Question

Derive the expression for maximum safety speed with which vehicle should move along a curved horizontal road.state the significance of it

Answer 1

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.

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Answer 2

Answer:

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