Idealizations. Models or idealizations are
used in mechanics in order to simplify application
of the theory.
Most common types of idealization include
particle, rigid body and concentrated force.
Particle
A particle is a body that has a mass but a
size that can be neglected. For example, earth
orbiting around sun. The size of earth is
very small when compared to the size of the
orbit. So earth can be approximated as a particle
when analysing the orbital motion. Hence geometry
is not involved in analysis of a problem.
Rigid Body
Rigid body has already been discussed in previous
video. It is a combination of particles that
remained at fixed distance before and after
application of load.
Concentration Force
Effect of a loading can be approximated by
a point force on a body. This is valid only
when area of loading is less than area of
surface on which loading is placed. For example,
the loading area of hand placed on a wall
can be approximated by a concentrated force.
Newtons Laws
First Law
A body originally at rest or moving in straight
line with constant velocity will remain the
state provides it is not subject to unbalance
forces. As in a box at rest or a ball moving
in straight line. Key word here is straight
line which means that first law does not cover
the object moving at a constant velocity in
a curved path.
Second Law
A body acted upon unbalanced forces will experience
an acceleration in the direction of the unbalance
force, expressed as F equals m a, where m
is the mass of the body under unbalance force
Consider two springs pushing a sphere from
both sides, equally, such that the forces
are balanced. When one of the spring is removed,
the unbalance force produces acceleration
in the same direction of the unbalance force.
Third Law
Every action has an equal but opposite reaction.
Or in other words, the mutual forces of action
and reaction between two bodies are collinear.
A body of certain mass will generate tension
in the rope it is suspended by. The magnitude
of this tension will be equal, opposite and
collinear with the weight of that body.
Gravitational Law
All bodies in universe have a force of attraction
between them. For any two bodies at a certain
distance apart. Force equal to G, m 1 m 2
over r square, where G is universal constant
of gravitation. Physically G is force between
two 1 kg objects exactly 1 m apart.
Weight
For a body at earth surface, the force between
earth and the body will be given by F equal
to G m M e over R E square, as radius of the
body is very small as compared to radius of
earth. This R E is taken at sea-level and
45 degree latitude. Solving we get Weight
equal to mass times acceleration due to gravity.
Where g = 9.81 meter per second.
