Young's Modulus and Axial Elongation
For a uniform prismatic member in small linear tension or compression, Young's modulus gives Delta L = FL/(AY), with force, area, and material properties constant along the segment.
Why this shows up in the exam
Comparing wire extensions · Designing tension members · Finding modulus from load-extension data
Learn the idea
Axial extension grows with force and length but falls with area and Young's modulus. A long thin wire behaves like a softer spring than a short thick wire of the same material because more length deforms and less area shares the load.
🧠 Memory hook: More F or L stretches more; more A or Y stretches less.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Delta L = FL/(AY) — extension or compression magnitude of one uniform axial segment
- k_axial = AY/L — effective spring constant of a uniform wire or rod
- Delta L₁/Delta L₂ = (F₁ L₁ A₂ Y₂)/(F₂ L₂ A₁ Y₁) — ratio form that avoids unnecessary arithmetic
How to approach it
- 1Write FL/(AY) separately for each uniform segment
- 2Replace circular area by pi d squared over four when needed
- 3Take ratios before substituting numbers
Common slip-ups that cost marks
- •Using diameter rather than area proportional to diameter squared
- •Treating Young's modulus as geometry-dependent
- •Forgetting different tensions in different segments
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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