A wire 2.5-m long has a cross-sectional area of 2.5 mm². It is hung vertically, and a 4.5-kg mass is attached to it. By how much does the wire stretch if Young's modulus for that material is 2.0 x10¹¹ N/m²? A) 0.22 mm B) 2.2 mm C) 0.022 mm D) 0.72 mm E) 0.072 mm

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Quizplus · Accepted Answer

The correct answer is A because the wire stretches by 0.22 mm when a 4.5-kg mass is attached to it. This is calculated using the formula:stress = force / areastrain = change in length / original lengthYoung's modulus = stress / strainIn this case, the stress is:stress = (4.5 kg)(9.8 m/s^2) / (2.5 mm^2) = 1.76 x 10^7 N/m^2The strain is:strain = (change in length) / (2.5 m)The Young's modulus is:Young's modulus = 2.0 x 10^11 N/m^2Using the formula Young's modulus = stress / strain, we can solve for the change in length:change in length = (stress)(original length) / Young's moduluschange in length = (1.76 x 10^7 N/m^2)(2.5 m) / (2.0 x 10^11 N/m^2)change in length = 0.22 mm

A Wire 25-M Long Has a Cross-Sectional Area of 2