A solid copper cube of side 10 cm has Young's modulus of elasticity 1 0 11 N / m 2 and Poisson's ratio 0.32. First, It is subjected to a longitudinal force of 1000 N . Then it is subjected t

Question

A solid copper cube of side 10 cm has Young's modulus of elasticity $1 0^{11} N / m^{2}$ and Poisson's ratio 0.32. First, It is subjected to a longitudinal force of 1000 N . Then it is subjected to a pressure of $1 0^{8} Pa$ from all the directions. In the third experiment, It is fixed on the table and the block is pushed by a force of $10, 000 N$ , at the top.

TestHub · Accepted Answer

Stress = A F ​ = 1 0 − 2 1 0 3 ​ = 1 0 5 Strain = l Δ l ​ = Y s t ress ​ Δ l = 1 0 11 1 0 5 ​ × 0.1 = 1 0 − 7 m = 1 0 − 4 mm σ = l o n g i t u d ina l s t r ain l a t er a l s t r ain ​ Δ r = σ Δ l = 0.32 × 1 0 − 4 = 3.2 × 1 0 − 5 mm B = 3 ( 1 − 2 σ ) Y ​ V Δ V ​ = B p ​ Δ V = 1 0 11 1 0 8 ​ × 1 0 − 3 × 3 = 1.08 × 1 0 − 6 m 3  = 0.36 cc η = 2 ( 1 + σ ) Y ​ = 2 ( 1.32 ) 1 0 11 ​ A F ​ = η l x ​ x = 1 0 11 1 0 4 ​ × 0.1 × 1 2 ( 1.32 ) ​ ≈ 2.648 × 1 0 − 6 m

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