# Young's modulus of a hanging wire

1. Feb 13, 2015

### Westin

1. The problem statement, all variables and given/known data
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. [Broken]

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 [Broken] (the stiffness of one interatomic bond) can be related to the macro property Y. Determine the interatomic spring stiffness:

2. Relevant equations

Y=(FT/A) / (ΔL/L)

3. 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.

Last edited by a moderator: May 7, 2017
2. Feb 13, 2015

### Staff: Mentor

Watch those units. Also, arithmetic error.

Chet