Question

Centripetal Acceleration:

A car moving with a constant speed of 80 km/h enters a circular, flat curve with a radius of curvature of 0.50 km.  If the friction between the road and the car’s tires can support a centripetal acceleration of 1.20 m/s2, without slipping, does the car navigate the curve safely, or does it fly off the road? Perform calculations to justify your answer. Be sure to perform all the necessary dimensional conversions to mks units.

Answer 1

Let us first convert all the information in MKS units.

Radius of curvature (r)=0.50km=500m,

Speed of the car(V)=80km/hr=22.22m/s

The centripetal acceleration(a_{​​​​​​c} ) of the car moving along the circular road is given by

So let us plug in the values now

This acceleration is less than the acceleration that can be supported by the friction (1.20m/s^{​​​​​​2} ). So the car can safely navigate the curve. The centripetal acceleration and the centrifugal acceleration are equal in magnitude but opposite in direction. The friction tries to keep the car on the circular path while the centrifugal acceleration tries to throw the car off the road. But since the centrifugal acceleration is less than the frictional acceleration, the car can easily navigate the curve.