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 17.5 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

Answer:$\theta =57.37^{\circ}$

Explanation:

Given

Radius of curvature=20 m

Speed of cyclist=17.5 m/s

we know that velocity during a turn is given by

$v=\sqrt{\frac{rg\left (tan\theta +\mu_s\right )}{1-\mu_stan\theta }}$

where v=speed

r=radius  of curvature

$\theta$=angle of banking

$\mu_s$=coefficient of friction

g=acceleration due to gravity

here $\mu_s=0$

thus

$v=\sqrt{rgtan\theta }$

$\tan\theta =\frac{v^2}{rg}$

$tan\theta =\frac{17.5^2}{20\times 9.8}=1.562$

$\theta =57.37^{\circ}$