Dynamics HW7 solution 9th ed

Dynamics HW7 solution 9th ed - h / Jrf 5/30/07 6; é. ea? 9...

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Unformatted text preview: h / Jrf 5/30/07 6; é. ea? 9 PROBLEM 15.13 in Problem 15.12, determine the velocity and acceleration of comer B, assuming that the angular veiocity is 9 radls and increases a: the rate of 45 radIS". / 205 mm PROBLEM 15.12 The bent rod ABCDE rotatols obcaut a fine joining Points A and E with a constant angular velocity of 9 radfs. Knowing that the rotation is clockwise lag viewed from 19“, determine the veiocity and acoeforalion of fume: C, l minim 350%) n.9, \fi‘Q-wM—>4}“Ww Me i: 1513 mm jLJLfi girls 9-? {5‘4"DL'i7fM €[xlm/p( £0. T . h 460 mm A 1% A A fix/F :—,L{mi+lqmi +.Zm \ A. A A I: "— 21—. ' 1-, ' i. L a} 4’ ‘h 3, Q a 3) A '4' w * .x _u_ p . V3 “ (42x [‘3’er (cm Judge an i3er Irv: din 01‘s of rg~{Q-!:wi ‘3 Gambia; cn‘f F“ \ 3A “7/1/97 '/r “i” -.E PROBLEM 15.34 b A simpic friction drive consists of two disks A and Biinitialiy, disk A has a clockwise anguiar velocity of 560 rpm‘and disk B is at rest. it is known that: disk A wiii coast to rest-in 60 3. However, rather than waiting until both disks are at rest to bring them together; disk 8 is given a constant angular acCclcration of 2.5 malls2 counterclockwise. Determine (a) at what'itimc the disks can be brought together if they are not to siip, (b) the angular velocity ofcach disk as contact is made. c) For Miicarmla CLCCQiE’a/‘idgg, (diachm' 0:7cq, -\ «not \/= (“tau 3W flue is up diff-«ti 615" WP CW‘iLLd‘ VA:L/JS E. Ruhr: Fact/’3 O n (W o : moo/1W o f: 5/0....“ (50051!“ a “(mimics mum???- — yoMmC‘sfiigy 150+¢7,8’I317 [1 [-7.0‘Sééq; 19) g]: wo-ietf w 5 '8 :634‘21; , ' "frail 60a”; SOOrfM—~ L$1 “3.05636 9‘ “flagrng ‘ ——__ gory ' ' CM W/l/a‘l 1* f“ d. v PROBLEM'1536” In a‘centinuous‘ printing process, paper is drawn into the presses at a constant speed v. Denoting by r the radius of the paper‘roli‘arany given time and by}; the thickness of the paper, derive ‘aztexpression for the angular acceieracion of {he paper roli. LODKKUE .Crm M 52:13) “HLL, Circle. 04" +LQ ran :5 A: ml, Th2, Gwar‘ {-5 I934 "3 Kraut)“ 54:; mi“ of.» CME‘LavU'L VC‘flctl‘a' A Cfif'p‘fe—fm‘hak «pggt OQWQQA, e‘flxf (aux LC “fill-EU" ‘15 037k ‘ ‘10 v Jib T'w. wad-five “TIL b nurse’s geek-muse, swam o‘g {OH [53 QQgpr‘BaSeX ‘91 “‘45 “Maumv-L. (law til—A : ’bV dis (Li‘ITrl): ,bv M L 52 49* C?) Mfg/921%" M 53?: ZTfV’ ‘J‘V _. J") :-—V~— «2} 2 \/‘ [\C‘) "‘ r LO Q 34 ._ h!“— smméua gm ma, (0 1111-3 "EB ZTTV dotwcflj; ‘ _E:)f “27' ’ gjv 0" : +bcu7’ 7/1/0‘1 WM 1 A ibROBLEM 15.33 I The motion of rod AB is guided by pins: attached at A and B, which siide in the slats shown. At the instant shown, 6' = 40" and the din at 3 moves upward to the left with a Constant velocity‘of 6 injs; Determine (a) the angular velocity at" the rod, (3;) the 328106in of the pin at end A. I ‘ C\ J m <\ x, A A ‘ ' - Lo IL-EBéainbh {pH-32" M ,L‘ ’.\ J 4 ‘ 05 . T LOLA K LIT 2.015! @lfOJ a} > Ah \_ t"3/be 1 “GOV’WI) A A = V55 : a j, - élfiiLm-g‘i 1 50(—40wmj)- -— q} [Hfrgzmh :0 : 0 — H8'5‘5m~ w WLO Vvi ~ 42?}; M V/I/a‘l’ 7’3 6:6 ! PROBLEM 15.57 In the engine syaztem Shawn, 1:160 mm and 11:60 mm. Knowing that the crank AB rotates with a constant angular velocity of 1800 rpm deckwise, deienninc the velocity of the piston P and the angular velocin of the connecting rod when {a} 8 w 0. (b) 6 = 90“, K o 4 J+UOFWKJ corn/pr V3, 2 toooggxgommflmj : 4195 12:; M US] 695 5 rD/B :+lé(7MW‘ if A A f‘ Lfo + 63—wléommx. a = 4225.2 "2; (Ha/3LT 3 T- A A [7%.31mm 4 3+0 15.82 Knowing that at the instant ‘Ishown the angular velocity of rod AB is 15 rad/s cloc‘kwise, determine (a) the angular velocity of rod 319, ‘ (b) the velocity of the midpoint of rod BI); -- M: gimme— VW \me 3,? M/s I wee : 3.? "/5 6158'” 371 V/Z/M 1/?“ _ :PROBLEM15.87 ; Wee? Kn‘oivihg‘ that at the inswnt éhbxvn the velocity‘or collar D is 1.6 ‘m/s upward, determine (a) the angular velocity‘of ‘md‘ziD, (fame veiocity hf min: B," (c) the veibcity of Point A. \ B ' ' ' ‘ ‘ M) “£4 . [A . 1360111111 I I) _ '; ’ _ I r A - 1‘ 4 VB 1 : [5673} + (flax (—Bévmm @3300» + 3 #0 wt m3aoj) on) "78 "‘ ‘79 1* (lg/1; ‘ ‘ VB L Vb ‘65 K F5“) 0 ._ 4‘ f‘ f‘ V31. : )‘—‘w3//-77mm\) ’W/fOMMA tram-re. MFNémf‘ji“ g?" V5 : *HQM'Q 0 z 1.4 53 — 31/77“ to L4) 1 [éfla fax/J h 31!,77 um I ‘ sem‘tfl +0 “50(1); +£4.55 .ifi-OL Lem proLMWé; E oterj ‘ £1"; {5" ’gfi‘m‘fl [fliw’Ez/M-Cowj 0‘9 V“? M. T [\ ‘ VD :‘l. (pm/6 Aug/«Law VelocA-a 3"" V9," ‘ ~— _ , __v 4‘ 4 L I I I . Vii-wk rD/Lzmflvxfitimu) [4— 207.35 CLEJm-M .. I . ‘ 1,915; LU 31(..77 Maw ‘;v&;—{RVI‘\ (lite—90¢) C‘F 1"“0‘3m+ -‘ ma -z§ '5‘”? Ceq+cr B 3/2. M '7/2/0 ‘1 W“ epfl PROBLEM 15.105 A BOO~mm rod rests an a horizontai table. A forciel’fapplied as shown produces the foilewing accetemfionsz 3/, 23.611113; to the right, a=6 rad/’52 c0un£ércloc.kwis¢;gaé viewed fifbm‘abovc. Determine the acceleration (a) 0f Point G; (b) of Point 13. H “Vi/0? ‘er e48, PROBLEM 15.107 ‘ A IO-fl steel beam is lowered by'méans of two Babies unwinding at the same speed from overhead cranes; As‘thg: beam’appmaches the ground, the crane operators appiy brakes to stew down the unwinding motion. At the instant considered, the deceleration cf the cable attached at A is 32 fifs‘ whiic that of the cabin: attached at 8 is 5 Ms‘ betermine (a) the angular accctcration of the beam, (5) the acceleration of Point C. 4‘ k , @Ph _ *1 PROBLEM 15.117 ’L The 150-mm~ratiius drum r0113 witheut siipping on a beil that moves to the ieft with a constant velocity of 300 mmfs. At an. instant when the voice:in and acceleration oi‘the center .13 of Ihe drum are as shown, determine the accelerations of Points A, B, and C of the drum. l 1‘ a My} *5 I m x ‘h _ Va ‘ ’BOOM—f A 1' V45" L/D. *VMUKQM A - r\ ’- "waw/Lx «150*«41’ I. C J) ‘ 2300—750 Lt) :. :- ~—7/ | 150.3% 5 __ A w r -1 1A .4 h’ A __ _ ._ f ,_ v I 1 Ha ab’rOiC/D :qJJreéfian'Ha-‘J {2/43 a : Ia:— A “(If Ian I -— ‘3‘l 2- . C .1 + oCflx-LXC 5 (b)€,(5mj H A A ‘- 'iw: r i w: {\- Qa gLL-F '5 “U— + J - A' {x an‘fe Mam 55c " aid: 1‘ 01.4 J r\ a _——— ‘i' l M ’2) ant " s? _ _5_d 3) an : 3%: 7/1/07 ,/2 PROBLEM 15.12% a "Q 4 Knowing that at the instant shown rod AB has zero angular accelerafion and an anguiar velocity of 15 rad/s comiterclockwise, determine (a) the angular acceleration of arm [312“ (b) the acceleration of Point D. 40 * ..‘ ., f A \ ., 1 x" +7 0. $4 - our 9% w M? A X W” WWW/5 _. ’0: A 6L0 ‘ d _ _ 2 A A D? Walt—3'” ’Lfln‘~3m3> N. ’.‘ I A V 2 ’.‘ 1 4‘ (XE : \dbt (4:4 J +<>ZDE X: + Lf"nl,{)bg,(‘ +‘ 334 W05 3 “(my 01% : Ems 3M 4 “73-4 (0313),? 4 (—095 ‘7’9, + 3.". (A2062); \ /\ m > 4 A .4 V6: “WWW; '“ ‘éfiwflbgfli 60%“ J + 95" 5 r A K > x A A As ’} ’3\ 4‘ ' Vb: VB+ VD/B 1 4-»(1541 ‘1" WbbfifiKIOML 75- QOJ‘VL‘SA “‘5'” ,w . A /\ # up = {<20 é few comm + wag—x _ ' fl‘ 5 A A . 6 [ii VD A VE + Vo/g 8' 0 + QDEQ/X (#954; “3:4 38 1 B‘WDCL/‘Kq 120% WMFW of ago W «My was 1 “515 A o r + wast) . / ,LZ7 éO’g/+(Om/CJN>, Z'CUMHK 5 K N £03“ + 40Wb£ ' " Li 7g ' '60 5% ,m f 5 ' IOQJM) : #120 S" - \L K 3 '1 (4)03 1/3 Uba ? Ebwfa W M firm “MK WNW? M - 2 2 g) “700 $1403» tom 0‘01: 3 n * [Tina/b? J) MEMO” + £75 '31 r “335%” 4 5" (“0°51 WA 2. 34 \L 7- . , 1 3:” 5’» g + L, ‘q LL 97.. ('53 lows) b t 5 L ~ 70073;»: 3? DE _.__,____._—.——————— \ «Mo? 9 9 ,4 . __ _ _.._.____7< . ‘ E MD; :‘1469 ar‘LoC : (OSfl/s2 A . ’5 '2390 ft a +Lt L) : tlpipxl‘n + L’*‘4( 51 Q E 1 0r Wm ' we r 6? >Cwfi° z . _‘ . 2 A 13) l4 + [@619qu + 5%?)35 3?— A ms ‘3 ’3 TA 7/6/03 ‘ *3 2 A: PROBLEM ‘15.“38‘)r 7 by + v A wheel of radius r rolls.without'slippingalong the inside of a fixed cylinder of radius R with a cofistant angular velocity 0). Denotingby P the point of the wheel in contact with the cylinder at ' 2&0, derive expressions far thehcrizomal and'vertica! components ofthe veiocity of P at any time t. (The curve described by i’oint P isa hypocycioid.) bflfi‘mt 6 75 0.3 Showvfi 59w: w‘ugAs Pa“ wii’hopck Skyrhna J "HIM; arc, 0C, (5 6644‘ \L-o we, fC, ’H/wu : qu f3 (3 R4— CN— ‘v‘t mat W- ” (“pf—p * “a )c / i P t H” Pwmaflt m cor A 'f m -3? TM) E—F>M / F‘U Am PM”: + {’41}th We; ; {AW MM? 72 ...
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Dynamics HW7 solution 9th ed - h / Jrf 5/30/07 6; é. ea? 9...

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