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? question 9.6 machenical properties of solid
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Answered by
88
Shear ' s modulus (η) of aluminium = 25 GPa
= 25 x 10⁹ Pa
Shear's Modulus , η = shear stress / shear strain
⇒ (F/A) /(L/ΔL)
⇒ ΔL = FL/Aη
⇒ 9.8 x 0.1 / 10⁻² x (25 x 10⁹)
= 3.92 x 10⁻⁷ m
= 25 x 10⁹ Pa
Shear's Modulus , η = shear stress / shear strain
⇒ (F/A) /(L/ΔL)
⇒ ΔL = FL/Aη
⇒ 9.8 x 0.1 / 10⁻² x (25 x 10⁹)
= 3.92 x 10⁻⁷ m
Answered by
54
given,
side of a cube (l) = 10cm = 0.1 m
area of its face = (side length)²
= (0.1)² = 0.01 m²
normal force acting each face of cube = mg = 100×9.8 = 980 N
now,
shear modulus = shearing stress acting on this face/shearing strain acting on this face
25GPa ={ 980 N/0.01 m²}/strain
strain = 98000/25×10⁹
ΔL/L =3.92 × 10⁻6
ΔL = 3.92 × 10⁻⁶× 0.1 = 3.92 ×10⁻⁷ m
hence deflection of this face =3.92 ×10⁻⁷ m
side of a cube (l) = 10cm = 0.1 m
area of its face = (side length)²
= (0.1)² = 0.01 m²
normal force acting each face of cube = mg = 100×9.8 = 980 N
now,
shear modulus = shearing stress acting on this face/shearing strain acting on this face
25GPa ={ 980 N/0.01 m²}/strain
strain = 98000/25×10⁹
ΔL/L =3.92 × 10⁻6
ΔL = 3.92 × 10⁻⁶× 0.1 = 3.92 ×10⁻⁷ m
hence deflection of this face =3.92 ×10⁻⁷ m
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