# Hooke's Law Calculator

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

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## 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 x1 is 33 meters, x0 is 20 meters, Fx is 5 N.

Solution:

Step 1: Extract the data

Force = Fx =5 N

Spring equilibrium position = x0 = 20 meters

Distance from Equilibrium = x1 = 33 meters

Spring constant = K =?

Step 2: Calculation

K = - {Fx / (x1 – x0)}

Plugging in the values:

K = - {5 / (33 – 20)}

K = - {5 / (13)}

K = -0.385 N / m