The following concepts and definitions are basic to the study of
mechanics, and they should be understood at the outset.
·
Space is the geometric region occupied by the
bodies whose positions are described by linear and angular measurements
relative to a coordinate system. For three-dimensional problems, three
independent coordinates are required. For two dimensional problems, only two
coordinates are required.
·
Time is the measure of succession of events
and is a basic quantity in dynamics. Time is not directly involved in the
analysis of statics problem.
·
Mass is a measure of the inertia of a body,
which is resistance to a change of velocity. Mass can also be thought of as the
quantity of matter in a body. The mass of a body affects the gravitational
attraction force between it and other bodies. This force appears in many
applications of statics.
·
Force is the action of body on another.A force
tends to move a body in the direction of its action. The action of a force is
characterized by it magnitude, by the direction of its action, and by the point
of its application.
·
Idealizations or Models are used in mechanics in
order to simplify application of theory. A few of the more important
idealizations will now be defined. Others that are noteworthy will be discussed
at points where they are needed.
·
A particle
has a mass, but size that can be neglected. For example, the size of mars is
insignifcant compared to the size of its orbit, and therefore the mars can be
modeled as a particle when studying its orbital motion. When a body is
idealized as a particle, the principles of mechanics reduce to a rather
simplified form since the geometry of the body will not be involved in the
analysis of the problem.
·
A rigid-body
can be considered as a combination of a large number of particles in which all
particles remain at a fixed distance from one another both before and after
applying a load. As a result, the material properties of any body that is
assumed o be rigid will not have to be considered when analyzing the forces
acting on the body. In most cases the actual deformations occuring in
structures, machines, mechanisms, and the like are relatively small, and the
rigid-body assumption is suitable for analysis.
·
A concentrated
force represents the effect of a loading which is assumed to act at a
point on a body. We can represent a load by a concentrated force, provided the
area over which the load is applied very small compared to the overall size of
the body. An example would be the contact force between a wheel and the ground.
