A bicyclist traveling with speed v = 4.2 m/s on a flat road is making a turn with a radius r = 6.4 m. The forces acting on the cyclist and cycle are the normal force (Fn) and friction force (Ffr) exerted by the road on the tires, and mg, the total weight of the cyclist and cycle (see Fig. 8-56).
(a) Explain carefully why the angle θ the bicycle makes with the vertical (Fig.
8-56) must be given by tan θ = Ffr/FN if the cyclist is to maintain balance.
(b) Calculate θ for the values given.
(c) If the coefficient of static friction between tires and road is μs = 0.70, what is the minimum turning radius?

N. Fir (b) (a)