(^580) „„„„„ A Textbook of Engineering Mechanics
28.10.REACTIONS OF A VEHICLE MOVING ALONG A LEVEL CIRCULAR
PATH
In the last articles, we have discussed that whenever a vehicle is moving along circular path, it
is subjected to some centrifugal force. In order to avoid any unpleasant effect of the centrifugal force,
on the moving vehicle or passengers sitting in it, we provide some superelevation in the roadways and
railways. Now we shall discuss the effects of not providing any superelevation i.e. providing a level
circular path.
Fig. 28.5. Reactions of a vehicle.
Consider a vehicle moving on a level circular path, with O as centres as shown in Fig. 28.5.
Let m = Mass of the vehicle,
v = Velocity of the vehicle,
r = Radius of the circular path,
h = Height of the centre of gravity of the vehicle from the ground
level,
RA = Reaction at A (i.e. inner wheel)
RB = Reaction at B, (i.e. outer wheel) and
2 a = Distance between the reactions at A and B
We know that the centrifugal force, acting through the centre of gravity of the vehicle,
2
c
mv
P
r

We also know that the weight of the vehicle (equal to mg ) acting downwards through its centre
of gravity will exert a reaction equal to
2
mg
on A and B (because of symmetry).
Taking moments about A and equating the same,
22
B 2( )^1
mv v h
R a mg a h mag
rgra
⎛⎞⎛⎞
×= ×+⎜⎟⎜⎟⎜⎟⎜⎟×= +
⎝⎠⎝⎠
∴
2
1
2
B
mg v h
R
gra
⎛⎞
=+⎜⎟⎜⎟
⎝⎠