Biomedical Engineering Reference
In-Depth Information
P
F
Q
Figure 2.11
The force vector
F
resulting from the two force vectors
P
and
Q
.
Suppose that two thin wires are connected to a point. The first wire is loaded with
force
P
and on the second wire a force
Q
is applied. The total force vector
F
exerted on the point is calculated from
F
=
P
+
Q
.
(2.51)
See Fig.
2.11
for a visualization.
The force vectors may be written as
P
=
P
x
e
x
+
P
y
e
y
+
P
z
e
z
(2.52)
Q
=
Q
x
e
x
+
Q
y
e
y
+
Q
z
e
z
,
(2.53)
such that
F
=
(
P
x
+
Q
x
)
e
x
+
(
P
y
+
Q
y
)
e
y
+
(
P
z
+
Q
z
)
e
z
.
(2.54)
The magnitude of the resulting force vector is given by
(
P
x
+
Q
x
)
2
|
F
|=
+
(
P
y
+
Q
y
)
2
+
(
P
z
+
Q
z
)
2
.
(2.55)
Using the column representation the components defining the force vectors
P
and
Q
with respect to the Cartesian vector basis may be collected into, respectively:
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
P
x
P
y
P
z
Q
x
Q
y
Q
z
∼
=
,
Q
∼
=
,
(2.56)
