A pendulum is 0.80 m long and the bob has a mass of 1.0 kg....

A pendulum is $0.80 \mathrm{m}$ long and the bob has a mass of 1.0 kg. At the bottom of its swing, the bob's speed is $1.6 \mathrm{m} / \mathrm{s} .$ (a) What is the tension in the string at the bottom of the swing? (b) Explain why the tension is greater than the weight of the bob.

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Key Concepts

Force Decomposition in Circular Motion

In problems involving circular motion, forces are often decomposed into components to analyze motion. For a pendulum at the bottom of its swing, the tension is not only balancing the gravitational force acting downward but also providing the necessary centripetal force for the circular motion. This is why the tension in the string is greater than the weight of the pendulum bob.

Newton's Second Law in Circular Motion

This principle states that the net force acting on an object moving in a circular path is equal to the mass of the object multiplied by its centripetal acceleration. In the context of a swinging pendulum, the net inward force is the difference between the tension in the string and the gravitational force, which together account for the required centripetal force to sustain the circular motion.

Centripetal Force

Centripetal force is the inward force required to keep an object moving in a circular path. For a pendulum bob at the lowest point of its swing, this force is provided by the excess tension in the string above the bob's weight. It is calculated as the mass multiplied by the centripetal acceleration, which depends on the bob's speed and the length of the string.

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