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**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.
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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