Elastic Potential Energy
Elastic energy density for linear stress-strain (stress σ, strain ε) equals?
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About This Question
- Subject
- physics
- Chapter
- properties of solids and liquids
- Topic
- elastic potential energy
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
(1/2) σ ε
- Definition: Energy density is the work done in deforming a material per unit volume.
- Work Link: Work =∫Fdx=Area under Force-Extension curve.
- Volume-Normalized: For a linear elastic material (Hooke's Law), the stress-strain plot is a straight line through the origin.
- Geometric Calculation: The area under the triangle is 21×base×height=21×strain(ϵ)×stress(σ).
- Result: u=21σϵ. Also writable as 21Yϵ2 since σ=Yϵ.
This medium difficulty physics question is from the chapter properties of solids and liquids, covering the topic of elastic potential energy. It appeared in the 2025 exam.
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