On a banked race track, the smallest circular path on which cars can move has a radius of 119 m, while the largest has a radius of 155 m, as the drawing illustrates. The height of the outer wall is 15.5 m. Find (a) the smallest and (b) the largest speed at which cars can move on this track without relying on friction.
I already posted this twice, but each time it seems to have disappeared. 
Trying again ......
To cause any body to "orbit" in a circle you need a force always acting inwards and of magnitude $${\frac{{{\mathtt{mv}}}^{{\mathtt{2}}}}{{\mathtt{r}}}}$$
If it is to not rely on the tyres getting much grip, then it must be relying on the weight of the body having a component towards the circle centre. That's why the track is banked---to give a large component of weight directed towards the central point of the circular path.
Equate these two forces, in magnitude and direction.
I already posted this twice, but each time it seems to have disappeared.
Trying again ......
To cause any body to "orbit" in a circle you need a force always acting inwards and of magnitude $${\frac{{{\mathtt{mv}}}^{{\mathtt{2}}}}{{\mathtt{r}}}}$$
If it is to not rely on the tyres getting much grip, then it must be relying on the weight of the body having a component towards the circle centre. That's why the track is banked---to give a large component of weight directed towards the central point of the circular path.
Equate these two forces, in magnitude and direction.
