jj205-engineering mechanics unit 2
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JJ205-ENGINEERING JJ205-ENGINEERING MECHANICSMECHANICSForce VectorsForce VectorsApplication of Vector Addition
There are fourconcurrent cable forcesacting on the bracket.
How do you determinethe resultant force actingon the bracket ?
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Scalars and VectorsScalars and Vectors
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Vector OperationVector OperationScalar Multiplicationand Division
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Vector AdditionVector Addition
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Sine Law and Cosine LawSine Law and Cosine Law
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Basic TrigonometryBasic Trigonometry
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ExampleExample
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Resolution of a VectorResolution of a Vector
“Resolution” of a vector is breaking up avector into components. It is kind of like using the parallelogram law in reverse.
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Cartesian Vector NotationCartesian Vector NotationWe ‘ resolve’ vectors into components
using the x and y axes systemEach component of the vector is shown
as a magnitude and a direction.The directions are based on the x and
y axes. We use the “unit vectors” i and j to designate the x and y axes.
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Cartesian NotationCartesian NotationFor example,F = Fx i + Fy j or F' = F'x i + F'y jThe x and y axes are always perpendicular
to each other. Together, they can be directed at any inclination.
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Addition of Several Addition of Several VectorsVectors
Step 1: resolve each force
into its componentsStep 2: add all the xcomponents together
andadd all the y componentstogether. These two
totalsbecome the resultant
vector.Step 3: find the
magnitudeand angle of the
resultantvector.
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IllustrationIllustration
FR = F1 + F2 + F3
= F1xi + F1yj – F2xi + F2yj + F3xi – F3yj
=(F1x–F2x+F3x)i +(F1y+ F2y–F3y)j
= (FRx)i + (FRy)j
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Magnitude and DirectionMagnitude and Direction
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EXAMPLE 1EXAMPLE 1
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