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Unformatted text preview: PROBLEM 5.25 A T50 = g unifunn smelredishcminmacimularmofradiuasoﬂ mm
as shownTherodissupporbedbyapin utA andthe curdBC.Determinn
(a}1he tension in the cord, (1:) the reaction at A. SOLUTION ‘ D
Firstnote, from Figm'e 5.83: J? = 0’5 “Ema 1.5
=——m
v: = mg
= (0.?5 kg){9.31m!az)
= 7.353 N Also note that A ABD is an equilateral uimla
Equilibrium then (squirm (0}ZMA = D: [0.5 m  [1?5 m]cos30“](7.358 N) — [(0.5 mm soﬂrx = n or rm 21.4693N or Tm, 21.470»: 4 (b) ESP: 2 0: A, + [1.4698 Njcosﬁﬁ" = 0
or A; = 43.734911
2.3 = m 4y — ”LESSN +{l.4698 N]sin60° = 0
or Ay=6.085N thus A=6.13N 5.33.1“ d PROBLEM 5.23' '  : ' an: lhehpmngenemgswimiﬁCDishmtasshmmdisaﬂmhedwahmge
at C. Determine the lengthl. forwhichtheportionBCD ofthe wire is
horizontal. SOLUTION Fixst mm: that for equilibrimn the center ofgravify ofthe wire must lie on
a vertical line through C. ther. because them is hambgeneous, its
center of gravity will coincide. with the centroid ofd'le curlImpending line. Thus; EME = 0, which implies that f = I} ﬁsh=0 gu) (—3 m.}{s in.) + [4; in.)[lﬁ in.) = o L2 #144 in2 or;L=12.00in. 4 PROBLEM 5.58 '
\ E f . Damname mec'apacity, in gallona,'ofﬂ1epmh bowl shown if R =12 in.  L—u—A‘ SOLUTION The volume can be gmted by rotating the triangle and circular sector shown about the y axis Applying the
second theorem ofPappus~GuIdinus mdusmgFig 5 am, we have Since 1331 = 231m3
. 3526.03 in’
V = ——— =1526
23lin3fgal 3‘1 V=15.26gaH PROBLEM 5.61 For the beam and loading showi'l. detemiine (a) the magnitude and
mu lel‘r location of the resultant of the distributed load, {b}tl1e reactions at'the
beam supports.  SOLUTION
. Resultam R = R1 + R:
(:1) Have R] =‘(40lh’ﬁ)(l8ﬁ'} = 7201b
I 122 = %{1201wn}(13 ft) = 1080113
or R = 18001]:
The resultant is located at the centmid C of the distributed load 3
Have +3313: [1800 ME = [401m)[1m)(9ﬁ)+%(120 Ibm](18 fl](12 ft]
01' E = 10.8011 '
R = 1300 11:4
3 = 10.3%
(b) ”amaze: A,=u
+125 :0; Ay—tsoulbzo, Ay=13001b A=18001b§4 +321 A = o: M,{ —(1suolb}{10.s ﬂ] = 0
MT =19.4441bﬁ or M{ =19.44kipft ) 1 ...
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 Spring '08
 Chang

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