Slipping cycle

Classical Mechanics Level 2

A boy is driving his bicycle at a constant speed v on a circular horizontal path. To do so he turns the handle so that the front wheel makes an angle β \beta with the line joining centres of axles of wheels. Distance between the axles is. l . Coefficient of friction is same between both tyres and road. Find the Minimum friction so that the cycle doesn't slip is ( Take acceleration of free fall as g and assume center of mass of cycle and the boy equidistant from both axles)

8 l v sin ⁡ β g tan ⁡ β ( 4 + tan ⁡ β ) \dfrac{8lv \sin \beta}{g \tan \beta(4+ \tan \beta)} ( 6 v tan ⁡ β ) l g sin ⁡ β ( 4 + tan ⁡ β ) \dfrac{(6v \tan \beta)l}{g \sin \beta (4+ \tan \beta)} ( 8 ( v 2 ) tan ⁡ 2 β ) ( g l sin ⁡ β ( 4 + tan ⁡ 2 β ) ) \dfrac{(8(v^2) \tan^2 \beta)}{(gl \sin \beta (4+ \tan^2 \beta))} ( 8 ( v 2 ) sin ⁡ 2 β ) ( g l tan ⁡ β ( 3 + tan ⁡ 2 β ) ) \dfrac{(8(v^2) \sin^2 \beta)}{(gl \tan \beta(3+ \tan^2\beta))}

Arka Dutta by Arka Dutta , 19, India

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