A ball is held at rest at position A in Fig. P 5.127 by two...

A ball is held at rest at position $A$ in Fig. $P 5.127$ by two light strings. The horizontal string is cut and the ball starts swinging as a pendulum. Point $B$ is the farthest to the right the ball goes as it swings back and forth. What is the ratio of the tension in the supporting string at position $B$ to its value at $A$ before the horizontal string was cut?

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Key Concepts

Centripetal Force in Circular Motion

When an object moves along a curved path, such as a pendulum bob in a swing, it experiences centripetal acceleration that requires a net inward force. This centripetal force is provided by the tension in the string, and its magnitude increases with the speed of the bob.

Tension Variation in a Pendulum

The tension in the supporting string of a pendulum varies along its path. At a static or low-speed position, the tension primarily counteracts the weight of the bob. However, when the bob is moving and undergoing circular motion, the tension must also supply the centripetal force, resulting in a higher tension compared to the static case.

Energy Conservation

In mechanics, energy conservation is used to analyze systems where potential energy is converted to kinetic energy and vice versa. For a pendulum, the gravitational potential energy at a high position is converted into kinetic energy at lower positions, allowing the calculation of the bob's speed at various points in its swing.

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