A particle (charge = 8.7 pC) is released from rest at a point x = 5.4 cm. If a 46.2-uC charge is held fixed at the origin, what is the kinetic energy of the particle after it has moved 93.3 cm? Round your answer to 2 decimal places.

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**Question:**

A particle (charge = 8.7 μC) is released from rest at a point x = 5.4 cm. If a 46.2 μC charge is held fixed at the origin, what is the kinetic energy of the particle after it has moved 93.3 cm?

Round your answer to 2 decimal places.

**Solution:**
*[The following steps and equations are to be provided to understand and solve the problem]*

1. **Potential Energy Calculation:**
   - Calculate the initial potential energy (U_initial) at x = 5.4 cm.
   - Calculate the final potential energy (U_final) at x = 93.3 cm + 5.4 cm (since the starting point is not the origin).

2. **Kinetic Energy Calculation:**
   - Using energy conservation principles (initial potential energy converts into kinetic energy), determine the kinetic energy (K) after the particle has moved.

3. **Formulas Involved:**
   - Electric Potential Energy: \( U = \frac{k \cdot q_1 \cdot q_2}{r} \)
   - Kinetic Energy: \( K = U_{\text{initial}} - U_{\text{final}} \)
   Where:
     - \( k \) is Coulomb's constant (\(8.99 \times 10^9 \, \text{N·m}^2/\text{C}^2\)).
     - \( q_1 \) and \( q_2 \) are the charges involved.
     - \( r \) is the distance between the charges.

Make sure to convert all distances to meters and charges to Coulombs before using in the formulas.

**Attention:**
Show step-by-step calculations to ensure a clear understanding of solving the problem.
Transcribed Image Text:**Question:** A particle (charge = 8.7 μC) is released from rest at a point x = 5.4 cm. If a 46.2 μC charge is held fixed at the origin, what is the kinetic energy of the particle after it has moved 93.3 cm? Round your answer to 2 decimal places. **Solution:** *[The following steps and equations are to be provided to understand and solve the problem]* 1. **Potential Energy Calculation:** - Calculate the initial potential energy (U_initial) at x = 5.4 cm. - Calculate the final potential energy (U_final) at x = 93.3 cm + 5.4 cm (since the starting point is not the origin). 2. **Kinetic Energy Calculation:** - Using energy conservation principles (initial potential energy converts into kinetic energy), determine the kinetic energy (K) after the particle has moved. 3. **Formulas Involved:** - Electric Potential Energy: \( U = \frac{k \cdot q_1 \cdot q_2}{r} \) - Kinetic Energy: \( K = U_{\text{initial}} - U_{\text{final}} \) Where: - \( k \) is Coulomb's constant (\(8.99 \times 10^9 \, \text{N·m}^2/\text{C}^2\)). - \( q_1 \) and \( q_2 \) are the charges involved. - \( r \) is the distance between the charges. Make sure to convert all distances to meters and charges to Coulombs before using in the formulas. **Attention:** Show step-by-step calculations to ensure a clear understanding of solving the problem.
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