# How large a force is necessary to stretch a 2.0-mm-diameter steel wire (Y = 2.0 ´ 1011 N/m2) by 1.0%?

In order to calculate the force necessary to stretch a 2.0mm-diameter steel wire by 1.0%, we must first determine the Young’s Modulus (Y) of the material, which is a measure of its stiffness or resistance to elastic deformation. For steel, this value is 2.0 x 10^11 N/m2. We then need to calculate the cross-sectional area of the wire using A = pi * (d / 2)^2 where d is the diameter and pi is 3.141592. In this case, we get an area of 0.007854 m2.

We can now calculate the force required using Hooke’s Law (F = Y * A * deltaL / L). Where F is Force; Y is Young’s Modulus; A is Area; deltaL/L represents Delta Length divided by Initial Length as a percentage change in length due to stretching applied force.. Substituting our known values gives us a result of 1566 N or approximately 1570 N rounded up .This means that it would require at least 1570 Newtons stretch steel wire mentioned question certain amount ..

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