Biomedical Engineering Reference
In-Depth Information
Fig. 1.4
Vector force
F
represented by its
components
F
x
and
F
y
y
F
y
F
x
F
x
1.4 Resultant or Sum of Force Vectors
When two or more forces act on a body, it is possible to determine a force called
resultant force, which can produce the same effect as all forces acting together. For
this, we must know how to work with vector quantities. Some important rules are:
F
is the opposite vector of
F
with the same
magnitude (intensity or length) but opposite direction.
The multiplication of a vector
F
by a real number
n
is another vector
T
,
T
There is the opposite vector:
F
,
¼
n
nF
, same direction as
F
, depending on the sign of
n
; that is,
if
n
is positive,
T
will have the same direction as
F
, and the opposite direction, if
n
is negative.
The associative property is valid:
with magnitude
T
¼
ðF
1
þ F
2
ÞþF
3
¼ F
1
þðF
2
þ F
3
Þ
.
The commutative property is valid:
F
1
þ F
2
¼ F
2
þ F
1
.
A vector can be projected in a determined direction by using sine and cosine
relations of a right triangle.
1.5 Addition of Vectors
Four rules or methods can be used to add vectors.
1.5.1 Rule of Polygon
One of the vectors is initially transported, maintaining its magnitude and direction.
Then, the next vector is transported in a way that its origin coincides with the head
of a previous vector. The sum vector or resultant vector will be an arrow with its
origin coinciding with the origin of the first transported vector and with the
head coinciding with the head of the last vector considered, as shown in Fig.
1.5
.
