The formula to calculate the Elastic Constant (Young's Modulus) is:
\[
E = \frac{\sigma}{\epsilon}
\]
Where:
\( E \) is the Elastic Constant (Young's Modulus) in N/m²
\( \sigma \) is the Stress applied to the material in N/m²
\( \epsilon \) is the Strain experienced by the material (unitless)
Definition
Elastic Constant (Young's Modulus): A measure of the stiffness of a material. It defines the relationship between stress (force per unit area) and strain (proportional deformation) in a material in the linear elasticity regime of a uniaxial deformation.
Stress (σ): The force applied per unit area of the material.
Strain (ε): The proportional deformation experienced by the material.
Significance: High values of Young's Modulus indicate a stiffer material. It is an intrinsic property of a material that is independent of the amount of material or its shape and size.
Example
Let's say the stress (σ) is 200 N/m² and the strain (ε) is 0.01. Using the formula:
\[
E = \frac{200}{0.01} = 20000
\]
So, the Elastic Constant (Young's Modulus) is 20000 N/m².
Extended information about "Elastic-Constant-Calculator"
How to Calculate Elasticity
Definition: Elasticity measures how much one variable responds to changes in another variable.
Formula: \( E = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q} \)
\( E \): Elasticity
\( \Delta Q \): Change in Quantity
\( \Delta P \): Change in Price
\( P \): Initial Price
\( Q \): Initial Quantity
Example: \( E = \frac{20}{5} \times \frac{10}{100} \)
\( \Delta Q \): 20 units
\( \Delta P \): 5 dollars
\( P \): 10 dollars
\( Q \): 100 units
Elastic Constant Dimensional Formula
Definition: The dimensional formula of an elastic constant represents its physical dimensions.
Formula: \( [K] = [M L^{-1} T^{-2}] \)
\( [K] \): Elastic Constant
\( [M] \): Mass
\( [L] \): Length
\( [T] \): Time
Example: \( [K] = [10 , kg , m^{-1} , s^{-2}] \)
Mass: 10 kg
Length: 1 m
Time: 1 s
Find the Equation for Elasticity Calculator
Definition: This calculator finds the elasticity of demand or supply based on changes in price and quantity.
