Materials Science Lab: Verification of Young's Modulus
Investigate the **Young's Modulus ($Y$)** of materials—a measure of stiffness. This experiment calculates $Y$ from the stress and strain induced by a hanging load.
Key Equations & Concepts
▼$$ Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L/L} = \frac{F \cdot L}{A \cdot \Delta L} $$
Stress ($\sigma$) is in Pascals ($\text{Pa}$ or $\text{N/m}^2$). Strain ($\epsilon$) is unitless. Young's Modulus ($Y$) is in Pascals ($\text{Pa}$).
The **yield strength** ($\sigma_y$) is the maximum stress a material can handle before permanent deformation. **Breaking stress** ($\sigma_b$) is the stress at which the material fractures.
Experiment 1: Young's Modulus Analyzer (Ideal System)
Enter the measured data from a tensile test to calculate the material's modulus ($Y$).
Experiment 2: Stress Limit and Strain Challenge
Find the maximum stress ($\sigma$) and the required force ($F$) given material properties.
**Stress** ($\sigma$) is the internal restoring force per unit area ($F/A$). **Strain** ($\epsilon$) is the relative change in configuration ($\Delta L/L$). Young's Modulus is the proportionality constant in Hooke's Law ($\sigma = Y \cdot \epsilon$).
Elastic Limits and Material Behaviour
The **elastic limit** is the point beyond which the material will not return to its original shape once the deforming force is removed (it enters the plastic region).
A material with a **higher Young's Modulus** is considered **stiffer** (e.g., steel has a higher $Y$ than rubber) and requires much greater stress to produce a small amount of strain.
Besides Young's Modulus (longitudinal strain), materials also have a **Bulk Modulus ($B$)** (volume strain) and a **Shear Modulus ($G$)** (shape strain).
