### Understanding Hooke's Law and Elastic LimitA paperclip is bent so that it forms a straight piece of steel wire. The steel wire does not return to its bent shape. Is steel wire (in general) capable of following Hooke's Law?#### Multiple Choice Question:1. **No; Hooke's Law only applies to springs** **Explanation**: This option is incorrect. Hooke's Law is not exclusive to springs but applies to any elastic material within the elastic limit.2. **Yes; in this case the force to bend the paperclip exceeded the elastic limit but a smaller force would still let the paperclip return to its original shape** **Explanation**: This option is correct. Hooke's Law states that the force needed to compress or extend a spring by some distance \( X \) is proportional to that distance. However, once the applied force exceeds the material's elastic limit, the material deforms permanently and does not return to its original shape.3. **No; the paperclip does not return to its bent shape so it is not elastic** **Explanation**: This option is incorrect. The fact that the paperclip does not return to its original shape indicates that the elastic limit has been exceeded, not that steel wire is incapable of following Hooke's Law.4. **Yes; it can follow Hooke's Law without returning to its original shape** **Explanation**: This option is partially correct but misleading. While the steel wire can follow Hooke's Law within the elastic limit, failure to return to its original shape means that the elastic limit was surpassed, resulting in permanent deformation.#### Further Explanation:Hooke's Law is expressed mathematically as \( F = kx \), where \( F \) is the force applied, \( k \) is the spring constant, and \( x \) is the displacement. This law is applicable to any elastic material, including steel used to make paperclips, as long as the material remains within its elastic limit. Once the force exceeds this limit, permanent deformation occurs, and the material does not return to its original shape.#### Conclusion:Steel wire can follow Hooke's Law under normal conditions up to its elastic limit. Exceeding this limit results in irreversible deformation, as observed when a paperclip does not return to its bent shape after being straightened.This educational content covers the relationship between a paperclip's deformation and Hooke's

Hooke’s law states that for relatively small deformations of an object, the size of the deformation…

A paperclip is bent so that it forms a straight piece of steel wire. The steel wire does not return to its bent shape. Is steel wire (in general) capable of following Hooke's Law? O No; Hooke's Law only applies to springs Yes; in this case the force to bend the paperclip exceeded the elastic limit but a smaller force would still let the paperclip return to its original shape No; the paperclip does not return to its bent shape so it is not elastic Yes; it can follow Hooke's Law without returning to its original shape

A paperclip is bent so that it forms a straight piece of steel wire. The steel wire does not return to its bent shape. Is steel wire (in general) capable of following Hooke's Law? O No; Hooke's Law only applies to springs Yes; in this case the force to bend the paperclip exceeded the elastic limit but a smaller force would still let the paperclip return to its original shape No; the paperclip does not return to its bent shape so it is not elastic Yes; it can follow Hooke's Law without returning to its original shape

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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Question

### Understanding Hooke's Law and Elastic Limit

A paperclip is bent so that it forms a straight piece of steel wire. The steel wire does not return to its bent shape. Is steel wire (in general) capable of following Hooke's Law?

#### Multiple Choice Question:

1. **No; Hooke's Law only applies to springs**

**Explanation**: This option is incorrect. Hooke's Law is not exclusive to springs but applies to any elastic material within the elastic limit.

2. **Yes; in this case the force to bend the paperclip exceeded the elastic limit but a smaller force would still let the paperclip return to its original shape**

**Explanation**: This option is correct. Hooke's Law states that the force needed to compress or extend a spring by some distance \( X \) is proportional to that distance. However, once the applied force exceeds the material's elastic limit, the material deforms permanently and does not return to its original shape.

3. **No; the paperclip does not return to its bent shape so it is not elastic**

**Explanation**: This option is incorrect. The fact that the paperclip does not return to its original shape indicates that the elastic limit has been exceeded, not that steel wire is incapable of following Hooke's Law.

4. **Yes; it can follow Hooke's Law without returning to its original shape**

**Explanation**: This option is partially correct but misleading. While the steel wire can follow Hooke's Law within the elastic limit, failure to return to its original shape means that the elastic limit was surpassed, resulting in permanent deformation.

#### Further Explanation:
Hooke's Law is expressed mathematically as \( F = kx \), where \( F \) is the force applied, \( k \) is the spring constant, and \( x \) is the displacement. This law is applicable to any elastic material, including steel used to make paperclips, as long as the material remains within its elastic limit. Once the force exceeds this limit, permanent deformation occurs, and the material does not return to its original shape.

#### Conclusion:
Steel wire can follow Hooke's Law under normal conditions up to its elastic limit. Exceeding this limit results in irreversible deformation, as observed when a paperclip does not return to its bent shape after being straightened.

This educational content covers the relationship between a paperclip's deformation and Hooke's

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