Work done in Spring - Work, Energy & Power Video Lecture - Class 11

hello friends this video on work energy
and power
part 13 is brought to you by exam feel
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make sure that you have watched all the
videos from part 1 to 12 before going
ahead with path 13 here we will see work
done in a spring we will consider one
scenarios one by one so let us first
consider the scenario where we see that
the spring is stretched so when the
spring is stretched in that case X will
be positive that is the displacement
will be positive
however if s that is the spring force
will be negative then see here I have
purposely not included a diagram so that
you can visualize the diagram on your
own however you can always refer the
previous slide to get a reference of the
diagram spring when stretched means the
spring is getting elongated so in that
case X is positive and s is negative so
what would be the work done we know work
then is nothing but force into
displacement so work done in this case
because the force here is a variable
force which we discussed before this
force is variable force because it
depends on displacement X so this will
be equal to FS integration of FS into DX
from any X initial 2x final right so
this will be the work done so this will
be equal to what is f s F s is equal to
minus K into X DX and it will elongate
from which point to which point let us
say initially it was at 0 initially the
spring was at rest so let us say that
shellie X was equal to zero that is
initially the displacement was zero and
let us say that the maximum displacement
is X M so we can say a minus K X square
by 2 from 0 to X M so we can say this is
X M square divided by 2 so this will be
the work done for stretching the spring
from X is equal to 0 to X is equal to
some value X M correct what I would
suggest you is when you are doing this
you try to visualize the figure try to
draw the diagram on your own and try to
visualize the scenario in real time now
let us look at the second scenario that
is where the spring is compressed
now when the spring is compressed in
this case X will be negative therefore
the spring force will be positive
because spring force is always in the
opposite direction of that of the
displacement so in this case what will
be the work then many times the work
done in case of a spring is denoted by
WS this L subscript is used for the
spring so the work done in this case
will become F s into D X again here X
initial 2x final now in this case
everything else will remain the same it
will be minus K X DX what will be the
initial get initial will be X M and
final will be 0 because here the spring
was already stretched and now we have
compressed it that means it was already
stretched means it was at the position X
is equal to X M now from X is equal to X
M we are compressing into X is equal to
0 this is again we will get minus K X
square by 2 X M 0 so we get K X M square
divided by 2 so this would be the work
done in vessels now let us assume a
scenario so we considered both the cases
and this
during this stretch and when the spring
is compressed the funda remains the same
to calculate the work done just that you
need to know from where to where now let
us consider that we have a block which
is moved from X I X F that means the
initial position was X I and the final
position is X F so in this case what
would be the work done it is very simple
well 10 will be equal to integration F s
DX where X from X initial to X final so
this will be equal to integration of
minus K X DX X initial to X final so
this will be equal to minus K X square
by 2 X initial to X final so this will
be equal to minus K X M square by 2 plus
K X and square by 2 so this would become
the work done in moving the block from
initial position X I to final position X
F so now I hope it is clear how do we
calculate the work done in case of a
spring ok now let us go ahead and let us
see what all the rivers include all the
points which we studied about the spring
force right so the first thing we learnt
about spring forces the work done by
spring force in a cyclic process is
equal to 0 what do you mean by a cyclic
process cyclic process means the point
from where it starts it comes and ends
at the same point that means X initial
is equal to X final the initial position
is equal to the final
so what will data work that in this case
well then just now we found just now
just if you look at the last example in
the previous slide you will see that the
work done in moving an object from
initial position X adding the final
position X if that was given by this and
this was nothing but it came out to be
something like this minus K X F square
by 2 plus K X I square by 2 now if I say
that X F is equal to X I then what will
you get you put X F is equal to X I so
this will become X I square by 2 plus K
X I square by 2 so they both will cancel
out and we get work done is equal to 0
the next is if s is position dependent
that we already saw because F s the
value of the spring force as well as the
direction of spring force depends on the
displacement and what is displacement
displacement is nothing but position
next is spring force is a conservative
force what is a conservative force
conservative forces of course in which
work done in moving from one point to
another point is independent of the path
in this case you can see that the work
then depends only on the initial point
and the final point it does not depend
upon the path which is taken to reach
the final point from the initial point
right so what we see F s depends only on
X I X F and it depends on X I X F and
not on the path I am sorry it is not F s
it is not FS and talking about it is WS
the work then does not depend on the
path the work then depends only on the
initial position and the final position
there put the force associated with this
work done is a conservative force right
so any force which is associated with
the work which does not depend upon the
but between the initial and final point
is quite a conservative force so the
spring force is a conservative force it
is position dependent force and it is
zero in a cyclic process thank you
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