Math Problem Statement
A steel wire 15 m long hanging vertically supports a tensile load of 2000 N. Neglecting the weight of the wire, determine the required diameter if the stress is not to exceed 140 MPa and the total elongation is not to exceed 6 mm. Assume E 200 GPa.
15m
2000 N
Solution
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Math Problem Analysis
Mathematical Concepts
Mechanical Engineering
Stress and Strain
Hooke's Law
Formulas
Stress: σ = F / A
Cross-sectional area of a circle: A = πd^2 / 4
Elongation: ΔL = FL / AE
Diameter from stress: d = √(4F / πσ)
Diameter from elongation: A = FL / EΔL, then A = πd^2 / 4
Theorems
Hooke's Law
Suitable Grade Level
Undergraduate Engineering
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