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# Hooke's Law Calculator

To use Hooke’s law calculator, enter the values, and hit calculate button

## Hooke’s Law Calculator

Hooke’s law calculator is used to calculate the force, distance, spring constant, and spring equilibrium position using the principles of Hooke’s law.

## What is Hooke's Law?

Hooke's Law states that the force needed to extend or compress a spring is directly proportional to the distance it is stretched or compressed. This law applies as long as the material remains within its elastic limit.

**Formula:**

Mathematically, Hooke's Law can be expressed as:

**F = -k * x**

Where:

- F represents the force applied to the spring.
- k is the spring constant, also known as the stiffness constant.
- x denotes the displacement of the spring from its equilibrium position.

## Elasticity and Deformation:

### Elasticity:

Elasticity is the ability of a material to regain its original shape and size after the removal of external forces. This property is vital in understanding the behavior of materials under stress.

### Types of Deformation:

Deformation can be categorized into two types:

- Elastic deformation
- Plastic deformation.

Hooke's Law governs elastic deformation. It is reversible while plastic deformation involves permanent changes in the material's shape.

## Hooke's Law in Young's Modulus:

### Defining Young's Modulus:

Young's Modulus, also known as the modulus of elasticity, measures a material's stiffness when subjected to tensile or compressive forces. It relates stress to strain and helps characterize the material's behavior.

### Stress and Strain:

Stress refers to the internal resistance experienced by a material, while strain measures the resulting deformation. Hooke's Law is integral in determining the proportionality between stress and strain.

## Mathematical examples:

**Example 1:**

Find out the spring force constant if x_{1} is 33 meters, x_{0} is 20 meters, F_{x} is 5 N.

**Solution:**

**Step 1:** Extract the data

Force = F_{x }=5 N

Spring equilibrium position = x_{0 }= 20 meters

Distance from Equilibrium = x_{1 }= 33 meters

Spring constant = K =?

**Step 2: **Calculation

K = - {F_{x} / (x_{1} – x_{0})}

Plugging in the values:

K = - {5 / (33 – 20)}

K = - {5 / (13)}

K = -0.385 N / m