**Transcription for Educational Website**### Idealized Data for a Spring's DisplacementThis section explores the relationship between the displacement of a spring from its equilibrium position, denoted as \( x \), and the external force applied to it, \( F_{\text{ext}} \). The data is presented in the table below:| \( x \) (cm) | \( F_{\text{ext}} \) (N) ||--------------|--------------------------|| 0 | 0.0 || 5 | 1.0 || 10 | 2.0 || 15 | 3.0 || 20 | 4.0 |#### Tasks:**a. Graphical Representation:**Draw a properly scaled and carefully labeled graph of \( F_{\text{ext}} \) versus \( x \). Make sure to do this by hand without using software like Excel.**b. Hooke's Law Analysis:**Determine if the spring follows Hooke’s Law by analyzing the linearity of the graph. Justify your reasoning.**c. Spring Constant Calculation:**Calculate the spring constant \( k \).**d. Work Done on the Spring:**Shade the following areas on your graph:- The area representing the work done in stretching the spring from a displacement of 0 cm to 5 cm.- The area representing the work done from a displacement of 15 cm to 20 cm.**e. Explanation of Work Differences:**Explain why the amount of work done in the second case (from 15 cm to 20 cm) differs from the first case (from 0 cm to 5 cm), even though the change in displacement is the same for both.### Graph and Diagrams Explanation:- **Linearity of Graph:** A straight line indicates that the spring follows Hooke's Law, which states that force is proportional to displacement (\( F = kx \)).- **Slope of the Line:** Represents the spring constant \( k \).- **Shaded Areas:** - Calculate the area under the graph for each section to determine the work done, given by the formula \( W = \frac{1}{2}kx^2 \).Understanding these concepts is crucial for comprehending the principles of elasticity and mechanical work in physical systems.

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a. Draw (DO NOT use excel or other software to do this!) a properly scaled and carefully labeled graph of Fext, vs. x for this data. 1.0 10 2.0 b. Does this spring obey Hooke's Law? Why or why not? 15 3.0 c. What is the value of its spring constant k? 20 4.0 d. Shade the area on the graph that represents the amount of work done in stretching the spring from a displacement or extension of 0 cm to one of 5 cm. Also shade the area on the graph that represents the amount of work done in stretching the spring from a displacement or extension of 15 cm to one of 20 cm. Exploin whu the

a. Draw (DO NOT use excel or other software to do this!) a properly scaled and carefully labeled graph of Fext, vs. x for this data. 1.0 10 2.0 b. Does this spring obey Hooke's Law? Why or why not? 15 3.0 c. What is the value of its spring constant k? 20 4.0 d. Shade the area on the graph that represents the amount of work done in stretching the spring from a displacement or extension of 0 cm to one of 5 cm. Also shade the area on the graph that represents the amount of work done in stretching the spring from a displacement or extension of 15 cm to one of 20 cm. Exploin whu the

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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Instantaneous Power

Power is defined in physics as the amount of energy transmitted or transformed per unit time. The watt is the unit of electricity in the International System of Units, equivalent to one joule per second.

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**Transcription for Educational Website**

### Idealized Data for a Spring's Displacement

This section explores the relationship between the displacement of a spring from its equilibrium position, denoted as \( x \), and the external force applied to it, \( F_{\text{ext}} \). The data is presented in the table below:

| \( x \) (cm) | \( F_{\text{ext}} \) (N) |
|--------------|--------------------------|
| 0 | 0.0 |
| 5 | 1.0 |
| 10 | 2.0 |
| 15 | 3.0 |
| 20 | 4.0 |

#### Tasks:

**a. Graphical Representation:**
Draw a properly scaled and carefully labeled graph of \( F_{\text{ext}} \) versus \( x \). Make sure to do this by hand without using software like Excel.

**b. Hooke's Law Analysis:**
Determine if the spring follows Hooke’s Law by analyzing the linearity of the graph. Justify your reasoning.

**c. Spring Constant Calculation:**
Calculate the spring constant \( k \).

**d. Work Done on the Spring:**
Shade the following areas on your graph:
- The area representing the work done in stretching the spring from a displacement of 0 cm to 5 cm.
- The area representing the work done from a displacement of 15 cm to 20 cm.

**e. Explanation of Work Differences:**
Explain why the amount of work done in the second case (from 15 cm to 20 cm) differs from the first case (from 0 cm to 5 cm), even though the change in displacement is the same for both.

### Graph and Diagrams Explanation:

- **Linearity of Graph:** A straight line indicates that the spring follows Hooke's Law, which states that force is proportional to displacement (\( F = kx \)).
- **Slope of the Line:** Represents the spring constant \( k \).
- **Shaded Areas:**
- Calculate the area under the graph for each section to determine the work done, given by the formula \( W = \frac{1}{2}kx^2 \).

Understanding these concepts is crucial for comprehending the principles of elasticity and mechanical work in physical systems.

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