Students Let's solve the Question the
question is a block  lying on an
inclined plane has a weight of 50 Newton
there is an inclined plane like this and
a block is placed here who's weight is 50
Newton that means I can say that the
mass of the block is 5 kilogram it just
begins to slide down when inclination of
the plane with the horizontal is 30
degree that means for 30 degree it just
begins this motion that means if I put
the inclined plane block is here and the
angle is 30 press it it starts moving
down if I bring this inclination to a
lower level by decreasing the angle then
if I place it if not splayed so that
particularly what is given in the
question is the minimum angle of its
motions that means what that means if I
increase the angle greater than 30
degree then also it will start moving so
this 40 degree is called the angle of
repose the 30 degree is called the angle
of repose what is the angle of repose is
the minimum angle of the incline plane
where you place the block is start
sliding obviously if it starts lightning
as suppose that this is start studying
as 37 degree D then obviously it will
also start sliding up more than 37 38 39
because of the sliding winds more than
that also it will start sliding if I
decrease that below that angle that
means if I decrease below 37 suppose
then through notch like so we have to
solve this question like this since 30
degree here is the angle of repose
this is the solution
because at this angle it starts sliding
decreasing the angle do not slide
increasing the angle also it will slide
to that minimum angle is the coefficient
of friction now what I will do adjusting
the free body diagram of this block this
is M all right the block is having mass
and irrespective of whether the block
passes a more to M doesn't matter much
because at the end we will see that this
independent is theta is independent of
the mass of the block let us see how it
is done this is the weight which will
act vertical downward this is the
direction in which the connection let if
the component of this mg will be like
this I call this angle of 30 degree as
theta so this angle also in the theta so
this component is mg cos theta and this
component is and the sine theta so we
did component of the gravitational force
acting on the block the block starts
sliding so that is an external force
which tries the block to move in that
inclined plane so this is the external
force because of the friction the
friction obviously will be acting in the
upward direction the friction would be
in the upper direction that is F F force
of static friction and the operation
when you say that it is just begin to
slide is motion whenever you will find
what like the just begins that means is
balancing this and this will balance
that balances it
so therefore
this source of static friction is at
this and design theta it starts as
motions on balance these two obviously I
would also balance these two components
this ng cos theta and this I would have
to balance it if I balance it what I
will get
so first of all and balance the force of
static friction equals to M D sine theta
similarly a balance and M D cos theta
and because and I will divide these two
equations okay let us divide the two
equation and see what I'll get so
interesting point is if you divide the
two equation the M will get cancelled FS
over n is mg sine theta for mg cos theta
okay
I am just writing this woke up previous
slide from here only okay if you divide
that then mg will get canceled out so
therefore I told you in the beginning it
is independent of the mass of the block
that is placed so finally you are
getting here is a tan of theta and what
is FS FS is office mu s into M divided
by M and also you get cancelled and you
get mu s as tan of theta this means what
the coefficient of static friction is
equal to the tangent of the angle of
repose it is what angle it is that angle
on which the block placed on the client
surface starts moving down therefore
into question we are asked to find the
coefficient of static friction
and we got this at the formula the
coefficient of static friction is
tangent of theta and theta and the
question is given 30 degree therefore mu
s is equal to tan of 30 degree which is
1 upon root 3 so this is the answer to
this question so this is the answer
thank you very much
