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iffiFL

TEKNOLOGIPETRONAS

COURSEDATETIME

VAB 1023 STATICS F RIGID ODIES22 MAY2007 TUESDAY)9.00AM 12.00NOON 3 hours)

INSTRUCTIONSO CANDIDATES

1.2.3.

AnswerFIVE 5)out of SIX(6)questionsn the AnswerBooklet.BeginEACHanswer n a newpage.Where applicable,showclearly teps aken n arriving t the solutions ndindicate LL assumptions.Indicate learly nswershatarecancelled,f any.Do notopen hisQuestion ooklet ntil nstructed.

4.5.

Note : There are THIRTEEN 13) pages n this QuestionBooklet ncludingthe coverpage.

Universit.i Teknoloqi PETRONAS

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i\AB1023+J"

What s a vector? f ,or6' ' 12markslDefine Cartesianector orm.

[2 marks]The position f pointA on the building ndpointB on theantenna avebeen measuredelative o the electronic istancemeter EDM)at O.Assume he coordinateor point O is (0,0,0).Answer he followingquestionsased n heFIGURE 1(c).

^-^tt'fup,c.

l

F+,

FIGUREQ1(c)What are he coordinates f pointA?

ii . Whatare hecoordinatesf pointB?

Determinehe position ector rom A to B and

[2 marks]

[2marks]it'smagnitude.

2

1i l .[4 marks]

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rI\VAB1023

The mastOA n FIGURE 1(d) s supportedy three ables amely B,AC andAD. lf cableAB is subjectedo a tension f 500N,determineffetensionn cablac-c, fr and he verticalorceF whichactsat the mastalongtsaxison hecollar t A.

[8 marks]

iiI

FTGURE1(d)

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iI\AB1023

a. Explainwhat a moment f a force s,then explainhow ts magnitudesdeterminedy scalarormulation.

[2 marks]b. Explainhe"right-hand-rule"ndetermininghedirectionf a moment.

[2 marks]lf the resultantmoment f the hree orces hown n FIGURE 2(c) aboutpoint is M = 4.8kN.m clockwise),eterminehemagnitudef F.

o')- g qin oo ( t) -o-tt

FIGUREQ2(c)[4 marks]

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VAB 1023

FIGUREO2(d)shows frameacteduponby a forceF givenby hevector(50i-20j-B0k)Answerhe ollowing.

FTGURE2(d)Find he position ector rom C to D

[2marks]

Find heunit ector longCA[2 marks]

i i i . Determine he vectorand the magnitude f the momentof the forceF about hetsaseineCAof the ripod.

[8 marks]

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The cablesexert he forcesshownon the pole npole s supported y a ball-and-socketointat itsforces ie n a horizontallane.

Draw he reebodydiagram f thepole.

ii. Determinehecomponentsf reaction t A.

FIGUREQ3(a)

VAB1023

FIGURE 3(a). Tlsebaseand he applied

[2 marks]

[12m'arks]

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Theadiculatedraneboomshownn FIGUREN and ts masscenter s at G. lf it supportsfollowing uestions

a3(b)has'aweight f O2Sloadof 3000N,answerhe

FTGURE3(b)

il .

Draw he reebodydiagram f the boom.[2 marks]

Determinehe orceacting t the pinA and he compressionn thehydraulicylinder C.[4 marks]

'-'

,l|l

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VAB1023

state he assumptions ade or designinghe members'andonnectiqnsof a truss' [2 marks]

AFinkrooftrussis|oadedasshowninF|GUREo4(b).MemberBHisperpendicularoACandmemberDF s perpendicularo CE'

48 KN

FTGUREO4(b)

DeterminehesupporteactionstA & E' [3 marks]

ii. ldentifyheTHREE 3)zero-force embers nd ndicate hy'[3 marks]

iii. Calculatehe forces n members B' BC'.AH & BH using hemethod f oints tA & B. [4 marks]

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VAB1023

A truss s loaded s shown n FIGUREQa(c). The ointsB, C, D & E aieexactly bove hecentre f spansAl, lH,HG & GFof the russ.

30 kN

FIGUREQa(c)

i. Determinehe reaction t the support .[2 marks]

ii. Calculatehe orces n he members D,CH & Hl using hemethodof sections'

[6marks]

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VAB1023

a. State he rules egardinghe characteristicsf bodiessubjectedo dystatic riction.

[3 marks]

b. The300-Nboard, m long, s placed cross hechannel nda 450-Nboyattemptso walkacross s shown n FIGUREOs(b). lf thecoefficientfstatic riction t A and B is,p, = 0.4,determineloy ll t ne willget romA(thedistance ) before he boardslips. The nclined ideof the channelhasa slope2 verticalo 3 horizontal.

FTGUREsF)[7marks]

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IVAB1023

The wedgeshownat B in FIGUREas(c) is used o level he floor'of abuilding.The angleof the wedge s '1BoThe coefficient f static rict ionbetween he wedgeand the two surfacesof contact r, lr . = 0.3. Neglectthe size and weight of the wedge and the thicknessof the beam. Ahorizontal orce P is applied o move the wedge as shown. Answer hefollowing.

FIGUREs(c)

Draw the free body diagram of the beam and determine hereact ionsatA&8.[6 marks]

Draw the free body diagramof the wedgeand determine he forceP.

[4 marks]

i l.

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b.

VAB1023

State he TWO(2) theorems f Pappus nd Guldinusegarding urfadeareaandvolume f anyobject f revolution.

[4 marks]

Locate hey-coordinatef the centroid f the areabetweenhe parabola2,, =tand thestraightiney, = x, shownnFIGURE 6(b).

FTGURE 6(b)[6 marks]

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VAB1023

with'a circular oleIGUREQ6(c)gives he crosssectionof a beamhaving radius f 25mm.

GtFIGURE 6(c)

i. Determinehe moment f inertiaor the beamcrosssection boutthex axis.

[5 marks]ii. Determinehe moment f inertiaor the beamcross dction bout

they axis.[5 marks]

ENDOF PAPER

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