Hooke's Law Calculator

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, F_x is 5 N.

Solution:

Step 1: Extract the data

Force = F_x =5 N

Spring equilibrium position = x₀ = 20 meters

Distance from Equilibrium = x₁ = 33 meters

Spring constant = K =?

Step 2: Calculation

K = - {F_x / (x₁ – x₀)}

Plugging in the values:

K = - {5 / (33 – 20)}

K = - {5 / (13)}

K = -0.385 N / m