A force of 40 N is applied at the end of a wire 4m long and produces an extension of 0.24mm. If the diameter of the wire is 2.00mm, calculate the; (i) stres...
Question 1 Report
A force of 40 N is applied at the end of a wire 4m long and produces an extension of 0.24mm. If the diameter of the wire is 2.00mm, calculate the;
(i) stress on the wire; (ii) strain in the wire.
Answer Details
A force \(F = 40\,\text{N}\) stretches a wire of length \(L = 4\,\text{m}\), producing an extension \(e = 0.24\,\text{mm} = 0.24\times10^{-3}\,\text{m}\); the wire diameter is \(2.00\,\text{mm}\), so radius \(r = 1.00\times10^{-3}\,\text{m}\).
Cross-sectional area:
\[ A = \pi r^{2} = 3.142\times(1.00\times10^{-3})^{2} = 3.142\times10^{-6}\,\text{m}^{2} \](i) Stress on the wire:
\[ \text{stress} = \frac{F}{A} = \frac{40}{3.142\times10^{-6}} = 1.27\times10^{7}\,\text{Nm}^{-2} \](ii) Strain in the wire:
\[ \text{strain} = \frac{e}{L} = \frac{0.24\times10^{-3}}{4} = 6.0\times10^{-5} \](Strain is a ratio and has no unit.)
Download The App On Google Playstore
Everything you need to excel in your exams
Personalized AI Learning Chat Assistant
200,000+ Exam Questions Across IGCSE, JAMB, WAEC & NECO
Over 3,900 Lesson Notes
Offline Support - Learn Anytime, Anywhere
Green Bridge Timetable
Literature Summaries & Potential Questions
Track Your Performance & Progress
In-depth Explanations for Comprehensive Learning