### Understanding Work and Potential Energy in a Variable Force FieldA variable force \( F(x) = \left(\frac{4.0}{x}\right) \, \text{N} \) acts on a particle as it moves along the positive x-axis.#### (a) Calculating Work Done- **Problem:** Determine how much work (in joules) the force does on the particle as it moves from \( x = 2.5 \, \text{m} \) to \( x = 5.2 \, \text{m} \).- **Solution:** The work done is calculated to be **2.93 J**.#### (b) Finding Potential Energy- **Problem:** Selecting the potential energy to be zero at \( x = 1 \, \text{m} \), find the potential energy \( U(x) \) for this force. Use \( x \) as necessary. Assume \( U(x) \) is in joules and \( x \) is in meters. Do not include units in your answer.- **Solution:** The potential energy \( U(x) \) is calculated to be **5.37** at the point specified.For each problem, the required calculations involve integrating the force function and understanding the relationship between work, force, and potential energy in a conservative force field.

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Description: ### Understanding Work and Potential Energy in a Variable Force FieldA variable force \( F(x) = \left(\frac{4.0}{x}\right) \, \text{N} \) acts on a particle as it moves along the positive x-axis.#### (a) Calculating Work Done- **Problem:** Determine

Given data: The work done by the force on the particle is: W The potential energy for the given…

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(a) How much work (in J) does the force do on the particle as it moves from x = 2.5 m to x 5.2 m? 2.93 (b) Picking a convenient reference point of the potential energy to be zero at x = 1 m, find the potential energy for this force. (Use the following as necessary: x. Assume U(x) is in joules and x is in meters. Do not include units in your answer.) U(x) = 5.37

(a) How much work (in J) does the force do on the particle as it moves from x = 2.5 m to x 5.2 m? 2.93 (b) Picking a convenient reference point of the potential energy to be zero at x = 1 m, find the potential energy for this force. (Use the following as necessary: x. Assume U(x) is in joules and x is in meters. Do not include units in your answer.) U(x) = 5.37

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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