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Unformatted text preview: ,0,6), and C (5,2,4), in meters, and the forces F1 of Given the three points A (0,4,3), B (O
B and P2 of magnitude 100 N in the direction of magnitude 50 N in the direction of A
AC, as shown: Z a ( 030) (9)
a.) Calculate the vector sum F1 + F2
A
f (5% K, g ’2
W ” g v” a; A g 'ﬁgiékN 131+}?2 = b.) Calculate the component of F2 in the AB direction. 33 g a W "3 a gw “‘3 5;} a"? A a “’1’ WE ‘ f c «a 5% 4/ ,M7j%ﬁ', f5; .fﬁii‘: 3e? 33! a:% is? A}? £9 2:; E2] f, a v’ Three forces are applied at the end of a hook in order to P remove the post shown. Determine the magnitude P and 500 N e
the angle 9 of the force so that the resultant of these three forces is a 1 kN vertical force acting straight up. {"3 M F a 3 give?) ii V 53:23:” == gm 4 z: s 2;: A
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g 3§§S§sﬁafggg€ﬁw IVE; V i What horizontal force, F, must a worker exert on the rope to position the 50—kg crate directly over the trailer? QWXWMMM‘MWWMWMWW’WWMWE if??? at
a?
wt“
m
{1:
2%?” wt”? “r”
{éggrwﬁfﬁﬁgéiﬂg‘
t; Ag « M M
5 P: Egg)? R5 mi} Three forces act at point A as shown. Force P has a
magnitude of 600 1b and acts along the line AB.
Force Q has a magnitude of 200 1b and acts along C
the line AC. And force S is described by the ,4
equation shown in the ﬁgure. " g
a) Determine the vector equation in rectangular E 3 m
I
l
l
I components for P.
b) Determine the vector equation in rectangular
components for Q. '
c) Determine the magnitude of force S. éw'ub: ? IE AAB (9:20015 AM f R; .— A
s =/l/$/Z‘+(pojnv15(ak i1; 691?; A g 9’ & a)F7nd= @Px’ii‘tij‘tpa" Fxf’ / a X7
Pg =(goan(oo =Boo/b x x
BC}, #900 améo =5/m lb 7% = nycgﬂo =5/9.(mo70 : 3981c a». '
P}, =5I‘M, Smﬁ’O =33‘7’.0 ll; d: rm P=395r£~33q14+ 300 k lb A A A A __ L/AJ'ZE A 4
5) ma: and WM we woke 2,“ ‘0'8’: Wk :200/6/018?+0l(0k) = /é0f +1202 112 Three forces act on the bracket at shown Where the
magnitudes of F2 and F3 are known to be 80 1b and 5211)
respectively. Determine the magnitude F1 and direction 9 so
that the resultant force is directed along the positive 11 axis and has a magnitude of1321b.
Givon‘ F2 ‘ 3’0 le9 F; r 52 [A l [b
[2' = 232 up Ru. ,3 1:362
End: 7:73 )9 j Fz‘EOib s
\e H
zfzé A 5 A
name? “Pane; + 80L +x'§(52>é +7452) 2:53.416 wee = /27.2 «1» Esme =Z7Z/A ‘~gm9+4/3:35.3 —~—r Flame :/Z.7/é jg. mike , 272 ’5 We =23? 6%?" ﬂ .— '’ I /b
FTSM W? = 27.2 ll; F7 30 o Given magnitudes P = 200 N and v = 300 m/s directed
as shown in the figure 21.) Find the rectangular components of P. b.) Find the rectangular components of V. 5 m,"
c.) Find the component of force vector P that acts I I
in the direction of velocity vector v. A," ~“‘ étVt‘zﬁ: 19‘2wa
V‘= $30 We 2:260 élnl/O N
:/28.5(0 N (+53) a) ﬁnd: 518:??‘ng‘fgi: =ZOOcao 9’0 N p : PX), émgo z men /~2‘) N
P); 3 PX (0330 .2 /32.¢78 N — 223.47? ~ 87.7%" + 178.392 m/s “Mat The gusset plate is subjected to the forces of four members as shown. If the
magnitude of F is .12 kN, determine the magnitude T of the force in member B and its proper orientation 9 for equilibrium. The forces are concurrent at
point 0. ' i
5'" F“ _f,\
.f . r v  1" 2” 5 '5
Fig? grit/tilibfiﬁm 0? m :1}: C 2}” w
sf E K“ W t!" g i 5:7: “.25.; K15: U/
I W " 5:: < ‘ “Mt—k Ifmc/ Ii
4i::§ 3" “ [gar/‘5‘} id (“M70 . :’ if»; 5 {EX
3%: '7'" {3 wggaé/G «=4? $5275 gin/5% I
4: f” :: “‘1 :: ii}: " 13171:?“
2 Z?‘/ O
i (K; (a M
qtlgfé\ /J (3 xi, /
{My} xy ffﬁa I}; 5;; km é
to: 3:59.? 'l'he pillar shown supports a vertical 30 N force at F. The bottom of the pillar is supported at C by 2 rods and 2 cables as shown. The
tension in cable CA is 160 N and the tension in cable CE is 90 N. Neglecting the weights of the pillar, rods and cables, determine the
magnitude of force in members CD and CE required to maintain static equilibrium. aim: Ea :i‘GO N ) £5590N35y5/rm I.” fimﬁb } FIND: E0255 Engi/Ibrlbbm Z}? = O 9325:"; £525 "‘ F85 SmZ’O '5 70 N F55 :: 3(3OM — a; (c1520) = 5. 50M ’§E60520> "F29 SanO ‘3 5
F20 (EECon , 5,
EEISON'3(/9’ 3ON \ ‘/
O : 904500 f EE(§)'ED 32:72.0 5
SON' 55950520 70 M
*5m 20) = 30 N SHIV) (mZO 4.1 Which equation describes the X component of P? y ‘ \
circle one
a) Ppéem e) P6 (30) cos(50)
b) P 81 30) i) P sin(30) 008(50)
c) P 6 (50) ﬂP c (30) 8111(50)
d) P £50) a 51n(30)81n(50)
K/ 4.2 Which force does NOT produce a moment about point A? circle one
P R s
Q Q
R P 7 T A 4.3 Which vector below is NOT a unit vector? circle one a) 0.342i — 0.587 j + 0.734k b) o.911i + 0.135j + 0.390k //'\ c)l\0.459i + 1.321 ’ — 0.198k
xvi} :1 d) 0.282i + 0.681 j + 0.676k a) 0.586i + 0.575j + 0.571 k Three cables are used to Support the 800 N box. Determine
the force developed in each cable for equilibrium. (7 Won 3 W = 800 N 1 5/46er I}: ifaz‘ﬂZr/Mb
Final: 7:38 377%,7749 A 17a 1A» Z
FED
E8 )’ x
.7.
4/: 800M
A
X A , “22‘71A+qkp4/’—£2_i
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22mm“)! r4
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2E=o ~7zsg+mf+7zb §L’§j+gl<>Xook N o
l 7;" “3177‘” to 72c=é7ap=%02w>‘900/V
. v" _2. __ 2
j: 1,413 Ewan ~ O '35 :éﬁwsé—{lm} 350A;
3
k‘ ém‘Soo =0 '9 EVEKXOO) =/zoou You walk from point A to point B along level sidewalks of length 51 and s2 and your friend takes
the straight path through a level ﬁeld. The distance your friend walks is: A) equal to the arithmetic sum of s; and s;
(i.e. the distance you walk) B Friend’s B) greater than the arithmetic sum of S} and $2 @ D) greater than the vector sum of 51 and $2 greater than either s1 or s; but less than the
arithmetic sum of $1 and $2 Which of the following is NOT an external effect?
Deformation B) Motion C) State of rest D) Support reactions When dealing only with EXTERNAL effects on a rigid body, a force may be treated as what kind
of vector? E) Equivalent vector
F) Fixed vector G) Free vector @ Sliding vector QC.) For questions a) to d) indicate whether the magnitude of the ,
component of force F along line AB (FAB ) will increase, B t, "6 5?
decrease or stay the same. Circle the correct response. '
\‘ l.’
‘." a) If the point of application of the force moves from B to C, F AB will: ix" . ' 9 B "\ Increase Decrease Stay the Same y \ C x, F
\. f
\:
\ b) If the angie 8 between F and line AB decreases, FAB will: Decrease Stay the same c) If the point of application of the force moves from B to A, FAB will: _/
Increase Decrease Stay the same ‘t X "e F
A
d) If the force is opposite in direction, i.e. points toward C, FAB will: I ’ 9 F
B
Increase Decrease Stay the same \ ................  c ................  \X j].
“A A 450 lb crate is supported by the rope—andpulley
arrangement shown. Determine the magnitude and
direction of the force F that should be exerted on the
free end of the rope to maintain static equilibrium. M Assume the pulleys are frictionless and each pulley
diameter is negligible. 69m: WthO t _
END: Fr} Q) 7%; (3:5an @263» Z thW My 5?": :0 Re 2630 237% F = 4/50 g/bwé 3W “Maia/6L [Fl 2 /éé 1b
9: 5340 degrees m The magnitude of T; = 300 N. 5'2 Using the geometry as shown in the figure i\ 21.) Find the rectangular components of T1 . ‘i \ I b.) Knowing that the resultant of the 3 forces at B is a . \/
vector directed along the y axis from B to A, ﬁnd l , l the magnitude of the tension T2 and the resultant R. "\ 60 / a.) Knowing that the resultant of E and 152 is a vertical force of 800 N, find the ué A
‘ .. .‘m:;f’* ‘\
magnitudes of F1 and F2 (33%“. g 31,4“ ’
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7/ 5g>ﬁ4§igwé
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gt; :7§’3>
g,
11:11: 703 N and 1122!: J22 Rf} Find the Component of F1 in the direction of F2 / ﬁg" A
gas?“ b.) ﬂag/’32 “f, A 4 . —~
.w x ﬂ 3555;» : $7325 453%.“:3/1
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4:52, 5; 3: Ff : jgﬁg‘x’ For the bracket as shown: g f,
a.) Determine the moment of P about the origin. FEM? me / 4+ f,
ﬁe:
X ___} WK'MKV'""‘“KM/“w”“‘wW'WK/wm AB) Mot BC atom Prinaoaﬁ. axi$ &} rw ; g 3 f3 NM» ' ‘J diéee’hbnjiw \ Z f f 3? f: ‘ ’:
f“ ” MAMWWVVM;W 3 it; (at g a e x as *2? j 5
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g; ~ [Mrs Sgt/WW t“; W mgr/5;”? “1%! a {’f‘ g a e:
5} g “e ; «em 5 i 3 .
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wk e; 2
W a: g S
Q 3 J :1: e A”? I
, ‘2 "'T ., i 5..» 17 ,. Mr A raw: 5
W mva g: 3 e X r» £535 +2223 new /
533% 35.3 «W?
b.) Determine the moment of P about the AB axis
gé‘vibf M ...
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