Question 9.6:
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?
Solution:
Edge of the aluminium cube, L = 10 cm = 0.1 mThe mass attached to the cube, m = 100 kg
Shear modulus (η) of aluminium = 25 GPa = 25 × 109 Pa
Shear modulus, η = Shear stress / Shear strain = (F/A) / (L/ΔL)
Where,
F = Applied force = mg = 100 × 9.8 = 980 N
A = Area of one of the faces of the cube = 0.1 × 0.1 = 0.01 m2
ΔL = Vertical deflection of the cube
∴ ΔL = FL / Aη
= 980 X 0.1 / [ 10-2 X (25 X 109) ]
= 3.92 × 10–7 m
The vertical deflection of this face of the cube is 3.92 ×10–7 m.
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