Conservative & Non-Conservative Force - Work, Energy & Power Video Lecture - Class 11

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before going ahead with part 10 we will
now study conservative and
non-conservative forces what is the
conservative force force with the
property that the work done in moving a
particle between two points is
independent of the path taken so this is
the most important point if I say
conservative force
that means the let us suppose we have a
particle we move the particle from point
A to point B now whatever path we are
following to take this particle from A
to B the work done in taking the
particle from A to B will be independent
of the nature of the path between these
two points that means so that force
which is associated with these kind of
work that is quite a conservative force
examples of conservative forces gravity
elastic forces electric forces because
if you see in case of gravity the force
of gravity exists between any two
objects right but it doesn't depend upon
the work done between these two or chips
follows which part it is independent of
the path between the two objects
similarly the elastic forces or the
electric forces which operates between
different charged particles that is also
independent of the path between any two
points on the other hand when I talk of
non conservative force it is a force
with the property that the work done in
moving a particle between two points
depends on the path taken that means if
you follow one part the force will be
something if you follow some other path
the food force will be different now
example of non conservative forces
friction friction is would be the best
example of non conservative force
let us now study
servation of mechanical energy for
conservative forces just we already know
that cut conservative forces are those
forces in which the work done between
the initial point and the final point is
independent of the path followed between
the two points now what is mechanical
energy kinetic energy and potential
energy together is known as mechanical
energy when I say mechanical energy I
mean to say kinetic plus potential
energy till now we have discussed what
is kinetic energy how do we calculate
kinetic energy what is potential energy
how do we calculate potential energy so
I think it is the best time when we can
discuss the topic on conservation of
mechanical energy
when I say conservation what I mean when
I say conservation I mean to say that
the total mechanical energy in a system
will always remain constant that means
total mechanical energy in a system will
always remain constant no matter what
may be some of the kinetic energy will
get converted to potential energy
potential energy getting converted to
kinetic energy or things like that but
then the total mechanical energy at any
point of time will always remain
constant now here what we'll do I'll
just prove that whatever I am saying is
correct so here we will prove that the
total mechanical energy remains constant
okay now according to the work-energy
theorem we studied work energy theorem
right w/e theorem so what did we study
in work energy theorem we studied that
change in kinetic energy is equal to
work done now what is well then burden
is nothing but force into displacement
now let us suppose we considered that
the force is a variable force so it will
be f of X into Delta X right if Delta X
is the displacement now also we know
that the relation we know the relation
between work and potential
the change in potential energy is equal
to the negative of birth then correct so
this we can write minus of FX Delta X so
from this is equation number 1 this is
equation number 2 so what do we get from
1 & 2 let us suppose we add equation 1
with 2 so what do we get from left hand
side Delta K plus Delta B and from right
hand side we get f of X Delta X minus f
of X Delta X so this is equal to 0 so we
get Delta or a plus B is equal to 0 that
means the change in kinetic plus
potential energy is equal to 0 now what
is kinetic plus potential energy kinetic
plus potential energy is mechanical
energy so the change in mechanical
energy is equal to zero change in
something is equal to 0 what does that
mean that means that something is not
changing at all change in mechanical
energy is zero means that the mechanical
energy is not changing that means the
mechanical energy is remaining constant
and that is what we wanted to prove
right so what did we see we saw from
work energy theorem we know that change
in kinetic energy is work done also we
know that change is potential change in
potential energy is equal to minus of
birth turn now we added both the
equations and we found that the change
in mechanical energy is equal to zero
that is the total mechanical energy in
our system is constant now let us look
at certain important points to be noted
regarding all that we have studied so
far please note that not all forces are
conservative we already discussed there
are two categories of forces one is
conservative and the other one is non
conservative
so conservative forces I'll quickly
review conservative forces are those
forces which are associated which
results in a work done which does not
depend on the path between initial and
final points whereas non conservative
forces
results in a work done which depends on
the path followed between initial and
final points so not here in this chapter
we talked mostly about not mostly in
fact we talked only about the
conservative forces right but there are
forces which are not conservative
examples of non conservative forces are
friction friction is an example of a non
conservative force
the second thing is zero of potential
energy is arbitrary what do we mean by
zero of potential energy you would have
observed that by solving questions while
deriving concepts we assumed that let us
suppose that the value of putting people
you already told that the potential
energy V is a function of H HS height
height or many of us also denoted by X
that is displacement so the potential
energy is a function of H now this V of
H is taken as zero it all depends on the
convention we take many times we assume
that V of H is equal to zero at H is
equal to zero so that is just a
convention we assume that here H is
equal to 0 so V of H is equal to 0 for
example I will give you certain examples
which we have taken before we always
assumed that on earth surface potential
energy is equal to 0 right by PD we
assume that because we considered that
height is equal to 0 on the Earth's
surface why did we say that height is
equal to 0 on the earth surface because
we considered
Earth's surface as the reference because
there is no standard fact that you have
to take this surface as the reference so
it is completely arbitrary it is
completely up to you which reference you
think similarly while we were discussing
the energy mechanical energy and
potential energy for spring in case of
the spring we considered that the
equilibrium position we considered that
at equilibrium position x is equal to
zero right in case of a spring what we
considered we considered that let us
suppose this is the equilibrium position
X equal to 0 this is the maximum X equal
to n this is minus X n so the body is
moving like this so we assume that the
equilibrium positive at equilibria in
position X is equal to 0 therefore the
potential energy is equal to zero at the
equilibrium position right so the zero
of a potential energy completely depends
on the Convention which we follow so it
is saying that zero of potential energy
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