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# IF BANKING OF ROAD IS THETA R IS THE RADIUS AND U IS THE COEFF OF FRICTION THEN FIND THE RANGE OF SPEED FOR SAFE DRIVING ON IT.

SAGAR SINGH - IIT DELHI
879 Points
11 years ago

Dear student,

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.

All the best.

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Sagar Singh

B.Tech, IIT Delhi