Question

Please write the expression for the maximum speed of a vehicle on a horizontal curve Road

Answer 1

maximum safetey speed on horizontal road=

Explanation:

Let

the mass of vehicle =m

maximum speed of vehicle = v

radius of curve path= r

acceleration due to gravity= g

and coefficient of friction=

During the motion of the vehicle the centrifugal force and frictional force will be in opposite direction to each other.

Hence in the equilibrium position the centrifugal force will be equal to frictional force and they will balance each other.

Hence, centrifugal force = frictional force

=> v=

hence, the maximum speed of vehicle should be v=

Answer 2

Refer attachment

Explanation:

The various forces acting are

1)Normal,N

2)Weight of the vehicle,mg

3)Force of friction,f

All the forces are resolved into components and

For vertical direction, since no vertical acceleration, the net upward and downward forces are equal.

But horizontally there is net centripetal force.

since centripetal force has the tendency to pull things towards the centre the limiting friction (FL) has to be greater than centripetal force.

For horizontal road, just

Use centripetal force is less than or equal to friction.

I have attached both banked and horizontal road derivation so that you understand it well.

Hope it helps you!!!!