Engineering Mechanics

(^578) „„„„„ A Textbook of Engineering Mechanics
Let m = Mass of the body in tonnes,
r = Radius of circular path in m,
v = Velocity of the body in m/s, and
θ = Angle of the bank.
We have seen in the previous articles, that whenever a body is moving along circumference of
a circle, it is subjected to the following forces :

1. Its own weight = mg


2. Centrifugal force

mv^2

r

=

From the geometry of the figure, we find that

2

Centrifugal force^2

tan

Weight of the vehicle

mv

r v

mg gr

⎛⎞

⎜⎟⎜⎟

θ= =⎝⎠=

It may be noted from the above expression that the superelevation is independent of the mass

of the body.

Example 28.8. A circular automobile test track has a radius of 200 m. The track is so

designed that when a car travels at a speed of 90 kilometres per hour, the force between the automobile

and the track is normal to the surface of the track. Find the angle of the bank.

Solution. Given : Radius of the track (r) = 200 m and speed of the car (v) = 90 km.p.h.

= 25 m/s.

Let θ = Angle of the bank.

We know that

(^22) (25)
tan 0.3189
9·8 200
v
gr
θ= = =
×
θ = 17·7° Ans.
28.8. EFFECT OF SUPERELEVATION IN RAILWAYS
Fig. 28.4. Superelevation in railways.
In case of railways, the outer rail is raised with respect to the inner rail of the track. The amount
by which the *outer rail is raised is known as superelevation. The general practice, to define the
superelevation, is to mention the difference of levels between the two rails as shown in Fig. 28.4.

• In some countries, the outer rail is raised from the centre line by half the superelevation ; and the inner
  rail is also lowered from the centre line by half of the superelevation.