In this Young’s Modulus guide, we will show you how to find Young’s Modulus in just a few simple steps.
We will also help you understand what Young’s Modulus is, and explain the stress and strain formulas while we’re at it.
What is Young’s Modulus?
How is it related to the stiffness of a material?
How to calculate stress, strain, and E in physics and engineering? Find all the answers here and make learning easy! You will also see real-world applications to understand where and how it is used.
Young’s Modulus Calculator
Calculate Young’s Modulus (E = Stress / Strain)
Result:
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Young’s Modulus (E) Explained
Understanding the Formula
Young’s modulus (E) is a measure of the stiffness of a material. It is calculated using the formula:
E = Stress / Strain
Breaking Down the Components:
1. Stress (σ) – The force applied per unit cross-sectional area:
σ = F / A
- F = Applied tensile force (in Newtons, N)
- A = Cross-sectional area (in m²)
- σ = Tensile stress (Pa, N/m²)
2. Strain (ε) – The relative deformation of the material:
ε = ΔL / L
- ΔL = Change in length (Lf − L, in meters)
- L = Original length (in meters)
- ε = Strain (dimensionless)
Real-world Applications of Young’s Modulus
| Material | Typical E (GPa) | Application |
|---|---|---|
| Steel | 200 | Construction beams, rods, mechanical components |
| Aluminum | 70 | Aircraft frames, automotive parts |
| Copper | 110 | Electrical wires, plumbing pipes |
| Rubber | 0.01-0.1 | Elastic seals, tires, flexible components |
| Glass | 50-90 | Windows, structural panels, screens |
Worked Example
Problem Statement:
A tensile force of 10,000 N is applied to a steel rod with a cross-sectional area of 0.0001 m² (1 cm²). The original length of the rod is 2.0 meters, and it stretches by 0.001 meters (1 mm). Find the Young’s modulus of the steel.
Solution:
Step 1: Identify the known values
- Force, F = 10,000 N
- Cross-sectional area, A = 0.0001 m²
- Original length, L = 2.0 m
- Change in length, ΔL = 0.001 m
Step 2: Calculate Stress (σ)
Stress formula: σ = F / A
σ = 10,000 / 0.0001 = 100,000,000 Pa = 100 MPa
Step 3: Calculate Strain (ε)
Strain formula: ε = ΔL / L
ε = 0.001 / 2.0 = 0.0005 (dimensionless)
Step 4: Calculate Young’s Modulus (E)
E = Stress / Strain = 100,000,000 / 0.0005 = 200,000,000,000 Pa = 200 GPa
Answer: The Young’s modulus of the steel rod is 200 GPa.
FAQs
What is Young’s Modulus?
n simple words, Young’s Modulus tells you how stiff a material is. It shows how much a material will stretch when you apply a force to it.
What is the difference between stress and strain?
Stress is the force applied on a material per unit area, and strain is how much the material actually stretches or deforms because of that force.
What are the units of Young’s Modulus?
Young’s Modulus is measured in Pascals (Pa), or in bigger units like kilopascals (kPa), megapascals (MPa), or gigapascals (GPa).