Force Vector

Engineering Mechanics: Statics in SI Units, 12e
2
Force Vectors Part 2

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Chapter Objectives

• Cartesian vector form • Dot product and angle between 2 vectors

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Chapter Outline

1. 2. 3. 4. 5.

Cartesian Vectors Addition and Subtraction of Cartesian Vectors Position Vectors Force Vector Directed along a Line Dot Product

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2.5 Cartesian Vectors

• Right-Handed Coordinate System

A rectangular or Cartesian coordinate system is said to be right-handed provided: – Thumb of right hand points in the direction of the positive z axis – z-axis for the 2D problem would be perpendicular, directed out of the page.

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2.5 Cartesian Vectors

• Rectangular Components of a Vector

–

A vector A may have one, two or three rectangular components along the x, y and z axes, depending on orientation – By two successive application of the parallelogram law A = A’ + Az A’ = Ax + Ay – Combing the equations, A can be expressed as A = Ax + Ay + Az

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2.5 Cartesian Vectors

• Unit Vector

– Direction of A can be specified using a unit vector – Unit vector has a magnitude of 1 – If A is a vector having a magnitude of A ≠ 0, unit vector having the same direction as A is expressed by uA = A / A. So that A = A uA

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2.5 Cartesian Vectors

• Cartesian Vector Representations

– 3 components of A act in the positive i, j and k directions A = Axi + Ayj + AZk *Note the magnitude and direction of each components are separated, easing vector algebraic operations.

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2.5 Cartesian Vectors

• Magnitude of a Cartesian Vector
A'2 + Az2

– From the colored triangle, A =

2