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In the arrangement of the first figure, we gradually pull the block from x = 0 to x = +3.0 cm, where it is stationary. The second figure gives the work that our force does on the block. The scale of the figure's vertical axis is set by Ws = 2.0 J. We then pull the block out to x = +7.0 cm and release it from rest. How much work does the spring do on the block when the block moves from x;= +7.0 cm to (a) x = +3.0 cm, (b) x = -2.0 cm, and (c) x = -7.0 cm?

In the arrangement of the first figure, we gradually pull the block from x = 0 to x = +3.0 cm, where it is stationary. The second figure gives the work that our force does on the block. The scale of the figure's vertical axis is set by Ws = 2.0 J. We then pull the block out to x = +7.0 cm and release it from rest. How much work does the spring do on the block when the block moves from x;= +7.0 cm to (a) x = +3.0 cm, (b) x = -2.0 cm, and (c) x = -7.0 cm?

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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### Understanding and Analyzing Graphs #### Graph Description In the provided graph, the horizontal axis (x-axis) represents the distance \( x \) measured in centimeters (cm), while the vertical axis (y-axis) represents the work \( W \) measured in Joules (J). The curve shown on the graph indicates a quadratic relationship between the distance \( x \) and the work \( W \). As \( x \) increases from 0 cm to 3 cm, the work \( W \) increases non-linearly, suggesting that the work done grows at an increasing rate as the distance increases. #### Input Fields for Calculation The following sections provide fields where you can input numerical answers and their corresponding units for specific calculations related to the graph: 1. **Field (a)** - **Label:** Number - **Input Box:** [ ] - **Unit Dropdown Box:** Select Units 2. **Field (b)** - **Label:** Number - **Input Box:** [ ] - **Unit Dropdown Box:** Select Units 3. **Field (c)** - **Label:** Number - **Input Box:** [ ] - **Unit Dropdown Box:** Select Units These input boxes can be used to answer questions or perform calculations related to the data presented in the graph. Be sure to select the appropriate units for your answers from the dropdown menu provided.
Transcribed Image Text:### Understanding and Analyzing Graphs #### Graph Description In the provided graph, the horizontal axis (x-axis) represents the distance \( x \) measured in centimeters (cm), while the vertical axis (y-axis) represents the work \( W \) measured in Joules (J). The curve shown on the graph indicates a quadratic relationship between the distance \( x \) and the work \( W \). As \( x \) increases from 0 cm to 3 cm, the work \( W \) increases non-linearly, suggesting that the work done grows at an increasing rate as the distance increases. #### Input Fields for Calculation The following sections provide fields where you can input numerical answers and their corresponding units for specific calculations related to the graph: 1. **Field (a)** - **Label:** Number - **Input Box:** [ ] - **Unit Dropdown Box:** Select Units 2. **Field (b)** - **Label:** Number - **Input Box:** [ ] - **Unit Dropdown Box:** Select Units 3. **Field (c)** - **Label:** Number - **Input Box:** [ ] - **Unit Dropdown Box:** Select Units These input boxes can be used to answer questions or perform calculations related to the data presented in the graph. Be sure to select the appropriate units for your answers from the dropdown menu provided.
**Understanding Work Done by a Spring: An Explanation** In this lesson, we explore the work done by a spring on a block in various positions. **Initial Setup:** - We start by pulling the block from \( x = 0 \) to \( x = +3.0 \) cm, where it remains stationary. - The schematic diagrams illustrate the block's movement and the forces acting on it. - The second figure provides a visualization of the work done by our force on the block, with the vertical axis scale set by \( W_s = 2.0 \, \text{J} \). **Objective:** We need to find out how much work the spring does on the block when we move it from an initial position \( x_i = +7.0 \) cm to the following positions: - \( x = +3.0 \) cm, - \( x = -2.0 \) cm, and - \( x = -7.0 \) cm. **Diagram Explanation:** ### Figure (a): This diagram shows the initial stationary state: - The block is attached to the spring. - No force (\( F_s = 0 \)) is applied as the block is at \( x = 0 \). ### Figure (b): This diagram illustrates the movement process: - \( x \) is positive. - A hand applies a force to pull the block towards the right from the equilibrium position. - \( F_s \) (spring force) is negative, opposing the direction of displacement \( \overrightarrow{d} \). - The spring is stretched as the block moves from the equilibrium position. ### Figure (c): This diagram shows compression of the spring: - \( x \) is negative. - A hand applies a force pushing the block towards the left from the equilibrium position. - \( F_s \) (spring force) is positive, opposing the direction of displacement \( \overrightarrow{d} \). - The spring is compressed as the block moves left of the equilibrium position. **Key Concepts:** - When the block is displaced in the positive \( x \)-direction, the spring force \( F_s \) is negative (opposes the displacement). - When the block is displaced in the negative \( x \)-direction, the spring force \( F_s \) is positive (also opposes the displacement). - The work done on the block by the spring depends on the displacement
Transcribed Image Text:**Understanding Work Done by a Spring: An Explanation** In this lesson, we explore the work done by a spring on a block in various positions. **Initial Setup:** - We start by pulling the block from \( x = 0 \) to \( x = +3.0 \) cm, where it remains stationary. - The schematic diagrams illustrate the block's movement and the forces acting on it. - The second figure provides a visualization of the work done by our force on the block, with the vertical axis scale set by \( W_s = 2.0 \, \text{J} \). **Objective:** We need to find out how much work the spring does on the block when we move it from an initial position \( x_i = +7.0 \) cm to the following positions: - \( x = +3.0 \) cm, - \( x = -2.0 \) cm, and - \( x = -7.0 \) cm. **Diagram Explanation:** ### Figure (a): This diagram shows the initial stationary state: - The block is attached to the spring. - No force (\( F_s = 0 \)) is applied as the block is at \( x = 0 \). ### Figure (b): This diagram illustrates the movement process: - \( x \) is positive. - A hand applies a force to pull the block towards the right from the equilibrium position. - \( F_s \) (spring force) is negative, opposing the direction of displacement \( \overrightarrow{d} \). - The spring is stretched as the block moves from the equilibrium position. ### Figure (c): This diagram shows compression of the spring: - \( x \) is negative. - A hand applies a force pushing the block towards the left from the equilibrium position. - \( F_s \) (spring force) is positive, opposing the direction of displacement \( \overrightarrow{d} \). - The spring is compressed as the block moves left of the equilibrium position. **Key Concepts:** - When the block is displaced in the positive \( x \)-direction, the spring force \( F_s \) is negative (opposes the displacement). - When the block is displaced in the negative \( x \)-direction, the spring force \( F_s \) is positive (also opposes the displacement). - The work done on the block by the spring depends on the displacement
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