A rock of mass m=1.5 kg is tied to a string of length L=2.0...

A rock of mass $m=1.5 \mathrm{kg}$ is tied to a string of length $L=2.0 \mathrm{m}$ and is twirled in a vertical circle as shown in Eigure $5.10 .$ The speed $v$ of the rock is constant; that is, it is the same at the top and the bottom of the circle. If the tension in the string is zero when the rock is at its highest point (so that the string just barely goes slack), what is the tension when the rock is at the bottom?

Key Concepts

Gravitational Force

Gravitational force is the force of attraction exerted by the Earth on an object, directed toward the center of the Earth. In problems involving vertical circular motion, gravity plays a significant role because its direction relative to the object's motion changes at different points along the circle, affecting the net force acting on the object.

Tension Force in Circular Motion

Tension in a string or rope provides the pulling force that contributes to the centripetal force necessary for circular motion. In vertical circular motion, the effective tension force changes with the position of the object because it must counteract the gravitational force in addition to providing the centripetal force. At different points in the motion, the tension is either augmented by or opposing gravity, resulting in variations in its magnitude.

Uniform Circular Motion

Uniform circular motion occurs when an object moves in a circle at a constant speed. Although the speed remains constant, the direction of the velocity vector is continually changing, which means the object is experiencing an acceleration toward the center of the circle. This acceleration is crucial for maintaining the circular path of the object.

Centripetal Force

Centripetal force is the net force required to keep an object moving in a circular path by constantly directing the object toward the center of the circle. This force is provided by various means depending on the context—such as tension, gravity, or friction—and its magnitude is given by the product of the mass and the square of the speed, divided by the radius of the circle.

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