JJ205-Engineering Mechanics Unit 2

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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