Elasticity
is the property of a material by virtue of which it is able to come back to its
original position after removing the external force applied on it. Depending on
the nature of the material every body has elastic nature up to some extend.
External force applied on the body tries
to change the shape of the body and that’s why it is called as deformation
force.
Within the elastic limit, the molecules of the body pull themselves back to its original position due to the force of attraction between molecules of the body and it is called as a restoring force. Within the
elastic limit the magnitude of the deformation force shall be equal to the
restoring force.
The
restoring force is there simply because the molecules of the material are having
a strong force of attraction among them to keep them together.Theoretically after removing the applied external force all the particles shall
come back to their original positions and hence there shall not be any change in
the shape of the body.This kind of the body is called as a perfectly elastic
body. But practically no body in the nature is perfectly elastic. Because of
the external force application the distance between the molecules increases
slightly which leads to the increase in the size of the body.
We
can say that more the increase in the
size of the body, less the elastic
nature of the body has and vice versa.
No body
in the nature is perfectly elastic. Among all the available bodies the best
elastic body is Diamond which will try to protect its shape in the best
possible way. The molecular force of attraction among the molecules of the body
are the basic reason behind the elastic force. The molecules behave as if like
connected with a mass less kind of the Springs which are having the restoring
force. Thus the Springs always tries to get back to the original positions and
hence the body also always tries to come back to original position. If the body
is unable to come back to its original position ,after removing the applied
external force then the kind of a body is called as a plastic body.
No body
in the nature is also perfectly inelastic or plastic. In fact nothing perfect
exists in the real life there are only there for the sake of reference in the
books.
To
study the elastic nature of a given material we shall define two terms called
stress and strain. Stress is defined as the restoring force acting on a body
per unit surface area and strain is
defined as the ratio of change in the dimensions of a body to its original dimensions.
We
have a law called Hooks law. As per this
law, within the elastic limit stress acting on a body is directly proportional
to the strain. And hence the ratio of stress to the strain is constant and the
ratio is called modulus of elasticity. It depends on the nature of the material
but not on the values of stress and strain.
Young's
Modules
Depending
on how do we apply the stress on a body that are three different types of
stress and correspondingly there are three different types of strains also.
If the stress is applied on a thin wire,it is called longitudinal stress which acts along its length.The change in the
dimensions also happen in majority along its length and the corresponding
strain is called longitudinal strain. As the stress is directly proportional to
strain longitudinal stress is also directly proportional to longitudinal strain
and the proportionality constant there is called Young's modulus.
The
stress applied on a body depends on the load that we have applied at the bottom
and in that case in the place of the force we can consider the weight of the
body itself. Here area of cross-section depends on the shape of the wire and in
general if it is a circular shape we can consider the area of the circle.
When
the same forces applied on a steel and rubber wire of similar physical
dimensions, it is quite easy to notice that the expansion the rubber wire is
more than that of the steel. As elastic modulus is inversely proportional to
increase the length of the wire,we can conclude that the steel is having more
elastic nature than that of the rubber.
That
is the reason why we say still is more elastic than the rubber.
Problem one and solution
A
copper wire of length 2.2 m and a steel wire of length 1.6 m are having the
same diameter of 3 mm and are connected end-to-end. When a load is applied the
net elongation is found to be due 0 .7 mm find the load applied as well as the
elongation of the each wire?
We
can solve this problem basing on the definition of young's modules of the material itself. It is very clear from the defamation of the wire in length
of the wire is directly proportional to the length of the wire as well as
inversely proportional to young's modulus the material. As modulus of elasticity is different materials are given in the problem,we can solve the problem
becomes simple as shown below.
Suppose
instead of the area of the wire if the mass and density of the wire is given in
the problem in solving, that is also quite simple because area is the ratio of
volume per length . We can further apply it volume as the ratio of mass to the
density.
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