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
on a banked road in this banked road for banking this
outer side of
road is slightly elevated up above the horizontal.
this elevation is provided because as we studied in the previous case that on a flat road if
we increase the speed of car then it will skid in outward direction , so on lifting
the outward edge in the upward direction we can say the road is banked and due to banking
the normal reaction is slightly tilted . Like if we take the cross section, this figure
is showing the cross section of this banked road. where this outer edge of road is elevated,
above the horizontal. such that the road is making an angle theta with the horizontal.
So in this situation.
the weight of car, m-g is acting in downward direction and if it is taking a turn in a circle of radius r , it
will experience an outward centrifugal force m-v square by r
in outward direction in rotating reference frame