# Hooke's Law math

#### meikamae

I have a math project on Hooke's Law and I have found a lot of information on the subject. The problem is, I'm in the tenth grade and none of it seems to make sense to me. I have never taken a physics class, and yet I have been assigned to do a project on a Law that is definately related to physics. Is there any simple way of explaining Hooke's Law?

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#### maximus

hooke's law is the direct relationship between an applied force and the change in the leangth of a spring. the equation is F=-kx, where x is the stretch leangth in the spring and k is the spring constant. (units for k are newtons per meter (i think!!, don't bet your life on it))
basically, an item hanging from a spring must be balanced by an upwards force caused by the spring called restoring force. \
hope that helped...

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#### Tom Mattson

Staff Emeritus
Gold Member
Hi, and welcome to PF.

As it happens, Hooke's law is not that difficult to understand. Have you played with a Slinky before? If so, then you probably know that if left undisturbed, it sits at a certain length. If you compress it and let it go, it will try to return to that length, but will undergo damped oscillations. If you stretch it out and let it go, the same thing will happen.

The force that acts to push/pull the Slinky back to its original length is called a restoring force, and Hooke's law says that this force (F) is proportional to the displacement (x) from the original length, or:

F=-kx

Here, k is the proportionality constant (unique to each spring), and the minus sign indicates that the force points in the opposite direction as the displacement.

In other words, if you displace the spring this way: --->
the restoring force pulls back this way: <---
and vice versa.

#### maximus

Originally posted by maximus
F=-kx
and the negitive sign is there to show that the direction of the restoring force caused by the spring is opposite from the direction of the stretch of the spring (or slinky, whatever).

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