A hanging wire made of an alloy of titanium with diameter 0.05 cm is initially 2.7 m long. When a 15 kg mass is hung from it, the wire stretches an amount 1.68 cm. A mole of titanium has a mass of 48 grams, and its density is 4.54 g/cm3. Based on these experimental measurements, what is Young's modulus for this alloy of titanium

Explanation:

Young's modulus of elasticity Y = stress / strain

stress = force / cross sectional area

= weight of 15 kg / π r²

= 15 x 9.8 / 3.14 x ( .025 x 10⁻² )²

stress = 74.9 x 10⁷ N / m²

strain = Δ L / L , Δ L is change in length and L is original length

Putting the values

strain = .0168 / 2.7 =.006222

Young's modulus of elasticity Y  = 74.9 x 10⁷ / .006222

= 120.88 x 10⁹ N / m² .

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