Hooke's law - why k is constant

In summary, Hooke's Law states that the force (f) applied to an object is directly proportional to the spring constant (k) and the change in length (x). The linear region of deformation, where the spring returns to its original length, is where this law applies. If the force is increased beyond this region, the spring will experience plastic deformation. The constant k does not change as the object compresses or stretches, but it does mean that the spring becomes harder to compress the more it is compressed. This is because the force must be increased to compress the spring further.
  • #1
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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  • #2
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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  • #3
What exactly do you mean by the linear region?
 
  • #4
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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  • #5
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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  • #6
As an object compresses or stretches what happens on the atomic level?
 
  • #7
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.
 

1. What is Hooke's law?

Hooke's law is a principle in physics that describes the relationship between the force applied to an elastic object and the resulting deformation or change in shape of the object.

2. Who discovered Hooke's law?

Hooke's law was first described by the English scientist Robert Hooke in the 17th century.

3. Why is k considered a constant in Hooke's law?

K is considered a constant in Hooke's law because it represents the stiffness or elasticity of a material and remains the same regardless of the force applied to the object.

4. How is k determined in Hooke's law?

K can be determined experimentally by measuring the force and corresponding deformation of an object and then calculating the ratio between them. It can also be calculated using the material's Young's modulus, which is a measure of its stiffness.

5. Is Hooke's law applicable to all materials?

No, Hooke's law is only applicable to materials that exhibit elastic behavior, meaning they can return to their original shape after deformation without permanent damage. Materials such as rubber and metal springs follow Hooke's law, while materials like plastic and glass do not.

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