QUESTION 8Consider a cylindrical specimen of some hypothetical metal alloy that has a diameter of 8.0 mm (0.31 in.). A tensile force of 1000 N (225 Ibf)produces an elastic reduction in diameter of 2.8 x 104 mm (1.10 x 10° in.). Compute the modulus of elasticity for this alloy, given thatPoisson's ratio is 0.30.Attach FileBrowse My ComputerBrowse Content Collection

Given:- Consider a cylindrical specimen of some hypothetical metal alloy that has a diameter of 8.0 mm (0.31 in.). A tensile force of 1000 N (225 lbf) produces an elastic reduction in diameter of 2.8 x 10 -4 mm (1.10 x 10 -5 in.). Compute the modulus of elasticity for this alloy, given that Poisson's ratio is 0.30.Solution:- A cylindrical specimen of some hypothetical metal alloy is stressed in compression. Diameter of an alloy = 8 mm. Tensile force F = 1000 N Elastic reduction in diameter = 2.8 x 10 -4 mm. Poisson's ratio = 0.30.From the equation:- (1) stress σ = FA0 (2) Hooke's law: σ = E∈z E = σ∈z (3) Specimen area in cylindrical shape :- A0= πd22 (4) Lateral and axial stains in Poison's ratio:- v = -∈x∈zv =- ∆dd∆ll0From the above given equation:- E = σ∈z = FA0-∈XV = - 4Fπd2×v∆dd E=4Fvπd∆dSubstitute these values in the above given equation: We get, E = 4×1000×0.3π×8×10-3×2.8×10-7E = 17.05×1010 The modulus of elasticity for this alloy = 170.5 Gpa.

Answered: Consider a cylindrical specimen of some…