Question

derive the expression for velocity of moving car while banking the curve ​

Answer 1

Answer:

The phenomena in which the edges of the curved roads are raised above the inner edge to provide the necessary centripetal force to the vehicles so that they take a safe turn. The various terminologies used in the case of banking of roads are:

Banked Turn – It is defined as the turn or change of direction in which the vehicle inclines towards inside.

Bank Angle – The angle at which the vehicle is inclined is defined as the bank angle.

In the next section, let us look at the formula for the angle of banking.

Explanation:

Angle of Banking Formula

The velocity of a vehicle on a curved banked road v=(rg(tanΘ+μs))1−μStanθ−−−−−−−−−√

For a given pair of roads, and tyre μs=tanλ, where λ is the angle of friction, the velocity of a vehicle on a curved banked road is v=rgtan(Θ+λ)−−−−−−−−−−−√

The safe velocity on an unbanked road is given by the expression vmax=μ×r×g−−−−−−−−√

The expression for the angle of banking of road is given by Θ=tan−1v2rg

The expression for the safe velocity on the banked road is given by vmax=rgtanΘ−−−−−−−√

Centripetal Force F = mv2/r = mω2r

Roads are most often banked for the average speed of vehicles passing over them. Nevertheless, if the speed of a vehicle is lesser or more than this, the self-adjusting state friction will operate between tyre and road and vehicle will not skid.