Obtain an expression for the maximum speed with which a vehicle can negotiate a curved smooth road banked at an angle theta with proper diagram.
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Explanation:
Consider a car of mass "m" moving on a banked road of radius 'r'. The various forces acting on the car are: (i) The weight of the car which acts vertically downwards i.e., ω = mg ....(i) (ii) The normal reaction R of the road acts perpendicular to the road. Neglect the force of friction between the tyres of the car and the road. Now resolve the normal reaction R of the road in the two components: (a) R cosθ which is equal opposite to mg i.e., R cosθ = -mg ...(ii) (b) R sinθ which acts towards the centre of the circular path and provides the necessary centripetal force ({mv2 i.e., R sinθ = {mv2 Dividing (iii) by (ii) we get tanθ = v2/rg ⇒ v = (rg tanθ)1/2 which is the safe speed of the car for given value of 'r' and 'θ' on a circular banked road.Read more on Sarthaks.com - https://www.sarthaks.com/571760/obtain-expression-maximum-speed-with-which-vehicle-safely-negotiate-curved-banked-angle
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Answer:
To make the turning of vehicles on the curved road safer, the outer edge of the road is raised above the inner edge making some inclination with the horizontal.This is known as banking of roads
