Acyclist is rounding a 18-m-radius curve at 13 m/s . what is the minimum possible coefficient of static friction between thebike tires and the ground?

The minimum possible coefficient of static friction between the bike tires and the ground is 0.96

The parameters given in the question are;

radius= 18

velocity= 13 m/s

acceleration(g)= 9.81

Therefore the coefficient of static friction can be calculated as follows

= velocity²/acceleration × radius

= 13²/9.81 × 18

= 169/176.58

= 0.95

Hence the minimum possible coefficient of static friction is 0.96

link

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:

where the term on the left is the frictional force, while the term on the right is the centripetal force, and where

is the coefficient of static friction

m is the mass of the cyclist+bike

is the gravitational acceleration

is the velocity

is the radius of the trajectory

By re-arranging the equation and solving for , we can find the minimum possible value of the coefficient of static friction:

volume: 22

density: 7.04

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