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Unformatted text preview: Problem 2—?9 Given 1‘1, r:, and rs, determine ihe magmmde and direction Df 1' = 2r] — I: + 313. Given:
M ’ 4 ‘ f3 ‘1
1~l:—4}m P}: [I‘m 132—2131
'~ 3 ' k—jz' x 5 ,
Solution:
1‘ = 211 — r: + 3}
“ ll
1‘ = —14]m . = 31.5 m
a 26 J
{3‘11 ‘5 {at} (59.5‘
ﬂ = acosf' i ﬂ = 116.4 deg
k lrl ,.  J
a J"; 3r £34.14 a Problem 2—32 Express the position vector 1‘ in Cartesian voctor form: then detonﬂioe its mang and
coordinate direction angle5. Given:
a = 4 to
E: = Sm
r: = 3 m
d = 4m _ 
Solution: ,
—c "I —3 r
1‘ = —a'—b r: —12 m
(I 4 Problem 2—92 Determine the magnitude and coordinate direction angles of the resultant force acting at point A. Given:
F; =15UN
u
,1“ "a
F2=2ﬂﬂN ‘
F:
azljm " x {1
524m , x
c = 3111
d = 2m
2 = 3m
6' = 613 deg
Solution: Deﬁne the position vectors and then the forces ecosliﬁ'ii r 33
. "AB r
LAB = a + esinigi = Ir l = h
L —E: .1 AB R —m1.4 ,:
C x r 119.4 ‘w
"AC
LAC = a — d F}; = F2 Ir l F21. = —19_9 N
x —b . AC $159.2 ,
Add the forces and find the magnitude of the resultant
/ 1514 I
FR = Fh. + F21. FR = 33.9 N IFRI = 315 N
k—26ﬂﬁ ,4 Find the direction cosine angles for“ rr F “a few [5:11
_. I? i = aces? R ] e = ":45
' I t IFRI “J L J Liaise I .
xi"; deg 3—..___—r" Problem Z—lﬂﬂ Determine the position (I, y, [I] for ﬁxing cable BA so that the resnitant of the forces exerted on the
pole is directed along its axis, ﬂour: 3 toward 0, andhas magnitude FE. Also, what is the magnitude offorce F3?
IGiven:
F} = EDD N
F2 = 4130 N
FR = 1900 N azlm Solution:
Initial Guesses
F3=1N x=11n y=ln1 Given Problem 2—103 Each of the four forces acting at E has magnitude F. Express each force as a Cartesian vector
and determine the resultant force. Units used:
W = m3 N
Given: F=23kN Solution: Find the position vectors and
then the forces a E] 3'
FEB
l‘EB = 9 FEB = F
rEB
x —r:' ,I
.r _b“.
1H: = a ‘ FEE” = F lrEcil
kﬂu rEc.
.1 _5 W.
IE” 2  —::I  FED = F IIEDI
x _C J TED Find the resultant sum FR = FEA + FEB + FEC + FED K12 ‘
FEB: 3 EN .1‘ —24 ., (—12 1. lx—24,
K—12
FED: —3 EN
k—E‘i
' U
FR = 0 kN .k —9ﬁ ,1 ...
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 Spring '08
 THAKKAR

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