A simple pendulum consists of a 50 cm long string connected to a 100 g ball. The ball is pulle

step 1 So in this question, we're trying to find out the tension in the string when the pendulum bob is

A simple pendulum consists of a 50 cm long string connected...

A simple pendulum consists of a $50 \mathrm{~cm}$ long string connected to a $100 \mathrm{~g}$ ball. The ball is pulled aside so that the string makes an angle of $37^{\circ}$ with the vertical and is then released. Find the tension in the string when the bob is at its lowest position.

Key Concepts

Simple Pendulum

A simple pendulum is a model in classical mechanics consisting of a mass (often referred to as a bob) attached to the end of a lightweight, inextensible string, which swings under the influence of gravity. Its motion is typically analyzed using small-angle approximations and principles of energy conservation, making it a fundamental system for studying periodic motion and harmonic oscillators.

Conservation of Energy

The principle of conservation of energy states that the total energy in an isolated system remains constant, transitioning between potential and kinetic energy. In the context of a pendulum, when the bob is displaced from its equilibrium position, gravitational potential energy is stored, which is converted into kinetic energy as the bob swings downward. This conversion is key to determining the speed of the bob at various points in its trajectory.

Gravitational Force

Gravitational force is the attractive force acting between two masses and, in the context of a pendulum, it is the force that imparts a downward pull on the bob. This force, often expressed as mg (mass times the gravitational acceleration), influences both the pendulum's potential energy and the overall dynamics of the system.

Centripetal Force

Centripetal force is the net force required to keep an object moving in a circular path, directed towards the center of the circle. For a pendulum at the lowest point, the bob’s circular motion necessitates an inward (centripetal) force, which is provided by the tension in the string. This concept is essential for understanding how the bob's velocity and the curvature of its path contribute to the overall forces in play.

Tension Force

The tension in the string of a pendulum is the force transmitted through the string that supports the weight of the bob and provides the necessary centripetal force for its circular motion. At the lowest point in the pendulum's swing, the total tension is the sum of the force required to balance the gravitational pull (mg) and the additional force needed to keep the bob moving in a curved path, making it a critical quantity in the analysis of pendular motion.

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