Properties of Matter – Stage 1 (Page 4)

Elastic Potential Energy, Stress in Wires & Practical Applications

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1. Elastic Potential Energy (Strain Energy)

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

Elastic Energy = Work Done

U = ½ × Stress × Strain × Volume

Important Formula:
U = (½) (F × ΔL)

• Valid only within elastic limit
• Energy is fully recoverable

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2. Elastic Energy per Unit Volume

This quantity is known as energy density.

Energy Density = U / V = ½ × Stress × Strain

JEE Tip:
This formula is directly used in objective questions.

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3. Stretching of a Wire Under Its Own Weight

When a wire is suspended vertically, different sections experience different tension.

Elongation = (ρ g L²) / (2Y)

• ρ = density of material
• L = length of wire
• Y = Young’s modulus

Key Point:
Average force acts at the midpoint of the wire.

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4. Wire Suspended With a Load

If a load M is attached at the end:

ΔL = (M g L) / (A Y)

• Directly proportional to load
• Inversely proportional to area

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5. Effect of Temperature on Elasticity

• Elasticity of most solids decreases with temperature
• Rubber shows opposite behavior

Reason:
Increased thermal agitation weakens restoring forces.

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6. Applications of Elasticity

• Bridges and buildings (load distribution)
• Suspension cables
• Vehicle shock absorbers
• Spring balances
• Earthquake-resistant structures

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7. Important IIT-JEE Observations

• Breaking stress ≠ Young’s modulus
• More elastic ≠ stronger
• Steel is more elastic than rubber
• Elastic limit depends on material & treatment

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Stage 1 – Page 4 Summary

• Elastic energy and energy density
• Stretching of wires (with load & self-weight)
• Temperature effect on elasticity
• Real-world applications

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Stage 1 – Page 4 Completed ✅
Next: Stress–Strain Curve, Breaking Stress & Material Behaviour – Page 5