For a vehicle moving on a banked curved road, using free body diagram $(FBD)$, obtain the formula for the maximum safe speed $(v_{max})$.
For a vehicle moving on a banked curved road, using free body diagram $(FBD)$, obtain the formula for the maximum safe speed $(v_{max})$.
In figure $(a)$ A road banked through angle $\theta$ and having radius $\mathrm{R}$ is shown.
Figure $(b)$ shows the vehicle moving on a circular track.
Three forces act on it.
$(1)$ Weight of the vehicle. $(2)$ Normal reaction force. $(3)$ Frictional force acting away the road's surface.
Taking the components of normal reaction force.
$(1)$ $\mathrm{N} \cos \theta$ along vertical direction.
$(2)$ $\mathrm{N} \sin \theta$ along horizontal direction.
Taking the components of frictional force.
$(1)$ $f \sin \theta$ acting in downward direction.
$(2)$ $f \cos \theta$ acting along the horizontal direction.
In figure $(a)$ A road banked through angle $\theta$ and having radius $\mathrm{R}$ is shown.
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