Chapter 10, Problem 39A

Friction is needed for a car rounding a curve. But if the road is banked, friction may not be required at all. What, then, supplies the needed centripetal force?

To determine

To Explain: The source of centripetal force.

Explanation of Solution

Introduction:

Centripetal force is the net force that causes uniform circular motion. The direction of centripetal force is always towards the center of curvature. The magnitude of this force is,

  $\begin{array}{c}{F}_c=m{a}_c\\ =m\frac{v^2}{r}\\ =mr{\omega }^2\end{array}$

Where,

m is the mass.

v is velocity.

r is radius of curvature

  $\omega$ is angular velocity.

Consider free body diagram of a car on the banked road. Assume that there will be no friction.

Where,

Mg is the weight of car

N is the normal reaction.

From free body diagram, it is observed that the horizontal component of the normal force is directed towards the center of curve and this component will provide the centripetal force required.

Conclusion:

Thus, in the absence of friction, a car will take a turn on the banked road due to normal force horizontal component.