A cylindrical specimen of a hypothetical metal alloy is stressed in compression. If its original and final diameters are 30.00 and 30.04 mm, respectively, and its final length is 105.20 mm, compute its original length if the deformation is totally elastic. The elastic and shear moduli for this alloy are 65.5 and 25.4 GPa, respectively. Express the answer in mm to five significant figures.

The original length is 75.793 mm.

Explanation:

Strain = shear modulus ÷ elastic modulus

shear modulus = 25.4 GPa

elastic modulus = 65.5 GPa

Strain = 25.4 ÷ 65.5 = 0.388

Final length = 105.20 mm

Let y represent the original length

Strain = (final length - y)/y

0.388 = (105.20 - y)/y

0.388y = 105.20 - y

0.388y + y = 105.20

1.388y = 105.20

y = 105.20/1.388 = 75.793 mm

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