Section 2.4 Addition of a System of Coplanar Forces (page 32)
CARTESIAN VECTOR IN TWO DIMENSIONS (page 1)
Section 2.4 Addition of a System of Coplanar Forces (page 32)
CARTESIAN VECTOR IN TWO DIMENSIONS (page 2)
• Rectangular components of a vector
!F =!Fx+!Fy
!Fx
and
!Fy
are the rectangular components of
!F .
• Cartesian unit vectors
!i is a dimensionless vector of length one
which points along the positive x-axis.
!j is a dimensionless vector of length one
which points along the positive y-axis.
!i and
!j designate the directions of the x and y axes.
• Cartesian vector
Write
!Fx= F
x
!i F
x= F cos!
!Fy= F
y
!j F
y= F sin!
Then
!F = F
x
!i + F
y
!j
= F cos!
!i + F sin!
!j
Section 2.4 Addition of a System of Coplanar Forces (page 33)
RESULTANT OF A SYSTEM OF FORCES:
CARTESIAN VECTOR METHOD (page 1)
• We want to determine the resultant F
!"
R of a system of forces
!F1,!F2,!F3.
That is, we want to determine the magnitude and direction of F
!"
RR where
F
!"
R = !F
!"
Section 2.4 Addition of a System of Coplanar Forces (page 33)
RESULTANT OF A SYSTEM OF FORCES:
CARTESIAN VECTOR METHOD (page 2)
• Method: Write
!F1,!F2,!F3 as Cartesian vectors:
!F1= F
1x
!i + F
1y
!j
!F2= F
2x
!i + F
2y
!j
!F3= F
3x
!i + F
3y
!j