.3! + 47/ = 20.5 (if - 0)
'2.1./: 28./0 Z/:: 5.30 Yn/s
)
zr:: 5:44 H/.5ec
I3/120 I I -+p , Lc:f 5 = /er7g/-h 0';:
~ bar~1, • S ~ -1 F= force On bu//er
On grouud; worlr dOr?c JFdS ="c 5 = "'!""rnv'0 ....· 2
On veh/c/e: WOY;' do",: SroJ,cds z:{;v(Si-d)=.i.rnV2-f-fO Jo 2 Qv
u/M~"'~ ,,:: d/:;f'once Irav~/cd by veh;clc c/un'n5 ""',.'ct: 0./ ,;:;n·r1J
eu t ,f =- ut t.£;;v = rrJ o"v .50 ~>f= Yn ~I/ ut = rrt ccV
SlnC<! q", •.. t =- ch"""3e /'n ve/ou/y = V
7hu5 Y'rlwt I"!'pa'.sen/-s C:lCl'clecl tAJork c/O'1e 0..,
buller by ~Q.5O'" ".I' t-hc rnover1fe"l rf 0/ Hu ,5"""
4000
J = 0.0294 rn or J= 29.4"""",(f)
when LJT=o I/.U=-o2f, t-3
-J3Xd'X 1-800=0)
3-..3(zt£-fG&) + Roo~ v
1IS= 10.33 I;". ~. (&;-J)
3//22 r F'= k x: ) wheY> F= 9 lb . .K = <t1J =- 31'n.o
Zr:- u- ~T' jt - ) - FdX + ~Oy = i 8'0 (lj'2_0)(;Z)
4J ",'U 32.2
t -j3Xclx. -f- 6'0((;)= ~80 lj''' if I~' ,ft/s~cy=!: 3 32.2 I
Z3 2. 480 Z 2.
so rs -2(i5-3~+4~0 :::32.21/, V=IOA6
v- = 3. Z 3 il/.5ec
---~--- ------
(up)
(/"'A-r..
7S:s~-30s + 9" 10.5 (S)"
or 75"s"-30s +2.75:0
.30 ~ hoz -4(7S)(Z. 75) .30:1: 8,66Ss :2(75) /50
= 0.1423 '" or 0.257 on
3/12"'[ U=Q = LlT-f-Lll.j f-.:::J~..JT= .L 3(V-~02) = .1.v2
2 2Llv.: = - 3 (9.5'/)( 0.8) :::- 2.3•.54 J
LJ~ = ; 200 ([VO~Z+O.G2- 0.4]2 - [0. ff-O.4t): 20 J2 Z; •. /.O=.l...z.rZ-23.54-+20, V:2.3Grn.5, tr=:/.54i'n.5
2
(I; )
LlT-fLlY "-0·..L",.,.2.-""9(h_ .!:..)-o9 '2. -,Ij-
trZ .•. 2 9 (h _ ..t. )Y2
IF;: m a . N+ ~ :: ,."a~11 n » -v2 .,
wh.re a,,:: c.rYr= 2.9(t--/i-)
SO N~ ,.,gI2(~-j;.)-7t]:: 1>'9{2~-It]Fe,. m r 0.25 kg, r= O./Sm, h" 0.6 "',
N· 0.25 ('1.1112 ese - ~J =- 14.42 No , /s .,q:
3/133 U = Ll T f- LJ Veof- ~ ~ for $Y-,"r~Yn
U = 40 (1,5)c..o::> 30° = SZ 96 J, 2. e
LlT= - 2 V -::;V
LJ~ = ; 24[(jZZ-II'sZ -/5/- (2-/.5/]:: <I J
Ll v.; = 2.(9,81 )/.5 co: 2.9.43 J~ 2 ~ ~
..50 51.<76 ~ V- r 9 -I- 29.-9-31
V z: 13 ..ss, V=3.6fi> S
3/134 AT == f (Z.$){£:43 -I-:-i') = 3.15 J
A V. - -}30[rIi.sarI.21-o.9l'_ (/ii:7P+I.Z2 '-0,.,/1•• 10.23 J
A~ = 2.S(9.81)(-O.'l) & - 22.1 J
U.: UI=.:1T+.I1~ +A~ j VI -3.15,.10.2.3 -22.1
lit .: - 8. 6'1 J
IUri=f,;"ds; 8.{,9:F. •.!o.'1Z+I.S"", ~,,=4.lf7 N
...-....----.-----..---.----::-----1LlT Lit.{ 0 /IT- / 3 (9 ')2-1- :9::: )' LJ - Z3t?Z /z9
I 2 '45[ '])2-r : 32.Z( 12 zo
:::O.04-367e2 .:/1-/6
Llt.{ = -J (.!-) _2(4.5+4.5)J ./2 12
- IS- !Cf 'L- - -:j:' ~ - 3. 7S;r - 10
·2 •2. 2.0.04,3(,7& -3.75'= OJ (9 = gs. 8'7 (rad/sec)
Cl = 9.27 raclpec
3//35f3/b
·-4.5"-V=o
3
2e
3/13[? Th~ syskrn IS c.ons.:rYC-r/ve So
LJTf-LlVe f-,.ej':9'=o )' 5pnny :s!"eft:.J., ::'13-IZ=II;"
ilT= ; 3;.2 (VB 2_ s ") :::-0.0466 l-;/-2.":'S/ ./r-I/'
Llv.;; = 2 (.!.. /o~/2. - o)..!. = 0 i33 ;/1-11:>e 2 JZ'
LlV::::: 3(-5'1,2) =-1.250 /I-If,J :2
ThuS O.04{'{, '13 -z.9.'1'1 -f o.IJ~ -/'250::- 02.
0.0466012=3.3'18) -z.;;2=72.91- (.ff/sec)
z.;s = 8.54 /1j.5eC
= L Sin 8 -f- -:z( J- sin i9
L~f ;0 = trlOSS ;=,- l/r};; /"-I"1,9t1?
Gzl-_'X-/2 .LIL§ rLlT=O~ LI~ 15 Nud "E I-hc /~n.!Jl-h .x..
drY//OPI'"y Cl 6,'sre:;.nc.e hLll§= -;03X-h ::::- /-'..9[L)(s/~e -I- ;2(/-.5/~61)J
LlT= ; ~L vL
Thus -~3[LX: $/1'1& I- -f2.(/-.5/~&)] -I--jjJLVL= 0
V=- YZ9.x. [SI"76~ - L (J- SIn &}2L J
Ll T +-Ll ~ t: .dL{. = oLJT= i3;2 (vl:.. 0) z: 0,12.42. 7/2
Llv'::-8 /:;'-:Coc,60Q
::: -5./1--/6:3 12
Llv.:: = ..L4 ( 30v'z -30)2c: 2 --1-2 --. - 0
= 2..I'1-5".:If - 11,
.500.IZ42u2-5-1-Z.l45=0
zr2= 2.3.0 (,ff/SC(/
if = 4-.79 ./fJs=.
Ll~-fL3T=oL~f? =,.,..,,,,,,5 of CJ,~/'"
per unit knJIJ.,
~3i~21~--: ~~~-~~:-~-~---" ""-:J e"T I 2 • Z Z
LJ c: ;:;YY7V- -0 = in? ("268) = 2rnb~-
Lll:9'= -m3(26) -= -2h7.$"
/rJ/';la/ s:lrel-ch t1/eqch.5pnn3 for e=-O IS
bVZ -b z: srrz-»Ll ~ '" 2(i k ['l-z'- ...,']) =- k( 62._" 2 [IZ _1]2) -=- 2(1/2. -1)kbZ
- 2.'2 ~ )k'2./f-Jt.lS 2mb () - 2m3h f- 2(IZ-f 0 =0
,92", gib - (f2-J)kjrn &='/9/b-(IZ-I)k//"Yl
1_ 9W1",-~---~ (1"2 -I)!,
h m LlTrLl~ f-Ll~:::o
o /nr~rvo/ 8=60" 10 6= 90°b ,-----V=O / '.2
8, .9 LlT=Zrn(o(})Ib, /' I/'_ ( L 6 0) tn!)bI L.J "(, - OJ5 0 - Q c.os 0 ,,- ----, .J " Z
k 5pr;l?y COl/I? re S5/0/7 IS
(AB) - (A8)() = 90' 6=60°
.::: 6Vz -6 == 6((z-l)
.LJ~=~k[6({2-/}]2 =: jkb'2(3-ZYi.)Th I 2.' 2
05 -2 m I;, 29 - ~ -f ..!..kh2(j-2'ii.)::.0- 2 z
8
A
3//_~ rVe:Jlecr LJ~ ; L1Ve=O~2{i)Jdl-b)Z.
= -1-4 (.; bZ+X2 - hf"
4T=in?v2-o)" A/SOl .5"lj/n~!JS o/em"'''~ 5Prf~.7A8 /S A-~ 1)/"
5ub.5.r/r",,/~ /n L1~-f-LIT=0 ¥ ,ger
rn-v2"" 2bk(/b2+x.2 _b)Z~ v-=YI!f{~ -b.)
--------------------------Ymox =:» :for y = Of SO 2gy ~ f!:y2(/- C~2) = 0
Hence (y . '::0) Y. =rng b2-""In J i'J.'1.Q.)( - ---zk 6'J.-c.
3//47/..1 T +.t1 v., == 0 ~ :::_ Ir7gRZ
,,) ~ r
Z...!m (IT -- [7/00]%)'" 9.8/ (io~~(j600lm(637o)'(-'-__/_)
£3 7200 I~ 000
i USZ- 25.2(/O~}:: 394 (IO~) (km/ht
'B ::: 2'7 000 k•••/h
3//48'1 ~T -r: Ll ~ = 0
/ ( 2 2) rYI.:J122 tn;}R 2Z rn if - Z{; - ---- f- -- z: 0r R
Lel 27= 0 :for r == oo f/ JeT
- V; 2. 9 rJ ? r-: .r::-;;2 f- ,'- I 0'0 = y2.J/'C.
= VZ'-x-9,-. 8-Z-4-x-6-3-7-a-, -I a--=-3
'" /1 /90 o+/s z: .!.!.:.!! km-Is
13//5"01LlT = irn (v;/- V;;2) =i3;'~[7600Z-foool.l (~:::l=-10.00(10
6) if-I/'
!J'v:. == -m!} R. 2.(~ - .!..) = _ 48(J~5"'d>"'f5zg0)1..-/- - __1_)~ ~ ~ (40og 3983
= 6.Z/~ (10') .:II-Ib
U=- - P(Z50)(52.f?o) := -I. 320P (106) .H-Ib
U = LIT,.. LJ 11..'9 . -/.320P::: -10.00 I- 6.218 p= 2. [17/6) )
3/15/1
Max 8 , R. occur for ..1 T:r 0
-m9x+fJcx~=O, x=~= 2""9. R=J:~.: Z""Q-Jc-~ .I
3//53 Let ~ =0 ,'" in/tiall"H/f/on (X'=O)
X r d~t:or""a /:'-on 01 spr,'"s
.1~ +A~ +t1T =OJ LI~:= -"'<ix, .1~:'ikx', /J.T" imtrl.
-""g x: + i k x Z ..f i m er ,. = 0
Formax. ~ ~md(v2)=m'J-kx=O X= A192 dx 1 K
$0 V'I.:= ~(('"<J.J2. - -'-1c[m9J2) I !!:..La if:: J fm",., r· le. 2 k. le' ik
...3'//541 X%+tj·.=if:7f2, xx+,/~ .• O
AT +..1 ~ •• 0 j i '"(,(,.+ tj r) + m1 ('1 - c;;.) = 0
X 60(1 -I- X 21.) z: 2('1.8;)( o. , _ 'J), 0.Cf:tx Z = l'U,2 /o.q y'_,,'1'I yr Iff /
Fer "'4)(. x, d6<Z) = 19.62 (H a ~ 3<1'2) _ 00'9 0,61 ff 7 J. j
$0 'I::" 0z..h m 1/ X2", /9.1i.2(~ _ 0.108)= 1"1.(,2 ff0.61 ff .,q-/ ~O
IT. -" ,( c 1!9.lt2ff • 0.962 •••/$~"'.x Y- ",0
~3//5.sjy Fy~.
t/w~~fFx-~x
~dV= -F·o'r = _ (_nwZjdr
- - I
;:;;= FCD$/9 = _rUJ'Z ~ '" _ XGLJ~
.t; = I='.$/n9:: _rw2 L := _ y wZ
r
3Fx.:: 0 = oFy .50 /Ie/q' /;'~y 8X.
Conser"a :h'yt!
r1/, r. :;;! J / 2 2r c.../ raJ a. r == 2'''' a»
."
1-=---;-I--------------------~3~/,~/:-=G::.':G'J·1f:: §~::.(_t</ -f / s: f)"J3//
601 ~ 2-2T = /6 kN '" /1 t ~_i + .30 t.:!·AR'------- 0
JL~4't= rY1.L1V')' (16000-LJR)9=/oOOO(t050-I000'Jj Fol' 1:.35, f=lf(.J')!.·-f30(3)j =(62J-f9~' N
LlR= S68' N s,6 rf F "".j;C:zZ+ 902: /ts. 3 tJ
I ,1--0
2
3/15"81 Jf ;--;t~--:'Ll ~X
~
)/5:000 44('1000 -R /2. := .3;2 1.50.30
,/000 /"~__ ;e= 460/6
3/;591 ~ ~--->r /Z-F dt =' MA"
0.09- a.o s:- Z 6000 == s (v- - 20),J Ir= - 4.00 ••../s
01' er:::: 4.00 ,.,/s f 0 the /./';.
46,'185t: = 17.63x/06
1:= 375" Sec. or r = 6.2S m;"
1>19 = 200 (/. (,Z) = 324 N
T::: /8 000/10 ~ UOO N
t-:« -=mLl"r
(.324-/J'OO)t := 2aO(I.S-4S)
re; .5. $11 5
" \ITII
If
3//631 flFd't::: nuJ v> RAV (IO-/Z Ir••oh) ~ /so kiV(z50 000-/80000 ) t z: /5 (/06) (12-/0) 1:':2
t -= 220 5 or t= 3.7 mm
JIr;. tit s: m Ll'ifx.
W (,S;)t z: ~ (24-[-/2])32.2
t·":: 2.11 sec
3/20 I
3/22 I
Q'O£3 :30 ~=28
->-Clr--. X
n-7y Y
zr:;= yY1C{)C)' 28.51',,30"- e 5/'1'730°
= t'YYl a
28 ces 300
f f3 co.:;30"- 1'Y1,J = 0
B f/ 5.c:i a = !J/3{3,Ellmina/e
For corY'/4',3<= ,;/ Cy//nder
raken r0..3~rherL;::;'= rnqx»rr=> Cl)(: 3 S/n 19
3/2G I1--y....J, W=m3 ~>
30'''· ~\
I~--_ Fe.=-O
/ \ 45" -"x.'45°\
ZF=rnq, ')G' x. )
mq cos (45°f30) = m a Co545°
a= 9 (.0575° = 9:?lf 0.2S88cos 451> 0.707 I
= ,3,59 ;n/..:; 2
3//681 ./2F dt"' YYl LlZ5 J'
Yt( ZT )
~
' 2(SO~Z+I5VJ<2+fOO)<2+Z00x2.
: -(IOOxZ -.50,,2 +25'0><2 +/SOxZ) -7(9.P/)IOI t - '1(,/. sr)
rV == 7 (if - [- /.Z 7)2000 - //00 - ?83 =: <J (V+I.2.)
72 V= 0.70 rn./s u.p
..3//671 If, fj ;-ockei- burns otAl al'l er: 2% s}
5" f_la/ i,"p"lfe on s/ed cI••r''''9 3 s is
'(/CO)(I03) - 3R N·.5
J2:F dt or ffI Acr; 600 (IOl) -.3R. .,. 3(ro3)(/so)
R" 50 kN
3/1701 Jz,c de::. yY}.dl{ ,n. t )
P~Jt. Se:::'""""~;x:. (900..il - 196Z-f) t=-200(3- [-z))z.;;=.2 /0 .'V= 3 '3 ,3~ I· ,n/S -1:-=/3.135m/5
'looN
200(9.;1)=/962 N
&= mY]-'.,£ = J? 7°/0 _
3d 4t.bIJolr'~T~
_V'
fZFdf ,,-LlG; -T{o,S)= 30 (u,-u;,)
rre.s ) = 50 ((/- v;,)
0.ST(3~ +~)= (u--r.r;,J- (V;-u;,JJ if-er; = 0.0267 T
8 ut if-V"" /0 "'/.5 J SO T= -'-"- = 3 75 NI 0.0267
3//731 I~ Nod- ~o~_s =h_nP=25t P P= F=;U,v = O.4(9f?I)
-~ 0:: 3"1.2 AI(.oVMIc.h a cc",,,, at: 39.2.
9'?/A/ /O~ 4=157s4-
JZIf: cH = ,.,.,LJVJ• J(25"t- -39.Z)dt: = 10 (v--O)
/.57
IZ.s (42_1:572) - 3'i.Z( «-r s r ) s: 10Z/
10 if: 73.8 V= 7. 38 tn/s
3/1741 (9=::1--_..J150oo 1o
~~L20,000 11.
~--XB F'"
I~10.r:
1Ff p(Tau/er)
mn '0. I=- .5:71 oJ
Ji r=; dt -= IYZ A v;.[3s;ooOxO.0995 - 2FJS
:0 3S;OOO~ ? 44)--- 0- ,,0-32.2. 30
F= 4'130 Ib
[p- 4'130 +/S}OOO x o. 0995]S-
- 15000( 44)- ---L--.: 0 - 20 -32.2 .]0
P = 704 Ib .r fen3/on)
3/176i./Fdr =~t = Y1-'I L1y
F== 0.20([1 &'cos Z.OO]t' ~[!8 S/~, ZOO]/ - [-12/])- 0.04 - -
z; S( !8<O.9397J+lJ><O.3420j -t 121:)
=- 30(4_8J~i -f- I.OZ(./) AI
F=30'/4.'i19lf-I.C>2(;2= /47.f? IV
(3= hl?-/~/U' = 10...,-11.026 =- 12.02°)( 4./?/9
t---.---:-/---r,,-------------------c-t 3//83 1 r 4 t L~' - 2-t_i - 3t !! rri3//7.5'1 Irnpu/4~ J= ,-n,Av c: rrr zr;
",.x In. = S frJ~h~r~ v=o or P.:=R",.;fvll
V=!:"::. gt-j -Z/-31:! rn/SG=mv= ,j-(f?t-i:. -Z!..'-3!:!) N·s
H=- r~(j= (4t}; -2tj-3i/s)>:S(IN!:' -2!-3f;:)- - -:: 5[i(6i-';:;i) fj{24t1.fIZt') f.6:(-nz+16tZ)]
=- zot'2.(-3j-f2!!) N'Y"r1'5
!Y'i= d = 40 -t (-3! -f Zis) N· rr)
f/ fOY t::: 3 5) ij:::/80(-3/-I Z!r) /V'''''''S
ldl =fao V31:f2i :: 64q N' Y'l1. S
JM!= 4-0(3)/3'2+-27.=433 N'm
3/INI /o(q. '8'/) IV
.3//8'01 T = 600 cos & . (9 = 7,,0 ra-d~-IS--S-O-4-t-=-IO-a'i-B-f--~FT~y ) '7/ ~
17/2JL/§ clt =rn .d~J' /600 co5B (!Ji, dB) :::Z60(z.:y-o)
Tr/2 0 tJ 98./NGOOD . ) 6000 ~=»: Sin (90 z: 260'5- I 'j;' = -2-6-0-17-=. 735 m/s OO~4:'0~--- :
f--- II 4{)L, ---II I I~----r---------------------------------------t 0 ': I
3/1?/IJ,,60lbl{;=zOH/sec 0 1.% 4 7 I
----~/ ~L1t ~P:::4D<h \~~\/ £5=0) N- 60 cos30o-40S;n30o=O
»: y\. N.= 7Z.0 Ib FOr Iotal I"Ylcflcl'? LJV-::'0, 50
X-j;: 0.2t.J t.J O.ZlJ=- /4-4 le JOO~4"1.0S(4_1.96) +-40(7-4) -4'1.o~-LJt :::0L1t=-ss4s
3//7 71 /.!.;::;' dt c; rn L) i'{
Jf. 644)-/0 sm 77t dt = --' - (zr : S
32.2o
I
+;;:C05TTt]=Z(if-S)) !..Q(-J-I)=2(V-5'j If=/.?/7:ffn TT } sc.:o
FOr t= Z s<t:c, /Jet' 1r>'''j7u/se "0 So cr=o-///,5c=c.
So
LIv1.. = Ho 0 o =~(mr&"r)) dt
or d (r1.d) = 0dt
SO r?j = co r» sf.
f2,c;, dt- = m L1~ ) [60 5Jn 30° - 40 cos 30° - /4.4] t== ~ (0 - 20) t:~I. 96 sec
32.2 )
!5/0C;;-' hC3/rJ 5 ;10 ~'lOve
tuhen T= F=rW=O.S(98.1)=4'loSA/
tvh/~h occ a r s Cl tt z: ~4= /·96 5I /00
MOJ<:.ve/oc/ty reached byb/cc.k OCCurS at l!= 4- s
3/1S's-1 rz~ dl = rn..1ux/ SJ.:p heJ""s 10 ""<lVS whenZT.= ..3(9. J'/)~) T = /2.74 IrN\.~T T,kIJ Wh"C~ o c c u r=J (1,1 t _ 12.74-2
\ I~._- = 1.~3 SIt.7-/- --
N3(w) ,
I< tJ ;;;. 00 ( Z ,f, s--~ /.5135
jz ~ <!If = 4/~;'12. 74 (2.-1.:>93)'; 16(6--21-3('1.FIJ!lr;;-IS'fJ)
= 27.4 h/·s
Thus ZZ4 == .3 (tr-o). er: '1./3 "'/S
1------,..-----------------------13/1.5>61 rtz,c C/t = In Llv': .J X. )(.,
ojTr/w
J Kt c.o5 wto ~ [cos wt
w2.
dt = yn (V-x. -0)
]frlW
+ wt SI;" GUt = ¥VJU)c.o )
fJ-Fy dt z: rYJ L1Z)t )'
TT/wJKt -Sin cut dt-= rn IV; -0)
o 'iT/wJ<. [05/;'" wt - wt cos wt] = YYl ify 1/ = ~WZ 0) Y ""'II:-<-'Z
y'~rL Vd _ K. '~U--=' vii. f '-Y - --zY4-!-TT'rrr co
.3//981 For sjsl e,.., <I/' d,r'{; ",Pr<l'/uf;/e A G ~ 0
So IJ'O(..3000)+ 0 = !/O(ISoO)+960cr: er'". 21'/ •••/s
3//931 LlH =0 060..-1 cenlel- 0/ earlhr:
YY/ V:p r.p :: YYI ~ I::" if = V PI A P fA
6371 1- .300 = 2.6 926 frm/;.,-z-:::; z: 2 ~1.37 (,37 I r 600
3/;911 LlG = o : /(}O (/ S-) = /20 V- z.r= 1Z. z» ./I/.5~'I) J
- ~ 2.. = F:lm;: ~ - ,C(J' ,0- ~a if -= Zasl a. I' 12.0/3 -')"-..1-t -2/20,# _ /2.5 _
120 ,h 32.2,P- - Z(~C) ) ~- 0,030
3//94J h= r(I-CoS8) = 2 (I-Co..s 20°)==- 0.12.06 m
rl~";.~~_d:~:o,~:o~;~?)::;:~£;:;.71<~_ •.._r -r u:» 77/ rn/s'V' T
Al/r = r-r: /_.!'=I_ i(30.06)r1,53'8)2
T T -ffJO.06)(770)2
=/- 0.00/99(; = 0.998 or 99.11%
3//761 ZM cH ==-0 SOI~~--~-~----~----~~------~==~--~=========-_t~--~,0 03//.§>91 I ".,po.cl V',;>/oc/f"y '{;;:~ =.,!Z(9.J'IJ(;'2) !
.,.~,S •••/st1G ;::OJ -f.oo(4. rs )» 0 ~ (400 +250) V"
cr= 2.99 ••.•(s
3//90 I LlG =-0)' 58'0 (IS-OOO) - (SOO'Z-3 f-flO(I:Jo'SO)f
=0Z(i= 14 '1'12 km/h
Ho = conslant
r"':h • '370 +-390 = 6 760 k •••r: == 2(13 ".2.0) - ~ 760,..•."
'" 20 210 k••.•
For W" C<ln.t-"'n t ,
6760 (33 no);:: If 720'li : 20 U0"A
'A = 11 2'lO b.,,/h
VB: 19 S40 k",/J..
3//98 11J,-=~-V-~! tru~-;;-?{.= V;el - if
= 5- if km/"[____~~~ tvf.9-"-V
G,'""ha/ = G:h;"QI:= 0
LlG = 0,;--------1
Ciz=O.sg
u;:= v'2~~=Y2.(0.5><9, 81) >< /. Z
:= 3,43 rn/sQ.O(3;OV-l-O = 8'(2,80) +(6+0.06)3,43
V= 720 rn/s
F:=rYl4)' Q,=O.S3
V, =: V2<21 S, = V'Z-(O-. S-x-q-, 6'-/-)"-0-.-8
= 2.f!O Mls
3//97 [ A 55urnc no cho~.!Je. /n QXT~/'n&l/
/orc<".5 Qc'hny (7Vl r:w3 -.h"--3<" Sys/<"n7
if=: ve/ouj 0/ /i-» . z.;:;:::- ve/oC/jr c,/ .hc,,;yc
ug=Uf2L]6==0' (500 (-'9r:>o)6,,/.6CfO =5cJOU-f"ioo(zr-l-z)
) v:. fj'. S'S/I/,f~c or 2/"·= ~ = £24- /rnofs~ 690 __' _
3/20/ r
_J
LlG =0,
IO(S-V) == 240 ~ if= 0.20 krn/h
'2.V= 2aS
j
3/2031 (Q.j·Ll0 = O· YY1. -(-.;) + 0 = rn~ f rr7VF.J/
1----," ------.- ....-.-.------------------1 v;, f 'lJ'6 = 4-3/2001 z:__ ~ -K <1T/r=O.6D)· O.60'iYYl.(42)«1mz:;2fjrnu;/
c=J c=J ~ ~2.fVfJ2= 9,G
50Iye ..51;""ulfaneDusy i Jef
(4-ua)"fV(/=9,6) Z:;Z-4Z-;;+3.Z=O
~= ::t: iv +2_ 4(J.Z) z; 2. 1: o,f?94
(SolI) v,s= 2.8?4 .H/sec c( t;;;= 4--2.8'94 = 1./06 H/s",
(SoUT) ~=I/06,Hh~c ~ t;;04-/,I06=2.GJ?4,:H/su
-5o/JZ /',.-.,/>o5s;6/~ .5/nce ~ h'lusl be > ~Thu 5 ~ = 2, S'9 ./~/J"C
.8e.:fore A/fer
(h) /=0,lnif;;'; /0 "/m;'/ C:Onc/n">"",.,
LI &- '" 0)' h'7 (4) ."..0 = 21'Yl -vc J Vc = 2 .:/'//s<"c
An,;Ju/ar fl1o':"t"~run'> etoe>vr&~nrra/ -?x/s /.,S c:~"se'J/~d So
. dH = eTt ( J'n r k) ::0
rrt (2rtVelr I- r2d",):~
L,c = m Cl ',c = rn rUJ:2n n /(/ 7.~)
d{/=dT' -Fdr;d -zl??r<-Uj/ J
_ h7rw2dr ;::m (rC<.l2dr of- r~dUJ)
z; h7(rUJ~r .•..rZwt2~d.r])'" -.n1Nu"dr (ch~ck)
~3/zoslll_. ficd/ = c.ons/ant· mr'w :0 ,..,r2wr er: ~ I' -a ~
.$0 r/N, ::'i2~ ) (.300 7/r'{O) ",(300 i/~""IV; 270"'/~;,
U=.1T+L. v.:'J' U=2..!.4fio.3J.. :/.70 2".}2_10.3 6 '(0 2,,:f1) 2 1<' 2 '0/ (. 2 '0/ J
+ 2(4)(~fl)[O.3 -/f - 0.3 fJ= 48.0 +.5'.('2 c .5"6.' J
3/z061
3/2081 L_~F---- x.
--i(O.4}(8)- ~(O.4)(IOJ::: 2.(V-4)j if= 2.2 ;-nls
+j
. 3/21/1 fiFclt z: fYJ~----';;-:-~.--;·t-:761 (v-~[-IOS//7300J)r y Y) .32,2 I .y
V cly t ,t zor y = -v-r- =2 -5 Y= ( (2t-s)clt z: t <s t:a t: J .
fi;r y = 0 J (t -5) t = 0 Jt- =.5 s~c
1500'4,?,2'16-V:) 1/=0./44 k•.•.3/21.id ZF.. =lna .~., I ) I h "'" /
kl'Yl/h0'" U; = 40. I ~~
5
1500(48.1.52) = 501500 tFz
UZ = 0. /44 H-""-/h
Or ~ = 4<).0 V>1M.-/S
\'-- ~7
~-__,r_--- ------- -------- ..----.-- ------
3/2071 __ ~ ''--2 --x/0 kA/ R
{zF de = m LI 'Z7' - (/0000 f-R.) 8' = 20 000 (3-15).LS-:'-zJ.i. x X) .3.6
/0 000 r: R = /54-33
12=543'3 N or /2= 543 k.tv'
2N s» ·n .30· =- 2. S(O.I:;)(~OO (,2,,-;/.0 /N" l4i'tJ IJ
~t"r M
75"0 ('1. fl) ¥It 0.2",
1~~~ r A1__•__F_Z__O__N__.~ ~~ R lp
3/2 It; 1 (a) AT:O, .6Vg+.6Ve=Oj Z(9.81)h-iI20(O.S)!O :\b
h - 0.764 "., (3.--V\h~lo e
Load' ZF=rnC{) Y 'Y
.500(9.&>1) -T= 300(1. 35)
T=- 4230 A./
a "5 t:Dnrta,n! Ior ConI' ani M) SO
J1V-" r 20.1; a =- 2 (4) s: /. I.2S ""/52.
J[F~m4j .2T-7So(9.1I}. 7S0{l.I.2S)
Ta4/00N
LM'" 0; 0.2 (4/ooJ-M= 0
(b).1T+A~ +A~-=O;
-}2 1/'2 'f' 2 ('1. 8/)x - i 120[(0.Sl-(os ...•jJz z ~O
I/' -= 40.4-)( - 60x 12$$".,./", x!:O.,S'",
d{IJ''Z.)/dx =40.4-120..: =0 /or m4X. .r; X= 0.336"..
E/-v;,._:: /(40.4 -'o[ain"J)O.3':U, :: 2.1'.1 "'/5
From .so/wf/~w7 10 Pro O. 2./1442e2-h2 2
Cl = W I:( = - 2eu/r Y hZ-eZ (;
£,c; = mar)' Nc::>s;'3 -P:: lYlC(r
£~ = mt?6')' N s/;'" (3 - R = m<f6'
£/I~/";I?"t:' N 1/ ,3cr
-/?:: 1'Y1(~ - C(rrc;r?;a)- P f'anj3
'l. '22e -b e) 2 Pe
So l2=rn(Ze f- V6'Z.-ez Vbz_cz eo t- Yb2_et
2 62 P,-e= n1r?W z 'Z -T' ,~
b -e vb2-e
a=i.:J
2LL =2.K~ L.L=X><.'2. ).. .:2) ••
L L I-L s: XY. -f x. wh"rc X" 0.. .z '2 _ (.<. Xl.,)/
a=L=(x..-L)/[- X-Tz'X. L
=- L'-><'\:.'2.= h2.v1.
L3 L3f7:,r: x.. =- /2 W1 h =-/6;on L = 20..-n - 2
. " ) a.=/6(S'):08/2.»: = V"= .:rJo'Yl/5 203 . 0,.,.. ~z..F=Y'Y1a.)· T-4<:J(9.'i?I)=4<J(O.8'O)) T=4Z4N
3/2221 flFa't. mAy!",/..•
flF dC = .fjE.~e .fIn pt <It
o
~h~~ er- ge -i£p f/'S,t':frl'/'
f-::!/E"e cos;o r: dto frlz,b
= ~e [- ii- cO'l't +-i/;s,;.,»t]" = ;~ (i 'i)
So ; ~(!~j ) : n-! U (~ - {-7ii) +-/ (~ - 7)]
3/2241
I!ence T= f'.Jr(S/n B - lB/TT)
if, A/lon-1t!!n1 0/ ,1""'$/0,. T aNurI"'/lg~"cy ,P0/"I A /s z~r~ iJuTA
/~, .W \ I ,:,. a. """OV'I"~ ,Iu:u"r. 4/se:. /7>O""f!'",t
W) >:~'~allow-I //x~d ,P0//1' 0 /.5 nor zero.o ';/ tu ThU$ (:1/1.;1,://armo"","n/"'''''
0.t\A v-;;; ~ <> /~ rl° r c o~ !7,.rvi!' d. A/so'-:I..-<':....------:l~-..( £"C / 0 on parr/J::/~ J So
Ao ~ C<.{, I,ru:ar rno,-nt!!'n ru~ /$ nc>T
CO/1S'~"I/~d .
/5 con~~rvld.BuT ~nt!!'rgy
~ co z: ro W =-r 0
""-
- __ LV
-';;-4.& 0)
(J..1 = ----
3/z71 f{ = rrlCl)t;
Y ,,25(9.111)fI./ A <:0,5/5"-25(9.9/),5/,,1.50
a'f..~2.9 = 25(2)l9.1?/)\ ~'j..\ .-----&A A = 25(9,(1/)(2 r O.Z5"6'~)
0.9657= .574 AI
,,,,\
/3 '[F = o· 8 _25/9.8'1 )c.os /5"_ S74 SIn /S·y J =0
8= 574 ro.ese r) r 25(9. '!?1)(o.96S9)
=- 3ii'SA/
3jZ'? J ~ ---)<T •. 300k~ R.
IF =ma~· 300 -O.Scr 0: 2 al( ~J
or (300 -O.S.,.) dxI( Vf dx ,,21 trdtr
• •• Joo-O.Str4"0
X = 2p.~t [ 300 - 0.511' - s eo 6. (3oo-o.s.rJ]o
_ 8.00 [-200 - 300 P,,~]~(JO
= 1.001:200+ 300 (1.'0'1'1)]
R. = O.S IT k N
r 2 crd..,..
•• /0.37 •••
3/291 F,~N F.= 2'2 -17$OJC = 17S0(O.IS-X), /(/•••2'1.
:~~,.tl)N - I(~'~) I~~""<I"i /7S0rO./S-X)-19 .• 2/" •.24
t" "'" a=12/.4-.f7Sx",sI 1 0 o.rs: 'I I
v: •. IS
F Jeraer ·fa.dx;!, u-du-" [(121.-I-17S>t)d;c
•. IS!C" •• 121.4~-67sr/ .= 1.37, er=- 4.09 ••../sz 2- •
x,= Z,:)/ m
3/3/1 ~9L L~=W1Q.)t)·f 1-x. -'1 p P -I' f.J >' = ?L C{)(
~v I..t t ppgx. JV-dV =/4')(. dxpg (L -)C) 1'3>' 0 0
tr': frLp _ ~9)(.)dx = ..E _ ;U!JL 1/= Y.2P -/'.3L2 - J (/": L (J e: J P
o -------------MIn. vo/~e or P -fo <:nswre p"5;-II';~ aCC6/en::>n';",
.3/..321 z;:; = rr» Cl.x.
P-/"-jJ.J (L -x.)=jJL Cl",tf L
JV-dff =/0)(. dx.o 0
IS ~/"'.= ~?,L
= I?-3L
vJVdifo
v-~ .2.. x.2.] L = .!l.. (L 2_i/j2 L 2. 6 ZL
V= V"~L-(-/---A-1.)------- ---.
3/46 I:rt .ff:.=mq . N-3220= 3Uo (44)2.~~ __,- . ~ -t~~J ~220 ~ n n; 32.2 /00
3/40 1 {I? (a) ~ t-!= 3220 + 1936Z-r;,=ma". R.+2ft1.II):2(-f·a)'· t 44.:H/sec .:::5/60Ib
~ I 0.5 p= 100 Ft ~alJ , 3220 Va.
2(t,,)}/ I!.:z 92.2-/'1.62= 72.SN (b) i+n. L!h=m{(n; 3220-1610= 32:2100: v,n ])"""'fI v-2::/G/O) V-=40.IZ;ffjsec
~,...1/= 27.4 nll/hr
3/41 I £1=:= n'7C1" . 2 5-2= ~ ..:!:-2n J' 32.2 P
32fJ = /.) = /. 99 ./f
3'2.2(0.5
3/42 I ),n1jtN::Ori
£'h= rnCl,,; rH3 - 0 =V=-~J-=V (/.8)(9.81)
=VJZ6C, ~ 4.20"..,/5
3/43 1 .J::: .fur ..race .3rav~ raT-l"on",,/acc.~/cY~7"/e>,..on carlh
I l.F::n)t7I1·rnc.=YYlrw2 to=).9/rn ) J I
'I W .!T."0~ eo= Y T =0 /, /07 rCld'/~
! c8:J--p
_ So A/= /./07 ...§E = /0.57 ~v/rnJ;"t---=----~ p = Yt1.J 21T
r:« f? rn
3/441__ ~':"'9/+
300MlI"'9 ~ to ('1.11) N,,
'"
I;;; . '"~"i It,," v 'if"'1 + '"9/-1 =- hf v-~ I/,:: '" .,.'.r~
So f:: -f (30(] /J.6)"- $66..5r9.~/) ..,
3/451 :
:rz11I
V__ x= .Irt>?j'
~mg
L/h= mC1"J' /rYrly _n;y z: ""'7 ;2V\JL(h--t)
V=V,jL (/r-I)
3/48' I A·~(9.5>')N LF.:.::rn an h 2T ~ T Cl.er». 8'1) ;. 2T ~ = o. e 3.18
/0.3th:/'1. .••." 0.5 0.3'--- ----~0.4m o.4YY' 1.2r=/9.12.)T=I5.9N
Z;::=YYl/: . A/- JllOCos30o= /&'o (go) 7.r7 "'"/]) -.32.Z 90
A/=- /8'0(0.866 f 2.21) = 553 /h
LP'; =: m Qn = 0; T '- rn~ ea» .300
:: 0
T '= =s v'3/2
k= T/r = V3 j.!- = 3/z2 V3 --
3/58 11: c_rh -""4" j
I,5", Ij~..;o I
I :'O"--"'::"'~I, I TI I ,.,---
<+,.,I mq
~r;= 01 T CDS '0" = "'9tAn 10' '" (3'+/O.$in ~o')AJ"
9."1~'1:: /.244 [r •.d/S) 1) ~,II /.//S ~
sor N: /./IS{60J _ /tJ.65" reYj...i"
2r -
3/60 I t2n::: riJ2 = 0,1$ (300 :;) 2 = 148,0 rn/sz
L;:;= rnq~;, To:. 3 (148,0 CO..5 -?So)
= 3/4 N.£)/mcPon 0./ ,...."';<:n".o.... /~~S nor
c;hpV~ acct:l.) h~nct: hq~ h"
I;,//'-f~"ce <?Y/ T or le·.t
3/61 I c?=rif = 0,150 (120):: 1[lyY/I.sZt
1.;::;' = n?CfJ(; T= 3 (lff CO:5 4,st»
::: .3 fj', 2 '"
LF= rn a = 0 ._/2....!... +- 38. 2 _rI n j (2 v'2-0
,€::: 38., Z AI
3/ b31r s: 2 t- '3_3-; ~4 /n.~-;:.-~-~t?~3~-;" -: I 2. t- i"s~ J J"ec.Z
. r' 17t •.&= 2 so·, ~ e '"/7C05_ e - 772 . 7le2 I 2.) --2.5/1"72For- t = z sec J r = /41r}. / ;-::: 2.1 ;n';'J~c) ;-.= 24 In/scc 2-
e= 0) &=-7Tn:Jcr,/jcc.) &=0
~= I?'I (;'-r& 2.) :: ~ .: (24 _ /4Lr-rr] 2.);c -0. S91 16r ~1~ .
£= rn (rg' r2":.9) = 2-. .: (0 r 2 (2.1 )(-J7 ))' ~ -0 683<9 32,21;1. . 16
F= V ,c; Zf I{,a s: y 0.5'1/ 1.+ O. b 8'3 2. = 0..903 16
z;;; r rn/:t"j - O.S m9 -0.3 (O.U5 "7} = "., q..:
a.• = - 0.760 'J,,' = O,.!6" 'J -.2 (- 0.760 'l)26'
•. ',13('1.'1) = s o.r ( ••./s)~"= 7. 7S •.•.Is
p= 4 16
3/67 le:: 6 flu/Is ", •cow st: I 2£:' m (rB r: 2ra)
e '~" m9
/ r ~yp= 0.5'( 0 f- 2 [0,8]6) :: 7. G8 AI: rnJ = 0, [I (c;. fi'1) = 7. 86-N'
F=;-t-N \:P A/==-Y7.t;8Zf 7?SZ: /0..91) 11/
mg "'\:/11 F="uN = 0.4(/0.98) = 4.3'1 N(5pr~'13 ../cyc.es not sh"U/n)
3/66> J i:II
!
J:::>L JI (onc JOfC~ C?9,,,,Qr,on)
• 0 8 /0 ):2 0sr- = rn a;; R CoS 30~- t? SlY! 30 ., - -(TT Cos 30L./).: /' ) 32. Z 12
(r 0 IOTTZ)/2= g f4Yl 30 r -- = 6.G616.32.2x/2
..3/73 J r.;r 100 + 10 si" '(12)t ,"m
;. • 720 cos 7Z / "' •••Is, r >: - SI. 84 si" 72/ ••/s'
RJr r ••.•••xlmu""> si" 721=/, co s 7.21=0
t/ ar =-;: -r4.JZ = -.5"1.8-1- - 0.110 {1.2r =-67.7 ",/s'ZF,. ~"'4ri R-19.1= 0.1(-~7.7)
= -'-.77 N
R.= /'1./-1.77= 12 ..B N
J -rnJ 51'n(9 == ;-n ~ ) ~ = -.Js;nS11" 30"
JVdU- =J~d(r(;)
'if 0o 30"
; (V~ V;') =if-Ioy S;/? & C/B)
o 300
= -/0.J (- GO se)"~ (V-z_ 64) = _ 9&'./ (1- o. ?66)2
VZ:;. 64 - 26.29 = 37.71
V- = 6. /4 rn/s
R - rn!} GOS @ = YYI V'lrR = 30(9. ?I)(O. ?66) 1- .30(37. 71)}0
= 2.54.9-1- 113./
(Rc/a)
----_ .._---
01' (/=11.1'1 I"" •• /s
z F" " ma,,; rn'l;: rn ;;~. I/~ = gf, u~/ij"At tOf ,,{ hCAmp d:J/dx;: 0
4 radiuJ of Ct.lrvafu,.t! is
r = (d'o/dx2r' wh(Zre '1" b sin :Z:":!Jt '" .2rrh co,r3!!:..!! dRy = _ 4rr}, sin ;2rrx&Ix L L' d>('l- LZ L
Af t Pp 01 hump X = .:f, s/» Zi.!T)( = /"1d1..t,lf- ,_ 47Tl.l:, L ~y- d,,'- -1- -zr i fJ,uJ' cr""ilii 1b
le.•n,
--+:~-AI- ,bolto,,", of dip IF" = ,"an
At!3 Zr::"""q , N-rnq == rYl ~'J n #'J) J ,
N = rr:.7 f r»: -/-2Y>1.J ) Ai = Trr +- 3n7.J
,iI.
£F=W7C(r' -202. == 10 (r·-I/.66)r ) )
:::;:.-1/. 36 ./1 /.5~C2
r = -~. €'4 .:ff/.5~~