Calculate the centripetal force exerted on a vehicle of mass...

Calculate the centripetal force exerted on a vehicle of mass $m=1500 .$ kg that is moving at a speed of $15.0 \mathrm{~m} / \mathrm{s}$ around a curve of radius $R=400 . \mathrm{m} .$ Which force plays the role of the centripetal force in this case?

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Key Concepts

Friction

In practical scenarios such as a vehicle turning on a curved road, the frictional force between the tires and the road surface usually serves as the centripetal force. This frictional force acts horizontally towards the center of the curve, providing the necessary inward force that keeps the vehicle traveling along the circular path without sliding outward.

Uniform Circular Motion

Uniform circular motion refers to an object moving along a circular path at a constant speed. Although the speed remains constant, the continuous change in direction means the object experiences an acceleration, known as centripetal acceleration. This acceleration is provided by the centripetal force acting towards the center of the circle, ensuring the object remains in circular motion.

Centripetal Force

Centripetal force is the net force required to keep an object moving in a circular path. It is always directed towards the center of the circle and is given by the formula F = mv²/R, where m represents the mass of the object, v is its speed, and R is the radius of the circle. This force is essential for maintaining the circular motion, continually changing the direction of the object's velocity.

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