A hanging wire made of an alloy of titanium with diameter 0.43cmcm is initially

Question

A hanging wire made of an alloy of titanium with diameter 0.43cmcm is initially 9mm long. When a 42kgkg mass is hung from it, the wire stretches an amount 1.78cmcm. A mole of titanium has a mass of 48gg, and its density is 4.54g/cm3g/cm3.

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

b.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 2.60×10-10mm for titanium. The micro quantity ks,iks,i (the stiffness of one interatomic bond) can be related to the macro property YY. Determine the interatomic spring stiffness:

ks,i=ks,i=

Explanation / Answer

formula for young moduls is

Y = stress/ strain

stress = F/A = mg/ pi r^2 = 42(9.8)/ pi ( 0.43* 10^-2 m/2)^2 = 28343179.9141 N/ m^2

strain = del L/L = 1.78* 10^-2 /9 = 0.001977m

Y = 28343179.9141 N/ m^2/ 0.001977m= 14.33 * 10^9 Nm^2 or 14.33 GPa

(b)

ksi = Yd = 2.6* 10^-10 m ( 14.33 * 10^9) = 3.72 N/m

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