Bicycling is fun until it isn't

Classical Mechanics Level 5

A boy is driving his bicycle at a constant speed on horizantal ground. To do so he turns the handle so that the front wheel is making an angle \(\theta \) with the line joining the centres of the axles of the wheels. The distance between the axles is \(l\). Coefficient of friction is same between both the tires of the road. Calculate the minimum coefficient of friction between the road and the tires so that the bicycle does not slip.

Details and assumptions :

-Assume mass centre of the cycle and the boy equidistant from both the axles and acceleration of free fall is \(g\) - Velocity of the bicycle is \(v\)

If the answer is in the form \(\mu=(\frac{av^{2}(tan\theta)^{e}}{gl(sin\theta)^{d}(a+btan^{2}\theta)})^{c} \) the find a+b+c+d+e


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