A hanging wire made of an alloy of titanium with diameter 0.28cm is initially 7m

Question

A hanging wire made of an alloy of titanium with diameter 0.28cm is initially 7m long. When a 48kg mass is hung from it, the wire stretches an amount 1.13cm. A mole of titanium has a mass of 48g, and its density is 4.54g/cm Based on these experimental measurements, what is Young's modulus for this alloy of titanium? Y = 7.6472GPa Submit Answer Incorrect. Tries 4/5 Previous Tries 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 2.60x10- 10m for titanium. The micro quantity ksi (the stiffness of one interatomic bond) can be related to the macro property Y. Determine the interatomic spring stiffness: ubmitnswer Incorrect. Tries 1/5 Previous Tries

Explanation / Answer

We know, stress = tension force/ cross sectional area

therefore, stress = (48kg*9.81m/s2)/ (1.4*10-3)2 = 76472326.13

Also, strain = change in length / length = 0.0113/7 = 1.61*10-3

Y= stress/strain = 4.75*1010

For interatomic spring stiffness, ksi:

Y= ksi/diameter

therefore ksi= Y*diameter = 4.75*1010*(2.60*10-10) = 12.35

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