Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsMARCH 20242 Marks
Question
Derive an expression for maximum speed moving along a horizontal circular track.
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Answer
To derive the expression for the maximum speed (v max) of an object moving along a horizontal circular track without slipping, we consider the balance between the centripetal force needed for circular motion and the maximum static friction force, which prevents slipping. The equation gives the maximum speed: v max $=\sqrt{\mu_s g r}$ Where: - vmax is the maximum speed, - $\mu_{ s }$ is the coefficient of static friction between the object and the track, - g is the acceleration due to gravity, - r is the radius of the circular track. This formula indicates that the maximum speed is determined by the track's radius, the gravitational force, and the friction between the track and the object.
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