# A turn of radius 20 in is banked for the vehicles going at a speed of 36 km/h. If the coefficient of static friction between the road and the tyre is 0.4, what are the possible speeds of a vehicle so that it neither slips down nor skids up?

Let us assume that the path has an inclination of θ.

There is no movement in vertical direction. So,

If the vehicle is not to be slide up then the friction must reinforce the overall force. That means the direction must be towards mgsinθ. So, the condition will be,

From these equations we get;

Now we need to find tanθ

So, the velocity will be,

For, not to skid down the condition will be

Doing the similar calculation we will find v=54 km/hr.

So, if we move the vehicle with a speed in between 14.7 km/hr to 54 km/hr the forces will be enough to avoid skidding down and not sufficient to skid up.

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