Engi 1313 mechanics i
This presentation is the property of its rightful owner.
Sponsored Links
1 / 20

ENGI 1313 Mechanics I PowerPoint PPT Presentation


  • 56 Views
  • Uploaded on
  • Presentation posted in: General

ENGI 1313 Mechanics I. Lecture 07:Vector Dot Product. 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

Download Presentation

ENGI 1313 Mechanics I

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Engi 1313 mechanics i

ENGI 1313 Mechanics I

Lecture 07:Vector Dot Product


Chapter 2 objectives

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 07 objectives

Lecture 07 Objectives

  • to examine the concept of dot product


Overview of dot product

Overview of Dot Product

  • Definition

  • Laws of Operations

    • Commutative law

    • Scalar Multiplication

    • Distributive law


Overview of dot product cont

Overview of Dot Product (cont.)

  • Dot Product of Cartesian Vectors

Go to zero


Application of dot product

Application of Dot Product

  • Angle between two vectors

    • Cables forces and the pole?

      • and ?

Component magnitudes


Application of dot product cont

If A||has + sense then same direction as u

^

Application of Dot Product (cont.)

  • Component magnitudeof A on a parallel or collinear linewith line aa

    • Recall

Component A||


Application of dot product cont1

Application of Dot Product (cont.)

  • The vector A|| canbe determined by:

Vector A||

Application of Dot Product for Component A||

Multiply by Unit Vector ûto obtain Vector A||


Application of dot product cont2

Application of Dot Product (cont.)

  • For force vector F at Point A: What is the component magnitudeparallel (|F1|) to the pipe (OA)?


Application of dot product cont3

Application of Dot Product (cont.)

  • For force vector F at Point A: what is the component magnitudeperpendicular (F2) to the pipe (OA)?

    • Method 1

    • Method 2


Comprehension quiz 7 01

Comprehension Quiz 7-01

  • The dot product of two vectors results in a _________ quantity.

    • A) scalar

    • B) vector

    • C) complex number

    • D) unit vector

  • Answer: A


Example problem 7 01

A

Example Problem 7-01

  • For the Cartesian force vector, find the angle between the force vector and the pole, and the magnitude of the projection of the force along the pole OA


Example problem 7 01 cont

A

Example Problem 7-01 (cont.)

  • Position vector rOA

  • Magnitude of |rOA|

  • Magnitude of |F|


Example problem 7 01 cont1

A

Example Problem 7-01 (cont.)

  • Find the angle between rOA and F


Example problem 7 01 cont2

A

Example Problem 7-01 (cont.)

  • Find magnitude of the projection of the force F along the pole OA


Comprehension quiz 7 02

Comprehension Quiz 7-02

  • If the dot product of two non-zero vectors is 0, then the two vectors must be ______ to each other.

    • A) parallel (pointing in the same direction)

    • B) parallel (pointing in the opposite direction)

    • C) perpendicular

    • D) cannot be determined.

  • Answer: C


Comprehension quiz 7 03

Comprehension Quiz 7-03

  • The Dot product can be used to find all of the following except ____

    • A) sum of two vectors

    • B) angle between two vectors

    • C) vector component parallel to a line

    • D) vector component perpendicular to a line

  • Answer: A


Comprehension quiz 7 04

Comprehension Quiz 7-04

  • Find the dot product (PQ) for

    • A) -12 m

    • B) 12 m

    • C) 12 m2

    • D) -12 m2

    • E) 10 m2

  • Answer: C


Classification of textbook problems

Classification of Textbook Problems

Hibbeler (2007)


References

References

  • Hibbeler (2007)

  • http://wps.prenhall.com/esm_hibbeler_engmech_1


  • Login