Please derive the equation : , v = root (rg tan theta ) . Please tell where to use it . No links

Dear student,
For the vehicle to go round the curved track at a reasonable speed without skidding, the greater centripetal force is managed for it by raising the outer edge of the track a little above the inner edge. It is called banking of circular tracks.

Consider a vehicle of weight Mg, moving round a curved path of radius r, with a speed v, on a road banked through angleθ.

The vehicle is under the action of the following forces:

  • The weight Mg acting vertically downwards

  • The reaction R of the ground to the vehicle, acting along the normal to the banked road OA in the upward direction

The vertical component R cos θ of the normal reaction R will balance the weight of the vehicle and the horizontal component R sin θ will provide the necessary centripetal force to the vehicle. Thus,

R cosθ = Mg …(i)

R space sin space theta space equals space fraction numerator M v squared over denominator r end fraction   ..........(ii)

On dividing equation (ii) by equation (i), we get

fraction numerator R space sin space theta over denominator R space cos space theta end fraction equals space fraction numerator M v squared divided by r over denominator M g end fraction tan space begin inline style space end style begin inline style theta end style begin inline style space end style begin inline style equals end style begin inline style space end style fraction numerator v squared over denominator r g end fraction

v=rgtanθRegards

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