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28 • CH"'PfE~ 2 FORCE VECTORS PROBLEMS .2-1. If 8 - 30" and T - 6 kN. determine the magnitude of Ihe rC$ullant force acting on Ihe 1.')'1.'0011 and its dir.::clion measured clockWise from the posi tive .( axis.. 2-2. If (J _ fI.'f' and T _ 5 tN . determine Ihe magniludl.' of the resultant force acting on the eye boll and its direction meflSurcd clockwise from Ihe posi li\'c .J axis.. 2-7. If foB - 2 kN and the re~ultanl force acts along the positive" axis. delermine Ihe magnitude of the resultant force and the angle 9. "2-3. If thc resultant force is required to aet along Ihe posilh'e" uis and ha"c a magnitude of S kN.dclermine the required magnilude of f Band ils direc.ion 9. 2-3. If the magnitude of the resultant forre is 10 be 9 kN directed along Ihe posit;"c xaxis,octcrminc the magnitude of force T ~Iing on the eyebolt and ils :Ingle O. T ~-IJI-~-··' Probs. 2-718 ('robs. l- l/lIJ . 2-4. Determine Ihe magniUlde of the resultant forcl.' acting on Ihe bracket and ils direction measured oo\mtcrdod:wisc from Ihe po$it;I'C II a_~is. ·Z- 5. Rcsoll'c FI inlo components along llie" and v axes. and determine the magnitudes of these components. 2-6, Rcsol,·c F! ;n10 components along Ihe " and 1/ axes., and delCrnl;ne Ihe nlaJllillldcs of Ihcse oo"'pQnenl$. ' 2-9. 1lIc plDIC is subjttled to the t,,·o forces at A and 8 as shown. If 9 - «1'. determine Ihe magnitude of the resultant of these two forces and its direction measured clock,,·ij.C from the horizontal. 2-10. Determine the angle of 9 for connecting nlcnlbcr A to lhe plate 5() Ihat the resultant force of f A and f a is directed Iiorizontally to.he right. Also.. wll." is the nlagnitude of lhe rcsUI13n! force? • ~ F. _ f>kN l' rob!<.l-4I5I6 I'ml~ 2-9/10 2.3 2- 11. If the tellsioll in the table is 400 N. detennine tbe tn:Igllitudc and di rection of the resultant fon:e acting on the pulley. This angle is the same angle 0 of lille AB on the tailboard bind:.. 29 V{CTOR AOOl110N 01' FO!tC€s !-14. [ktennine the design angle 0 to" s 0 s 90") for strul JI B so that the 4OI).Ib horizontal force has 3 component of 500lb directed from A to ..... ards C. Wh at is the component of force acting along member AB? Take <b - 4Q". !-15. Delennine the design angle <b to" s <b s 90") bet"'ecn StrulS AB and lie so thai the 4OI).Ib horizoncal force has a tomponem of 600 lb which aclS up 10 the left. in Ihe same direction as from B to,,·ardsA.Takc 8 - 30". , .100 Ib A " c I' roo. !-Il !'rob!>. !-14I15 *2- 12. The devke is used for surgical replacement of the knee jomt, If the force 3"illg along the kg is 360 N. de tennine its componen ls along the .f and y ' axes. *2-16. Resolve t'l inca components along the" 8nd u axes and (\ctermi ne the magnitudes of these tOnlponents. oZ_IJ. The device is used for surgical replacement of the knec joint. If the force acting alollg the leg is 360 N. de termme it5 components along the.t· and axes. 02-17. Resolve f ! into components along Ihe" and u axes and dete rmine the magllHudes of these componenls. r F, - ZSON !'rob§.. 2- IUIJ !'robs. 2- 16117 30 CH"'PfE~ 2 FORCE VECTORS 'l'he truel: is to be lowed using IWO ropes. Delcnn;nc the magnitudes of forces f " and FII acting on each rope in order 10 dC"clop a resultant force of 950 N directed along 2- 1 ~. lite positive:r axis. ScI 6 .. 50". 2-ZJ. If 0 - 30" and 1-2 - 6 kK (\ctermine the magnitutk of the resultant fom: acting on the plate and its dircrtion measured dock"isc from the positi"exaxis; .·R 2- 19. The truck is \0 be lowed using two ropn. If the resultant fOIT(: is 10 be 950 N. directed along the posit'I'c:r axis. determine llie magniludcs of forces FA and FJI aCling on each rope and the angle II of Fs so thallh c magnitude of FII is a m;II;"'''"" FII acts at 20" from the ~' :uis as showo. is directed along a · 2-24, If the resultant force line mea su red 75' clockwise from the positi"e x axis and the magnitude of F2 is to be a minimum. determine the magnitudes of F R and ••~ and the angk 0 s 90". , - - ... ~ Prob. 2- 18I19 I'robs. 2- lJI24 · 2-20. If 4> _ 45°, Fl .. 5 ~N. and the rcsuhaot (orIX is 6 tN dira:lcd along the Jl'O$ith'c )' axis.. determine lhe required magnitude of Fz and ils direction 11. ' 1-21. If It> .. 3l)" and the !'e.,ullan! fon:c is 10 be 6 k.N directed along !he positive y axis.. determine the magnilUOCs of F , and Fz and the angle 0 if '"1 is required 10 be a minimum. If <I> - 30", FI - 5 kN. and the resultant force is 10 be direcled along the positil'e y a~i!. delenninc the magnitude of the resultant force if '"i is to be D minimum. Also. what is '"1 and the angle 8"! 2- 22. "robs.. 2-211/1 1/21 °z.-2S, Two forces f j and f t act on the Kreweye. If their lin..-s of aenon ar..- at an angle 9 apart and the magnitude of each force is FI - 1-i - F, determine the magnitude of the resultant force FR and the angle bel,,'eCn . '/1 and .'\' I'rob. 2-25 2.3 l-16. 'Ibe log is being towcd by two tractors , I and n, (}ctcrmine Ihe magniwdes of the \1'10 10"'ing forces t"" and ) "/1 if it is required that the resultant force ha"c a magnitude 1'" '" IOkN and be direCled along the.l axi'!. Sct 0 _ ISO. 2-Z7, 111e resultant .'" of tbe two foren acting on the log is to be directed along the positive.l a.~is and rum: a magnitude of I0 kN. determine the angle tl of the cable, aHaehcd 10 B such Ihal lhe In.1gnitude of foTCt Fa in this (;lblc is a minimum , What is tl\o;> magnitude of the foTCt in each (;lblc for this siluation'! l-3Il, 'iliree chains aCI OII lhc bracke t slICh thatlhey create a resultant force ha,ing a magnitude of 500 Ib, If two of thc chains are subjected to knO"ll forces. as shown. determine the angle Ii of the third chain measured d oc kwis<: from the positive A' a~is. so that the magnitude of force .' in this chain is a ",;",'mllm , All forces lie in the .t-)' plane. What is the magnitude of .~! lIillr. First find the rcsulta nt of the 11'10 known forces. Force )" acts in this direnion . , I '" I'robs. 2-21>127 0l-l8. l'hc heam is to be hoisted using twO chain'!. Deter, mine the magnitudes of foTCts t"" and .'~ acting 00 each ell-1in in order to de,'clop a re:lultant fom: of 600 N directed along the posilive)' a.~is. Seltl '" -15°. 02-29. 111(' beam is to be hoisted using t"'O ehains. lf the resultanl force is to be 600 N directed along the positi,"C " axis. determine the magnitudcsofforecs F" and .'"acling on each chain and thc angle Bof . "/1 so thaI the magnitude of ) "/1 is a minimllm. FA aCtS M 3fr from the)' uis. as shown. ,• 31 V{CTOR AOOl110N 01' FO!tC€s I' rob. 2- 30 ""'" 2-J I, Three cableli pull on Ihe pipe such thatlhe}' create a rcsul\3nt for~e havi ng a magnitude of 900 lb. If two of the abies arc subjeetcd to known forces. assho"'n in the figure. determine the angle /I of the third cable so thm Ihc m.1gn itude of force F in this ~able is a m;lIjlll"'". All forces lic in the x-y plane. Whm is the magnitude of F? "ml: Firsl find the resultant of the two known forces. ,, , '9-----. Probs. 2- 2lII!9 l'roh. 2- J I 38 • ."2-7. CH"'PfE~ 2 FOR CE VE CTORS FUNDAMENTAL PROBLEMS RC50I,'c each fOTCC acting on the post into ils.r and y romponcnls. , I ."2- 111. If the resultant force aCling on the bracket is \0 be 750 N directed along the 1', .. ..100 N posi' h~ x axis. dcu:rmim: the magnitude of F and ils direction O. , Fl-' t'241. Dc\cmunc Ihe magnilud<: and direction of Ille resultant force. F'2-11. If Ihe magnitude of Ihe resultant force aCling on lhe bmekcl is 10 1M: 80 lb direclcd along Ihe /J axis. determine the magnitude of F and ils direction O. 15c>...J~"-N-'---' Fl- I I "2- 9. O"lCmlinc the magnitude of llie rcsultant forre aCling on Ihe corbel and its direction II measured counterclockwise from Ilte.r nis. , I !-"2-12. Dclcnninc the magnitude of the rcsullam force :md its dire<:lion 0 mcasur... d rounlcrclockwise from lhe positive .f axi5. Fl - 4001b Fl - I! 2.4 • AoolllON OF A SYSTEM OF CoPlANAR FO!tC€s 39 PROBLEMS *2- 32. Determine llie magnitude of llie rcSUllan! force acting on Ille pin and ils di rection measured dock " 'isc from the positil·"' .r axis. 2-35. The oontac\ IlOint bel""Cen the femur and tibia bonn or the leg is 3\ A. lf a ,·crlie.. l forr:e of 1751b isllpplicd al this poin!. determine the romponcnls along the .r and y axes. NOle Ihal tile y component rcprcscnl~ the noroml force on Ihe load·bearing rcgioll of Ille bones. BOlh Ihe x and y componenls of Ihi5 forcc cause s)'lIo\;al nuid 10 be squeezed OUI ofille bearing space. "''' 1"011.2-32 I' rob. 2-35 02-.B. If 1', _ 600N Dnd 4> - 30". deteml;nc the magnitude of the resuhant force :lCling on the eyebolt and its dircClion measu red clod\\isc from Ihe posith'c x axis. l-J4. If the magnitude of Ihe resultant force actin g on lite cycboll is 600 Nand ilS direction measured clockwise from Ihe positive ,r 3.'(;$ is 8 - W. determine Ihe magnitude o f .'\ and Ihe angle <1>. 0Z-J6. If <b - 30" and F! .. 3 kN.dclcmlinc: the magnitudc of the resultant force OCIing on the plate and ilS direction 6 measured clockwise from the posilivcx axi5. ' 2-37. If thc magnitude for Ille rcsultant force actillg on lite plale is required to be 6 kN and its d ireel;oll measured clockwise from Iltc posi li,'c x axis is 6 - JO".de lermille lit e magnit ude of F2 and il$ dire<:tion 4>. Z-38. If 4> - 30" and tile resultant fortt acting on Ihe gusset p13tc is directed olollg Ille positi>'c x axis. determine lite magnitudes of t"2 and Ihe resultant fortt. ~ Prohs. l-3J1)..1 l'rOIlS.2- J6f37/JIS kN 40 CH"'PfE~ 2 FOR CE VE CTORS If d> - 30" and Fl - 250 lb. determi ne Ihe magnitude of the resultant force acting on the bracket and 2-39. DClcmlinc the magnitude of FI and its direction (I so Iha\ the resullanl forte is din:clcd \'crlicalir upward and has a magnitude o(SOI) N. ils diredion measured clockwise from the positi,'e of axis. *2-40. Determine the magnitude and direction measured coun terclockwise from the posit;,·c x a:cis of the re$uhanl force of the three forres acting on the ring A . Take . 2-44. If the magnitude of the rC$ultant force acting on the bradel is 400 Ib directed along the positive x axis. determine the magnitud~ of F t and its direction </>. f '\ - SOONandlJ - 20· , 2-43. .2-45. If the resul tant force act ing on the bracke t is to be directed along the positive.T axis and the magnitude of . ' 1 is required to be a minimum . determine the magnitudC$ ofche rcsultam force and F L' , I'robs. 2- 39/40 '2-4 1. Determine the magnitude and direction /I of F8 so thaI Ihe rC$ullam force ;s dirc(lcd along the posilj"C y axis lind has a magniHldc of ISO) N. 2- 12:. Iklcrminc the magnilUdc and anste measured counterclockwise from lhe positil'c )' uis of the resultant force acting on the bracket if F . - 600 Nand fJ - 20' , F, .. 260 Ib 2-46. The three concurrent forces acting on the sere'" e~'e produce a resultant force 1'/1 - O. lf " 2 F Land t't is to be 90" from . '2 as shown. detumine the required nmgnilude of Fl expressed in terms of FLand the anll-Ie 8. i " I',eobs. 2..... 11-'2 I'rob. 2-46 2.4 t·" 2_ 17. Dctcnnine the ma" utude of and 1t5 direction 6 so that thc resultant force is dm~ctcd alon, the posiu,'~ .l .lXI' and has a rnapitude of 1250 N. 0l-4ll. Dt:1~rminc the magrutude and dn«tlon measu red f,om the posiu,'c x u's of the resullant force acting on the ring al 0 if 1'" _ 750 Nand tJ '" 45". AooInof.I Of,. Sm£M Of' C()IV.N.tJt FOIIICES 41 2-50. The thrcc forces are apphed to the brackct. DelumlOc thc runge of values for thc rnagnitu<tc of force P so thai the resultant of the three forces docs nOl c:c~ecd 2400N. ~ollntcr~lock ... ,se , l'rub. 2-511 2-51. If 1'1 - ISO N and ~ - 30". det~nnl~ the rnagmludc of lhe resultant force acting on the brnctet and ilS direction mcasUt«! dod: ..-I:SC from thc pailti'~!l a.ris. ' ~'.I. Dcl~nnine thc magnitude of Ih~ r~sultanl force and liS dlr«1ion measured OOIIn terdockwise from th e poslti'·c .r a:..1 , °1_5l. If the m3'"'tude 0( thc resultant fOKe aclln, 01\ the brxkc l IS to be:.ISO N direcled alon, the posiu,'c I/.IX~ de tcnnmc the magnitude of " , and its directlon~. 02-53. If the resultant force 3("\ing on thc brKket IS rcquir.::d to be: a minimum.detcrminc the magnitudes of F, and 11K: resultant force. ScI ~ '" 30". " "'F. '" SO Il! "rob. 2---4'.1 Probs. 2- 51/SU.!iJ 42 CH"'PfE~ 2 FOR CE VE CTORS l_~ 'Ibree forces act on tile brad;ct IXtcrminc th~ magnitude and dircClion 6 of t'l so that the resultant force is directed along the p<l6iti\"c II axis and has a magnitude orso lb. 2-55. If f : '" ISO Ib and II .. 55~. determine the magnitude and di reCTion measured clockwise from the positive .r a~is of the resultant force of lhe three forces acting on the bracke t. ' 2-57. Determine tbe magnitude of force f so tllat Ille resultant [orce of llie three forces is as small as possible. What is Ihe masnitudc of Ihis smallest resultant force'! , IHN , F, _ SOII> --, I'rob.2-57 '" • " " I' robs. 2-5-1155 2-58, Expre§5 each of Ihe Ihree forces aCling on Ihe brackC I 11'1 Carlcsi an ,-celor form wilh .('spectto Ihe;t and }' :ues. Determine Ihe R'l3gninlCie and direction 0 of 10-1so Ihal Ihe re~ulmnl force is dircded along the posilh"e;t' axis and h3S a magniludc of Fit - 600 N. *2-56. 111c tllrc~' concurrent forces acting on the post produce a resullam force t'R .. O. If F: .. F ,. and f l is \0 be 90" from .' z as shown,determine the rcquir... d magniwdc of F} expressed in terms of F, and the angle 6. J , I"~ II' '--, ", l'rob. 2- 56 Prob. 2- 511

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