study material-physics-mechanics-work power energy
Work Power Energy -6
Banking of Roads:
When vehicle go through turnings, they travel along a nearly circular arc. There must be some force to produce the required centripetal acceleration. Centripetal force is provided to the vehicle by following three ways.
- By friction only
- By banking of roads only
- By friction and banking of roads both.
1) By friction:
Let a car of mass m is moving at a speed v is at horizontal circular arc of radius r.
And fL= limiting value of f = 
N = mg (N=mg)
For a safe turn without sliding,
So if m and r is fixed the speed of the vehicle should not exceed 
and if v and r is fixed then coefficient of friction should be greater than 
2) By banking of roads only:
To avoid friction outer part of road is some what lifted compared to the inner part.
Fig (29)
From figure (29) NSin
= 
and NCos = mg
From this we get, Tan = 
At two speeds car does not slide down even if track is smooth.
3) By friction and banking of road both:
If a vehicle is moving on a circular road which is rough and banked also then magnitude of N and direction plus magnitude of friction mainly depends on the speed of the vehicle V-
- f is outward if v = 0
- f is inward if v>
- f is outward if v <
- f is zero if v =
a) When the car is at rest f is upward-
Fig (30)
b) Now when the car is given a small speed v, ------- equation (1) becomes
Illustration:
A turn of radius 20m is banked for the vehicle of mass 200kg going at a speed of 10m/s. Find the direction and magnitude of frictional force acting on a vehicle if it moves with a speed a) 5 m/s b) 15 m/s assume the friction is sufficient to prevent slipping ( g = 10m/s2).
Solution:
a) The turn is banked for speed v = 10 m/s therefore 
As the speed is decreased force of friction f acts upwards
Fig (31)
Substituting
, v=5 m/s, m=200kg, r=20m
b) Here force of friction f will act downwards
Substituting v=15 m/s,
, m=200kg and r=20m we get
