Answer: 0.96
Explanation:
The frictional force, in this problem, provides the centripetal force that keeps the cyclist in circular motion in the curve. Therefore, we can write:
[tex]\mu mg = m\frac{v^2}{r}[/tex]
where the term on the left is the frictional force, while the term on the right is the centripetal force, and where
[tex]\mu[/tex] is the coefficient of static friction
m is the mass of the cyclist+bike
[tex]g=9.81 m/s^2[/tex] is the gravitational acceleration
[tex]v=13 m/s[/tex] is the velocity
[tex]r=18 m[/tex] is the radius of the trajectory
By re-arranging the equation and solving for [tex]\mu[/tex], we can find the minimum possible value of the coefficient of static friction:
[tex]\mu = \frac{v^2}{gr}=\frac{(13 m/s)^2}{(9.81 m/s^2)(18 m)}=0.96[/tex]
