shawn kenny, ph.d., p.eng. assistant professor faculty of engineering and applied science memorial...
TRANSCRIPT
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