forces physics problem - Please Help ASAP

Question

Suppose you ride a bicycle in a 21.6-m-radius circle on a horizontal surface. The resultant force exerted by the surface on the bicycle (normal force plus frictional force) makes an angle of 13.8° with the vertical.
(a) What is your speed?

(b) If the frictional force on the bicycle is half its maximum possible value, what is the coefficient of static friction?

Answer 1

Since the bicycle is not sliding outwards, the net force in the horizontal direction is zero.   The normal component of the force is just mg and the horizontal component is then Fhor = mg(tan 13.8).

(a)This horizontal force must counter the centripetal force so

mV^2/r = mg(tan 13.8)      V^2 = 2*r*g*tan 13.8 = 104m/s

(b)  The horizontal component for max friction is 2*Fhor = 2*mg(tan 13.8).  Fn = mg.  So

u = (2*mg*tan 13.8)/mg = 0.491