Acivil engineer plans to design a curved ramp such that a car may not have to rely on friction to round the curve without skidding. the roadway is tilted toward the inside of the curve. suppose the designated speed is v and the radius of the curve is r. at what angle should the curve be tilted?

Explanation:

let \theta be the inclination at which curve is tilted

v is the speed of car and R is the radius of curve

m is the mass of car

Suppose R is the reaction offered by road to car

Resolving R in x and y direction we get

will balance weight and will provide the necessary centripetal Force

thus  ------------1

 ----------------2

Divide 1 & 2 we get