Formula of Coefficient of Elasticity

Young's Modulus Formula:

\[ E = \frac{\Delta L}{L} \times \frac{F}{A} \]

Change in Length (ΔL):

Original Length (L):

Force (F):

Cross-sectional Area (A):

m²

Young's Modulus (E):

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1. What is Young's Modulus?

Young's Modulus (also known as the modulus of elasticity) is a mechanical property that measures the stiffness of a solid 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.

2. How Does the Calculator Work?

The calculator uses the Young's Modulus formula:

\[ E = \frac{\Delta L}{L} \times \frac{F}{A} \]

Where:

\( E \) — Young's Modulus (Pa)
\( \Delta L \) — Change in length (m)
\( L \) — Original length (m)
\( F \) — Applied force (N)
\( A \) — Cross-sectional area (m²)

Explanation: The formula calculates the ratio of stress (force per unit area) to strain (change in length per original length) in a material under tension or compression.

3. Importance of Young's Modulus

Details: Young's Modulus is crucial in engineering and materials science for predicting how materials will deform under load, designing structures, selecting appropriate materials for specific applications, and ensuring safety in construction and manufacturing.

4. Using the Calculator

Tips: Enter all values in consistent SI units. Change in length and original length in meters, force in Newtons, and cross-sectional area in square meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of Young's Modulus values?
A: Values range from about 1 GPa for rubbers to over 200 GPa for steels and up to 1000 GPa for diamonds.

Q2: How does Young's Modulus relate to material stiffness?
A: Higher Young's Modulus indicates a stiffer material that deforms less under the same load, while lower values indicate more flexible materials.

Q3: Is Young's Modulus constant for a material?
A: It's generally constant for small deformations within the elastic limit, but can vary with temperature, processing, and material composition.

Q4: What's the difference between Young's Modulus and shear modulus?
A: Young's Modulus describes tensile/compressive stiffness, while shear modulus describes resistance to shear deformation.

Q5: Can this formula be used for all materials?
A: It applies to isotropic materials within their elastic limit. For anisotropic materials or large deformations, more complex models are needed.