,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,MOMENT OF A COUPLE,Todays Objectives,:,Students will be able to,a)define a couple,and,b)determine the moment of a couple.,In-Class activities,:,Check Homework,Reading Review,Applications,Moment of a Couple,Concept Review,Group Problem Solving,Attention Review,MOMENT OF A COUPLE,A couple is defined as two parallel forces with the same magnitude but opposite in direction separated by a,perpendicular distance d,.,The moment of a couple is defined as,M,O,=F,d (using a scalar analysis)or as,M,O,=,r,F,(using a vector analysis).,Here,r,is any position vector from the line of action of,F,to the line of action of,F,.,MOMENT OF A COUPLE,(continued),The net external effect of a couple is that the net force equals zero and the magnitude of the net moment equals F d,Moments due to couples can be added using the same rules as adding any vectors.,Since the moment of a couple depends only on the distance between the forces,the moment of a couple is a,free vector,.It can be moved anywhere on the body and have the same external effect on the body.,EXAMPLE-SCALAR APPROACH,Given,:Two couples act on the beam and d equals 8 ft.,Find:,The resultant couple,1)Resolve the forces in x and y directions so they can be treated as couples.,2)Determine the net moment due to the two couples.,The x and y components of the top 60 lb force are:,(4/5)(60 lb)=48 lb vertically up,(3/5)(60 lb)=36 lb to the left,Similarly for the top 40 lb force:,(40 lb)(sin 30,),up,(40 lb)(cos 30,)to the left,The net moment equals to,+M=-(48 lb)(4 ft)+(40 lb)(cos 30,)(8ft),=-192,.,0 +277,.,1 =85,.,1 ftlb,EXAMPLE-SCALAR APPROACH,EXAMPLE VECTOR APPROACH,Given,:A force couple acting on the rod.,Find,:The couple moment acting on the rod in Cartesian vector notation.,1)Use,M=r,F,to find the couple moment.,2)Set,r,=,r,AB,and,F,=14,i,8,j,6,k,N.,3)Calculate the cross product to find,M,.,A,B,r,AB,=0,.,8,i,+,1.5,j,1,k,m,F,=14,i,8,j,6,k,N,M,=,r,AB,F,=,i,(-9 (8),j,(-4,.,8 (-14)+,k,(-6.4,21,)N,m,=-17,i,9,.,2,j,27.4,k,N,m,=,N,m,i,j,k,0.8 1.5 -1,14 -8 -6,A,B,EXAMPLE VECTOR APPROACH,CONCEPT Review,1.,F,1,and,F,2,form a couple.The moment of the couple is given by _.,A),r,1,F,1,B),r,2,F,1,C),F,2,r,1,D),r,2,F,2,2.,If three couples act on a body,the overall result is that,A)the net force is not equal to 0.,B)the net force and net moment are equal to 0.,C)the net moment equals 0 but the net force is not necessarily equal to 0.,D)the net force equals 0 but the net moment is not necessarily equal to 0.,GROUP PROBLEM SOLVING SCALAR APPROACH,Given,:Two couples act on the beam.The resultant couple is zero.,Find,:The magnitudes of the forces P and F and the distance d.,1)Resolve the 300 N force in x and y directions.,2)Determine the net moment.,3)Equate the net moment to zero to find d.,GROUP PROBLEM SOLVING SCALAR APPROACH,From the definition of a couple:,P=500 N and,F=300 N.,Resolve the 300 N force into vertical and horizontal components.The vertical component is(300 cos 30,)N and the horizontal component is(300 sin 30)N.,Now solve this equation for d.,d=(1000+60 sin 30,)/(300 cos 30)=3,.,96 m,It was given that the net moment equals zero.So,+,M=-(500)(2)+(300 cos 30,)(d)-(300 sin 30)(0.2)=0,GROUP PROBLEM SOLVING VECTOR APPROACH,Given,:,F,=25,k,N and -,F,=-25,k,N,Find,:The couple moment acting on the pipe assembly using Cartesian vector notation.,1)Use,M=r,F,to find the couple moment.,2)Set,r,=,r,AB,and,F,=25,k,N.,3)Calculate the cross product to find,M,.,r,AB,=-350,i,200,j,mm,=-0.35,i,0.2,j,m,F,=25,k,N,=,M,=,r,AB,F,=,i,(-5 0),j,(-8.75 0)+,k,(0)N,m,=-5,i,+8.75,j,N m,N,m,GROUP PROBLEM SOLVING VECTOR APPROACH,ATTENTION Review,1.A,couple,is applied to the beam as shown.Its moment equals _ N,m.,A)50B)60,C)80D)100,2.You can determine the couple moment as,M,=,r,F,If,F,=-20,k,lb,then,r,is,A),r,BC,B),r,AB,C),r,CB,D),r,AC,3,4,5,1m,2m,50 N,End of the Lecture,Let Learning Continue,