tutorial assignment 2 - part a.pdf

Post on 08-Oct-2015

774 views

Category:

Documents

3 download

Embed Size (px)

TRANSCRIPT

  • 10/14/2014 Tutorialassignment2partA

    http://session.masteringengineering.com/myct/assignmentPrintView?assignmentID=1206301 1/14

    Tutorialassignment2partADue:12:20pmonThursday,October9,2014

    Youwillreceivenocreditforitemsyoucompleteaftertheassignmentisdue.GradingPolicy

    MomentofaForceVectorFormulation

    LearningGoal:

    Tousethevectorcrossproducttocalculatethemomentproducedbyaforce,orforces,aboutaspecifiedpointonamember.

    Themomentofaforce aboutthemomentaxispassingthroughOandperpendiculartotheplanecontainingOandcanbeexpressedusingthevectorcrossproduct, .InaproperlyconstructedCartesiancoordinatesystem,thevectorcrossproductcanbecalculatedusingamatrixdeterminant:

    Noticethattheorderoftheelementsofthematrixdeterminantisimportantswitchingrows2and3ofthedeterminantwouldchangethesignofthemomentfrompositivetonegative(orviceversa.)

    PartAMomentduetoaforcespecifiedbymagnitudeandendpoints

    Asshown,amemberisfixedattheorigin,pointO,andhasanappliedforce ,thetensionintherope,appliedatthefreeend,pointB.

    Theforcehasmagnitude =180 andisdirectedasshown.Thedimensionsare

    =0.250 , =1.70 , =2.30 ,and=1.10 .

    Whatisthemomentabouttheoriginduetotheappliedforce ?

    ExpresstheindividualcomponentsoftheCartesianvectortothreesignificantfigures,separatedbycommas.

    Hint1.Howtocalculatethemomentabouttheorigin

    WeneedtoexpresstheforceandthepositionvectorofthefreeendofthememberasCartesianvectorsthenusethevectorcrossproducttofindthemoment.

    Hint2.ExpresstheforceasaCartesianvector

    Theforcehasmagnitude =180Nandisdirectedasshown.ExpresstheforceasaCartesianvector.

    ExpresstheindividualcomponentsoftheCartesianvectortothreesignificantfigures,separatedbycommas.

    ANSWER:

    ' '

    Sg'.

    . Sg'

    J

    .

    4

    4

    K

    .

    5

    5

    L

    .

    6

    6

    '

    /

    4

    N 4

    N 5

    N

    6

    N

    '

  • 10/14/2014 Tutorialassignment2partA

    http://session.masteringengineering.com/myct/assignmentPrintView?assignmentID=1206301 2/14

    Hint3.ExpressthepositionvectorofthememberasaCartesianvector

    ThememberisanchoredatpointOandhasitsfreeendatB.Expressthepositionvector asaCartesianvector.

    ExpresstheindividualcomponentsoftheCartesianvectortothreesignificantfigures,separatedbycommas.

    ANSWER:

    Hint4.Identifythedeterminantofa3by3matrix

    Whichofthefollowingcorrectlyexpressesthedeterminantofthematrix?

    Hint1.Expansionbyminors

    Themethodofexpansionbyminorscanbeusedtocalculatedeterminantsoflargematricesbyreducingthemtoalinearcombinationofdeterminantsof2by2matrices.Forcalculatingmoments,thebestchoiceofminorsisthetoprowbecauseithastheunitdirectionvectors.Thecomponentsarethengivenbythedeterminantofthe2by2matrixleftafter"crossingout"therowandcolumncontainingtheminor:

    Thedeterminantofa2by2matrixisgivenby

    andeachterminthesumwillalsocontainaterm ,where and aretheindexoftherowandcolumnoftheminor,respectively.

    ANSWER:

    99.9,135,64.6' < J KL> /

    0#

    0.250,2.30,1.100# < J KL> N

    .

    .

  • 10/14/2014 Tutorialassignment2partA

    http://session.masteringengineering.com/myct/assignmentPrintView?assignmentID=1206301 3/14

    ANSWER:

    Correct

    PartBMomentduetoaforcespecifiedasaCartesianvector

    Asshown,amemberisfixedattheorigin,pointO,andhasanappliedforce ,thetensionintherope,appliedatthefreeend,point .

    Theforceisgivenby.Thedimensions

    are =1.35m, =1.80m,and =1.05m.

    Whatisthemomentabouttheoriginduetotheappliedforce ?

    ExpresstheindividualcomponentsoftheCartesianvectortothreesignificantfigures,separatedbycommas.

    , *J ,)K *)L

    J

    )

    K

    *

    L

    ,

    * ,J ) ,K ) *L

    J

    )

    K

    *

    L

    ,

    , *J ,)K *)L

    J

    )

    K

    *

    L

    ,

    , *J , )K * )L

    J

    )

    K

    *

    L

    ,

    * ,J ) ,K ) *L

    J

    )

    K

    *

    L

    ,

    , *J , )K * )L

    J

    )

    K

    *

    L

    ,

    0,126,263 / N

    '

    ' /J /K /L

    4

    5

    6

    '

  • 10/14/2014 Tutorialassignment2partA

    http://session.masteringengineering.com/myct/assignmentPrintView?assignmentID=1206301 4/14

    Hint1.Howtosetupandcalculatethemoment

    TheforceisalreadyexpressedasaCartesianvector.WeneedtoexpressthepositionvectorofthefreeendofthememberasaCartesianvectorthenusethecrossproducttofindthemoment.

    Hint2.ExpressthepositionvectorofBasaCartesianvector

    Basedonthedimensionsgiven,expressthevectorfromOtoBasaCartesianvector.

    ExpresstheindividualcomponentsoftheCartesianvectortothreesignificantfigures,separatedbycommas.

    ANSWER:

    ANSWER:

    Correct

    PartCMomentduetotwoforces

    Asshown,amemberisfixedattheorigin,pointO,andhastwoappliedforces, and ,appliedatthefreeend,pointB.

    Theforcesaregivenbyand has

    magnitude155 anddirectionangles ,,and .Thedimensionsare

    =1.30 , =1.85 ,and =1.20 .

    Whatisthemomentabouttheoriginduetotheappliedforces?

    ExpresstheindividualcomponentsoftheCartesianvectortothreesignificantfigures,separatedbycommas.

    Hint1.Howtosetupandcalculatethemoment

    Force isalreadyexpressedasaCartesianvector.BecausethepositionofpointBisgivenintermsofcomponents,wealsohave .Weneedtoexpresstheforce asaCartesianvector.Thenetmomentabout duetobothforcesisthevectorsumofthemomentsduetoeachforce.Calculateindividualmomentsbysettingupadeterminantforeachforcethensumtheresultscomponentwisetofindthenetmoment.

    1.35,1.80,1.050# < J KL> N

    221,58.5,385 / N

    '

    '

    /J /K /L'

    '

    / C

    D

    E

    4

    N 5

    N 6

    N

    '

    0# NJ NK NL '

    '

  • 10/14/2014 Tutorialassignment2partA

    http://session.masteringengineering.com/myct/assignmentPrintView?assignmentID=1206301 5/14

    Hint2.Expresstheforce asaCartesianvector

    Force hasmagnitude155 anddirectionangles , ,and .ExpressthisforceasaCartesianvector.

    ExpresstheindividualcomponentsoftheCartesianvectortothreesignificantfigures,separatedbycommas.

    Hint1.Thedirectionangles

    Thedirectionangle istheanglebetweenthevectorandthepositivexaxis.Thedirectionangle istheanglebetweenthevectorandthepositiveyaxis.Thedirectionangle istheanglebetweenthevectorandthepositivezaxis.

    ANSWER:

    Hint3.CalculatethemomentduetoforceF1

    Whatisthemomentabouttheoriginduetotheappliedforce ?

    ExpresstheindividualcomponentsoftheCartesianvectortothreesignificantfigures,separatedbycommas.

    ANSWER:

    Hint4.CalculatethemomentduetoforceF2

    Whatisthemomentabouttheoriginduetotheappliedforce ?

    ExpresstheindividualcomponentsoftheCartesianvectortothreesignificantfigures,separatedbycommas.

    ANSWER:

    ANSWER:

    '

    '

    / C

    D

    E

    C D

    E

    124,82.1,44.3

  • 10/14/2014 Tutorialassignment2partA

    http://session.masteringengineering.com/myct/assignmentPrintView?assignmentID=1206301 6/14

    Correct

    Therearetwowaystoapproachthisproblem.One,themethodusedinthistutorial,istofindthenetmomentasasumofmoments,i.e.,calculateamomentforeachappliedforcethenusevectoradditiontofindthenetmoment.Equivalently,wecouldhavefoundthevectorsumoftheforcesthencalculatedasingledeterminantusingtheresultantnetforceandthepositionvectortofindthenetmoment.Thesetwomethodsproducethesamenetmoment.(Youmightfinditaninterestingexercisetoconfirmthis.)

    PrincipleofMoments

    LearningGoal:

    Toapplytheprincipleofmomentsandtheprincipleoftransmissibility.

    Asshown,aropeisattachedtoa highshedthatistoberelocated.AmanpullsontheendoftheropeatpointAtheropeisattachedtotheshedatpointB.Asthemanpullsontherope,itcreatesanangle withthehorizontal.Theendoftheropeislocatedat fromtheshedand offtheground.Themanpullsontheropewithaforceofmagnitude .

    PartA

    Whatis ,thecontributiontothemomentaboutpointOmadebythexcomponentoftheforce atpointA?Whatis ,thecontributiontothemomentaboutpointOmadebytheycomponentoftheforce atpointA?Whatisthetotalmoment duetotheforce aboutpointO?AssumethatmomentsactingcounterclockwiseaboutpointOarepositivewhereasmomentsactingclockwisearenegative.

    Expressyouranswersnumericallyinpoundfeettothreesignificantfiguresseparatedbycommas.

    Hint1.Howtoapproachtheproblem

    Theprincipleofmomentssimplifiestheprocessofcalculatingamomentbyseparatingaforceintoitscomponents.Tocalculatethetotalmoment,addthemomentsthatresultfromtheseparatecomponents:

    Here, and arethexandycomponentsoftheforce .AssumethatmomentsactingcounterclockwiseaboutpointOarepositivewhereasmomentsactingclockwisearenegative.

    ( GU

    J

    4 GU

    5 GU

    MC

    4

    '

    5

    '

    '

    Sg' Sg Sg Sg.

    '

    '

    '

    '

    '

    '

    '

    4

  • 10/14/2014 Tutorialassignment2partA

    http://session.masteringengineering.com/myct/assignmentPrintView?assignmentID=1206301 7/14

    Hint2.Findanexpressionfor

    WhatisthecontributiontothetotalmomentaboutpointOfromthexcomponentoftheforceatpointAintermsoftheforce ,theangle ,andthedistances and ?

    Expressyouranswerintermssomeorallofthevariables , , ,and .

    Hint1.Findanexpressionfor

    Whatis ,thexcomponentoftheforce,intermsoftheforce'smagnitude andtheangle ?

    Expressyouranswerintermsof and .

    ANSWER:

    Hint2.Findthemomentarmofthexcomponentoftheforce

    Whatisthemomentarmfor ,thexcomponentoftheforce ?

    ANSWER:

    ANSWER:

    4

    J 4 5

    J 4 5

    4

    4

    J

    J

    =4

    DPTJ

    '

    4

    '

    4

    5

    5

    5 4 UBOJ

    4

    =

    4

    DPTJ5

    5

  • 10/14/2014 Tutorialassignment2partA

    http://session.masteringe

Recommended

View more >