24. On a banked race track, the smallest circular path on which cars can move has a radius of 112 m, while the largest has a radius of 165 m, as the drawing illustrates. The height of the outer wall is 18 m. Find (a) the smallest and (b) the largest speed at which cars can move on this track without relying on friction.

 

Banking angle can be found from

 

So we know the bank angle.  Now exam the free body diagram

 

Acceleration vertically is zero, car is not moving off the track in an upward direction.

 

 

 

 

 

 

 

For the smaller radius

 

 

For the larger radius

 

 

 

 

Please send any comments or questions about this page to ddonovan@nmu.edu

This page last updated on January 11, 2020