Question

A civil 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?

Answer 1

Answer:
`\theta =\tan ^(-1)((v^2)/(gR))`

Step-by-step 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

`R\cos \theta` will balance weight and
`R\sin \theta` will provide the necessary centripetal Force

thus
`R\sin \theta =(mv^2)/(R)` ------------1

`R\cos \theta =m g` ----------------2

Divide 1 & 2 we get

`(R\sin \theta )/(R\cos \theta )=(mv^2)/(mgR)`

`\tan \theta =(v^2)/(gR)`

`\theta =\tan ^(-1)((v^2)/(gR))`