### Force (N) vs. Inverse Distance Squared (m^-2)This graph depicts the relationship between force, measured in Newtons (N), and the inverse of the distance squared, measured in meters inverse-squared (m^-2). The horizontal axis (x-axis) represents the inverse distance squared, while the vertical axis (y-axis) represents the force.#### Key Details:- **Equation of the Line:** The linear relationship displayed in the graph can be expressed with the equation: \[ y = 2011.3x \] where \( y \) is the force in Newtons and \( x \) is the inverse distance squared in meters inverse-squared.#### Graph Explanation:- **Data Points:** The data points are observed to align closely along a straight line, demonstrating a linear relationship between force and inverse distance squared.- **Slope:** The slope of this line is 2011.3, indicating that for each unit increase in the inverse distance squared, the force increases by 2011.3 Newtons.- **Axis Labels:** - **X-axis:** Ranges from 0 to 27 m^-2. - **Y-axis:** Ranges from 0 to 60000 N. This graph and its linear relationship reflect an important physical principle often seen in fields such as gravitational force or electrostatic force, where the force is inversely proportional to the square of the distance between two objects or charges.### Practical Applications:Understanding this relationship is crucial for calculating forces in physics, engineering, and related fields, especially in designing systems involving gravitational or electrostatic interactions. ### Coulomb's Law and the Coulomb Factor, \( k \)In an experimental setup, a student measured the Coulomb force between a positive charge (+400 μC) and a negative charge (-600 μC) at varying distances. The objective was to ascertain the Coulomb factor, \( k \).**Experimental Procedure:**- Charges used: +400 μC (positive charge) and -600 μC (negative charge).- Various distances were used to measure the force between these charges.**Data Analysis:**- The student plotted the measured force (in newtons) against the inverse square of the distance (in inverse squared meters). - The resulting graph, along with the trendline, is depicted in Figure 2a.**Determination of \( k \):**- From the analysis of the graph (illustration shown in Figure 2a), the value of the Coulomb factor \( k \) is extracted.**Possible Values for \( k \):**1. \( 8.98 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)2. \( 8.88 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)3. \( 8.78 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)4. \( 8.68 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)5. \( 8.68 \times 10^8 \, \text{Nm}^2/\text{C}^2 \)6. \( 8.99 \times 10^8 \, \text{Nm}^2/\text{C}^2 \)7. \( 8.38 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)8. \( 9.08 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)**Figure Analysis:**While the figure itself (Figure 2a) is not detailed here, it typically involves a graph plotting the force (y-axis) against the inverse square of the distance (x-axis) with a linear trendline. The slope

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A student measured the Coulomb force between a positive charge (+400 µC) and a negative charge (-600 µC) for different distances between them. The student plotted the force (expressed in newtons) as a function of the inverse distance squared (in inverse squared meters) with the goal of extracting the Coulomb factor, k. The resulting graph, including the trendline, is shown in Figure 2a. Based on this graph, the value of k is: 8.98 x 109 N m²/c2 - 8.88 x 109 N m²/c2 - 8.78 x 109 N m²/c2 8.68 x 109 N m²/c2 8.68 x 108 N m2c2 8.99 x 108 N m2c2 8.38 x 109 N m21c2 9.08 x 109 N m²/c2

A student measured the Coulomb force between a positive charge (+400 µC) and a negative charge (-600 µC) for different distances between them. The student plotted the force (expressed in newtons) as a function of the inverse distance squared (in inverse squared meters) with the goal of extracting the Coulomb factor, k. The resulting graph, including the trendline, is shown in Figure 2a. Based on this graph, the value of k is: 8.98 x 109 N m²/c2 - 8.88 x 109 N m²/c2 - 8.78 x 109 N m²/c2 8.68 x 109 N m²/c2 8.68 x 108 N m2c2 8.99 x 108 N m2c2 8.38 x 109 N m21c2 9.08 x 109 N m²/c2

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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