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horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.040 kg, the string has length L = 1.1 m and negligible mass, and the bob follows a circular path of circumference 1.0 m. What are (a) the tension in the string and (b) the period of the motion?

horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.040 kg, the string has length L = 1.1 m and negligible mass, and the bob follows a circular path of circumference 1.0 m. What are (a) the tension in the string and (b) the period of the motion?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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The figure shows a conical pendulum, in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.040 kg, the string has length L = 1.1 m and negligible mass, and the bob follows a circular path of circumference 1.0 m. What are (a) the tension in the string and (b) the period of the motion?

### Pendulum Motion: Understanding Circular Motion In this illustration, we have a classic setup to study pendulum motion and circular dynamics. **Diagram Explanation:** 1. **Cord:** - The pendulum setup features a cord, which is a string or rod that attaches the bob to the fixed point at the top. The cord allows the bob to swing freely in a circular path. 2. **Bob:** - The bob is the weight, often a spherical object, at the end of the cord. It represents the mass that is in motion during the pendulum swing. In this diagram, the bob is purple. 3. **L (Length of the Cord):** - The variable \( L \) represents the length of the cord. This length is measured from the fixed point at the top to the center of mass of the bob. It is a crucial parameter as it affects the period and frequency of the pendulum's motion. 4. **r (Radius of the Circular Path):** - The variable \( r \) denotes the radius of the path that the bob takes as it swings. This is the horizontal distance from the point directly below the fixed point to the bob's position. 5. **Circular Path:** - The green circle represents the circular path traced out by the bob as it swings around the fixed point in a conical shape. The circular path is perpendicular to the segment that represents the radius \( r \). ### Key Concepts: - **Simple Pendulum:** A simple pendulum consists of a bob attached to a fixed point via a cord or rod, free to swing in a two-dimensional plane. The motion is typically periodic and can be described using principles of harmonic motion. - **Conical Pendulum:** In a conical pendulum, the bob moves in a circular path in a horizontal plane, creating a cone-shaped figure. This motion can be analyzed using the principles of circular motion and centripetal force. Understanding pendulum dynamics is essential in fields ranging from basic physics to engineering, as pendulum movements are foundational examples of periodic motion and can be extrapolated to study more complex systems.
Transcribed Image Text:### Pendulum Motion: Understanding Circular Motion In this illustration, we have a classic setup to study pendulum motion and circular dynamics. **Diagram Explanation:** 1. **Cord:** - The pendulum setup features a cord, which is a string or rod that attaches the bob to the fixed point at the top. The cord allows the bob to swing freely in a circular path. 2. **Bob:** - The bob is the weight, often a spherical object, at the end of the cord. It represents the mass that is in motion during the pendulum swing. In this diagram, the bob is purple. 3. **L (Length of the Cord):** - The variable \( L \) represents the length of the cord. This length is measured from the fixed point at the top to the center of mass of the bob. It is a crucial parameter as it affects the period and frequency of the pendulum's motion. 4. **r (Radius of the Circular Path):** - The variable \( r \) denotes the radius of the path that the bob takes as it swings. This is the horizontal distance from the point directly below the fixed point to the bob's position. 5. **Circular Path:** - The green circle represents the circular path traced out by the bob as it swings around the fixed point in a conical shape. The circular path is perpendicular to the segment that represents the radius \( r \). ### Key Concepts: - **Simple Pendulum:** A simple pendulum consists of a bob attached to a fixed point via a cord or rod, free to swing in a two-dimensional plane. The motion is typically periodic and can be described using principles of harmonic motion. - **Conical Pendulum:** In a conical pendulum, the bob moves in a circular path in a horizontal plane, creating a cone-shaped figure. This motion can be analyzed using the principles of circular motion and centripetal force. Understanding pendulum dynamics is essential in fields ranging from basic physics to engineering, as pendulum movements are foundational examples of periodic motion and can be extrapolated to study more complex systems.
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