Two hard rubber spheres, each of mass m = 16.2 g, are rubbed with fur on a dry day and are then suspended with two insulating strings of length L = 4.60 cm whose support points are a distance d = 2.85 cm from each other as shown in the figure below. During the rubbing process, one sphere receives exactly twice the charge of the other. They are observed to hang at equilibrium, each at an angle of 0 = 10.7° with the vertical. Find the amount of charge on each sphere. (Enter your answers from smallest to largest.) с C Need Help? Read It

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### Problem Statement

Two hard rubber spheres, each of mass \( m = 16.2 \, g \), are rubbed with fur on a dry day and are then suspended with two insulating strings of length \( L = 4.60 \, cm \) whose support points are a distance \( d = 2.85 \, cm \) from each other as shown in the figure below. During the rubbing process, one sphere receives exactly twice the charge of the other. They are observed to hang at equilibrium, each at an angle of \( \theta = 10.7^\circ \) with the vertical. Find the amount of charge on each sphere. (Enter your answers from smallest to largest.)

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### Diagram Explanation

The diagram shows two spheres labeled as mass \( m \) hanging from insulating strings of length \( L \). The strings are attached to a horizontal support, and the points of attachment are a distance \( d \) apart.

- Both spheres are suspended and hang away from each other forming angles \( \theta \) with the vertical.
- The distance between the support points from which the strings are hanging is \( d \).
- The length of each string (from the support point to each sphere) is \( L \).
- The angles formed by the strings with the vertical are represented as \( \theta \).

### Data and Variables:
- Mass of each sphere (\( m \)) = \( 16.2 \, g \)
- Length of insulating strings (\( L \)) = \( 4.60 \, cm \)
- Distance between support points (\( d \)) = \( 2.85 \, cm \)
- Angle with the vertical (\( \theta \)) = \( 10.7^\circ \)

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### Input Fields for Charges

| Charge (C) on first sphere | Charge (C) on second sphere |
|----------------------------|-----------------------------|
|                            |                             |

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### Help Section

- **Need Help?:** If you need assistance solving the problem or understanding the concepts, click on the "Read It" button for detailed explanations.

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**Note:** Ensure to explain all steps leading to the solution, focusing on the principles of electrostatics and equilibrium of forces to find the charges on the spheres.
Transcribed Image Text:### Problem Statement Two hard rubber spheres, each of mass \( m = 16.2 \, g \), are rubbed with fur on a dry day and are then suspended with two insulating strings of length \( L = 4.60 \, cm \) whose support points are a distance \( d = 2.85 \, cm \) from each other as shown in the figure below. During the rubbing process, one sphere receives exactly twice the charge of the other. They are observed to hang at equilibrium, each at an angle of \( \theta = 10.7^\circ \) with the vertical. Find the amount of charge on each sphere. (Enter your answers from smallest to largest.) --- ### Diagram Explanation The diagram shows two spheres labeled as mass \( m \) hanging from insulating strings of length \( L \). The strings are attached to a horizontal support, and the points of attachment are a distance \( d \) apart. - Both spheres are suspended and hang away from each other forming angles \( \theta \) with the vertical. - The distance between the support points from which the strings are hanging is \( d \). - The length of each string (from the support point to each sphere) is \( L \). - The angles formed by the strings with the vertical are represented as \( \theta \). ### Data and Variables: - Mass of each sphere (\( m \)) = \( 16.2 \, g \) - Length of insulating strings (\( L \)) = \( 4.60 \, cm \) - Distance between support points (\( d \)) = \( 2.85 \, cm \) - Angle with the vertical (\( \theta \)) = \( 10.7^\circ \) --- ### Input Fields for Charges | Charge (C) on first sphere | Charge (C) on second sphere | |----------------------------|-----------------------------| | | | --- ### Help Section - **Need Help?:** If you need assistance solving the problem or understanding the concepts, click on the "Read It" button for detailed explanations. --- **Note:** Ensure to explain all steps leading to the solution, focusing on the principles of electrostatics and equilibrium of forces to find the charges on the spheres.
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