Question

Find the maximum speed at which a car can turn a curve 30m radius on a level road. Coefficient of friction between tyres and the road is 0.11?

Answer 1

A car can safely turn a curve when all the forces acting on it are in equilibrium. The main two forces to be considered while turning is the centrifugal force which depends upon the speed of the car and the frictional force acting between the road and the tyre of the car.

Complete Step By Step Answer:
When a car turns a curve, centrifugal force acts on it. When a car turns, the friction force on the spun wheels of the car provides centripetal force needed to move circularly. As centripetal force works at constant speed on an object that moves in a circle, the force acts inward as the speed of the object is tangentially pointed to the circle. The car safely turns when the centripetal force equals the frictional force.
Centripetal force $=$ frictional force
$\dfrac{{m{v^2}}}{r} = m\mu g$
${v^2} = \mu gr$
${v^2} = 0.11 \times 9.8 \times 30$
$v = 5.68m/s$
The maximum speed with which the car can turn is $5.68m/s$.

Note:
Usually roads are banked on turnings for safe turnings. Banking of roads is described as the edges elevated for curving roads over the inner edge to ensure that the cars are equipped with the required centripetal force to make their turn safe. The angle of inclination of the vehicle is defined as the angle of the bank. A centripetal force is a force that allows a body to follow a curved road. It is always orthogonal to the motion and to the fixed point of the immediate centre of the path curvature.