derive an expression for the maximum safety speed limit for the vehile moving along horizontal curved road
Answers
Answer:The equation "µ = v^2 / rg" gives the maximum velocity with which the car can take a turn of radius rs, when the coefficient of friction between the tyres and the road is equal to r.
Explanation:
If R1 and R2 are the normal reactions of the ground on the two tyres of a car of weight Mg, going around on a circular turn of radius r, with velocity v, on a level road, then
F1 = µR1 and F2 = µR2
Where, µ is the coefficient of friction between the tyres and the road
The total force of friction provides the necessary centripetal force, i.e.
F1 + F2 = Mv^2 / r
µR1 + µR2 = Mv^2 / r
µ ( R1 + R2 ) = Mv^2 / r ---- (i)
The total normal reaction balances the weight of the car, i.e.
R1 + R2 = Mg ---- (ii)
From equations (i) and (ii), we have
µMg = Mv^2 / r
µ = v^2 / rg
The above equation gives the maximum velocity with which the car can take a turn of radius rs, when the coefficient of friction between the tyres and the road is equal to r.
hope it helps u
Explanation: