Question

A 333.3m velodrome track has a banking angle of 32 degrees. What speed (in km/h) can a 61.4kg cyclist travel along this track assuming there is no fricition? Assume the radius of the velodrome track is 20.0m.

Answer 1

Align y-axis vertically upward and x-axis horizontally to the left. Apply Newton's second law:

$$Ox: F_c-N\text{ sin}32°=0,\\ Oy: N\text{ cos}32°-mg=0.\\\space\\ \rightarrow N=\frac{mg}{\text{cos}32°}.\\\space\\ \rightarrow F_c=\frac{mv^2}{R}=N\text{ sin}32°=\frac{mg}{\text{cos}32°}\text{ sin}32°,\\\space\\ \rightarrow v=\sqrt{gR\text{ tan}32°}=11.07\text{ m/s}.$$

In km/h this is

$$v=11.07\cdot\frac{3600}{1000}=39.8\text{ km/h}.$$