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6. Two identical charged particles of mass 70 grams are at the ends of strings that are the same length t= 10 cm attached to the ceiling. The charged particles repel, as shown in the sketch below: The angle between the strings is o = 20°. Use force analysis to develop equations that describe the balance of forces along both the horizontal and the vertical directions. If we let the symbols 'FG' and 'FE' represent gravitational and electric force magnitude, type the symbol in the first answer box that corresponds to the force that balances out the tension along the - direction. In the second answer box type in the symbol for the force that balances out the tension along the , direction. FTy L Not yet correct, tries 6/18 Submit All Answers Hint: Try to work purely symbolically without substituting any numbers. Draw a free body diagram that shows the forces acting on one of the charged particles. There should be three forces: gravitational, electric, and tension from the- string. The tension from the string is at an angle, so redraw it in terms of its components. Identify the component that balances against gravity and the other component that balances against the electric force.

6. Two identical charged particles of mass 70 grams are at the ends of strings that are the same length t= 10 cm attached to the ceiling. The charged particles repel, as shown in the sketch below: The angle between the strings is o = 20°. Use force analysis to develop equations that describe the balance of forces along both the horizontal and the vertical directions. If we let the symbols 'FG' and 'FE' represent gravitational and electric force magnitude, type the symbol in the first answer box that corresponds to the force that balances out the tension along the - direction. In the second answer box type in the symbol for the force that balances out the tension along the , direction. FTy L Not yet correct, tries 6/18 Submit All Answers Hint: Try to work purely symbolically without substituting any numbers. Draw a free body diagram that shows the forces acting on one of the charged particles. There should be three forces: gravitational, electric, and tension from the- string. The tension from the string is at an angle, so redraw it in terms of its components. Identify the component that balances against gravity and the other component that balances against the electric force.

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**Problem 6: Charged Particles and Force Balance** Two identical charged particles of mass 70 grams are at the ends of strings with the same length \( \ell = 10 \) cm, attached to the ceiling. The charged particles repel each other, as illustrated in the sketch below: [Illustration: Two strings meeting at the ceiling, extending downward at an angle, with repelling charged particles at the ends.] **Details:** - **Angle Between Strings:** \[ \theta = 20^\circ \] - **Task:** Use force analysis to derive equations for the balance of forces along both horizontal and vertical directions. - **Symbols:** - \( FG \): Gravitational force magnitude - \( FE \): Electric force magnitude **Instructions:** 1. **Determine Forces:** - Input the symbol in the first answer box (\( F_{Tx} \)) for the force that balances the tension along the \( x \)-direction. - Input the symbol in the second answer box (\( F_{Ty} \)) for the force that balances the tension along the \( y \)-direction. 2. **Hint:** - Work symbolically without using numbers. - Draw a free body diagram for one charged particle. - Include three forces: gravitational, electric, and string tension. - Decompose the tension into components to identify those balancing gravity and the electric force. **Answer Boxes:** - \( F_{Tx} = \) [Input Box] - \( F_{Ty} = \) [Input Box] *(Note: Not yet correct, tries 6/18)* This problem is designed to help you understand the forces acting on charged particles and the importance of force decomposition in solving physics problems.
Transcribed Image Text:**Problem 6: Charged Particles and Force Balance** Two identical charged particles of mass 70 grams are at the ends of strings with the same length \( \ell = 10 \) cm, attached to the ceiling. The charged particles repel each other, as illustrated in the sketch below: [Illustration: Two strings meeting at the ceiling, extending downward at an angle, with repelling charged particles at the ends.] **Details:** - **Angle Between Strings:** \[ \theta = 20^\circ \] - **Task:** Use force analysis to derive equations for the balance of forces along both horizontal and vertical directions. - **Symbols:** - \( FG \): Gravitational force magnitude - \( FE \): Electric force magnitude **Instructions:** 1. **Determine Forces:** - Input the symbol in the first answer box (\( F_{Tx} \)) for the force that balances the tension along the \( x \)-direction. - Input the symbol in the second answer box (\( F_{Ty} \)) for the force that balances the tension along the \( y \)-direction. 2. **Hint:** - Work symbolically without using numbers. - Draw a free body diagram for one charged particle. - Include three forces: gravitational, electric, and string tension. - Decompose the tension into components to identify those balancing gravity and the electric force. **Answer Boxes:** - \( F_{Tx} = \) [Input Box] - \( F_{Ty} = \) [Input Box] *(Note: Not yet correct, tries 6/18)* This problem is designed to help you understand the forces acting on charged particles and the importance of force decomposition in solving physics problems.
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