Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI 1313 Mechanics I Lecture 08/09:Vector Dot Product

ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng. 2 Administrative Note Final Examination ENGI 1313  December 6, 2007  (700pm-930pm)

ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng. 3 Chapter 2 Objectives to review concepts from linear algebra to sum forces, determine force resultants and resolve force components for 2D vectors using Parallelogram Law to express force and position in Cartesian vector form to examine the concept of dot product

ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng. 4 Lecture 08/09 Objectives to apply dot product in a vector mechanics problem

ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng. 5 Example 8-01 Problem  Determine the projected component of the 80-N force acting along the axis AB of the pipe.

ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng. 6 Example 8-01 (cont.) Problem Objective  Projected component Dot product  Data needed Cartesian force vector for force F Position vector for pipe segment AB

ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng. 7 Example 8-01 (cont.) Cartesian Force Vector, F  Recall L06 Slide 14 Force vector directed along a line  Define point P Force F along line AP  F AP No structural element needed P

ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng. 8 Example 8-01 (cont.) Obtain force vector F AP F AP P

ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng. 9 Example 8-01 (cont.) Find force component parallel to pipe segment AB  Need unit vector P F AP

ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng. 10 Example 8-01 (cont.) Find force component parallel to pipe segment AB P F AP û AB

ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng. 11 Classification of Textbook Problems Hibbeler (2007)

ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng. 12 References Hibbeler (2007) mech_1