Young Modulus - Mechanical Properties of Solids Video Lecture - Class 11

hello friends this video on mechanical
properties of solid part 7 is brought to
you by exam feel calm no more fear from
exam please make sure that you have
watched all the videos from part 1 to
part 6 before going ahead with Path 7
now we will study about elastic moduli
when I was explaining you about the
Hookes law I told you that stress is
equal to a constant into strain that
constant o is known as the elastic
modulus so here after we will discuss
about what basically its elastic modulus
elastic modulus is the ratio of stress
and strain so this is very much clear
from my previous statement right what I
had told while I was explaining in books
law I told that stress is equal to a
constant of proportionality into string
and this constant of proportionality is
the elastic modulus right so from this
we can say that the elastic modulus is
equal to stress by strain so we can say
that the elastic modulus is the ratio of
stress and strain elastic modulus is a
characteristic value of each material
characteristic value voltage mean by
this this means that for a particular
material the elastic modulus will be a
specific pattern let us suppose if I
talk of gold gold we have a specific
value of elastic modulus if I talk of
rubber rubber will have a specific value
of elastic material sorry
elastic modulus so that means the value
of elastic modulus is a characteristic
of each material each material will have
its own elastic
less value so if we look at this graph
we can see that elastic modulus is
stress by strain that means if you look
at this region where coops law is obeyed
if you see that region you can see that
stress by strain is the elastic modulus
that is the slope of the straight line
would be elastic modulus now let us look
at the different types of elastic
modulus now if you see what I am trying
to do is I am trying to relate
everything together if you see when we
talked of stress we found that there
were three types of stress right one was
the aqua toodle stress tangential stress
got shearing stress and then the third
one was the volumetric stress similarly
when we talked of strain we had three
kinds of strain longitudinal strain
tangential stream and volumetric strain
now when we talk of elastic modulus
again we have three types of elastic
monuments the first one is Young's
modulus second one is shear modulus and
the third one is bulk modulus so there
are three types of modulus of elasticity
so we will discuss each of them in
detail so let us start with young's
modulus so the young's modulus as you
can see from the name it is derived from
the name of the scientist jung who
derived it or who define me they are
after it is known as young's modulus of
elasticity so what is Young's modulus it
is basically the ratio of longitudinal
stress to longitudinal strain I already
told you that modulus of elasticity is
stress by strain so when it comes to
young's modulus it only talks about
longitudinal stress and longitudinal
strength so the ratio of longitudinal
stress to log it internal strain it is
denoted by capital y generally we denote
Young's modulus by capital one so the
Young's modulus is equal to the
longitudinal stress by longitudinal
strength
right so what is longitudinal stress we
generally denote the longitudinal stress
by Sigma and we do not longitudinal
strain by epsilon so they are just
letters to denote throughout the journal
stress and longitudinal string it is
better if you remember this notation so
that it will be easier for you when you
refer some book for numericals or
something so this is longitudinal stress
and this is longitudinal screen so what
is longitudinal stress it is nothing but
force per unit area so this is force per
unit area
what is longitudinal strain it is the
change in length divided by the original
length right so we get F L divided by a
Delta n so this is your Young's modulus
this is the expression mathematically
for Young's modulus so greater Young's
modulus means larger forces required to
produce a small change in length so from
this you can say that if the Young's
modulus this more Young's modulus is
more means force will be more and the
change in length would be less that
means greater Young's modulus would mean
that greater force will be required to
produce a small change in length so if I
say that there is a material with
greater Young's modulus that means you
will have to produce more force to
produce even a small change in length
unit of Young's modulus is Newton per
meter square or Pascal why so because it
is longitudinal stress by strong eternal
strain we know that strain has no unit
because it is the ratio of two
quantities so it has no units and
longitudinal stress is force per unit
area so force per unit area that is unit
the forces Newton and unit of area is
meter square so it is Newton per meter
square or Pascal metals have
comparatively greater Young's modulus by
just now I told you right
metals are the materials which are quite
tough right so if you want to produce
the small change in length in a metal
you will have to provide a large amount
of force
so therefore the Youngs modulus is more
that means in case of metals to produce
a small changing length you will have to
provide a very high or very huge amount
of force so that means the Youngs
modulus of elasticity for metals is more
now let us look at certain applications
based on Young's modulus why do you
think is steel preferred over offered in
structural designs if you see against
any structural designs if you see the
structures which are built ahead in
there I think the the flyovers the
bridges or those kind of constructions
which we generally see around us so in
those kind of constructions the
industrial constructions you see that
steel is preferred over copper however
both our metals so what is the factor
that decides which metal is more
suitable for structural designs so this
answer is quite depending on Young's
modulus so steel is preferred over
copper because steel is more elastic
than copper what do you mean by more
elastic it means that if there is the
slight deformation in the length of the
steel due to contraction or expansion it
can come back to its original dimension
but in case of copper it is as if it
being less elastic those Lex abilities
are not there therefore greater force
would be required to produce small
changes in length so since copper is
very less elastic so greater force would
be required to produce small change in
length therefore we prefer steel over
copper by the first steel is more
elastic and cop
so if it is more elastic it is that we
need in the sense that if there is a
slight change or slight deformation in
the length it can come back to its
original form and as we already told
that in case of metals their Young's
modulus is high that is we need to
provide core force to produce a very
small change in length so that we is
also Stevens but now how do we determine
the value of Young's modulus so
experimentally the expression was
derived to determine the value of
Young's metal Young's modulus of the
material of a wire it is suppose we have
a wire it is made up of say some metal
or some material so if you want to
determine the young's modulus of that
particular material how do you determine
that
so an experiment was an experiment set
experimental setup was made to determine
young's modulus
there was a support from that support
those strings are hung on that we have
hung two vessels two buckets or results
about a reversal on each of them will
placed one apple each right so as of now
if you see carefully both the strings
are of the same length and both the
apples and line on identical vessels at
the same height now what we do we
increase we have also kept a metre scale
on the wire on one of them just to
calculate the length or the change in
length like soon so for now this wire is
the reference file so it is the
reference okay now what we do we
increase the number of apples in the
second one so as we increase the number
of apples to three the weight increased
because of this increase in weight we
found that this
three it moved in the downward direction
if you see again you see that the string
this yl got stretched it got stretched
and it went down so there was a change
in length of this wire so now I
understood why did we keep this meter
scale as reference just to measure the
change in length so this will measure
the initial length so that change in
handa measured compared to the original
position right this was the change in
length so this goes there was a change
in length say Delta n right so using
this experiment the value of Young's
modulus was determined now what was
Young's modulus Young's modulus as per
definition is stress by strain right so
what is stress stress is denoted by
Sigma strain is denoted by epsilon to be
precise it is wrongly Dudamel stressed
by longitudinal strain so now this
strength longitudinal stress is force by
area and longitudinal strain is change
in length by original length right so in
this case the change in length is Delta
let us suppose that the original length
was in it is a whole original length is
n so this will be equal to now what
would be force the force which is acting
here is what it is nothing but mg which
is acting downwards in G's acting
downwards so here force which this is
the force which is causing this stress
and strain the story of stress and
strain here is created only because of
this force when you increase the number
of actors the force which is acting
downwards due to acceleration due to
gravity increases so the force will be
mg what will be the area area is nothing
but the area of cross section of this
wire however it is a very thin wire but
still it will have some cross section so
this area would be nothing but
five R square where R is the values of
this wire so this would be PI R square
this divided by Delta L by M so we can
say it is nothing but mg L divided by PI
R square into Delta L so this would be
the value of Young's modulus so this is
how we can evaluate the value of Young's
modulus of of the material of a thin
wire now we'll go ahead and look at
certain problems on the basis of what we
studied so far so let us look at problem
number one thank you please visit exam
few calm to watch free educational
videos try free online tests get the
best quality study materials study from
the best tutors and mentors and much
more thank you once again