(Conceptual- Planar Kinetics) How to maintain the position

[daphnelee-mh]

Homework Statement

attached below

Relevant Equations

attached below

Relevant equations :

Kindly advise whether this approach is correct, I am not sure whether the friction force should be considered.

 

[Lnewqban]

You can consider a combined center of mass, rather than one for bike and one for rider.
The actual location of that CM is more or less by the knees of the rider.
The contact patch of the front tire can be considered a fulcrum.
The front brake is working, the bike is deccelerating and there is a horizontal friction force vector at the contact patch, pointing rearwards.

For a short period of time, there are two moments in perfect balance (zero angular velocity):
1) One is clockwise and is induced by the vector weight times horizontal distance between CM and contact patch.
2) The second one is counter-clockcwise and is induced by...