Question

State the formula for optimum velocity of a vehicle along a curved banked road with friction.​

Answer 1

Explanation:

Hint:In this question, we need to find the maximum speed of the car at which car doesn’t skid while moving in a circular banked road. We basically balance all the factors of the forces exerted on a car in x-axis direction and y-axis direction.

To solve any balancing problems, whether motion is translational or rotational, we always balance forces acting along x-axis and y-axis.

In case of rotational motion, we balance torques acting on the body.

Complete step-by-step answer:

Several formulas used in our calculations are-

Gravitational attraction force – mg

Frictional force (f) – acting between car’s tire and road, and parallel to the slope of road

Normal force (N)- It is a reaction force of the gravitational force exerted by the road on car

Centripetal force (mv2r)(mv2r) - acting towards the center of the circular path followed by the car.

Let’s take inclination angle A of road with respect to the x-axis as shown in the above diagram. Now we can balance all the x-axis and y-axis factors of forces. Refer to the figure.

(1) Balancing all the forces acting along the x-axis-

fcos(A)+Nsin(A)=mv2rfcos⁡(A)+Nsin⁡(A)=mv2r

Substituting the value f=μNf=μN into equation, we get

μNcos(A)+