Question

A velodrome is built for use in the Olympics. The radius of curvature of the surface is 20.0 m. At what angle should the surface be banked for cyclists moving at 15.5 m/s? (Choose an angle so that no frictional force is needed to keep the cyclists in their circular path. Large banking angles are used in velodromes.)

Answer 1

`\theta=50.79^(\circ)`

Step-by-step explanation:

The radius of curvature of the velodrome, r = 20 m

Speed of cyclists, v = 15.5 m/s

Let
`\theta` is the angle at which the surface should be banked. The horizontal and vertical forces acting on the cyclists are as follows :

`F_x=(mv^2)/(r)`

`F_y=mg`

From the above two equations,

`tan\theta=(v^2)/(rg)`

`tan\theta=((15.5)^2)/(20* 9.8)`

`tan\theta=1.225`

`\theta=50.79^(\circ)`

So, the angle at which the surface is banked is 50.79 degrees. Hence, this is the required solution.