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 f_L= 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

Related Guides