# What is the spring stiffness?

Did you study physics well at school? Do you know the basic physical laws and would be able to simply take and calculate, for example, the spring stiffness? Let's start with theoretical knowledge. Spring stiffness is a coefficient connecting the elongation of an elastic body and the force of elasticity resulting from this elongation. The stiffness of the spring is also called the coefficient of elasticity or the Hooke coefficient, since the spring stiffness refers specifically to Hooke's law. What is the force of elasticity, which is mentioned in this law? The force of elasticity is the force that arises during the deformation of the body and counteracts this deformation.

## Mathematical method

How to determine the stiffness of the spring or, in the terminology of a science such as physics, the coefficient of spring stiffness? To do this, you need to know a simple formula by which the spring stiffness is calculated. This formula, or rather Hooke's law, looks like this: F = | kx |, where k is the coefficient of elasticity of the spring, x is the extension of the spring, or, as it is also called,the amount of deformation of the spring. And the value denoted by the letter F, respectively, is the elastic force, which we calculate. To find out what the spring stiffness is, it is necessary to measure two other quantities, indicated in the formula, using standard mathematical laws. Then you just need to solve the equation with one unknown.

## Experimental method

To understand how to find the spring stiffness, or rather, to determine the spring stiffness coefficient experimentally, the following manipulations should be performed. You need to deform the body by applying force to it. The simplest form of deformation is compression or tension. The stiffness coefficient shows exactly what force must be applied to the body in order to elastically deform it per unit length. We are now talking about elastic deformation, when the body takes its original shape after making an impact on it. In order to conduct this visual experiment you will need the following things:

- calculator,
- a pen,
- notebook,
- spring,
- ruler,
- cargo.

So, fasten one end of the spring vertically, and leave the other free. Measure the length of the spring and record the result in a notebook (this will be the value of x1).Suspend a weight of one hundred grams to the free end of the spring and again measure the length of the spring, write down the value (x2). Calculate the absolute elongation of the spring (the difference between the values of x1 and x2). At low compression and tension, the elastic force is proportional to the strain. Here we are already applying the Hooke's Law, according to which Fupr = | kx |, where k and is the stiffness coefficient. In order to find the stiffness coefficient we need, the tensile force must be divided by the spring extension. We find the tensile force as follows: Fupr = - N = -mg. It follows that mg = kx. So, k = mg / x.

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