Young's modulus of a hanging wire

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SUMMARY

The discussion focuses on calculating Young's modulus for a titanium alloy wire with a diameter of 0.5 cm and an initial length of 6 m, which stretches 1.44 cm under a 60 kg load. The formula used is Y = (FT/A) / (ΔL/L), where A is the cross-sectional area calculated as A = πr². The user encountered issues with unit conversions and arithmetic errors in their calculations, which are critical for obtaining accurate results.

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Homework Statement


A hanging wire made of an alloy of titanium with diameter 0.5cm is initially 6m long. When a 60kg mass is hung from it, the wire stretches an amount 1.44cm. A mole of titanium has a mass of 48g, and its density is 4.54g[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/144/char3D.pngcm3.

Based on these experimental measurements, what is Young's modulus for this alloy of titanium?

Y=


As you've done before, from the mass of one mole and the density you can find the length of the interatomic bond (diameter of one atom). This is 2.60×10-10m for titanium. The micro quantity ks[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/100/char3B.pngi (the stiffness of one interatomic bond) can be related to the macro property Y. Determine the interatomic spring stiffness:

ks[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/100/char3B.pngi =

Homework Equations

Y=(FT/A) / (ΔL/L)

The Attempt at a Solution



A=pir^2
A=pi(.25)^2
Stress = (60)(9.8)/.1963
Y= (588/.1963) / (600/1.44)

I thought everything was set up right.. Need assistance on part 2 also, thanks.
[/B]
 
Last edited by a moderator:
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Watch those units. Also, arithmetic error.

Chet
 

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