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A charge Q₁ =-6.7nC and mass m₁ = 5.2x10-20 kg is fixed in position and an electron is released from rest at a distance of ro = 4.3m from charge Q₁. Determine the speed of the electron when it has moved a distance of d=33cm from its initial position (in km).

A charge Q₁ =-6.7nC and mass m₁ = 5.2x10-20 kg is fixed in position and an electron is released from rest at a distance of ro = 4.3m from charge Q₁. Determine the speed of the electron when it has moved a distance of d=33cm from its initial position (in km).

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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A charge Q1 =-6.7nC and mass m1 = 5.2 x10-20 kg is fixed in position and an electron is released from rest at a distance of ro =4.3m from charge Q1. Determine the speed of the electron when it has moved a distance of d =33cm from its initial position (in km/s I need to show all work look at correct answer
### Educational Content on Electrostatic Force and Motion **Problem Description:** A charge \( Q_1 = -6.7 \, \text{nC} \) (nanocoulombs) and mass \( m_1 = 5.2 \times 10^{-20} \, \text{kg} \) is fixed in position, and an electron is released from rest at a distance of \( r_0 = 4.3 \, \text{m} \) from charge \( Q_1 \). Determine the speed of the electron when it has moved a distance of \( d = 33 \, \text{cm} \) from its initial position. The final speed should be expressed in \( \text{km/s} \). **Responses:** - **User Answered:** 419.208 \(\text{km/s}\) - **Correct Answer:** 592.8952 \(\text{km/s}\) with a margin of error of \(\pm 1\%\). **Explanation and Concepts:** 1. **Electrostatic Force:** - Electrostatic force is given by Coulomb's Law, which states that the force between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between their centers. 2. **Energy Conservation:** - As the electron moves in the electric field, the potential energy changes to kinetic energy. Using the conservation of energy, the potential energy lost by the charge can be equated to the kinetic energy gained. 3. **Conversion Between Units:** - Remember to convert measurements into consistent units, such as meters for distance and seconds for time, before calculating speeds and energies. This example illustrates concepts of electrostatic forces, conservation of energy in electric fields, and the dynamics of charged particles. Understanding these principles is crucial for solving similar physics problems involving motion in electric fields.
Transcribed Image Text:### Educational Content on Electrostatic Force and Motion **Problem Description:** A charge \( Q_1 = -6.7 \, \text{nC} \) (nanocoulombs) and mass \( m_1 = 5.2 \times 10^{-20} \, \text{kg} \) is fixed in position, and an electron is released from rest at a distance of \( r_0 = 4.3 \, \text{m} \) from charge \( Q_1 \). Determine the speed of the electron when it has moved a distance of \( d = 33 \, \text{cm} \) from its initial position. The final speed should be expressed in \( \text{km/s} \). **Responses:** - **User Answered:** 419.208 \(\text{km/s}\) - **Correct Answer:** 592.8952 \(\text{km/s}\) with a margin of error of \(\pm 1\%\). **Explanation and Concepts:** 1. **Electrostatic Force:** - Electrostatic force is given by Coulomb's Law, which states that the force between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between their centers. 2. **Energy Conservation:** - As the electron moves in the electric field, the potential energy changes to kinetic energy. Using the conservation of energy, the potential energy lost by the charge can be equated to the kinetic energy gained. 3. **Conversion Between Units:** - Remember to convert measurements into consistent units, such as meters for distance and seconds for time, before calculating speeds and energies. This example illustrates concepts of electrostatic forces, conservation of energy in electric fields, and the dynamics of charged particles. Understanding these principles is crucial for solving similar physics problems involving motion in electric fields.
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