Environmental Engineering Reference
In-Depth Information
any acceleration vectors to the side of the diagram. Figure 2.11 shows a free-body
diagram for a topic in static equilibrium on a table. The weight of the topic and
the normal force from the table are in opposite directions. The condition of static
equilibrium implies that the magnitudes of these two forces are equal and that the
acceleration of the centre of mass is zero.
N
a
=
0
m
g
Figure 2.11
Free-body diagram for a topic in static equilibrium on a table.
2.3.2 Three worked examples
In order to illustrate the methodology that we presented in the last section we
will work through three specific examples. Like so often in physics, it is useful
first to work through problems that are selected because they really help to develop
an ability to apply the key ideas and principles that we have spent so much time
developing. The problems are not chosen because they represent particularly excit-
ing phenomena. The study of exciting things comes later, once one has a grasp of
the key ideas. In this section we shall take a look at the motion of a pendulum,
two spaceships connected by a cable and two masses hung over a pulley.
Example 2.3.1
When the bob of a pendulum is made to describe a circular orbit in
the horizontal plane, rather than executing the usual oscillatory motion in a vertical
plane, it is known as a conical pendulum. Determine the period of revolution of a
conical pendulum of mass m and length l which makes an angle α to the vertical
(see Figure 2.12). Ignore the mass of the pendulum string.
Side view
a
From above
l
R
R
Figure 2.12
Geometric diagram of a conical pendulum.
