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:
Edge of the aluminium cube (L) = 10 cm = 0.1 m
Mass (m) = 100 Kg
Shear modulus of aluminium (η) = 25 GPa = 25 x 109 Pa
Shear modulus (η) = Stress/strain = F/A/L/ΔL
Where, Force (F) = mg = 100. x 9.8 = 980 N
Area of the one faces of the cube = 0.1 x 0.1 = 0.001 m2
Vertical deflection of the cube = ΔL
Therefore, ΔL = FL/Aη = 980 x 0.1/10-2 x 25 x 109 = 3.92 x 10-7
The vertical deflection of the faces of the cube is 3.92 x 10-7
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