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The graph shows the potential energy curve (blue), and mechanical energy (red) of an object. If the object starts at x = 8 m, and is moving to the left, where will it turn around? %3D

The graph shows the potential energy curve (blue), and mechanical energy (red) of an object. If the object starts at x = 8 m, and is moving to the left, where will it turn around? %3D

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
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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The graph displays the potential energy curve (blue line) and the mechanical energy (red line) of an object. It is used to analyze the motion of the object. The task is to determine the turning point of the object as it moves to the left, starting at a position of \( x = 8 \, \text{m} \). ### Detailed Explanation of the Graph: - **Axes**: - The horizontal axis represents the position \( x \) in meters (m). - The vertical axis represents energy in joules (J). - **Curves**: - **Blue Curve (Potential Energy, \( U \))**: Shows the variation of potential energy with position \( x \). At \( x = 8 \, \text{m} \), the potential energy is below the mechanical energy line, gradually decreasing to a minimum around \( x = 2 \, \text{m} \). - **Red Line (Mechanical Energy, \( E_{\text{mech}} \))**: This is a horizontal line representing the total mechanical energy of the system, which remains constant as the object moves. ### Interpretation: The object's kinetic energy is determined by the difference between the mechanical energy and the potential energy at a given position. The object will turn around where its potential energy equals its mechanical energy, resulting in zero kinetic energy. - **Turning Point**: The object will turn around at approximately \( x = 3.0 \, \text{m} \), where the potential energy curve intersects the mechanical energy line. ### Multiple Choice Options: - 2.0 m - 1.0 m - 0.0 m - 5.0 m - **3.0 m** (correct answer) This analysis is essential for understanding energy conservation and the concept of turning points in potential energy wells.
Transcribed Image Text:The graph displays the potential energy curve (blue line) and the mechanical energy (red line) of an object. It is used to analyze the motion of the object. The task is to determine the turning point of the object as it moves to the left, starting at a position of \( x = 8 \, \text{m} \). ### Detailed Explanation of the Graph: - **Axes**: - The horizontal axis represents the position \( x \) in meters (m). - The vertical axis represents energy in joules (J). - **Curves**: - **Blue Curve (Potential Energy, \( U \))**: Shows the variation of potential energy with position \( x \). At \( x = 8 \, \text{m} \), the potential energy is below the mechanical energy line, gradually decreasing to a minimum around \( x = 2 \, \text{m} \). - **Red Line (Mechanical Energy, \( E_{\text{mech}} \))**: This is a horizontal line representing the total mechanical energy of the system, which remains constant as the object moves. ### Interpretation: The object's kinetic energy is determined by the difference between the mechanical energy and the potential energy at a given position. The object will turn around where its potential energy equals its mechanical energy, resulting in zero kinetic energy. - **Turning Point**: The object will turn around at approximately \( x = 3.0 \, \text{m} \), where the potential energy curve intersects the mechanical energy line. ### Multiple Choice Options: - 2.0 m - 1.0 m - 0.0 m - 5.0 m - **3.0 m** (correct answer) This analysis is essential for understanding energy conservation and the concept of turning points in potential energy wells.
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