F2x
F2y
(2.1)2
( 17.6)2
314.2
Vectors
ANALYTICAL METHOD OF VECTOR ADDITION
Rev. 0
Page 29
CP-02
Step 3:
Sum the x and y components.
F = F + F + F
Rx
1x
2x
3x
F = 69.9 lbf + (-25 lbf) + (-42.8 lbf)
Rx
F = 2.1 lbf
Rx
F = F + F + F
Ry
1y
2y
3y
F = 56.6 lbf + 43.3 lbf + (-117.5 lbf)
Ry
F = -17.6 lbf
Ry
Step 4:
Calculate the magnitude of F .
R
F =
R
F =
R
F =
R
F = 17.7 lbf
R
Step 5:
Calculate the angle of displacement.
tan = F /F
Ry
Rx
tan = -17.6/2.1
tan = -8.381
= tan (-8.381)
-1
= -83.2o
Therefore,
F = 17.7 lbf at -83.2 or 276.8 .
R
o
o
Note: A negative angle means a clockwise rotation from the zero axis.
It is left to the student to try the previous example using the other methods of vector addition
described in earlier chapters.
