ENGI 1313 Mechanics I

ENGI 1313 Mechanics I Lecture 08/09: Vector Dot Product

Administrative Note • Final Examination ENGI 1313 • December 6, 2007 • 1900-2130 (700pm-930pm)

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

Lecture 08/09 Objectives • to apply dot product in a vector mechanics problem

Example 8-01 • Problem 2-119 • Determine the projected component of the 80-N force acting along the axis AB of the pipe.

Example 8-01 (cont.) • Problem Objective • Projected component • Dot product • Data needed • Cartesian force vector for force F • Position vector for pipe segment AB

Example 8-01 (cont.) • Cartesian Force Vector, F • Recall L06 Slide 14 • Force vector directed along a line • Define point P • Force F along lineAP FAP • No structural element needed P

FAP Example 8-01 (cont.) • Obtain force vector FAP P

FAP Example 8-01 (cont.) • Find force component parallelto pipe segment AB • Need unit vector P

FAP Example 8-01 (cont.) • Find force component parallelto pipe segment AB ûAB P

Classification of Textbook Problems Hibbeler (2007)

References • Hibbeler (2007) • http://wps.prenhall.com/esm_hibbeler_engmech_1

ENGI 1313 Mechanics I