Properties of Matter – Stage 1 (Page 10)

Elastic Energy & Stress–Strain Curve (JEE Essentials)

                                              
Picture used in matter of properties

1. Elastic Potential Energy

When a material is deformed within elastic limit, work done is stored as elastic potential energy.

Elastic Energy per unit volume = ½ × Stress × Strain

Unit: J/m³ (same as pressure)

2. Energy in a Stretched Wire

For a wire of length L, cross-section A, extension ΔL:

U = ½ × (Y × A / L) × (ΔL)²

JEE Tip:
Energy ∝ (extension)² → doubling extension → energy becomes 4 times

3. Stress–Strain Curve (Ductile Material)

The stress–strain graph shows how a material responds to applied stress.

Region Meaning
OA Hooke’s Law region (linear)
A Proportional limit
B Elastic limit
C Yield point
D Ultimate tensile strength
E Breaking point

4. Key Definitions (Very Important)

  • Proportional Limit: Stress ∝ strain
  • Elastic Limit: Material regains original shape
  • Yield Point: Large strain without increase in stress
  • Breaking Stress: Stress at fracture

5. Brittle vs Ductile Materials

Ductile Brittle
Large plastic deformation Almost no plastic region
Copper, Steel Glass, Cast iron

6. Area Under Stress–Strain Curve

Area under the stress–strain curve up to elastic limit = elastic energy per unit volume.

JEE Favorite:
Slope of OA = Young’s modulus

7. Resilience & Proof Resilience

  • Resilience: Ability to absorb energy elastically
  • Proof Resilience: Max energy absorbed without permanent deformation

Proof Resilience = (½ × Stress × Strain) × Volume

8. JEE Fast Facts

  • Steel → high Young’s modulus
  • Rubber → high strain, low stress
  • Breaking stress ≠ ultimate stress
  • Elastic energy depends on shape & material

Stage 1 – Page 10 Summary

  • Elastic energy formulas
  • Stress–strain curve interpretation
  • Ductile vs brittle comparison
  • Resilience concepts

Stage 1 COMPLETED ✅
Next: Stage 2 – Advanced Applications & Numericals

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  7. Properties – Part 7
  8. Properties – Part 8
  9. Properties – Part 9
  10. Properties – Part 10
  11. Properties – Part 11
  12. Properties – Part 12
  13. Properties – Part 13
  14. Properties – Part 14
  15. Properties – Part 15
  16. Properties – Part 16
  17. Properties – Part 17
  18. Properties – Part 18
  19. Properties – Part 19
  20. Properties – Part 20
  21. Properties – Part 21
  22. Properties – Part 22
  23. Properties – Part 23
  24. Properties – Part 24
  25. Properties – Part 25

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