Ahanging magnesium wire with diameter 2.1 mm (2.1 × 10-3 m) is initially 1.15 m long. when a 104 kg mass is hung from it, the wire stretches an amount 8.46 mm. a mole of magnesium has a mass of 24 grams, and its density is 1.74 g/cm3. find the approximate value of the effective spring stiffness of the interatomic force.

The approximate value of the effective spring stiffness of the inter atomic force is 11.32 N/m.

Explanation:

Given that,

Diameter of wire = 2.1 mm

Initial length = 1.15 m

Mass = 104 kg

Stretching length = 8.46 mm

Mass of mole of magnesium =24 g

Density = 1.74 g/cm³

We need to calculate the diameter of magnesium

Using formula of diameter

Put the value into the value

We need to calculate the stress

Using formula of stress

We need to calculate the strain

Using formula of strain

We need to calculate the young modulus

Using formula of young modulus

We need to calculate the approximate value of the effective spring stiffness of the inter atomic force

Using formula of effective spring stiffness

Put the value into the formula

Hence,  The approximate value of the effective spring stiffness of the inter atomic force is 11.32 N/m.