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# Statics MEM202

Drexel

GPA 3.65

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This 83 page Class Notes was uploaded by Jada Daniel on Wednesday September 23, 2015. The Class Notes belongs to MEM202 at Drexel University taught by AndreiJablokow in Fall. Since its upload, it has received 34 views. For similar materials see /class/212387/mem202-drexel-university in Mechanical Engineering at Drexel University.

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Date Created: 09/23/15

5 Solutions 44915 12309 511 PM Page 320 2010 Pearson Education IncUpper Saddle Pl 7 NT exist No 5 1 Draw the freeebody diagram of the soekg paper roll w 39 h has a cente fmass a G and resb on the smooth blade of the paper hauler Explain the signiticance oteach tcrce acting on the diagram See Fig 57717 w509395149039 Th1 Sllnlfiunquot a bah For W is the u a 1391le wdghu on Ill pave mil N4 mm mmxmmdihhdemniuni mini 1me ll 5 2 Draw the freeebody diagram of member ABwhich is supported by a roller at A and a pin at B Explain the signiticance of each torce on the diagram See Fig 5417 Ah an nl plmenn mllu 11 H Van Dfpin on nabs 5 NA BX 8ft 4 5 Solutions 44915 12309 511 PM Page 321 mnv m quotmin ti n Tn Tme v midi Ry le exist No portion 5 3 Draw the freeebody diagram of the dunipsterD ofthe truck which has a weight of5000 lb and a center of gravity a G It is supported by a pin at A an a pinconnected hydraulic cylinder BC short link Explain the significance 39 77b oteach torce on the diagram See Fig 5 Th2 Signiflzanu clack ram w is me affa DryIvin wand on line dumpsu A and A an me pixA Indians on no dump in is iii hydnulic cylinda 3c union on dreamy 5 4 Draw the treeebody diagram of the beam which e suppom the 80kg loa and is supported by the pin atA and D J a cable which wraps around the pulley at D Explain the significance oteach force on the diagram See Fig 54b 4 5 4 Tlmofubknnm Av fnlunfpmnnbam Al maxim fan nfahhwn bum Zm 239quot l5quot 80 8IN 5 Solutions 44915 12309 511 PM Page 322 2010 Pearson Education IncUpper Saddle Pl 7 NT exist No 5 5 Draw the freeebody diagrarn of the truss that 39s 3 supported by the cable AB and pin c Explain the signiticance cteach torce acting on the diagrarn See Fig 57717 1h Signi cant of Bldh Forquot qmqmmepincmmunnmems V Zm Tquot 39mhtabbAH minnoans C IkNInd4kaumI lad fxlufexmlllpplhl muun I 2y Ihc mus 1250 lb is suspended trcrn a cable attached at B Explain the signi cance cteach torce acting on the diagram See Fig 57717 Tin Si ni mnu u Each Farce w is the arm of quotwhy wish on m been A zndA uerhepind rimnus unthzbooma 7 is ll ubk EC mu man an In boom l2501b am is Iii suspmdai laid man an 3911 beam 5 Solutions 44915 12309 511 PM Page 323 mnv m quotmin ti n Tn Tme v midi Ry er exist No portion 20 1b 5 7 Draw the freeebody diagram of the spanner wrenchquot subjected to the 2071b force The support at A can be considered a pin an the surtace of contact at B is smooth Explain the significance of each torce on the diagram See Fig 57717 L rN focal lindannwmlch A 39 W 701 5 3 Draw the freeebody diagram of member ABC which is supported by a smooth collar at A roller at B and short link CD Explain the significance oteach torce acting on the diagram See Fig 57717 Th Significant of am pm lv Li mesunoin colhnuninn on memba 45 N is me rollu snppm l motion on manneruc Fm Lr the shun link mnian on memberuc 15 kN i lh dfwlafulundzpp d unzan maslb ABC t m m is m e oomlcrmal applied oouplg mnmuu on me 5 Solutions 4491a 12309 511 PM Page 324 2010 Pearson Education IncUpper Saddle Pi 7 NT I exist No 5 9 Diaw the freeebody diagram ofthe bar which has a negligible thickness and smooth pains of Contact at A B and c 1aih the significance of each force on the diagram See Fig 57717 quot4 Myrtle Bluofwoodonbu whim nthad an m 5 Solutions 4491a 12309 511 PM Page 325 mmgt a quotFriquot ti n Tn TTnnv midi Ri vNT exist No portion 5 10 Draw the freeebody diagram of the winch which consists of a drum of ra 39 4 in It is pinconnected at in center c and at in outer rim is a ratchet gear having a mean radius of o in The pawlAB se as a tworforce member short link and prevents the drum from rotating Explain the signiticance of each orce on the diagram See 39 5417 qc inchingmm Fumulmlondmm lat mlfmnf hkmdmm 5 11 Determine the normal reactions at A and B in Prob 571 s Equallanl of Equilibrium By setting up the Indy In in the a a show one on obnin mu rwl solution for N Ind N I I D N 49055in 3039 0 N a 5 N A My 0 NA 490socs 20 u N 425 N An N I 0 Aa 5 Solutions 4491a 12309 511 PM Page 326 2010 Pearson Education IncUpper Saddle Pi 7 NT exist No 5 12 Determine the tension in the cord and the horizontal and vertical componenm of reaction at supportA 39 4 of the beam In Prob 5 gm o rm TG10 mum a TmeNIION Ala quao Aaso AstN Au oTEF 0 4 mioxsoiG m9u o 709quot A An 1 1 Pi p 1 man 13 Determine the horizontal and vertical componenm of reaction at C and the tension in the cable AB for the truss in Prob 55 Equation of Equilibrium The tension in II 93111 m be obtained 39 y by summing mums about point C mm 30 2 1sin 30quot4 32 4 0 539 Am 75 425w c sa9mso o 2 C1 1 J in c 5JILN Ans Tuo C589in30 3 40 kN All 5 Solutions 4491a 12309 511 PM Page 327 mmgt m quotFriquot H n Tn TTvmv aridl Rt vNT exist No portion 5 14 Determine the horizontal and vertical componenm of reaction atA and the tension in cable BC on the boom in Equuinu 21 Eq uiubriunr The are in table ac m be obuinni 39 y summing mnmuin hnnr poinlAr m 0 Tush nao uo 650oos zois lLSOsin swzo 0 T 110569lbllllrjp Am an o A uusssg o A 10106A lb 102 kip An lg 6501150 ll0569 A 61527lb615 kip Au Determine the horizontal and verticalcomponenm of reaction at A and the normal reaction at B on the spanner wrench in Prob 577 at IozN1IOUD Ar Jul mama Alll I anttr Aua 0 anon Am eTD 0 A 20 0 41413 A 5 16 Determine the normal reactions atA and B and the force in link CD acting on the member in Prob 578 Equalia nr 11 Equilibrium The nnnml reaction NA mu he ohmian by sunning mama about point C m o 15sin 60 6 25ms arm 4 None 493 NAsin 45 10n N 1059 HI L06 In An Au 0 l059cos45 2l5m60 Fw0 mm 4 T2 0 N L059sin tin 153M 60quot 0 N 42W 5 solutlons 44915 12309 511 PM Page 325 2010 Pearson Education IncUpper Saddle Pl 7 NT exist No 5 17 Deterrnine the normal reaotions at the points of oontaot atA B and c of the bar in Prob 579 Air 0 Nclin air lo sin 3039 0 N 517 b An ant o 10 cos W131732M5I131 5171 64 o N L39L39l B An p w quot5477 mammary2mm N I link All 1 Deterrnine the horizontal and vertioal componenm otreaotion at pin c and the toroe in the pawl of the winch in 10 omo Fl asnowo m Fquot a A006h4mh A F a 1 EF0 C4m5 5333 A a 1 trm soooC Aoo um grizzly All 328 5 Solutions 4491a 12309 511 PM Page 329 ti n Tn TTnn v midi Ry vNT mmgt m quotFriquot exist No portion 120er Woman when she is wearing regular shoes sti1etto heels Assume all her weight is placed on one and the reactions ooour at poinmt and B as shown 9mm i01575 N7o Tvyo N986 1100 Na2i4lh smhqishos Qua o mum Ni 45 0 NA 1M h NB500 l200 ND 20 anyoz 5 19 Compare the toroe exerted on the toe and heel of a an foot ML 1201b NW 1201b ig 075 in 375 in IZo lb 075111 375ni NA 0 5 5 Solutlons 4491a 12309 511 PM Page 330 2010 Pearson Education IncUpper Saddle Pi 7 NT exist No 5 20 The train car has a weight on4 000 lb and a center ofgmvity at G It is suspended trorn is tront and rear on the by six tires 1ocate at A B and c Deterni39 normal reactions on these tires if the track is assumed to be a smooth surtace and an e ua1 portion of the load is supported at both the tront and rear tires 24 000 lb wmao mam241mm chlsm lbauh39p Am Luann 1M 115o N4lskiu Am Turo 2N uoooo N 115 Ann 5 Solutions 44915 12309 511 PM Page 331 mnv or quotWu H n Tn Tme v nddl Rt er exlst No portlon 5 21 Determine the horizontal and verticalcomponenm of reaction at the pin A and the tension developed in cable BC used to support the steel frame C 7 Equations of Equilibrium From the free body diagram of the ame Flg a i the tension T quot39 quot L 39 39 39 39 quot equilibrium about point A 3 4 21 0 33T31 611 300 T 34452er 3462kN Ans 1 39 39 randvaxes 3 2Fx1 AX 346 5o Ax2077kN208kN Ans T2 F0 Ay 60 3462 io 5 A 8769kN 877kN Ans 5 Solutions 44915 12309 511 PM Page 332 2010 Pearson Education IncUpper Saddle Pl 7 NT I exist No 5 22 The articulated crane boom has a weight of 125 lb and center of gravity at G If it suppch a load of 600 lb determine the torce acting at the pin A and the torce in the hydraulic cylinder BC when the boom is in the position shown 241 o r m40 l39l inwm 124 4009 o F 41381b4l9Hp Ann Jar g 4188m40 o 4 320EIb121Hp An HEP 0 A 41835in40 600 125D A 1975 Ans 5 Solutions 4491a 12309 511 mmgt m quotWu trnTn PM Page 333 WM 7 add Ry vNT exist No portion NC can be obtaian by 5 23 The airstroke actuator atD is used to apply a force of F 200 N the member and vertical components of reaction at the pm A and t e force of the smooth shatt at c on the member at B Determine the horizontal 39 h Equatinns of Equilibrium From the free body diagram of member ABC Fig 1 A L l A 2444 0 2008m60 800 NC6002005in15 0 NC21260N 2st Ans U 1 randvaxes 321 Q Ax212r6000 15 20000560 0 A 105 N Ans T2 Fy 0 A 2126 sin15 2003in60 0 A 118N Ans 5 Solutions 4491a 12309 511 PM Page 334 2010 Pearson Education IncUpper Saddle Pi 7 NT exist No 5 24 The airstroke aotuator atD is used to apply a toroe of F on the member at B The normal reaotion of the smooth shatt at c on the member is 300 N Determine the magnitude ofF and the horizontal and vertioa1 oompone no of reaotion at pinA Equations of Equilibrium From the free body diagram of member ABC Fig a F L L Jam 0 F sin60 800 30m 600 2005in15 o F28222N 282N Ans e t t a 3213 0 AJE 30000s15 2822200s60 A 149 N Ans A 3oosin 15 28222sin 60 o A 157 N Ans 5 Solutions 4491a 12309 511 PM Page 335 mm m quotPrim n W Th TTan v add Ry vNT extst No pomon 5 25 The sooeloeleotrrool tmnsformerwith oerrterot gravity t G is supported by a pin a and a s h pad at Determine the horizontal and vertical oompoheho ot reac on at the pinA and the reaction ot the pad B on the transformer o 0 JAE g39a N3 and Ay L quotL 39 L W A e e L C2MA 0 NB3 3001r50 N3 150 h Ans Tszo Ely 3000 A 3001b Ans Ive rear r L 39 L raxi 31 z ISOAx0 AX 150 lb Ans 5 solutlons 44915 12309 511 PM Page 336 2010 Pearson Educatlon IncUpper Saddle Pl 7 NT exlst No 5 26 A skeletal diagram of a hand holding a load is shown in the upper tlgure If the load and the torearm have masses on kg and 12 kg respeotlvely and thelroenters of mass are looated at G1 and 62 determine the toroe developed in the bloeps CD and the horizontal and vertloal componenm of reaotlon at the elbow joint B The torearm supporting system oan be modeled as the strnotnral system shown in the lower tlgnre Equations omqnnnrrlnms PM the no body diam who structunl I Po 1 F 39 39 39 39 39 A 02 about pmnlB loo mm 135 mmA 65 mm gm o 2931100l3565l298l135 65 a sin 5 FCD13L25NI3IN Aux mdyaxes gm u 31250m75 BX0 B 3397 N 340N Ans my 0 lsl25sin7s 298llmash By 0 B IODMM 5 solutlons 44915 12309 511 PM Page 337 mmgt a quotFriquot ti n Tn TTnnv midi Ry vNT exist No portion 5 27 As an airplanes brakes are applied the nose wheel eaem two toroes on the end of the landing gear as show Deterrnine the horizontal and vertical componenm of reaction at the pin c and the toroe in strut tilrm 3 O4 f an 20 39m pit 0394quotquot E5 50quot Equalinlu of Equilibrium may by summing lamnun Ibmll pain C lec 0 21 61un 20 rum sweat 5cos swamquot 2039 o a oxs7motssam An kN 3637 m Ind sum rems alongx and y axu Using It mania v1th Tu 0 tumm sir c o c 616 W an 0 08mm so 2c 0 An 5 solutlons 44915 12309 511 PM Page 335 2010 Pearson Educatlon IncUpper Saddle Pl 7 NT I exist No 5 23 The 147Mg drainpipe is held in the tines of the fork litt Determine the norrnal toroes atA and B as functions of the blade angle 9 and plot the resulm of toroe vertioal axis versus 9 horizontal axis for 0 s 9 s 900 425 0 Mn L4m assumed 394 mm quotA 13quot lilBkN Am My m N 14IO 9 31m5390 9 quot N137 m8kN All I NB M M 39 N 131 m s 5 Solutions 44915 12309 511 PM Page 339 mnv m quotmin ti n Tn Tme v midi Rt er exist No portion 5 29 The mass of 700 kg is suspended from a trolley which moves along the crane rail from m to d 35 m Determine the force along the pinoonneoted knee strut BC short link and the magnitude of force atpin A as notion otposition P ot these resulm otFRC and FA vertical axis versus d horizontal axis 70751 t1 4 villa 0 c3lJ1w9al o n 5712Jd An 3 EC r2F 0 A 5711mm u A m3s1 I 139 amp w 5722Sd1oo9uo A md 6867 F s 343154 e um 6151 An Hm 5 Solutions 44915 12309 511 PM Page 340 2010 Pearson Education IncUpper Saddle Pl 7 NT exist No 5 30 If the toroe ofF 100 lb is applied to the handle of the bar bender determine the horizontal and vertionl componenm of renotion nt pin A and the renotion of the roller B on the smooth bnr my bender Fig 1 A and N can be uhhimd by writing the force equation of equilibrium T2F0 Ay1005in3m0 Ans mm o N am 60 5 100lt40 0 N5 lmoN I60kip Ans axis 25 amp Ax IMDIOOM30 0 Ans Ax l513l40N l51 kip 5 Solutions 4491a 12309 511 PM Page 341 mmgt a quotWu ti n in TTnnv midi R1 vNT exist No portion 5 31 If the force of the smooth roller at B on the bar bender is required to be 15 kip determine the horizontal and vertical components of reaction t pin A and the required magnitude of toroe F applied to the handle bender Flg a me Fun be obtained by Writing the moment equutiun orequiiihiium abuulpaintA 2141 0 lS OeosSt 5F40 0 F 9375 I Ans axlsi 251 l AV375w830quot 15000 A 4188 lb 142 kip Ans Trrym A 937SSinWD A 46875 lb 469 lb Ans 5 Solutions 44915 12309 511 PM Page 342 2010 Pearson Education IncUpper Saddle Pl 7 NT exist No 5 32 The jib orane is supported by a pin at c and rod AB 7 4 m Ifthe load has a mass on Mg with itsoenter of mass looated A at G determine the horizontal and vertioal componenm of reaotion at the pin c and the toroe developed in rod AB on the orane when r 5 m 3 2 m C 0 2 m B 7 4 h r it will oxen afurchAB w as Fig la From the free ebony diagram FAB can be oblained by writing 1h mumcnl rquanan ofequilibriurll about poim C X 2Mc 3 FAB E4 1 FM 02 2M98l5 0 quotA3 3832031N383kN Ans 25 cz IX 3832031 g 0 C 30 65625 N 307 kN 3 38 3703EJ 2000931 C D Cy 337219N 337kN Ans 209073951A 5 Solutions 44915 12309 511PM Page 343 mmgt a anu ti n Tn x Hwy 7 midi Ry v NT 5 lst No portion 5 33 The jib crane issupported by apin at Cand rodAB The rod can withstand a maximum tension of 40 kN If the load has a mass onMg with itscenter of mass located at G determine its maximum allowable distance r and the corresponding horizontal and vertical compouenm of reac ion t 39 rilwillexerl afameFAB Mquot39quot a Fm h r m u ruemmm equalion of equilibrium aheut point c 345 0 4O mm4 40 W01 2000981x D x522m Writing the fora oquuzious ofequilihrium along the x and y axes straw Cr Aoooo35o Cx 32000N 32kN Am TV 0 400mg 200m981cy 0 cy 4380N 43EkN Ans 4m 5 400ao A 45839quot 3 19 A 2000 96 A 343 5 Solutions 4491a 12309 511 PM Page 344 2010 Pearson Education IncUpper Saddle Pi 7 NT exist No 5 34 Determine the horizontal and vertioai oomponeno ot reaotion at the pinA and the norma1toroe at the smooth peg B on the mem er Equations of Equilibrium me ihe free lt body diagram of the member Fig a N L L J A 11 mm o NB0V46000E 30 D8 0 N3 1039r23N 104kN Ans r on axes LEE Q 600008 30 10392300 60 Ax 0 A1 0 Ans T 21quot 0 Ay 1039r2351n60 600 in30 0 Ay SOON Ans 5 Solutlons 4491a 12309 511 PM Page 345 mnv m n Friquot tr n Tn Tme v midi Pi v NT exist No portion 5 35 The framework is supported by the member AB Burg whi h resm on the smooth floor When loaded the pressure distribution onAB is linear as shown Determine the length d of member AB and the intensity w for this case wig T FIr rwoo Pr39mlb Muww QM 0 m ma 0 16 Au 5 lud lmm m 1 2 w 167 ram An 5 Solutions 44915 12309 511 PM Page 346 2010 Pearson Education IncUpper Saddle Pl 7 NT exist No 5 36 OutriggersA and B are used to stabilize the orane troni overturning when lifting large loads If the load to be lifted is 3Mg determine the maximum oorn angle 9 sot at the orane does not overturn The orane has a mass of 5 Mg and oenter of mass at 60 w ereas the boom has a mass of 06 Mg and center of mass at 63 an 0 s 9 7 4 3 981 95 sin a 07 06031 5 sin a 07 2 o E 16quot A 5 Solutions 44915 12309 511 PM Page 347 mnv a n mi N n Tn mquot v midi Rt 7 NT exist No portion he wooden plank resting between the buildings de ects slightly when it suppom the soekg boy This A iii B deflection causes a tri ngular distribution of load at is ends N having maximum intensities of WA and wR Determine W i W i and wR eaoh measured in Nm when the boy is standing W E 3 m from one end as shown Neglect the mass of the plank quot 7 03945 m 50 84705Al m 0 490505 o Ew 03915 o A 15m I I M l w 1136NmllkNm AII ll 3 em I Uquot I My o WAO65 lll16043 4905 a o 2 1003945 3 05 pm 14376 Nlm slumm All 347 5 Solutions 4491a 12309 511 PM Page 345 2010 Pearson EducationlncUpper SaddlePi 7 NT I exist No 5 33 Spring CD remains in the horizontal position at all times due to the roller at D If the spring is unstretohed when 9 0 n rnoket nohieves its e quot 39 position when 9 300 determine the stiffness k of the spring and the horizontal and vertionl oomponents of renotion ntpin nmitjnn 39 r 065in30 mquot39 39 39r39 F5Pkx03k Equa uns of Equilibrium From the free body diagram of the bracket Fig a the 21 e n n L e r A 1 s r r L 1 r ati mspec vely 2MA O 03kmS30 06 300005 30 045 SOOsin 30quot06 0 k1327r35NlmL33kNlm Ans T2Fo Ay 3000 A 300N Ans Using Ihe 55quot k 132735 N In and writing the force equation of equilibrium along the axis 2 a Ax 03132735 0 Ax 39821 N 398N Ans 5 Solutions 44915 12309 511 PM Page 349 mnv m quotFriquot ti n Tn TTvm v addl Ry er exist No portion 5 39 Spring CD remains in the horizontal position at all times due to the roller at D It the spring is unstretohed w en 9 0 and the stittness is k 1 kNm determine the smallest angle 9 for equilibrium and the horizontal and vertical oompone nm of reaction at pin A 06sin9 quot 39 39 L 39 39 39 F51 kt 150006sin9 QDOSin 9 Equations of Equilibrium From the free body diagram of the bracket Flg a the equilibrimn position 98nd Ay can be oblained by writing the moment equation of respectively 2114 A 0 9005in0 0058 06 300 sin 906 300uxs9045 0 5405in9 cme 1803in0 13500s6 0 Solving by trial and error yields 9 23083 231 Ans Trry0 Ay 3000 Ay sooN Ans 0 23083 39 1 39 quotquot the axis 125 a A 9005ln23083 Ax 352861 353 N Ans 5 Solutions 44915 12309 511 PM Page 350 2010 Pearson Educatlon IncUpper Saddle Pl 7 NT exlst No 5 40 The plattorm assembly has a weight of 250 lb and center of gravity at 61 If it is intended to support a maxim smallest counterweight W that order to prevent the platform trom tipplng o mammalaka HEM a Aoot21wln W7 a 5 Solutions 4491a 12309 511 PM Page 351 mmgt a quotPrivy n n Tn TTvmv midi Ry vNT exist No portion 5 41 Determine the horizontal and vertical componenm of reaction at the pin A and the reaction of the smooth collar B on the rod Equuunnmqunmmm memefmebodydiagmm A and N umbc mumcm Iqua a ufequiliblium about pninlA Ay73004500 A 75 MA 0 N54 in30 300l45030 N lb L u chums 324w Ax SLSD Ax8251b Au 5 Solutions 4491a 12309 511 PM Page 352 2010 Pearson Education IncUpper Saddle P 7 NT exist No 5 42 Determine the support reactions of roller A and the smooth collar B on the rod The collar is xed to the rod ABbut is allowed to slide along ro CD N amiss 9000 T 2F 0 N5 127279 L27kN qualion ofequilibrimn about point B 25 a 12721901545 A o x Ans 2545 mm mnmw wm M o M 7N m m 5 Solutions 4491a 12309 511 PM Page 353 mnv m quotFriquot n n Tn UM v arid Ry vNT exist No portion 5 43 The uniform rodAB has a weight of 15 lb Determine the force in the cable when the rod is in the position shown 5 H No gum 0 N5 tin 40 152s co m 0 N 3933 In Lin3950 Tcos m sgako 191 Am 5 44 Determine the horizontal and verticalcomponenm of force at the pinA and the reaction at the rocker B of the rved beam mg o N m 100w Ira scam 1039Z M 114279143N An ryr 0 A 5moole392mcmls39w790 A 342 mN A Lxr 9 l65minl F2005iuli 0 4 a 351 N An 5 Solutions 4491a 12309 511 PM Page 354 2010 Pearson Education IncUpper Saddle P 7 NT exist No of 2500 lb with a center of gravity at G If the crane 39 required to lift the 5004b rum determine the n rrna1 reaction on both the wheels at A and both the wheels at B when the boom is in the position shown 5 45 The floor crane and the driver have a total weight Fm n J 2445 0 2500l484500150m30 B4 NA21l4840 zzttl4ft 84 NA 1850401blr85kip Ann Trrym 185040 7500 500N5 0 N 114960 lhlISkip Ans 5 Solutions 4491a 12309 511 PM Page 355 mnv m quotFriquot n n Tn m v midi Ry vNT exist No portion crane to overturn when is boom is in the position shown 1 39 L 39 H thewlieelatAwill L A Mlnon w r L 34quot I the oor crane Fig a Wcan be obtained by writing the moment equation of equilibrium about point B GEM 0 250014 8 4 WUSOOS 30 84 0 W 533725 lb 534 kip Ans 5 Solutions 4491a 12309 511 PM Page 356 2010 Pearson EducationIncUpper SaddlePi 7 NT exist No 5 47 The motor has n weight of 350 lb Determine the 8501b toroe thnt enoh of the ohnins exerts on the supporting hooks I at A eglect the size of the hooks and the thiokness otthe benrn dinquot in quot H n m 1539 E a 9m 0 cole l 00SFccoslo 2 0 1 lama chinlW I inam F inlo39o 2 Tzr 9 BSOijlW mav gmlv0 3 Solving mm 2 and 3 yields F 321b 50 FLH llb An 5 43 Determine the toroe P needed to pull the soekg ro11er oVeI the smooth step Take 9 60 swan HIM o 50minthossa9uomzova33m memj Psin60 033l39 0 P441N An 5 Solutions 4491a 12309 511 PM Page 357 mnv m quotFriquot ti n Tn Tme v midi Ry vNT exist No portion 5 49 Determine the magnitude and direction 9 of the minimum tome P needed to pull the soekg when over the smooth step 05 Fm r N o o cos a 3356 Q2 0 50 981sin20 05 509 1m203903317 P005 9015 P sin 9 03317 0 23675 Pm No5 P sin 0337 0 P 23575 05 cm a 03317 sin a Fm Pnln div 723575 05m 9 02317 m a 0 HT 39 05 cos 0 03317 sin W 03317 quot9 F 8 316quot Am F 395 N Ans 5 Solutions 4491a 12309 511 PM Page 355 2010 Pearson Education IncUpper Saddle Pi 7 NT exist No a 0 The winch cable on a tow truck is subjected to n the cable is directed at 9 7 e ud both rear whee equilibrium The truck has a total mass of 4 Mg nd mass Center at G F 0 60m 60 F0 F5196N5i20kN An em a m 41 100611 2 woman mnx 039l5 o quotAswan1mm An 72 o 171364llf9llmm60 g o mane 1A9kN Am 5 Solutions 44915 12309 511 PM Page 359 mnv m quotFriquot ti n Tn Tme v midi Rt er exist No portion 5 51 Determine the minimum cable torce T and critical angle 9 which will cause the tow truck to start tipping ie for the normal reaction atA to Zero Assume that the truck is braked and will not slip at B The truck has a total mass of 4 mass center at G X dug tr 4ltf9ntzsl 1mm TmlDL5 o r quot out nine ll39 65 mt ninBOZ m0 a 0 as m s Iin tn sin9 2ux90 GInquot163 339634 An sum x 1er A r on suanz sin 514339 29 I 5 52 Three unitorm books each having a weight W and length a are stacked as shown Determine the maximum distance d that the top book can extend out trom the bottom one so the stack does not topple over W 41 4 i V Equl b lll Fur up two books in upper book will topple villa me I microfqu uflhisbonki m shorighturpoinu 39nllllf ll me 1 maximmdimmlmm R ld cnflhh hmkm puinIA is at Equallan u Equilibrium Farm em um noon the lap two books A w39 mpp1 Iboux will 3 Cum o Wa d Wd O d 7quot Am 5 Solutions 44915 12309 511 PM Page 360 2010 Pearson Education IncUpper Saddle Pl 7 NT exist No 5 53 Determine the angle 9 at which the link ABC is held inequilibrium if member BD mo es 2 in to the right The springs are originally unstretched when 9 0 Eneh gt kw 100 H m sprin has the stiffness shown The springs remain horizontalsince they are attached to roller guides m 0 F 6m9F 6eos8D Fc lv F r ka auJu qx aanlF 139 Iliumblquot nun h 5 Solutlons 4491a 12309 511 PM Page 361 mnv Hy nwn ti n Tn TTvm v midi Pl vNT exist No portion 5 54 The uniform rod AB has a weight of 15 lb and the spring is nnstretohed when 9 0 If 9 300 determine the stittness k of the spring cumin me mangle can in mine in givs I iZJJGH7321 22536L132ws120 3113 it Using Inzsin law sinlx Vsin 12039 aw 39 17in Equation of Equlllbn unl m on in die sinin Ian 5 Wind 39 aboulpoinlA direclly by sumnun alumni 9 ma 0 15m 30 l5Em 361l 30 1 1050 in Spring Farquot Farmulll m Iprillg manna x 37ls3 cm L Am 5 55 The horizontal beam is supported by springs at in gooN ends Each spring has a stiffness of k 5 kN m and is originally nnstretohed so that the beam is in the horizontal 39tion Deterrnine the angle of tilt of the beam ita load of 800 N is applied at point c as shown Equation 0 Equilibrium 39nicspring tomM um 11 cm bcohlailssi 500 N dmsaly iummmg rooms min pain la and A lupecIver 0 2M 0 loom 53 so in 53um ism o mnsootuo r2sssm J Syria ramm Applyth s 5 wellv I s 53333 It A 0JOG7 sum m I m 2quot 26667 A m 0105333 in F k Geamnry n mgkafu39lla is 5 Solutions 44915 12309 11 M Page 362 2010 Pearson Education IncUpper Saddle Pl 7 NT I exist No 5 56 The horizontal beam is supported by springs at is 800N ends If the stittness of the sprin at A is kA 5 kN rn determine the required stittness of the spring at B so that if the beam is loaded with the 800 N it remains in the horizontal position The springs are originally oonstrnoted so that the beam is in the horizontal position when it is unloaded O 01067 405335 4053 as m Equation of Equilibrium 39nIESp ng rums uA win an be AA 0 0 7m nhuinod direuly by sllmmhll momus alsompohns a MA mpeuinly M 0 8002l530 5 53313N EMA 0 lam lino 0 5 26667N Spring Furnmh Applying A g w hm AA 53333 26667 sum 010mi A 7 Guzman Requires A A Then 255 o 1067 k k 1500Nm250kNIn Am 5 Solutions 4491a 12309 511 PM Page 363 H n Tn WM 7 add Rt vNT mmgt m quotWu exrst No pomon 5 57 The smooth disks D and E have a weight onOO lb and 100 lb respectively Ita horizontal torce of P 00 lb is applied to the ce 39 etermine the normal reactions at the poinm of contact with the ground atA B and c N Fudth 121 roNquoto dug Nclm N39GO mama lat o N Gj N 0 125 so MGJvMmaN39GJo S pamml lulwi u dumb NA 250m An N a 91 A N l llb All 00b No P200Ib N220442 IL 5 Solutions 44915 12309 511 PM Page 364 2010 Pearson Education IncUpper Saddle Pl 7 NT exist No 5 53 The smooth disks D and E have a weight of 200 lb and 100 lb respeotively Determine the largest horizontal toroe P that oar be applied to the oeriter of disk E without oausihg the disk D to move up the iriolirie Forms 12 0 PN39 52 no nu 0 Nc IOO N so FwdEH7 lam 0 Ni a o oTlF 4 N GN MN39Gx WN ulnrr Solving P a 21m A quot 1621b An iv a 1431b A 00 b 200 lb 5 Solutions 44915 12309 511 PM Page 365 mnP av n Frill n n Tn TTan 7 add Pl 7 NT exist No portion 5 59 A man stands out at the end of the diving board which is supported by two springs A and 3 each having a stiffness of k 1 m In the position shown the board is horizontal If the man has a mass of 40 kg determine the angle oftiltwhich the board makeswith the horizontal after he jumps off Neglect the weight of the board and assume it 1 3 is rigid k m m A Q B Equatimu of Equilibrium Thcsyring fonuA and a m bcahuined d39 y summing mamaqu pain B and A lupenwdy 9 2M o a 39Z43 0 l1772N f m 0 Fl392440 r 156mm 4063 914 F 39m l in Spring Farnmla Applyth E wehave H771 15596 A mm 007343 A mm 010464 5 5 Gennmry nsmhomtu 39u 0 10164 0 07 aun I WJ10A An A 0 m4 64 m D A I z 0 39 I m 45007348quot a0eeoa7g45m 365 5 Solutions 4491a 12309 511 PM Page 366 2010 Pearson Education IncUpper Saddle Pi 7 NT exist No 5 60 The unitorm rod has n length 1 and weight W It is supported at one endA by n smooth wall an the other end by n oord ot ength s which is nttnohed to the wall as shown Show that tor equilibrium it is required that h 52 71531 34mm 11 Equilibrium m miml in madmanquot be obtained directly by summing moms Iqu pain A Q m 0 Tin0D Win o 1 mine 1 V wizi9 Usiugmsrnnnr m Wsius 1 uo m eoss o Wo sinGwsWO Zsin00 1 Gmnnny Applying amine law with sin iw e sin 5 we we h f rinc55in9 21 h J J Suhsu39m ng mm inm l yiclds III on tsm T 31 min rheminsiaw I h uum o o up nu 90 T A Emailing Eqs3 and 41 yiems 2h an I T 91 D 5 Solutions 44915 12309 511 PM Page 367 mnv m quotFrill ti n Tn mp v addl Ri iNl exist No portion 5 61 Ifspring BC is unstretched with 9 0 and the bell eiank achieves its equilibrium position when 9 150 C determine the tome F applied perpendicular to segment AD and the hoiizontal and vertical componene of reaction at pinA Spring BC iemains in the honzontal postion at all times due to the roller at c Spring Force Formula From the geometry shown in Fig a the stretch of spring 400 m4 BC when the bell crank rotates 9 15 about pointA isx 0300530quot 0300s 45quot 0aM768 m Thus the force developed in spring BC is given by FSp kx 2000004768 9535N Equations of Equilibrium From the free body diagram of the bell crank Fig b L i L A 4WA 0 95355in45 300 F400 0 F 5057N 506N Ans e 1 c1quot 39 Lrandy axess 21 t1 AJr 5057sin15 9535 o AXIOBA4N108N Ans T v3 0 Ay 5057oosISquot0 A 4884 N 488N Ans y I B 5 15 3039 5 Solutions 4491a 12309 511 PM Page 368 2010 Pearson Education IncUpper Saddle Pi 7 NT I exist No 5 62 The thin tad of length 1 is supported by the smooth tube Determine the distance a needed for equilibrium if the applied load is P 2quot 1 4r a 5U D N p c 2r iul ml Mao P 2 E A 391 r H mquot 95 o 1 i u 1 01a 1 47 0quot 4quot n39 a Hula 4r Am 5 Solutions 4491a 12309 511 PM Page 369 WM 7 midi Ry vNT mnv m quotFriquot ti n Tn exist No portion 5 63 The cart suppers the uniform crate having a mass 85 kg Determine the vertical reactions on the three casters at A B an C The caster at B is not shown Neglect the mass of the can Equalinru of Equuun39uu d y b S I 39nre Ilnrlml main Nccan be minim y ummg mulnaiu lbmllx uii 2M 0 NC L 13385045 0 N 2386 N289N Lu 0 83185013 28 64035 NA 07 0 NA 1100N113N Am 5 0 N 286 1l304 53385 o N 332 N 5 solutlons 44915 12309 511 PM Page 370 2010 Pearson Educatlon IncUpper Saddle Pl 7 NT exlst No 5 64 The pole tor a power line is subjected to the two z cable torces of 60 lb each torce lying in a plane parallel to th rey plane If the tension in the guy wire AB is 80 determine the x y z ccrnpcnenb of reaction at the fixed base of the po e 0 Eqnuimu nqul bdull 2r lx QbSOTinti wsin4s o 0r0 An 2Flr owanus eom45o o wln Anl mac qxno allo01h Am m 0 MaL awn Imam 4mm 0 Ma 94 an m 0 Ma eosln 4539M605i 45 04 0 Mo m 0 Mo 50sin45 l60iin45 10 Mb 5 Solutions 44915 12309 511 PM Page 371 nergt a quotWu H n Tn Um nddl Ry vNT exlst No pomon 5 65 If P 6 kN x 075 m and y 1 m determine z the tension developed in cables AB CD and EF Neglect the weight of the plate Equations oquuilihrillm From the flee lgtody diagram Fig a Ta and TE canbeoblzined uy quot 1 quotquot 39 L quot yaxes respectively 2M 0 TCD2610 T a 3 Ans 2490 man 0730 TE 225kN Ans c n t n 250 TAB 3225 60 TAB 075kN Am 2 5 Solutions 4491a 12309 511 PM Page 372 2010 Pearson Education IncUpper Saddle Pi 7 NT exist No 5 66 Determine the 1ooation x and y of the point of z app1ioation of force P so that the tension developed in oables AB CD and EF is the saine Neglect the weight of the plate Equations of Equilibrium FIUI39II the free e body diagram of the plate Fig a mm o L L and y39axas HZ ZRYFO y 0667m Ans my 0 27x T2 x0 x0667m Ans Z 5 solutlons 44915 12309 511 PM Page 373 mmgt m anu ti n Tn TTvmv midi Ri vNT exist No portion 5 67 Due to an unequal distribution of fuel in the wing t nks the oenters of gravity tor the airplane fuselage A ings B and are located as shown If these oornponens have weighs WA 45 0001b W 001b and WC 6000113 determine the normal reactions of the wheels D E and Fun the ground 2040 E0005Rn14 60003 a140 2M 0 800044 0007m4Rr27 230 gli 8000 6000 45000D SOME m2zskip Ans R22skip Ann R a 137 Anl 5 Solutions 44915 12309 511 PM Page 374 2010 Pearson Education IncUpper Saddle Pt 7 NT exist No as Determine the magnitude of force F that must be Eqna uns at Equilibrium From the free body diagram Flg ai r Hz 4 and 4y 39 39 39 l 39 39 y X and x39 axes and the fame equation of equilibrium along the yaxis F02759i810l o F 367875 N 368 N Ans w o Elms r O6 7598106 0 HI 40132 401 N Ans ZMxr 0 Az06 05 75981oi5 0 A2 33443 N 334N Ans IF o A o Ans Using the result F 361875 N and writing the moment equations of equilibrium about thesz axes x015 06 36787502 01 05 06 0 Bx468i20N 468N Ans AX 06 0t5 3678750iZ DJ 0 AX 100i33N100N Ans t quotquotv diagram 5 Solutions 4491a 12309 511 PM Page 375 mnv m quotFriquot n n Tn Tme v add Rt vNT exist No pomoh 5 69 The shaft is supported by three smooth journal bearings 21A 3 and c Determine the oompohehm of reaction at these hearings qula ans of Equilibrium From the free body diagmm Flg a Cy and CZ can be obtained by 1 L about the y axis 17 0 C 450o 450 N Ans ZMy Cz0909 90u0960006 0 CZ 250 N Ans Using the above results 2MC o 5403 ot925009o 9 o 9 45C06 90009 09 09 6000t9 0 Bl 1125 N 1125kN EMX o 60009 4stxo6 9ooto9250o9 Az09 09 o Ans thZ 3403 09 50009 4soto9 45009 09 o a 25 N Ans n 0 A25 sooo AX 475 N Ans 5 Solutions 4491a 12309 511 PM Page 376 2010 Pearson Education IncUpper Saddle P 7 NT extst No 5 70 Determine the tension in cables BD and CD and z the x y z components of reaction at the balleandesocket joint at A xquot 1 1513k1mt yquot 35011 1 1 Tu 023511 l 04286151 05571 n It huimilnmmnm Ta h c2351rmt amsr 1 ussnrmk w n n 217r u 11 023571 mx511 a o A e 042861ip 04mm 0 5 0 4 035111quot 01mm zoo 0 MA o 0 st r 15 05m rep 15 0 3001 035711 lnL5 118571 Tun L5 0 1 rm um An A mm An A a 0 An A noon Aug 376 5 Solutions 44915 12309 511 PM Page 377 mmgt a quotWu ti n in TTnnv midi Ri vNT exist No portion 5 71 The rod assembly is used to support the 2504b cylinder Determine the components of reaction at the ballrandr socket jointA the smooth journal bearing E and the toroe developed along rod CD The connections at c and D are ballrandrsocket joints r kn 39 directed along 39 m an and RP Fm n 39 39W diugmnin Canuinu veclmlann FA Axiij Azk FE ExlEzk w Lsmr1lh Fm 4m k Applying die force equalion at equilibrium 21 a FAFE 1705 Wll Axi ij AzkEi Ezk FDC lr Lsalr ll Ax EXAAZ E2 405 k a Fqualing jnd kwmpoucnts I AXEXD Ay0 2 AzEz FDC 7500 3 r Eandru Fig nmuslbedetzrmined rust m Hi 1jl iAE 2jln w l5l3jrt Thus MA o rt xFDC Mr 25le XW0 li ljx FDClr2jxEi Eklsi 3jx L50k 0 4x 25z 7SO375 FDC2Exi o 5 Solutions 4491a 12309 511 PM Page 375 2010 Pearson Education IncUpper Saddle P 7 NT exxst No Fanning LLand kmmpmcnm 4m 2Ez 750 o 4 375 Pm o 5 3925 0 6 Solving Fqs 1 through 6 yields Fm 3751 m ex 0 Ana E2 56251 M Ax o Ans Ay Au A2 625 lb Ans 5 Solutions 4491a 12309 511 PM Page 379 mmgt a quotFriquot H n Tn Um midi Rt vNT exist No portion 5 72 Determine the components of reaction acting at the smooth journal bearings A B and C moment equalion of equilibrium about me yaxis sz 0 450m4s cy o Cy SIKZOsz318N Am 2M o ciao 300 a C1 500 N Ans Ho8 450oos4snlto4 450rin45 os 043181004 someso4 a BI 27270N 273N Ans was 3182006 o HL i65N739N Ans nnnv Fl 0 AX23850 A 23865N 739 Ans IF 0 A1 Z7Z70500 1605in45 0 A 9030 N diagnm 5 Solutions 4491a 12309 511 PM Page 350 2010 Pearson Education IncUpper Saddle Pi 7 NT exist No 5 73 Determine the toroe components acting on the balle z andesocket atA the reaction at the roller B and the tension on the oord CD needed for equilibrium of the quarter D circular plate Equation nf Eqn lbriu mnamll wonu iuxun be a hint diroiaiy by summing mmquot lhmlukzx Indy lxes mpeaivdy 2M0 N3397m3 2003sin60quot0 gt N 31321 37 N Anl I nu 0 3502zoo3ms 60 A 30 A 33333 N 333 N All 2 0 1 37311333r333502m100D a 425 N Am m 0 A120 AM Ugo Ao Ans 5 Solutions 4491a 12309 511 PM Page 351 mnv m quotFriquot ti n Tn Tme v midi Rt vNT exist No portion 5 74 If the load has a weight onOO lb determine the x y z components of reaction at the balleandesocket jointA and the tension in each of the wires 39 quot 39 39 MA 439 Fin n inI znr ian vector form FA AxiijAzk w 2ouk1h FwanwFm PB FEFk Applying the force equation ofequilibrium nut nameFa FEW0 AiijevAzkHFBDkij DkF k200k0 4 3 A1 Ay Eliy AleFED FwFW 200 0 Equating i j and kwmpollems 410 1 A Jr 0 2 y 5 03 AZF5DFQFE 200O 3 1 must be dammined rusL ma mm rm 4i2ft m 4i4jrt m 2i4jft Thus MA 0 my mem XFa quotAE XFE39AG gtlt W0 4ixFHDk4i4jX Fcpj ka2i4jxF5k4iZix 200k gm 4rEF 400i 4F5D 455210 2FE meant 1515175 k 0 381 5 Solutions 4491a 12309 511 PM Page 352 2010 Pearson Education IncUpper Saddle P 7 NT exxst No Equating i j and k components 153Fw4Fg 4ooo 4 12 4mm Era 2F 800 o 5 35 6170 0 6 Solving Eqs 1 through 6 Fm 0 Ans FEF 100quot Ans Ans E02 lt50ft C 4 4 wjt 5 Solutions 44915 12309 511 PM Page 353 mnv m quotFriquot ti n Tn Tme v midi Rt er exist No portion i i 5 75 If the Cable can be subjected to a maximum tension z of 300 lb determine the maximum force FWhiCh may be applied to the plate Compute the x y z components of A lt reaction at the hinge A tor this loading 2 tt A m a 3m 3009 0 M 39 5 quot i Mir r 9001 Am quot 1 IF D A u Ans F 225 0 A 0 An mm 9oa3oo4 450 An Mn9w33000 MAxo Aquot mi 0 Mn 0 Au 5 76 The member is supported by a pin at A and a cable BC If the load at D is 300 lb determine the X y components of reaction at the pin A and the tension in e B C 1 TreI lkri Mu 2r Ar 2J c r 7 n X mquot 0 4 gJTc 0 5 0 AK Zme1iczu 2 we a 3006 s 71quot 6 u D m 0 Mi 3ootz 6y 4 o 3 6 2M tr Mn 1 a 75 0 0 Solving rquot Lojkip An 4 4501 An 4 900m An 4 a Ann M email I An MA 9001h fl All 333 5 Solutions 4491a 12309 511 PM Page 354 2010 Pearson Education IncUpper Saddle Pi 7 NT exist No 5 77 The plate has nweight oowithoenter ofgmvity at G Determine the distance d along line GH Where the verticalfor P075Wwillcause the tension inwire CD to become zero Equations 0f Equilibrium From the free body diagmm Fig a ux 0 TEFL W oi7sw doos45 o THrL OB39EWL05303Wd 0 I 075Wdsin45 75F o 10607Wd TEL0 2 Solving ms 1 and 2 yields d 0 550L T3 0583W E E 5 Solutions 44915 12309 511 PM Page 355 mnv m quotFriquot ti n Tn Tme v midi Ry er exist No portion 5 73 The plate has a weight of Wwitli center of gravity at G Deterrnine the tension developed in wires AB CD and EFif the force P 075Wis applied at d LZ Fqln nns uf Equilibrium Frum lh tree A body diagram Fig u T can b nblainrd by writing the inurneniequuu un ofeqnilihrium about 1 x axis L L L w u75w 45 Z 2005 w2 mm 0 TM l1402wll4w Auu yand y39axes L A it e L my 0 V2075w225iu45 1402W2 mayo 7 o570w L L TCDL114YL E w E 4175 Ta om9sw 5 solutlons 44915 12309 512 PM Page 386 2010 Pearson Educatlon IncUpper Saddle Pl 7 NT exlst No 5 79 The boom is supported by a balleandesocket joint atA and a gu 39 th SekN loads he in a plane which is parallel to the any plane determine the x y z componenm of reaotlon atA and the tension in the oable at B Equation 0 Equilibrium w 2Ssin 30395lT50 T 1661kN167 H Am 224 a 5H 305 5cm zos o swung m new Asmezo 5mwo A Ans gm 2 0 A151in3039 0 7 A mm Am zro A 16670 45mm An 5 Solutions 44915 12309 512 PM Page 357 mnv m quotmin ti n Tn UM v midi Ry er exist No portion 5 30 The circular door has a weight ofSS lb and a center of gravity at G Determine the x y z corn onenm of reaction at the hinge A and the torce acting along strut CB needed to hold the door in equilibrium Set 459 m Jsinu39n 3 Swim 6k 121lo 1111 at n rquot 212l ux21 5 3159 1 IF o x m Wyn o A I LAD Anl 5l12l 2F 3 D l A my 0 A 21m Au 25w 455 arco 42quot Au 4 39 v quota Lynne hus 0 m 0 ssm f maumwho my gt Ml saw It An 2 m rc 439 An I quot quota Wynn a Jourdan 16943931nu o M 0 Mil 5 Solutions 44915 12309 512 PM Page 355 2010 Pearson Education IncUpper Saddle Pl 7 NT exist No 5 31 The circular door has a weight ofSS lb and a center o ravity at G Determine the x y z componenm of reaction at the hinge A and the torce acting along strut CB needed to hold the door in equilibrium Set a 909 In 3JJ 6Hn lJ3a3quot6xv 4 i5 1 E 214m An 250 oJir a A 275h A 51 40 Au Mano ksse 6 F xo J m o m jmmm a M4 165154 It E 0 sslt3 Jmaho E Fc 67JGr am All m 0 Mr 57363 u Mnn An 2 67 3 0 mmgt a quotWu n n Tn TTnnv add Ry vNT 5 Solutions 4491a 12309 512 PM Page 359 exrst No pomon square hole of the collar Lt F 2m 7 40j e 75klb determine the x y z componenm of reaction atA and the tension in the cable I 4 s I F r v F k quot 14quot u 39d 14 12 2F z r o l A o u x r so A 01 n r a u c 2r 0 75 v 1r o 39 u x r 17 A A non Au 4 1 do An Bl 0 5071 4M u M 300hn AM ya a 1511l7512 91 a n M 0 Ann 12 4 m u o m12 l 13915 s l 417512 4 u o u JEDR A Eizoi i75kL 5 solutlons 44915 12309 512 PM Page 390 2010 Pearson Educatlon IncUpper Saddle Pl 7 NT 1 exlst No 43 MemberAB is supported at B by a cable and 21A b a smooth fixed square rod which ts loosely through the square hole ofthe collar Determine the tension in cable BC if the force F 745k lb quot20 at 350 Fuslmla A 5 Solutions 44915 12309 512 PM Page 391 mnv m quotmin ti n Tn Tme v midi Ry er exist No portion 5 34 Determine the largest weight of the oil drurn that the floor crane can support without overturning Also what are the vertical reactions at the smooth wheels A B and c for this caseThe floor crane has a weight of 300 lb with in center ofgmvity located at G 39 a 39 a a he wheel at Closes Conlacl with the ground Thus NC o Ans Applying the moment equalion of equilibrium about the y axis my o WlDoosJO 2 0 3009 0 W45L08lh451h Ans and the force equation of cquilibrinm along the zaxis 2M 0 N3ZS NA 25 o 1 230 NA N5 300 45L080 2 Solving ms 1 and 2 yields NAN3375541b3761b Ans 5 Solutions 44915 12309 512 PM Page 392 2010 Pearson Education IncUpper Saddle Pl 7 NT exist No 5 ss The circular plate has a weight W and center of gravity at in center If it is supported by three vertical cords tied to is edge determine the largest distance d trorn the center to where any vertical torce P can be applied so as not to cause the toroe in any one of the cables to become zero mmnunm m 0 murmur wtrmwPunmw no 5 so rcwr so mg ug WyoPrPdno dll MmEnO 1W 0 WOMENPUT 0 d39 2F 11 V d 6039 rux 1 dil An 5 Solutions 4491a 12309 512 PM Page 393 mnv m quotFriquot n n Tn UM v new Ry vNT exxstNo pomon 5 86 Solve Prob 5435 if the plate39s weight W is neglected Ammannun 2 u 12nrugrrdrmcou E m 72 quotP0 dzr Allmlrcoi ML 0 Pd50 d390 Thin anemowo 5 Au 2 5 Solutions 44915 12309 512 PM Page 394 2010 Pearson Education IncUpper Saddle Pl 7 NT exist No 5 37 A uriitcrrri square table having a weight W and sides m a is supported by three vertical le gs De termine the smallest far 5 vertical torce P that can be applied to is top that will cause it to tip over 42 QL 6 0 a aunquot 2 56 39 w E 1 4 sin16456539 0211 lt d xin 26569 0 72 l A C For P lull anemia suna 2Mquot a k W0Zm z P 04472 a P 05 An 5 Solutions 4491a 12309 512 PM Page 395 mnv m quotFriquot n n Tn UM v arid Ry vNT exist No portion 5 83 Determine the horizontal and vertical componenm of reaction at the pin A and the force in the cable BC Neglect the thickness of the members 5c 2quotzoa45450N we 0 FumW7450LS100l 0 Fl in N as N Am Imam L18558co30390 151N Anl 00 250 A18558sin3039 4ml000 A 4457 Am A 5 Solutions 4491a 12309 512 PM Page 396 2010 Pearson Education IncUpper Saddle P 7 NT exist No 5 89 Determine the horizontal and vertical componenm of reaction at the pin A and the reaction at the roller B required to support the truss Set F 600 N Equaliam 0 Equilibrium in mm mun N can he obtained 39 39 mums about what 2m tr 6006wo4oooamr 491 0 N509L17N5WKN All 0 3 0 4 5091J7ens 39D A36XJN360kN Au Tu 0 509Ll7lin4539 36mA 0 A noon mom LEA 1 i zin 4 z 2m 2 m I m N5 600 674 600A 5 90 If the roller at B can sustain a maxim m f 3 kN determine the largest magnitude ofeach of the three forces F that can be supported by the truss Equation of Equ ibriiun The unknown A mu cur heliumInd y summing Immull mi pumM m o nmmnm ax as39tz o mums at as L54 fa C 5 Solutions 44915 12309 512 P M Page 397 mmgt a quotWu H W Th Um midi Ry vNT e Xlst No portion 5 91 Determine the normal reaction at the roller A and 10 kN horizontal and verlieeleomporierm atpin B for equilibrium of the member l39 b um Th numln maninn NA an beohuined Hamlin n Equ diaealy by summing momenu thou puiru El 9 2M 0 1006 Jam 6039 60 N L2 12m16039 0 NA new m An 0XI390 5 5w330 0 5520kN TZI390 B8r0065inJD 100 500kN 5 solutlons 44915 12309 512 PM Page 395 2010 Pearson Educatlon IncUpper Saddle Pl 7 NT exist No 5 92 The shatt assembly is supported by two smooth journal bearings A and B and a short link DC If a oouple moment is applied to the shatt as s own deter 39n e oompone no of toroe reaotion at the journal bearings and the oe in the link The link 39es in a plane parallel to the yea plane and the bearings are properly aligned on the shaft m o 250 pm com075 contra pa ahwmzsmzlr a a P 101543 1 L02 An 2151 or A 0fl 101543 manna s o A msa 2olm An m 9 muu l l lani l 0 5 l9N m 20 0 A01 101543 EMMA 0 A 57251 51 N Am 9 57151 1015 m20quotB0 3 amquot All oz5casao39m 5 Solutions 4491a 12309 512 PM Page 399 mnv m quotFriquot n n Tn UM v add Ry vNT exxstNo pomon 5 93 Determine the reactions at the suppormA and B of the frame 5 kip Qty I am 160S6 1sAu 0 A 7V351 hp7JGHp Au 4mm 3oso B 5Hp A nustr B7357 S7l Z0 l a mm A 5 Solutions 44915 12309 512 PM Page 400 2010 Pearson Education IncUpper Saddle Pl 7 NT exist No 5 94 A skeletal diagram of the lower leg is shown in the lower tignre Here it oan be noted that this portion of the leg is lifted by the quadrioeps musole attaohe tot e ip atA lower leg determine the tension in the quadrioeps at c and the magnitude of the resultant toroe at the temnr pinD in order to hold the lower eg in the position shown The lower leg has a mass of 32 kg and a mass oenter at 61 the foot has a mass of 16 kg and a mass oenter at 62 val o Tail lalarm 329u4min1s39 i69ll7151in1539 o r loosuu L0 in An TEE 0 D IMJI sin HATJJGJD Lat I 0 Dm66N lanai Dloo632m1343o DwzoN p IDD 166 B4010 982N An 5 Solutions 44915 12309 512 PM Page 401 mnv m quotmin ti n Tn Tme v midi Rt er exist No portion 5 95 A Vertical force of 80 lb acts on the crankshaft Determine the horizontal equilibrium toroe P that must be applied tot e handle and the r y z components of toroe at the smooth journal hearing A and the thrust bearing BThe bearings are properly aligned and exert only toroe reactions on the shat mo P8 010o hum may tummuno n40lh m 0 B28lm100 a 3s7lb rno 4351 who A a 136 lh 250 so All mum Ann 200 Awlb 5 Solutions 44915 12309 512 PM Page 402 2010 Pearson Education IncUpper Saddle Pl 7 NT exist No The symmetrioal shelf is subjeoted to a uriitorm 1 ad of4 kPa Support is provided by a bolt orpiri looated at eaoli endA and A and symmetrioal braoe arms which bear against the smooth wall on both sides at B and B Determine e toroe resisted by eao bolt at the wall arid the normal toroe at B tor equilibrium Equation uf u ibriun Ech melts pus at its aid suppons hill or ylind lnldi m02075 we Nmquotamll mm N can be nbmed dueuly by summing uiuiuaus bDulpuinlA GZM NDl5 6000l0 N54DVN Anl A400N 725 0 A sooo Ay600N Theloiceru um by uranium is 5mm7zm Ans

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