Question

The edge of an aluminium cube is 10 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 100 kg is then attached to the opposite face of the cube. The shear modulus of aluminium is 25 GPa. What is the vertical deflection of this face?

Answer 1

Here, side of the cube,

L = 10 cm = 0.1 m

Area of each face,

A = (0.1)2 = 0.01 m2

Tangential force acting on the face,

F = 100 kg = 100 x 9.8 = 980 N

Shear modulus, η = Tangential stress/Shearing strain

Shearing strain = Tangential stress/ Shear modulus

= F/Aη = 980/0.01 x 25 x 109

= 3.92 x 10-6

Now, Lateral strain/Side of the cube = Shearing strain

Lateral strain = Shearing strain x Side of the cube

= 3.92 x 10-6 x 0.1 = 3.92 x 10-7 m

≈ 4 x 10-7 m