Measurement Uncertainty in Young's Modulus
For Y = 4FL/(pi d squared Delta L), the maximum fractional uncertainty is the sum of the fractional input uncertainties weighted by their absolute exponents.
Why this shows up in the exam
Designing wire-extension experiments · Selecting measuring instruments · Comparing dominant error sources
Learn the idea
Percentage uncertainties add with the powers appearing in the measured formula. A diameter error matters twice in a circular wire because area depends on diameter squared, while small measured extension often carries a large relative error.
🧠 Memory hook: Powers become error multipliers.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Y = 4FL/(pi d² Delta L) — Young's modulus from a circular-wire extension experiment
- delta Y/Y approximately delta F/F + delta L/L + 2 delta d/d + delta(Delta L)/Delta L — maximum first-order fractional uncertainty
- percentage error = 100(delta q/q) — conversion from fractional to percentage uncertainty
How to approach it
- 1Express the target as a product of powers
- 2Compute each fractional uncertainty
- 3Weight by exponents, add, and identify the dominant term
Common slip-ups that cost marks
- •Using absolute errors without dividing by readings
- •Forgetting the factor two for diameter
- •Treating original length and extension as the same measurement
🌟 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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