MEL1010 Engineering Mechanics Tutorial 2: Equilibrium Tuesday, 27 Aug 19 10 Marks Answer all of the following questions. Mention valid assumptions wherever applicable 1 Determine the force P required to begin rolling the uniform cylinder of mass m over the obstruction of height h. Problem 1 Problem 2 2 The spring of modulus k = 3.5 kN/m is stretched 10 mm when the disk center O is in the leftmost position x = 0. Determine the tension T required to position the disk center at x = 150 mm. At that position, what force N is exerted on the horizontal slotted guide? The mass of the disk is 3 kg. 3 A person is performing slow arm curls with a 20-lb weight as indicated in the figure. The brachia lis muscle group (consisting of the biceps and brnchiali s muscles) is the major factor in this exercise. Determine the magnitude F of the brachialis-muscle-group force and the magnitude E of the elbowjoint reaction at point E for the forearm position shown in the figure. Take the dimensions shown to locate the effective points of application of the two muscle groups; these points are 8 in. directly above E and 2 in. directly to the right of E. Include the 3.2-lb forearm weight which acts at point G. State any assumptions. (Solve this problem in FPS systems) Ans. Problem 3 Problem 4
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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)
Ans.
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.
Ans:
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?
Ans:
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