College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Question
**Educational Exercise: Circular Motion and Tension Calculation** In the image, a bead is attached to the end of a string and moves in a horizontal circle with a constant speed of 1.43 m/s. Key parameters are provided: the string's length \( L \) is 185 cm, and the bead's mass is 27.0 g. The angle \( \theta \) from the vertical is 19.0°. Air resistance is negligible. ### Objective Use two different approaches to calculate the tension \( T \) in the string. ### Graphical Explanation The image depicts a bead attached to a string, which is fixed at one end. The bead moves in a horizontal circle, indicating a conical pendulum. The diagram includes: - A vertical line from the fixed point to the bead, labeled \( L \) (the string length). - An angle \( \theta = 19.0^\circ \) shown between the vertical component of the string and the string itself. - A circle indicating the path of the bead’s horizontal motion. ### Problem-Solving Steps **(a)** Apply the GFS method to explain each step in solving the problem. **(b)** Create a Free Body Diagram (FBD) for the bead: - Identify and label all external forces acting on it. - Represent each force with an arrow. - Specify the x and y coordinate systems to be used for calculations. **(c)** Write Newton’s Second Law for the x direction: - Simplify using given information. - Solve for tension \( T \), providing answers to two significant figures. **(d)** Write Newton’s Second Law for the y direction: - Simplify using given information. - Solve for tension \( T \) to two significant figures. ### Answer Choices Choose the correct tension \( T \) from the following options, ensuring consistency between both methods: - 0.28 N - 0.23 N - 0.18 N - 0.31 N - 0.10 N ### Note We'll collaborate in class to sketch the FBD and apply Newton’s Laws for accurate tension calculations. Be cautious with units and rounding, as precision is crucial for correct results.
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Transcribed Image Text:**Educational Exercise: Circular Motion and Tension Calculation** In the image, a bead is attached to the end of a string and moves in a horizontal circle with a constant speed of 1.43 m/s. Key parameters are provided: the string's length \( L \) is 185 cm, and the bead's mass is 27.0 g. The angle \( \theta \) from the vertical is 19.0°. Air resistance is negligible. ### Objective Use two different approaches to calculate the tension \( T \) in the string. ### Graphical Explanation The image depicts a bead attached to a string, which is fixed at one end. The bead moves in a horizontal circle, indicating a conical pendulum. The diagram includes: - A vertical line from the fixed point to the bead, labeled \( L \) (the string length). - An angle \( \theta = 19.0^\circ \) shown between the vertical component of the string and the string itself. - A circle indicating the path of the bead’s horizontal motion. ### Problem-Solving Steps **(a)** Apply the GFS method to explain each step in solving the problem. **(b)** Create a Free Body Diagram (FBD) for the bead: - Identify and label all external forces acting on it. - Represent each force with an arrow. - Specify the x and y coordinate systems to be used for calculations. **(c)** Write Newton’s Second Law for the x direction: - Simplify using given information. - Solve for tension \( T \), providing answers to two significant figures. **(d)** Write Newton’s Second Law for the y direction: - Simplify using given information. - Solve for tension \( T \) to two significant figures. ### Answer Choices Choose the correct tension \( T \) from the following options, ensuring consistency between both methods: - 0.28 N - 0.23 N - 0.18 N - 0.31 N - 0.10 N ### Note We'll collaborate in class to sketch the FBD and apply Newton’s Laws for accurate tension calculations. Be cautious with units and rounding, as precision is crucial for correct results.
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