ES 226
Statics
Fall 2010
Class 2: Review of Vector Operations/Force Resultants
Material covered on September 1, 2010
Learning Objectives:
1. Resolve force vectors into Cartesian (rectangular or x-y) components
2. Determine the resultant force vector from two, three or more vectors using x-y components
3. Draw force vectors and resultants using the Parallelogram Law
4. Resolve a force vector into two components given their directions (line of action) (parallelogram)
Problems Discussed in Class:
1. Given: Three concurrent forces acting on the anchor.
Find: Magnitude and direction of the resultant force FR
2. Given: Three concurrent forces acting on a bracket.
Find: Magnitude and direction,  of F1 so that the resultant force is
directed along the positive x’ axis and has a magnitude of 1000 N.
Homework: Due on Friday, September 3rd
Problem 2-55, 2-56, and Problem 2/14 shown on the right.
Sections to Read in Textbook for next class:
Sections 2.2 – 2.4
ES 226
Statics
Fall 2010
Useful Math:
a + b + c = 180° (sum of angles)
x and y components of vectors
Extra Vector Practice – Given to Cartesian vectors a = 4i + 6j − 2k and b = 3i + 2k
a) Calculate a-b
b) Calculate a·b
c) Calculate a×b
d) Find the magnitude of a
e) Find the components of a unit vector parallel to a
f) Find the component of b in a direction parallel to a
g) Find the angle between a and b
Check answers:
a) i + 6j − 4k; b) 8; c) 12i −14j −18k; d) sqrt(56); e) (4i + 6j − 2k)/sqrt(56); f) 8/sqrt(56); g) θ = 72.75 degrees