Write the formula for the maximum safe speed | vedclass

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(A) For a vehicle moving on a flat curved road,the centripetal force required for circular motion is provided by the static friction force between the

Vedclass · Accepted Answer

$v = \sqrt{\mu_s r g}$

Vedclass · Answer

(A) For a vehicle moving on a flat curved road,the centripetal force required for circular motion is provided by the static friction force between the tires and the road.Let $m$ be the mass of the vehicle,$v$ be its velocity,$r$ be the radius of the curve,and $\mu_s$ be the coefficient of static friction.The required centripetal force is $F_c = \frac{mv^2}{r}$.The maximum available static friction force is $f_{s,max} = \mu_s N = \mu_s mg$.For safe turning,the centripetal force must be less than or equal to the maximum static friction force: $\frac{mv^2}{r} \leq \mu_s mg$.Solving for $v$,we get $v^2 \leq \mu_s rg$,which gives the maximum safe speed as $v_{max} = \sqrt{\mu_s rg}$.

Write the formula for the maximum safe speed of a vehicle moving on a flat curved road of radius $r$.

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