Lecture Notes: Physics - Young's Modulus, Work Done, and Energy Storage

Introduction

• Channel: Learn Physics
• Topic: Young's Modulus, Work Done, and Energy Storage

Key Concepts

Young's Modulus (E)

• Definition: Young's Modulus is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression.

• Formula:

  [E = \frac{\text{Linear Stress}}{\text{Linear Strain}}]

Work Done in Stretching a Wire

• Scenario: Consider a wire with length (L) and area of cross-section (A).

• To stretch the wire from 0 to L with a force (F):

  [\text{Work Done (W)} = \int_{0}^{L} F \cdot dL]_

Volume of the Wire

• Formula:

  [\text{Volume (V)} = A \cdot L]

Work Done per Unit Volume

• To calculate work done per unit volume:

  • Work is applied to deform a body
  • The energy spent is stored as potential energy in the body

  [\text{Work Done per Unit Volume} = \frac{W}{V} = \frac{1}{2} \cdot E \cdot \text{Strain}^2]

Energy Stored in the Wire

• The energy stored in the wire is equal to the work done in stretching it.
• This stored energy is known as potential energy.

Summary

• Young's Modulus (E): Linear stress over linear strain.
• Work Done to Stretch Wire: Integral of force over the length from 0 to L.
• Volume Formula: Area times length.
• Work Done per Unit Volume: Stored as potential energy, applying the formula (\frac{1}{2} E \cdot \text{Strain}^2).
• Energy Storage in Wire: Equals the work done in stretching the wire.