Question

Why do roads on mountains have inward inclination at sharp turns?

Answer 1

Banking on roads:

1. Banking on road is the best remedy for vehicles travelling at high speed along the curved road.
2. When a car is moving along a curved road; it is performing a circular motion since the curved road is an arc of a circle.
3. Centripetal force is a necessary force for circular motion. In absence of centripetal force, the car would move along tangents and circular motion is not possible.
4. In case, a car moves along a curved horizontal road, the necessary centripetal force is provided by the force of friction between the tires of a car and the road surface.
5. Suppose $\left(\mathrm{m}\right)$ be the mass of a car moving with speed $\left(v\right)$ along a curved road of radius $\left(r\right)$. Then, for a safe turn,

$\mathrm{Centripetal}\mathrm{force}\left(a\right)=\mathrm{Force}\mathrm{of}\mathrm{Friction}\left(f\right)$

Explanation:

1. The friction between the vehicle's wheels and the road surface generates the necessary centripetal force while driving over a horizontally curved road on a mountain.
2. If there is a lack of centripetal force, the car will tend to skid.
3. When the mountain roads have an inward inclination at sharp corners, the horizontal component of the normal response provides the centripetal force required for the vehicle's circular motion.
4. To generate the required centripetal force, mountain ranges have an inward inclination at acute corners. This is why mountain roads have an inward inclination at sharp turns.

Where,

$\left(\mathrm{mg}\right)$ represents the weight of the vehicle.

$\left(\mathrm{N}\right)$ represents a normal reaction.

$\left(f\right)$ represents the friction force.

$\mathrm{a}=\frac{{\mathrm{v}}^2}{\mathrm{r}}$is the centripetal acceleration.