The minimum velocity (in ms^-1 ) with which a car driver must traverse a flat curve of radius 15

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The minimum velocity (in ms^-1 ) with which a car driver...

The minimum velocity (in $\mathrm{ms}^{-1}$ ) with which a car driver must traverse a flat curve of radius $150 \mathrm{~m}$ and coefficient of friction $0.6$ to avoid skidding is (a) $60 \mathrm{~ms}^{-1}$ (b) $30 \mathrm{~ms}^{-1}$ (c) $15 \mathrm{~ms}^{-1}$ (d) $25 \mathrm{~ms}^{-1}$

The minimum velocity (in $\mathrm{ms}^{-1}$ ) with which a car driver must traverse a flat curve of radius $150 \mathrm{~m}$ and coefficient of friction $0.6$ to avoid skidding is
(a) $60 \mathrm{~ms}^{-1}$
(b) $30 \mathrm{~ms}^{-1}$
(c) $15 \mathrm{~ms}^{-1}$
(d) $25 \mathrm{~ms}^{-1}$

Key Concepts

Coefficient of Friction

The coefficient of friction is a dimensionless scalar value that represents the ratio of the frictional force resisting the motion between two surfaces to the normal force pressing them together. In problems of circular motion on a flat surface, this coefficient determines the maximum frictional force available, and hence the maximum speed at which the object can travel without losing traction.

Frictional Force

Frictional force is the force that opposes the motion or the tendency to slide between two surfaces in contact. In the context of circular motion on a flat surface, the frictional force provided by the interaction between the tires and the road is what supplies the necessary centripetal force to keep the car moving in a curved path without skidding.

Uniform Circular Motion

Uniform circular motion refers to the motion of an object traveling at a constant speed along a circular path. Even though the speed is constant, the direction of the velocity changes continuously, meaning that there is an acceleration directed toward the center of the circle. This concept is fundamental in understanding the forces required to keep an object moving in a circle, as the net force must always be directed inward to provide the necessary centripetal force.

Centripetal Acceleration

Centripetal acceleration is the acceleration directed toward the center of a circular path that is required to keep an object moving in that path. It is defined mathematically as the square of the velocity divided by the radius of the circle, and it plays a crucial role in analyzing circular motion because it links the speed of the object with the required inward force.

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