# 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 ..

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

It important note that this only applies cases where no additional forces such friction exist thus making calculation less precise .For example ,if surface used press against wire were rougher smoother than expected could potentially increase decrease number significantly depending upon situation .. Additionally ,factors like temperature humidity could also affect materials’ properties therefore requiring further calculations considerations order accurately predict exact amount energy needed deform given object ..

Overall ,Hooke’s Law provides invaluable tool helping figure out necessary amounts forces involved countless physical phenomena from everyday occurrences stretching bungee cords ballistic missiles launching satellites space .By utilizing scientific knowledge utilizing same appropriately individuals able make informed decisions regarding any particular project they may be working on thus leading better outcomes more satisfactory results all concerned

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