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College Of Engineering Electrical Engineering Department

College Of Engineering Electrical Engineering Department. Engineering Mechanics-Static Resultant of Force System Lecture-1 By Dr. Salah M. Swadi 2018-2019. Chapter Objectives. Parallelogram Law Cartesian vector form Dot product and angle between 2 vectors. Chapter Outline.

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College Of Engineering Electrical Engineering Department

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  1. College Of Engineering Electrical Engineering Department Engineering Mechanics-Static Resultant of Force System Lecture-1 By Dr. Salah M. Swadi 2018-2019

  2. Chapter Objectives • Parallelogram Law • Cartesian vector form • Dot product and angle between 2 vectors

  3. Chapter Outline • Scalars and Vectors • Vector Operations • Vector Addition of Forces • Addition of a System of Coplanar Forces • Cartesian Vectors • Addition and Subtraction of Cartesian Vectors • Position Vectors • Force Vector Directed along a Line • Dot Product

  4. 2.1 Scalars and Vectors • Scalar – A quantity characterized by a positive or negative number – Indicated by letters in italic such as A e.g. Mass, volume and length

  5. 2.1 Scalars and Vectors • Vector – A quantity that has magnitude and direction e.g. Position, force and moment – Represent by a letter with an arrow over it, – Magnitude is designated as – In this subject, vector is presented as A and its magnitude (positive quantity) as A

  6. 2.2 Vector Operations • Multiplication and Division of a Vector by a Scalar - Product of vector A and scalar a = aA - Magnitude = - Law of multiplication applies e.g. A/a = ( 1/a ) A, a≠0

  7. 2.2 Vector Operations • Vector Addition - Addition of two vectors A and B gives a resultant vector R by the parallelogram law - Result R can be found by triangle construction - Communicative e.g. R = A + B = B + A - Special case: Vectors A and B are collinear (both have the same line of action)

  8. 2.2 Vector Operations • Vector Subtraction - Special case of addition e.g. R’ = A–B = A + ( - B ) - Rules of Vector Addition Applies

  9. 2.3 Vector Addition of Forces Finding a Resultant Force • Parallelogram law is carried out to find the resultant force • Resultant, FR = ( F1 + F2 )

  10. 2.3 Vector Addition of Forces Procedure for Analysis • Parallelogram Law • Make a sketch using the parallelogram law • 2 components forces add to form the resultant force • Resultant force is shown by the diagonal of the parallelogram • The components is shown by the sides of the parallelogram

  11. 2.3 Vector Addition of Forces Procedure for Analysis • Trigonometry • Redraw half portion of the parallelogram • Magnitude of the resultant force can be determined by the law of cosines • Direction if the resultant force can be determined by the law of sines • Magnitude of the two components can be determined by the law of sines

  12. Example 2.1 The screw eye is subjected to two forces, F1 and F2. Determine the magnitude and direction of the resultant force.

  13. Solution Parallelogram Law Unknown: magnitude of FR and angle θ

  14. Solution Trigonometry Law of Cosines Law of Sines

  15. Solution Trigonometry Direction Φ of FR measured from the horizontal

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