Question

A solid copper cube has an edge length of 85.5 cm. How much stress must be applied to the cube to reduce the edge length to 85.0 cm? The bulk modulus of copper is 1.4 Times 10^11 N/m^2.

Answer 1

Bulk modulus of copper = B = 1.4 x 10¹¹ N/m²

Initial edge length of the copper cube = L₁ = 85.5 cm = 0.855 m

Final edge length of the copper cube = L₂ = 85 cm = 0.85 m

Initial volume of the cube = V₁

V₁ = L₁³

V₁ = (0.855)³

V₁ = 0.625 m³

New volume of the cube = V₂

V₂ = L₂³

V₂ = (0.85)³

V₂ = 0.6141 m³

Change in volume of the cube = $\Delta$V

$\Delta$V = V₁ - V₂

$\Delta$V = 0.625 - 0.6141

$\Delta$V = 0.0109 m³

Stress applied to the cube = P

$B = \frac{P}{\Delta V/V}$

$P = \frac{B\Delta V}{V}$

(1.4 * 1011) (0.0109) (0.625)

P = 2.441 x 10⁹ N/m²

Stress applied to the copper cube to reduce its edge length from 85.5 cm to 85 cm = 2.441 x 10⁹ N/m²