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

ENGI 1313 Mechanics I

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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 - PowerPoint PPT Presentation

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Shawn Kenny, Ph.D., P.Eng.Assistant ProfessorFaculty of Engineering and Applied ScienceMemorial University of [email protected]

ENGI 1313 Mechanics I

Lecture 08/09: Vector Dot Product

2 ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng.

Administrative Note

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

3 ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng.

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

4 ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng.

Lecture 08/09 Objectives

to apply dot product in a vector mechanics problem

5 ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng.

Example 8-01

Problem 2-119 Determine the projected

component of the 80-N force acting along the axis AB of the pipe.

6 ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng.

Example 8-01 (cont.)

Problem Objective Projected component

• Dot product

Data needed• Cartesian force vector for force F

• Position vector for pipe segment AB

cosBABA

uAcosAA ||

7 ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng.

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 FAP

• No structural element needed

r

rFuFF

P

8 ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng.

Example 8-01 (cont.)

Obtain force vector FAP

r

rFuFF

FAP

k212j34i6rAP

m60.131076r 222AP

m60.13

mk10j7i6N80

r

rFF

AP

APAPAP

Nk82.58j17.41i29.35FAP

P

9 ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng.

Example 8-01 (cont.)

Find force component parallelto pipe segment AB

Need unit vector

ABAPAPAB|| uFcosFF

P FAP

mk2j3i6rAB

AB

ABAB r

ru

m7236r 222AB

k2857.0j4286.0i8571.0uAB

10 ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng.

Example 8-01 (cont.)

Find force component parallelto pipe segment AB

P FAP

ûAB

ABAPAPAB|| uFcosFF

ABzAPzAByAPyABxAPxABAPAB|| uFuFuFuFF k2857.0j4286.0i8571.0uAB

Nk82.58j17.41i29.35FAP

2857.0N82.584286.N17.418571.0N29.35F AB||

N1.31F AB||

11 ENGI 1313 Statics I – Lecture 08/09© 2007 S. Kenny, Ph.D., P.Eng.

Classification of Textbook Problems

Hibbeler (2007)

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

References

Hibbeler (2007) http://wps.prenhall.com/

esm_hibbeler_engmech_1