Does the motion of a vehicle on a level circu | vedclass

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(B) For a vehicle moving on a level circular path of radius $r$,the necessary centripetal force is provided by the static friction $f_s$ between the t

Vedclass · Accepted Answer

No,it does not depend on the mass.

Vedclass · Answer

(B) For a vehicle moving on a level circular path of radius $r$,the necessary centripetal force is provided by the static friction $f_s$ between the tires and the road.$f_s = \frac{mv^2}{r}$The maximum value of static friction is $f_{s,max} = \mu_s N = \mu_s mg$,where $\mu_s$ is the coefficient of static friction and $m$ is the mass of the vehicle.For safe turning,the required centripetal force must be less than or equal to the maximum static friction:$\frac{mv^2}{r} \leq \mu_s mg$Dividing both sides by $m$,we get:$\frac{v^2}{r} \leq \mu_s g$$v^2 \leq \mu_s rg$$v \leq \sqrt{\mu_s rg}$Since the mass $m$ cancels out from both sides of the inequality,the maximum safe speed $v_{max} = \sqrt{\mu_s rg}$ is independent of the mass of the vehicle.

Does the motion of a vehicle on a level circular path depend on the mass of the vehicle?

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