Derive formula for mininmum speed on curved bank road
Answers
Some Formulae for Banking Roads
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, then the velocity of a vehicle on a curved banked road is: v=rgtan(Θ+λ)−−−−−−−−−−−√
The safe velocity on an unbanked road is: vmax=μ×r×g−−−−−−−−√
The expression for the angle of banking of road is: Θ=tan−1v2rg
Expression for the safe velocity on the banked road is: vmax=rgtanΘ−−−−−−−√
The expression for the angle of banking: Θ=tan−1v2rg
Answer:
Explanation:
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