Question

what is maximum speed of horizontal curve road ? write exprestion​

Answer 1

Answer:

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

Answer 2

What is maximum speed of horizontal curve road.

Answer:

[ expression refer in attachment ⤴]

• The Diagram is made in 1 dimensional and not in 3-d so to avoid the confusion.

• The Mathematical expression is shown in the diagram with the derivation of it. Also, two Important conclusions are shown.

• The Maximum velocity is √rgtanθ, where r is the radius of the curved path, g is the acceleration due to gravity.

• In this case, Friction is totally neglected. But this can also be taken in the given condition but for Maximum velocity we don't need to assume that.  

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