Obtain the formula for the maximum safe speed $(v_{max})$ of a vehicle on a level curved road.
Obtain the formula for the maximum safe speed $(v_{max})$ of a vehicle on a level curved road.
In figure $(a)$ vehicle is shown moving on a horizontal curved road. The mass of vehicle be $m$ and the radius be $\mathrm{R}$.
Figure $(b)$ shows the vehicle moving on a circular track. The vehicle experiences three kinds of force :
$(1)$ Weight in downward direction.
$(2)$ Normal Reaction force in opposite direction ' $w$ '. i.e., $\mathrm{N}=m g \ldots$ (1)
$(3)$ Friction force $f=\mu \mathrm{N}$ along the surface of road.
The friction between the tyre and the road surface provides the necessary centripetal force.
$\therefore \mathrm{F}_{\mathrm{C}}=f$
$\therefore \frac{m v^{2}}{\mathrm{R}}=f \quad \cdots(2) \quad\left[\because \mathrm{F}_{\mathrm{C}}=\frac{m v^{2}}{\mathrm{R}}\right]$
In order to move safely on this road, $\frac{m v^{2}}{\mathrm{R}}$ force is required and it should be equal to maximum frictional force.
$\left(f_{s}\right)_{\max } &=\mu_{s} \mathrm{~N}$
$=\mu_{s} m g[\because \mathrm{N}=m g]$
Where $\mu_{s}$ is the coefficient of static friction between the tyres of vehicle and the road.
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