Solved: A bicyclist traveling with speed v = 4.2 m/s on a

QUESTION:

A bicyclist traveling with speed \(v=4.2 \ \mathrm{m} / \mathrm{s}\) on a flat road is making a turn with a radius \(=6.4 \ \mathrm{m}\). The forces acting on the cyclist and cycle are the normal force \(\left(\vec{F}_{N}\right)\) and friction force \(\left(\vec{F}_{f r}\right)\) exerted by the road on the tires, and  \(m \vec{g}\), the total weight of the cyclist and cycle (see Fig. 8-56 ).

(a) Explain carefully why the angle  the bicycle makes with the vertical (Fig. 8-56 ) must be given by  \(\tan \theta=F_{f r} / F_{N}\) if the cyclist is to maintain balance.

(b) Calculate \(\theta\) for the values given.

(c) If the coefficient of static friction between tires and road is  \(\mu_{s}\) = 0.70, what is the minimum turning radius?

Equation Transcription:

v=4.2 m/s

r=6.4 m

()

()

tan  =

Text Transcription:

v=8.2 m/s

r=13 m

(vector F_N)

(vector F_fr)

m vector g

theta

tan theta = F_fr/F_N

mu_s