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

Answer:

maximum safetey speed on horizontal road=$\sqrt{cofficient\ of\ friction\times radius\ of\ curve\ road\times \ acceleration\ due\ to\ gravity}$

Explanation:

Let

the mass of vehicle =m

maximum speed of vehicle = v

radius of curve path= r

acceleration due to gravity= g

and coefficient of friction= $\mu$

During the motion of the vehicle the centrifugal force and frictional force will be in opposite direction to each other.

Hence in the equilibrium position the centrifugal force will be equal to frictional force and they will balance each other.

Hence, centrifugal force = frictional force

$=> \dfrac{m.v^{2}}{r}=\mu.m.g$

=> v=$\sqrt{\mu.r.g}$

hence, the maximum speed of vehicle should be v=$\sqrt{\mu.r.g}$