Hooke's law - why k is constant

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Discussion Overview

The discussion centers on the interpretation of Hooke's Law, specifically questioning why the spring constant (k) is considered constant despite the perception that materials become harder to compress or stretch as they are deformed. Participants explore the implications of this law in the context of elastic and plastic deformation, as well as atomic-level changes during deformation.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants express confusion about Hooke's Law, questioning the constancy of k and suggesting that materials become harder to stretch or compress as they are deformed.
  • One participant notes that Hooke's Law applies specifically to the linear region of a spring's elastic deformation.
  • Another participant seeks clarification on what is meant by the "linear region" of deformation.
  • A participant explains that the linear region is where the spring returns to its original length after the force is removed, and that exceeding this region results in plastic deformation.
  • One participant argues that a constant k implies that the spring becomes harder to compress as more force is applied, indicating a misunderstanding of the relationship between force and compression.
  • A question is raised about the atomic-level changes that occur as an object is compressed or stretched.
  • Another participant suggests a possible misunderstanding regarding the definition of x in the context of Hooke's Law, indicating that it refers to the total extension rather than an incremental change.

Areas of Agreement / Disagreement

Participants generally express disagreement regarding the interpretation of the spring constant and its implications, with multiple competing views on the nature of deformation and the behavior of materials under stress.

Contextual Notes

There are unresolved questions about the definitions of terms used in the discussion, such as the linear region and the nature of atomic changes during deformation. The discussion also reflects varying levels of understanding regarding the implications of a constant spring constant.

Who May Find This Useful

This discussion may be of interest to students and enthusiasts of physics, particularly those exploring the concepts of elasticity, material science, and the mechanics of springs.

member 529879
Hookes law says that f = kx where f = force, k = spring constant, and x = change in length. This doesn't make sense to me. Don't objects become harder to compress or stretch as they are compressed or stretched. For example, it is easier to stretch a rubber band when you first start stretching it. In other words, I don't understand why k is constant and doesn't change as the objects compresses or is stretched.
 
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Scheuerf said:
Hookes law says that f = kx where f = force, k = spring constant, and x = change in length. This doesn't make sense to me. Don't objects become harder to compress or stretch as they are compressed or stretched. For example, it is easier to stretch a rubber band when you first start stretching it. In other words, I don't understand why k is constant and doesn't change as the objects compresses or is stretched.

Hooke's Law applies to the linear region of the spring's (elastic) deformation.
 
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What exactly do you mean by the linear region?
 
Scheuerf said:
What exactly do you mean by the linear region?

The linear or elastic region of deformation is where the spring will return to its original length when the force is released: http://en.wikipedia.org/wiki/Hooke's_law

If you take it beyond that region, you will plastically deform it some. If you pull it past its elastic limit, it will be longer (than its original length) when you remove the force from it.
 
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Scheuerf said:
Hookes law says that f = kx where f = force, k = spring constant, and x = change in length. This doesn't make sense to me. Don't objects become harder to compress or stretch as they are compressed or stretched. For example, it is easier to stretch a rubber band when you first start stretching it. In other words, I don't understand why k is constant and doesn't change as the objects compresses or is stretched.

You're missing the point that a constant k does mean that the spring becomes harder to compress the more you compress it. If you apply a force, the spring will compress only so far. To compress it any further you must increase the force.
 
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As an object compresses or stretches what happens on the atomic level?
 
Maybe Scheuerf believes x to be an increment of extension. It's not that, but the extra length of the spring compared with its unstretched length.
 

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