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.2-1. If 8 - 30" and T - 6 kN. determine the magnitude
of Ihe rC$ullant force acting on Ihe 1.')'1.'0011 and its dir.::clion
measured clockWise from the posi tive .( axis..
2-2. If (J _ fI.'f' and T _ 5 tN . determine Ihe magniludl.'
of the resultant force acting on the eye boll and its direction
meflSurcd clockwise from Ihe posi li\'c .J axis..
2-7. If foB - 2 kN and the re~ultanl force acts along the
positive" axis. delermine Ihe magnitude of the resultant
force and the angle 9.
If thc resultant force is required to aet along Ihe
posilh'e" uis and ha"c a magnitude of S kN.dclermine the
required magnilude of f Band ils direc.ion 9.
2-3. If the magnitude of the resultant forre is 10 be 9 kN
directed along Ihe posit;"c xaxis,octcrminc the magnitude of
force T ~Iing on the eyebolt and ils :Ingle O.
Probs. 2-718
('robs. l- l/lIJ
. 2-4. Determine Ihe magniUlde of the resultant forcl.'
acting on
Ihe bracket and ils direction measured
oo\mtcrdod:wisc from Ihe po$it;I'C II
·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. _
l' rob!<.l-4I5I6
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:..
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
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.
!'rob§.. 2- IUIJ
!'robs. 2- 16117
'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;
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
l-16. 'Ibe log is being towcd by two tractors , I and
(}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
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'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.
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.
Probs. 2- 2lII!9
l'roh. 2- J I
RC50I,'c each fOTCC acting on the post into ils.r and
y romponcnls.
."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.
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.
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.
!-"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- 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.
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
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· ,
.2-45. 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',eobs. 2..... 11-'2
I'rob. 2-46
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.
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
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
~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.
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
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'!
F, _ SOII>
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.
II' '--,
l'rob. 2- 56
Prob. 2- 511
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