Can i get help with this problem ### Force and Extension DataThe table below displays the relationship between the force applied to a material and the resulting extension. This data is useful for understanding concepts related to elasticity and material behavior under different forces.| **Force Applied (N)** | **Extension (m)** ||-----------------------|-------------------|| -25 N | 0.125 m || -13 N | 0.065 m || 14 N | 0.070 m || 21 N | 0.105 m || 34 N | 0.170 m || 65 N | 0.325 m |### Explanation- **Force Applied (N):** This column indicates the magnitude of force applied to the material, measured in Newtons (N). A negative force might indicate compression, while a positive force likely represents tension.- **Extension (m):** This column shows how much the material extends under the applied force, measured in meters (m).This data can help in plotting a graph to observe trends, such as a linear relationship, which might indicate Hooke’s Law behavior in certain ranges. 1. Describe the pattern in your results. How is the force applied related to the extension? Give examples from the data you have taken.

Answered: Force Applied (N) -25 N -13 N 14 N 21 N…

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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Can i get help with this problem

### Force and Extension Data

The table below displays the relationship between the force applied to a material and the resulting extension. This data is useful for understanding concepts related to elasticity and material behavior under different forces.

| **Force Applied (N)** | **Extension (m)** |
|-----------------------|-------------------|
| -25 N | 0.125 m |
| -13 N | 0.065 m |
| 14 N | 0.070 m |
| 21 N | 0.105 m |
| 34 N | 0.170 m |
| 65 N | 0.325 m |

### Explanation

- **Force Applied (N):** This column indicates the magnitude of force applied to the material, measured in Newtons (N). A negative force might indicate compression, while a positive force likely represents tension.
- **Extension (m):** This column shows how much the material extends under the applied force, measured in meters (m).

This data can help in plotting a graph to observe trends, such as a linear relationship, which might indicate Hooke’s Law behavior in certain ranges.

1. Describe the pattern in your results. How is the force applied related to the extension? Give examples from the data you have taken.

Expert Solution

Step 1

Introduction:

The force is vector quantity. In simple harmonic motion due to spring action body attached to the spring is moved along the straight line path with to-and-fro motion. The restoring force is proportional to displacement of the body from mean position. The constant which decides the magnitude of applied force is spring constant.

Given data:

The given force applied and extension are related by the given table.

Formula used:

Relation between force, extension and spring constant is related by,

$\vec{F} = - K \vec{x}$

Where,

$\vec{F}$ - Restoring force due to spring

K- Spring constant

$\vec{x}$ - Extension

Negative sign indicate the direction of force and extension are opposite in direction.

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