MEL1010EngineeringMechanicsTutorial2:Equilibrium
Tuesday,27Aug19 10MarksAnswerallofthefollowingquestions.Mentionvalidassumptionswhereverapplicable1 Determine the force P required to begin rolling the uniform cylinder of mass m over the
obstructionofheighth.
Problem1Problem2
2 Thespringofmodulusk=3.5kN/misstretched10mmwhenthediskcenterOisintheleftmostpositionx=0.DeterminethetensionTrequiredtopositionthediskcenteratx=150mm.Atthatposition,whatforceNisexertedonthehorizontalslottedguide?Themassofthediskis3kg.
3 Apersonisperformingslowarmcurlswitha20-lbweightasindicatedinthefigure.Thebrachia
lismusclegroup(consistingofthebicepsandbrnchialismuscles)isthemajorfactorinthisexercise.DeterminethemagnitudeFofthebrachialis-muscle-groupforceandthemagnitudeEof theelbowjointreactionatpointE for the forearmposition shownin the figure.Take thedimensionsshowntolocatetheeffectivepointsofapplicationofthetwomusclegroups;thesepointsare8in.directlyaboveEand2in.directlytotherightofE.Includethe3.2-lbforearmweightwhichactsatpointG.Stateanyassumptions.(SolvethisprobleminFPSsystems)
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Problem3Problem4
4 DeterminetheexternalreactionsatAandFfortherooftrussloadedasshown.Theverticalloadsrepresenttheeffectofthesupportedroofingmaterials,whilethe400·Nforcerepresentsawindload.
Ans: 5 Theuniform400-kgdrumismountedonalineofrollersatAandalineofrollersatR.An80.kg
manmovesslowlyadistanceof700mmfromtheverticalcenterlinebeforethedrumbeginstorotate.Allrollersareperfectly freetorotate,exceptoneof thematBwhichmustovercomeappreciable friction in its bearing. Calculate the friction force F exerted by that one rollertangenttothedrumandfindthemagnitudeRoftheforceexertedbyallrollersatAonthedrumforthiscondition.
Problem5Problem6
6 Calculatethenormalforcesassociatedwiththefrontandrearwheelpairsofthe1600·kgfront-wheel-drivevan.Thenrepeatthecalculationswhenthevan(a)climbsa10-percentgradeand(b)descendsa10-percentgrade,bothatconstantspeed.ComputethepercentchangesnAandnBinthenormalforcescomparedwiththenominalvalues.Besuretorecognizethatpropulsiveandbrakingforcesarepresentforcases(a)and(b).
7 TheuniformI-beamhasamassof60kgpermeterofitslength.Determinethetensioninthe
twosupportingcablesandthereactionatD.
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Problem7Problem8
8 TheboomABliesintheverticaly-zplaneandissupportedbyaball-and-socketjointatBandbythetwocablesatA.Calculatethetensionineachcableresultingfromthe20-kNforceactinginthehorizontalplaneandappliedatthemidpointMoftheboom.Neglecttheweightoftheboom.
9 The shaft, lever, and handle are welded together and constitute a single rigid body. Theircombinedmassis28kgwithmasscenteratG.TheassemblyismountedinbearingsAandB,androtationispreventedbylinkCD.DeterminetheforcesexertedontheshaftbybearingsAandBwhilethe30-Nmcoupleisappliedtothehandleasshown.WouldtheseforceschangeifthecouplewereappliedtotheshaftABratherthantothehandle?
Problem9Problem10
10 Thespringofmodulusk=900N/misstretchedadistance𝛿=60mmwhenthemechanismisinthepositionshown.CalculatetheforcePminrequiredtoinitiaterotationaboutthehingeaxisBC.anddeterminethecorrespondingmagnitudesofthebearingforceswhichareperpendiculartoBC.WhatisthenormalreactionforceatDifP=Pmin/2?
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