Let us discuss skidding of an automoble while
taking a turn. Let us consider a circular track or we can consider that there is a straight
road on which a car is moving and taking a turn which is a circular arc of radius r . we
know that whwn a body is in a circular path just to maintain circular motion a centripetal
force is necessary or we can say that when a body is in a circular motion in a rotating
reference frame it experiences an outward centrifugal force.
Here this car was moving with a velocity v , when it takes a turn in a circle of radius
r we can say that in radially outward direction the car will experience a centrifugal force
m-v square by r and this centrifugal force will have atendency to skit the car in outward
direction on its wheel it will experience a friction in inward direction and if m-v
square by r is less than the friction then the car will take a safer turn it will not
skid. So we can state that for safe turning . without
skidding . the friction should balance m-v square by r and this friction should be static
friction . then only the car will be able to take a safe turn as the wheels will experience
an inward static friction and we can also say that for skidding. this m-v square by
r must be more than or=mu n that is the limiting value of friction , here we can say
that the normal reaction on car will be=to m-g.
we can also analyze this situation picorially here if we just draw the cross section of
the car . car will experience m-g in downward dierction on all of its wheel net normal reaction
will be in upward direction . car will experience a centrifugal force m-v square by r in outward
direction and its wheel will experience an inward friction which is balancing this m-v
sqaure by r, and at time of skidding the limiting value of this friction=mu n and here n=m-g
. so we can write this m-v square by r must
be less than=mu m-g. m cancels out. And we will get the value of speed=root of mu
r-g . so this is the maximum limit upto which , the car can take a turn without skidding
, if cars speed is more than or=root of mu r-g the car will skid . we can write here
for safe turning . speed of car must be less than root of mu r-g . this article you must
keep in mind, because this is important for various cases, whenever you will find a problem
in which an automobile is taking a turn. Now we will discuss skidding of an automobile
while taking turn on a banked road . in this figure you can see that a car is taking turn