in this illustration we'll, see about circling
inside well of death. here the situation is
state as a bike rider wishes to circle inside
a wooden vertical cylinder of radius 5 meter.
with a speed of 5 root 5 meters per second.
and we are required to find the minimum value
of coefficient of friction between tires and
walls of this well. here, in solution to understand
the situation if we draw the figure. it looks
like this. where inside a well if this is
the bike rider. whose riding inside a vertical
cylinder, in a circle, of radius r. so he
will be experiencing his weight in downward
direction. and normal reaction would be acting
inward which is providing the centripetal
force was circular motion, and rotating frame
we can consider it is experiencing a centrifugal
force m v square by r outward. and due to
normal reaction a fraction will act on it
in upward direction which will prevent it
from, falling down. so in this situation we
can write for. circular motion. 
inside. the cylindrical track. here we can
write the normal reaction is equal to m v
square by r. and for, safe turning. we can
write friction would be balancing m g. and,
the value of friction at its limiting value
would be mu, n. and value of n we can substitute
as m v square by, r. that is equal to m g.
here m gets cancel out, and the value of minimum
friction coefficient which will get, for safe
turning is equal to, g r by, v square if we
substitute the values g we can take as 10,
radius is given to us is 5 meter, and the
speed is 5 root 5 meters per second so on
squaring this 1 25. so this will be 10 by
25 or, this can be further written as 2 by
5 which is zero point 4 that will be the final
result of this problem.
