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?
Given, the edge of the aluminum cube is 10 cm . The mass attached is 100 kg . The shear modulus of aluminum is 25 GPa .
The shear force acting on the aluminum cube is,
F = m g
Substituting the values in the above expression, we get:
F = 100 kg × 9 .8 m / s 2 = 980 N
The shear modulus is given by the equation,
G = F L A Δ L Δ L = F L A G
Substituting the values in the above expression, we get:
Δ L = ( 980 N ) ( 0.1 m ) ( 0.1 m × 0 .1 m ) ( 25 × 10 9 N / m 2 ) = 4 × 10 − 7 m
Hence, the vertical deflection of the aluminum cube is 4 × 10 − 7 m .
Given, the edge of the aluminum cube is
The shear force acting on the aluminum cube is,
Substituting the values in the above expression, we get:
The shear modulus is given by the equation,
Substituting the values in the above expression, we get:
Hence, the vertical deflection of the aluminum cube is
