Question

A hanging titanium wire with diameter 2.0 mm (2.0 × 10-3 m) is initially 2.5 m long. When a 9 kg mass is hung from it, the wire stretches an amount 0.605 mm. A mole of titanium has a mass of 48 grams, and its density is 4.51 g/cm3. Find the approximate value of the effective spring stiffness of the interatomic bond.

Answer 1

To find the approximate value of the effective spring stiffness of the interatomic bond, calculate the stiffness constant of the titanium wire using Young's modulus.

Step-by-step explanation:

To find the approximate value of the effective spring stiffness of the interatomic bond, we need to calculate the stiffness constant of the titanium wire. The stiffness constant, or Young's modulus (Y), is given by the formula Y = F/A/L, where F is the force applied, A is the cross-sectional area of the wire, and L is the original length of the wire.

First, we need to find the force applied. The force can be calculated using the equation F = mg, where m is the mass and g is the acceleration due to gravity.

Next, we need to calculate the cross-sectional area of the wire. The cross-sectional area can be calculated using the formula A = π(r^2), where r is the radius of the wire.

Finally, we can substitute the values into the formula Y = F/A/L to find the Young's modulus of the titanium wire.