Art. 3/6 wow( Art/ D KIA/ EHC ENERGY
fhe f-/ rg c y/ /nder /5 / dfched i...
ARI' 3/7 POTENTIAL ENERGY NO. I
The Z-Kg cylinder i: re/ easea from re...
ARF 3/7 PorEA/ r/A z. ENERGY Alo. 2
A spacecraft of mass m is
orbit/ ng t...
ART 3/8 IMPULSE' AND MOMENTUM
The / .6-/ rg part/ cie has an init/ a/ ve/ ocity of
/0 m...
A t? 7.' 3/ 9 CONSER I/ A T/ OA/ o: MOM EN rom No. /
A zo-A-g b/ oc/...
Ani. " 3/9 CONSERVATION OF MOMENTUM N0.2
Each of the 4-/ rg bal/ s is mounted on the
frame of neg/ igib/ e mass and is mt...
APT 3// l / MPACT
Two spheres of eaua/ mass m are suspended by
' ivires of egua/ /ength l". The / eft-hahd sphere
is ...
Am? .3//2 CENTRAL-FORCE MGT/ ON
An earth . sate/...
ARra/ /a RELAT/ I/E MoT/ o/v
The point of . support B for the s/ 'mp/ e
penata/ um of mass m 0nd / ength Z has a
constan...
ART 4/2 GENERAL/ ZED / vewroivs secon/ o LAW
The two J-kg spheres s/ iae ...
ART. 4/3 WORK-ENERGY
The system of five ic/ entica/ spheres is *e/ easea'
from rest in the position shown ana moves
in ...
ART4/4 / MPULSE-MOMEA/ TUM
The three sma/ I spheres are we/ ded to the
/ ioht rig/ a' frame, which is ro rating in a
hor...
?Rvññl/ EM qui.
; Mx-HAL comNTloN .
, AT The : umur rm& tune/ u THE &Uu/ ET , HT &rafia/ B _mg EM(
- 'NCOMING MO...
?maca Ons ata. ? ) Maze.
&MO 2 (O z O.
Haga *Hoglmhhl z
-_ (mn 'V - 3:
Z(MVTK)bM4-cmL/ ZK)bWi ma* bm. ;- bum
: fjouxhk :...
ART. 6/3 T/ ?AA/ .S/ _AT/ DA/ (RECT/ L/NEAR)
7/)e uniform ma' AB / ls
placed on the nor/ zon/ a/
true/ r bea' and...
ART 6/3 TRANs/ _A T/ ON / CURV/ L/NEAR)
/ t a coup/ e M: /eo N-m / s app/ ied to the end ot
/ tn/ r AB w/ th the system ...
Am. " 6/4 F/ XED-AX/ s ROTA T/ ON N0./
The s/ ender oar of mass m and
/ enath Z is actea upon ay a tor-
sion spring at 0...
Aer 6/4 FIXED-AXIS nam T/ OIV A/ O. z
...
ART. ” 6/5 GENERAL PLANE MCT/ ON N0./
the uniform s/ en der bar AB
of mass m is re/ eased from
rest in the i/ ertica...
From / rin ema ti`c
ana/ ysis
aA: Zo<cosa
Kinetic diagram
Free-body diagram
Z...
ART 6/5 GENERAL IRLANE MOTION / /0. 2
Find the normai compo-
nent R of the contact force
atm( for the do-kg unba/ -
ance...
AR7T 6/5 GENERAL PLANE MorioN No.2 CONT
A/ ternatii/ e formu/ ation
Free-body diagram Kinetic diagram
...
ARt 6/6 WORK-ENERGY RELATiONs
Each ieg of the /5-/ rg piatform has a mass
of 3 kg. When a= o, each of the two springs
of...
ART 6/7 ACCELERA non neo/ w WORK- ENERGY
The uniform arm 0A nas...
ART 6/8 / MPULSE-MOMENTUM EQUAT/ ONS N0./
The 60-/ rg Whee/ with attached
hub has a radius of gyration
011200 mm about ...
ART 6/ 8 / MPUL se -MOMEA/ TU/ Vi' EQ uAr/ oivs No.2.
The homogeneaus . semicy/ ihder
is re/ eased from rest in the
posit...
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Kinematika dan Dinamika - Kerja dan Energi

kindin
Published on: Mar 3, 2016
Published in: Engineering      
Source: www.slideshare.net


Transcripts - Kinematika dan Dinamika - Kerja dan Energi

  • 1. Art. 3/6 wow( Art/ D KIA/ EHC ENERGY fhe f-/ rg c y/ /nder /5 / dfched in , o/ace w/ tn the 60 kA/ /m &pr/ ng com- 1 , oressec/ cv distance or' 20 mm, h' L j the tol/ o / o/ches ore s/ mu/ taneous/ y I ramal/ eng deferm/ he (d) the max- 20 mm . j@w«exQaw x x x / nvum he/ "ght y reached by the cy/ /nc/ er 0nd (b) the Ve/ oci/ y of the cy/ /nder when the spring ha; moved up/ g/mn The cy/ /nder fs not attached to / he . spring- For ent/ ?e system 0,: : = A7+AgtAl4 (a) U/ :Z=0, 11730, Agmvgh = ?Kathy Ag = 0- 2'- {60)(/ o wawa)? :-zz d Thus o = o + 8K? . wy-/ z = o, y: 0.529 m, =0 AT: gran/ lm* 415: aras/ Maone) = o. 942 a Alé= é(60)(/03)(O.006'Z- 0.020? = - ma: .x 777415 O = 4,2% 0.742- / aar akan, capyrlghto 1990 John WII-y l Sons, Inc, Merlam/ Kralge ENGINEERING MECHANICS, VOL 2 DYNAMICS, IIIE (Sl VERSION)
  • 2. ARI' 3/7 POTENTIAL ENERGY NO. I The Z-Kg cylinder i: re/ easea from rest against 0 coi/ ed spring of stiffness Ae/ zo N/ m which has been compressed a5m from its unconvpressed position. Find (a) the maximum height h reached . by the cy/ ihder above irs re/ ease position, and (0) the maximum l/ e/acity 2/ reached by the cyi/ nder. Spring mass is neg/ iy/ b/e. (a) For entire . system 4720 so Agmléw UI 2M. 3/)h-_?4//20)(a.5)2=o (o) ATtAlç +4143 = o j 52 27% en mx - g/ /eo)[(a5)*- (0.5-XM = o , f Z ziz= 404)( - 60% (assumes Ks 0.5 m) ? f/XLL 40.4 -/20X = O for max. U; X= 0.336 m U2: 40.4 (o. 336)-60{0. ssef, :r: ve. ro = JLIVI Copyrlylno 1990Jahn Wiley I sam, Inc. Meriam/ Kralga ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4IE (SI VERSION)
  • 3. ARF 3/7 PorEA/ r/A z. ENERGY Alo. 2 A spacecraft of mass m is orbit/ ng the moon in dn e/ /iptico/ porn as shown. /ts ye/ ocify at/ -l/ 's 3955 / rm/ h. By energy considered/ ons ca/ cu/ cvte its l/ e/ocity ot F! Consu/ t Table D/ z for' nec- essary moon data. f (From Tab/ e D/ Z, R= l738 krn and the . surface »va/ ae of lunar gravi/ _y / Ls y: /.62 07/52) For the energy equal/ on Z/ ,fgdfizllg iAg where U, _'z= o &Agga so . (177 AI_/ ,=0 3 a 2 _ ; rZ-/ mq"2.-Zlm[ / : ZLm/ /2o7X/ o3) dpn/ aig) mg* = -ZCmD/ ,f - (izovlr/ oil] _I J. z F z From Eo. 3//5 V= g = -mgêz 2 Jo AV? = -m3 (Eg); - ? Ri : -m{/ .6Z)(/738)/ /o3)(6,/ ) . i Thus zim[U, ;*-(/2o7)(/ o3)] -m(/6z)/ /73i){/ o')(c4) : o Cance/ /77 and . So/ VC for U; 4 581/ Z/ /;: VZ/5{/04 = /465 /77/5 or U/ ;-' 527.3 km/ h . .ILM capyrlghlo vmJohn Wllcyn Sons, Inc. Merlam/ Kraige ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4IE (Sl VERSION)
  • 4. ART 3/8 IMPULSE' AND MOMENTUM The / .6-/ rg part/ cie has an init/ a/ ve/ ocity of /0 m/ s in the horizonta/ x-y p/ ane irv the di- rection shown. A force in newtons given by F: 24/2 - 8 where t is in seconds is app/ ied to . the part/ cie 05 indicated, Find the magnitude of the ve/ acity of the part/ cie for t= ts and specify the direction 0/ the ve/ ocity. +F, N ja; at : mhz& / éitz/ z- e)dt = i6(zi; -[-5i(/0)]) l O esa/ s - 64 = zenjxie), zçvssm/ s 25:59 . so q/ z/OM/ y) . - gm/ s unchanged zr= 1//233/2 v* b” = /U 5x “““““ "X : "Izr = Lê. : axtan yg& tan Z33 I Copyrlghtoisnhhn wunyssom, Inc. MerIanI/ Kralge ENGINEERING MECHANICSNOL. 2 DYNAMICS, AIE (SI VERSION) a
  • 5. A t? 7.' 3/ 9 CONSER I/ A T/ OA/ o: MOM EN rom No. / A zo-A-g b/ oc/ r has a ve/ ocity of 5m/ .s to the right on a horizon ta/ surface when sfrhc/ r by a Z-/ rg project/ ie with 0 horizonto/ ve/ ocity of / OOm/ s. After impact the b/ och and embedded project/ ie are observed to have a ve/ oc/ ty of dm/ s when passing , OO/ ht 8 after . S// d/hg /4m past A. Co/ cu/ ate the Coefficient of / r/netic fr/ Ct/ bn , uk between the b/ oc/ r and the Jurfacc, Dur/ ng impact / irveor momentum is Conserved cgxwgr: 2(/ oo) 4 20/5) = eau; , dAn/ sed m/ s With constant aCce/ erotion g* = q; Z + 2 ax s 42 = /36424 zax (M), k= -6.07m/ s' -pk (2z)(? .8/) = zz / -6.o7) copyrights issaionn wiieyasons, inc. MarIam/ Kralge ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4/E (sl VERSION)
  • 6. Ani. " 3/9 CONSERVATION OF MOMENTUM N0.2 Each of the 4-/ rg bal/ s is mounted on the frame of neg/ igib/ e mass and is mtating free/ y at 90 rev/ mih about the vert/ ca/ with e =60.° / f the force F on the vertica/ contro/ md is increased to change e to 307 determine the new rotationa/ speed N and find the war/ r U done by F. Point 0 remains fixed Hvert, = const' 50 m/ izwi : mlezajzu f-ZM: = [Eg/ Ye I ”m (300 ? Wol = Kms' We, ^/ ~'^é = U=47*4*év watak? tztoigiiiaiéiivaiglzl + zetiietiijosç- o. 32'. ) u: 4ii0+e52 : ga copyrighie 1993 John Wiley a sam, Inc. Meriam/ Kralge ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4/E (SI VERSION)
  • 7. APT 3// l / MPACT Two spheres of eaua/ mass m are suspended by ' ivires of egua/ /ength l". The / eft-hahd sphere is re/ eased from rest in the dotted position. Determine the expression for the ang/ e p through which the wire ot the right~hand sphere swings after impact. The Coeffi- cient of restitution /5 e. Ehm/ nate Ufeget U; 2 But i/ :Vzgh so Z{= Vegr/ i- cos 0), gêvzgr/ i-casp) ___. .___V29r”`m5/3) : "e, p= co5"'[/ - (lçfii-casév] vzgr/ i-cos a) 3 * JLM . a : =~, .;: a=~': ::, .~. :: , Copyrighioissahhn Wiley& Song/ ne. Meriam/ Kralge ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4/E (SI VERSION)
  • 8. Am? .3//2 CENTRAL-FORCE MGT/ ON An earth . sate/ /ite which executes a po/ ar orb/ t comes with/ n /50 km of the north po/ e at / ts point ot c/ osest approach to the earth. /f the . sate/ /fte passes over the pole once every 90 mfn, ca/ cu/ ate / ts ve/ oc/ ty 2/ over the po/ e ana' / ts a/ t/'tuae h when _ / t passes over the eouator Given: R= 637/ km g = ci. 325 m/ s? per/ oo 7'= 90 mfn a3/z 503/40, 7'= z/7 R@- a3/2 a = 277 ? ~_--- 0050) 537/ 9.825003) ' I 503/43, 21429# 752-3- where r= /;, ,,-, ,=R*/5o / rm z- -3 2 2 I _ 1 U _ 2M ? Bb-Mo jawa) (6370 I 637/H50 Z(6654)] = 3034 00°/ fhm/ Nil, E05. 3/39, r, ,,-, ,=ar/ -e), e. -/- r 9513153 = 0. 0/993 . m/'n : /_ a 6654 Hecoso , 5033/39, ; '= mp7; Foro=90, r= aU-e? ) rhus r: 537/+h :6654 (/ -[o. o/493]2), h= 230 km JLM Cnpyrlghtd ma John wney a sam, Inc. MerIam/ Kralge ENGINEERING MECHANICSNOL. 2 DYNAMICS. 4IE (sl VERSION)
  • 9. ARra/ /a RELAT/ I/E MoT/ o/v The point of . support B for the s/ 'mp/ e penata/ um of mass m 0nd / ength Z has a constant hor/ zonta/ occe/ erot/ on a as shown. /f / t /5 re/ easeo' from rest re/ at/ 've to the mov/ no system w/ th B: Q determine the express/ on for the tens/ on T/ n the r cara / n terms of o. X From Eo. 3/46 Zf-m/ gayagfd) where / am/ j/; Zéê Kak/ Agio' 7% [t-a/ r] mg cos o: m (a . s/h 6' + 10') r / mg [n-d/ 'rj T-mg s/ 'no= m/ o cos 0 +10?) From / éf eo. to' = o cose - as/ n e . . . . . é . 5' I. But / o d0=/0 do 50 facto-a 24(gc056-05//7z9)dt9 o a wh/ ch o/ ves 492: ; (9 5//70 -o[/ -c0s0]) . Suost/ tute / nto 2/14 eo. o' get 7'= mg [sin e +93cos o +}72-(o5/ne-a[/ - cos 9D] or r: mo [ . as/ n e + / o/Wa cos a -2)] JAM cnpyrlghto 1990 John Wllny& Soni, Inc. Meriam/ Kralge ENGINEERING MECHANICS, VOL. 2 DYNAMICS, IIIE (SI VERSION): f]
  • 10. ART 4/2 GENERAL/ ZED / vewroivs secon/ o LAW The two J-kg spheres s/ iae on a smooth horizontal sur/ ace in the x-y p/ ane and are connected by the two identica/ springs of neo/ /o/ b/e mass. Co/ cu/ ate the x-'compo- nent_ of the acce/ eration of each sphere due to the action ot the so-N force apa p/ ied to the Junction ot the springs. Center ot mass G of the so/ v _ **MX system is a/ woys m/ away between spheres, so X- 60/77* ponent o/ accei. of each sphere eoaa/ s 06:& For system 2/55/7757” 60=Z/ s)ê, 5x): 0x = _ copyrights rsnuonn wnoya sans, Inc. MerIam/ Kraige ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4IE (SI VERSION)
  • 11. ART. 4/3 WORK-ENERGY The system of five ic/ entica/ spheres is *e/ easea' from rest in the position shown ana moves in the vertica/ ,o/ ane under the irit/ uence of grav/ ty. The two rig/ ci arms are tree/ y h/ nyea' to the upper sphere. Neg/ act friction and tina the ve/ ocity 2/ with which the upper sph ere str/ kes the horizonta/ surface. For system U: O= AIT+AIQ End spheres have no ve/ ocity. AT: 2[5/m{g)2]+2-'mz/ 'Z=4im2/2 _Q = _ -mg (ex/ g) 2V2'm9o _3_ 4 Av= ~2m 2 a ? g Thus o= mz/ Z-a/ Zmço U2= iJZ-ZQD, U'= Z T b copyrigme rm . iaim Wiley a sm, inc, MerIanIIKraIge ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4/E (SI VERSION) Upon impact m/ aa/ e spheres have ve/ ocity g 7 4
  • 12. ART4/4 / MPULSE-MOMEA/ TUM The three sma/ I spheres are we/ ded to the / ioht rig/ a' frame, which is ro rating in a horizonta/ p/ ane about a vertica/ axis through point 0 with an angu/ ar ve/ ocity o' =20 rad/ s. ii' a Coup/ e Mo=30 iv-m is app/ ied to the frame for ss, compute the new anya/ ar velocity 0.' 3 kg For entire assemp/ y 27%: ti, , #Mo d! : Ah; ;Ma/ tawar -A[Zm)i; tigév] = Zm)-i; ?2io' 30 (5) = [3(o.5)*+ 4/04/2 +3/o. 51709' '- 20) /50 =2.47/é'-2oi, JAM capyrtghw 199aJohn wllaya sam, Inc. MerIam/ Kralge ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4IE (SI VERSION)
  • 13. ?Rvññl/ EM qui. ; Mx-HAL comNTloN . , AT The : umur rm& tune/ u THE &Uu/ ET , HT &rafia/ B _mg EM( - 'NCOMING MOMENTUM : m * V bau& @ma: * 50%&- og- memacu& Haymbal = "WK = MwLbJVVuuLa/ ;R eo 2 A(t77o)(goo)clnff MHQ-Lamb (ruam, CoNDIT/ o/U. WK; Prada» , Arr Tue amran" TIME / rFTEz THE- samar HIT THE Ek& »Hub Been-m: :- ons NJITH 'me 8191:. . . - wrg. Bhg i; Mav/ NG a co 2
  • 14. ?maca Ons ata. ? ) Maze. &MO 2 (O z O. Haga *Hoglmhhl z -_ (mn 'V - 3: Z(MVTK)bM4-cmL/ ZK)bWi ma* bm. ;- bum : fjouxhk : mahma j L _ m& K h! 3 gmbmu`wkbuuq KLJXR>+CMRM *Wu* F” “' Cmbm# Imamat Ruma: ) 2 aza-w > [DUO > go 3-52- ; O < r- m; 3 [DUO . ,9_3?89foo 'z 9,5' mm oo 1 11-88 / Qéç 21;
  • 15. ART. 6/3 T/ ?AA/ .S/ _AT/ DA/ (RECT/ L/NEAR) 7/)e uniform ma' AB / ls placed on the nor/ zon/ a/ true/ r bea' and / eans on f/ yc Vert/ ca/ .back of the cab. /f Me coe/ f/'c/ en! of : fat/ c fr/ 'ct/ 'on az' each end /3 0.4, determine fhe max/ nian: acce/ eraf/ bn a e wn/ 'ch fhe frac/ r may have wit/ rom' . saba/ ne the roof When max. acce/ era/ /on / Is reached, .born ends 5/40, . $0 5:04& 4 @ham/ B ZF : o: Na-mg +0444 =0 I 2/3: = /770x: 0.4M, -Ml = ma iMar/ nad: me; cas 60°- 0.4M L cos 60: L _ a -4/44 . sm 50 = ma ; sm 5a Jo/ ve J 69.5. / n Jan/ rnowns A; 'ma, ada &ya; Ag: O. /36Zmy, Ago. 9461779, a. -o, z42_9 : gym/ S: K/ _nc-*f/ 'c ; $0 mag/ am A/ tema/ /I/ e/J/ EMG- 0 (ou/ d pe gsm( Can a mamenf : encer be fauna' psm/ m wea/ d e/ /xzz/ 'na/ e M. d* N, and y/ e/d cz m/ ec/ /Jz / n ane awar/ bn . P/Ans. Yes/ vu. : copyright& 1990 John wuoy l sam, Inc. Merlaln/ Kralge ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4IE (sl VERSION)
  • 16. ART 6/3 TRANs/ _A T/ ON / CURV/ L/NEAR) / t a coup/ e M: /eo N-m / s app/ ied to the end ot / tn/ r AB w/ th the system / h/'t/ a// y at rest, find the force supported oy the p/ n at C 05 the p/ ate / ffts on' / ts support with 0: 60? rhe / xn/ rs have ne g/ /gtb/ e mass. Ae: Z/ WA: o: /eo - 0.65* = o, 535300 N P/ ate: :gung . - 300 -3o/9. e/ jcos 3o°= 300 , q 4504 g; Z/ WB= /77g0; s (0. 6 cos 3076 - 30 (9. 8/)(o.45) t = 30 (z 5o4}(a. 45 cos 30°- o. 3 51/7 30°) FiLm] . .ILM copyugnto ma John Wlloyl sonmnc. MerIam/ Kralge ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4IE (SI VERSION) `
  • 17. Am. " 6/4 F/ XED-AX/ s ROTA T/ ON N0./ The s/ ender oar of mass m and / enath Z is actea upon ay a tor- sion spring at 0 which exerts a counterc/ oc/ vw/ se couple M on the oar as it sW/ ngs past the Vert/ ca/ pasition With an angu/ ar Ve/ oc- ity a). Write the express/ ons for the n- and t- components of the hearing reaction on the aar at this instan t. capyrlghw 1990 John Wiley l sam, Inc. Merlam/ Kralge ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4IE (SI VERSION)
  • 18. Aer 6/4 FIXED-AXIS nam T/ OIV A/ O. z 7he /600-/ r9 uniform beam rototes about A from rest at 0-0 under the act/ ah of the winch D which main- tains a constant tensian 73/5/01/ in the cab/ e. Find the tbrce atA when 0 = 45 Vs passed. e: alého-@j-Tvtf md ; I,; x 06:45. =67.5° j x T= /5//0')N -_I_ 2 * f* 53"” my: Zçwlrq-ao( Where an; /e0o/9.8/)N /5(/ o'/ /z . sin t; 4 f) - /500/2 t/ Js cos 0 3-' 0600)& Z é' é= 2.34 . Sina-II 43?) -/ .ZZ6'co$ a, 0& 45,: /. 292 red/ s? [ade -fédax 072 iEMs/ ntf-, cgj -izts cos ojaa 562: 73t[co5.; l : -msg 491-24554474 éjss/ .scnraaf/ s* Z5=man where cif-Fe' = 5/i3o7): 7.84 m/ sz A, , 4 /600/23//5//2 45° 4 /57/a3/ca5 6 25° = /sao/ zist) : m: 2/23/7767], where a: : F0 = 50273) -. - z79m/52 A, - / coo/ z E/ jcos 45° 4 /5//093/47 cz5°= /600/277) An= *4.27kA/ , A5270491( @A0454413 = . ILM copy/ mnta 1996 John Wiley& sam, inc. MerIam/ Kralge ENGINEERING MECHANICS, VOL. 2 DYNAMICS, IIIE (SI VERSION)
  • 19. ART. ” 6/5 GENERAL PLANE MCT/ ON N0./ the uniform s/ en der bar AB of mass m is re/ eased from rest in the i/ ertica/ p/ ane from the position shown. Find the initia/ angu/ ar acce/ eration oc. Friction is neg/ ipib/ e. Kihematics Qa-#QA t (ga/ AAJI [ga/ Ah, (UG/ AL _ . .O5 r QA *I LOG/ A it "I (ga/ q )n (a5A)n= Zw2:o, (06/'4 )n: 210150 since c0=o Kihetics ^ZiCx= mc7X: /I/ ;m/ Zo( cosa-Zie( cos 0) 5 0 _ -. _ ; -. z ~ Zia-may. Ai m0-n7( aas/ no; /77 --. I ' _ z , _ Z/ Ié-Ioc. A/ ZJ/ NQ Aizzcasa , z o( Join/ e three eouatiohs simu/ taheousiçr a get N, =mg [i- 55/2726) Mr? mg sin 20 capyriphtq 1990 John Wiley& sam, inc. MerIam/ Kralga ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4IE (SI VERSION)
  • 20. From / rin ema ti`c ana/ ysis aA: Zo<cosa Kinetic diagram Free-body diagram ZMA= io< + mad where 07:06: _QA 4 _UG/ A mQEIsina-Nztcasagémlzoc 4073431) -m [lot cas a)(zi cosa) = _ ' : -_Z. 25( max. A)? m/ loccosa Zotcosa) E/ iminate NZ e get _o<= êgsina izzi ““““ '_ ZMC: fai + mad ehm/ notes reference to M ei/ Z to obtain oc in one eouation A: 4 mêZ-ots/ ha/ -Zé sin êi-mê-Z-LY cosa/ é- cos 0) Z ' ___/ _ 2 Z mQZ-S/ U a-/ zmloc +mZoi cosagcosa) JLM capyrlghld mit John Wiley a sam, Inc. MerIam/ Kraige ENGINEERING MECHANIcS, VOL. 2 DYNAMICS, 4IE (SI VERSION)
  • 21. ART 6/5 GENERAL IRLANE MOTION / /0. 2 Find the normai compo- nent R of the contact force atm( for the do-kg unba/ - anced whee/ for the instant shown when w=2 rad/ s. The whee/ ro/ /s without s/ ipping, and its radius of gyration about the mass center 6 is 200 mm. w, = 30-(4. Sl) sin /5°= 75.2 N WA : some/ i cos i5'= 234 N r : 0.225 m, r`= 0.075m f. m/? *= 30/0200)? Azka-mz (awak-Fauz: 0075/2)? g' =0.3 mis? afra( / I - . 01250; KaG/ A); roc: 007504 0.075)? + azcsFe/ .zoc 24; : max: -F 4 76.2 : soioeesoc -0.3) Ffmc? , : /P-zza = 3o/ - 0.075 oc) soii/ e 3 eos. in 3 un/ rnowisisd get oc: i4 oz rad/ sz (ao= roc=3./5m/ s' for ho s/ ippino) F: -? .47N (opposite to direction shown) E721 copyrighio 1990 John Wllsy a. sam, Inc. MerIamIKraIga ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4/E (SI VERSION) JLM
  • 22. AR7T 6/5 GENERAL PLANE MorioN No.2 CONT A/ ternatii/ e formu/ ation Free-body diagram Kinetic diagram w, =3o{9. ti/ sin i5°= 76.2 N W530i? ti) cos i5°= 284 N r: o.225 m, r': o.o75m, f= m/? Z=3oi0.2)2=i.2 Aja-mz mao= mroc = 3oio.225)o( = 6. 750( N mfn( = 30(o. o75)o( = 2.250( N mfwz: 3o(o. o75)2*: a N ZMC: f o( + mad From FBD ZMC: 7c2io.225)+2s4i0. o75):3a40 / V-h? From Kp maa : 6. 75o<{0. 225) +2.25oi/0.o75)-9/0.225) = /.6'88o( -2025 N-m fhus v 38,46 = /.2o( + ican( -2.025, o(= i4.02 red/ s* Ztymay: R-2e4=3o/ -0.075)(i4.o2), (Note ayo/ dance of simu/ taneous so/ ution of eos. ) JLM capyriglite ml Jalin Wiley il sam, inc. Meriam/ Kralge ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4IE (SI VERSION)
  • 23. ARt 6/6 WORK-ENERGY RELATiONs Each ieg of the /5-/ rg piatform has a mass of 3 kg. When a= o, each of the two springs of, stiffness ir=7oa N/ m is unstretcned. /f a constant toraue M: /8 iv-m is app/ ied to one / eg as shown, starting from resi* with a= o, determine the angu/ ar i/ e/ocity u) of the / egs as they boss the position a = 45? U = A 7' 4- A IA 7" Ave U: Ma = ie/ i7/4)-i4.i4 d A r. 5/45/0450224 4A) -34/3)/ o. 40202 -45° . = 7.570022 4040502”. - / . 924012 A It, = -i5i9 êi)/ o.45-o. 3/ 3 ) - 4/3)/9 ei) i? - A é : 2/24) 700/o. 33)- 0457272: 20.5 u so i4./4=/ .924w2-Z~Z2 +Z6.6, coz: 7.67 / rad/ sf 60122.77 /2767/5 _MM capyrlyhtomaa Jalin Wiley& sonn, inc. MerIamIKraIgeENGINEERING MECHANIOS, VOL. 2 DYNAMICS, IIIE (SI VERSION)
  • 24. ART 6/7 ACCELERA non neo/ w WORK- ENERGY The uniform arm 0A nas a mass of 4-irg, and gear D nas a mass of 5/(9 witn radius of gyrat/ on aoout its center of 60 mm. Gear 8 is fixed . so does not rotate; but 0A and D are free to rotate in the Vertica/ ,o/ ane about their respective oearings. Find the angu- / ar acce/ erat/ bri oc of 0A Just after ras/ ease from rest in the horizonta/ position. du: d? ? au= 4 (9 e/ ){o. /5 de) + 5 (9. ei)(o. 30 ae) = eo. eo ae d -Qê = D-a/ Ol 30( ag; a/ gigcuz): [ow aw . - 1;o<dD=3'-(4)/ o.3)7x de = o./2oc ae a7g= défwzj* dz/ -miz/ Jcudwwnñdz? = feeds; + mêp d; = 5/0. o5)2(3o<)(3 ae) + s(o. 3a)(o. 3 ae) = o. 6/Zoc ae 777u5 20.60 oo = /a/ Z , Las/ acc ae , JL copyrlglne 1998 John wllcy a. sam, Inc. MarIam/ Kralge ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4/E (SI VERSION)
  • 25. ART 6/8 / MPULSE-MOMENTUM EQUAT/ ONS N0./ The 60-/ rg Whee/ with attached hub has a radius of gyration 011200 mm about 0 and is refeased from fest on the / hc/ /he with the Cord se- cure/ y Wrapped around V the huh and attached to A. Determine the ve/ ocity Jl* of the center O Jseconds after re/ ease. The static and Kine tic coefticients of frictioh are 00th eoua/ to 0.40. 25, = o: t? - sam. fi) sih 3020, A>= 294 iv r For eau/ Z ZMC= 0 wou/ d reauire $965 o. 3 isi: - o. /5/60)(9. si) cos so°= o, r=2o4 iv But F = ,L(/ ?=0.4/294/= //Z7 IV i? max so Whee/ .si/ ps with F= //7.7iV 3 sofyan/ v fii; dt= A6x : /[oo(4ei)co. s3o°-r-iiz7]dt= aora-o) O 3 / ZMO atm/ vo s/ [aisr- 0. Z25(/ /7.7}]C7l`= 5o(o.2)“(0_l/5 -o ) 0 / htegrate aha 50/1/6 5//77L/ /fO/7EOU5/y to get f: 3/4 A/ (const), copyrlghw muchn Wiley& sana, Inc. Merlam/ Kralga ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4IE (SI VERSION) JLM
  • 26. ART 6/ 8 / MPUL se -MOMEA/ TU/ Vi' EQ uAr/ oivs No.2. The homogeneaus . semicy/ ihder is re/ eased from rest in the position . shown and fai/ s with a l/ e/acity u' as i/ s corner A str/ kes ana' engages o f/ Lvea' / afch at' O. The cy/ inder then rofates about O. Determine the angu/ ar Axe/ oei& w of the cylinder irnmec/ iate/ y after impact. ,li/ so . find the fractiana/ energy / ass due ti; iinbact. [Why is / here a horizontal com- ponent of #arca of O during impact f) During impact / / ZModt : At/ o A O where ZM = mai* U '0 ' . ° _ Jdi-it' before dust after' /07/3051' 17/7749 /5 impact impact neg/ igib/ e, so [ZA/ é de' +0. mas bg, , = iga h/ o/: mur , Hailea) so w-'mVr/ [a For comp/ ate disk g = éizmy* t (Zmirz . - sim-z By s ymmetry, ;ér ha/ f dis/ r, . Z copyrlghlo 1990 Jann Wiley a. sam, Inc. Meriam/ Kralge ENGINEERING MECHANICS, VOL. 2 DYNAMICS, 4/E (SI VERSION)

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