# Hooke's law - why k is constant

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.

## Answers and Replies

berkeman
Mentor
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.

member 529879
member 529879
What exactly do you mean by the linear region?

berkeman
Mentor
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.

member 529879
PeroK
Homework Helper
Gold Member
2021 Award
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.

mic*, member 529879 and berkeman
member 529879
As an object compresses or stretches what happens on the atomic level?

Philip Wood
Gold Member
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.