A motorcyclist of mass m is to negotiate a cu | vedclass

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(B) For a motorcyclist to negotiate a curve of radius $r$ with speed $v$ safely,the centripetal force required is provided by the static frictional fo

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$\frac{v^2}{gr}$

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(B) For a motorcyclist to negotiate a curve of radius $r$ with speed $v$ safely,the centripetal force required is provided by the static frictional force between the tires and the road.The required centripetal force is given by $F_c = \frac{mv^2}{r}$.The maximum available frictional force is $f_{max} = \mu N = \mu mg$,where $\mu$ is the coefficient of friction and $N = mg$ is the normal force.For safe negotiation,the frictional force must be at least equal to the required centripetal force:$f_{max} \geq F_c$$\mu mg \geq \frac{mv^2}{r}$$\mu \geq \frac{v^2}{gr}$Therefore,the minimum value of the coefficient of friction is $\mu_{min} = \frac{v^2}{gr}$.

$A$ motorcyclist of mass $m$ is to negotiate a curve of radius $r$ with a speed $v$. The minimum value of the coefficient of friction so that the negotiation may take place safely is

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