Biomedical Engineering Reference
In-Depth Information
(b) Determine the length of
F
, using the specifications of
F
expressed in
{
e
1
,
e
2
,
e
3
}
and in
{
1
,
2
,
3
}
.
2.2
For the points P, Q and R the following location vectors are given,
respectively:
x
P
=
e
x
+
2
e
y
x
Q
=
4
e
x
+
2
e
y
x
R
=
3
e
x
+
e
y
.
The force vector
F
=
2
e
x
acts on point Q.
Q
P
F
x
Q
e
y
x
P
R
x
R
e
z
e
x
(a) Calculate the moment of the force
F
with respect to point P and with
respect to point R.
(b) Write the vectors, mentioned above, in column notation according
to the right-handed orthonormal basis
and calculate the
moment of the force with respect to the points P and R by using
Eq. (
1.35
).
{
e
x
,
e
y
,
e
z
}
2.3
Calculate for each of the situations given below the resulting moment with
respect to point P.
F
F
F
F
45°
F
P
P
P
2
P
P
F
F
2
2
F
F
F
(a)
(b)
(c)
(d)
(e)
2.4
On an axis a wheel with radius R is fixed to a smaller wheel with radius
r
.
The forces
F
and
f
are tangentially applied to the contours of both wheels
(as shown in the figure). Calculate the ratio between the forces
F
and
f
in
the case where the total moment with respect to the centroid P is zero.
