Question

A wire has a Young's Modulus of 4.2x10⁶ N/m² and a cross section radius of 0.005m. If its initial length is 1.0m, determine its length when a force of 50,000N is applied.

Answer 1

Given things:

Y = 4.2 x 10⁶ N/m²

r = 0.005m

L = 1m

F = 50000N

the youngs modulus can be given by the formula

where,

F = applied force

L = initial length

A = area of cross section of wire

l = change in the length

this is the extension in length the final length is the initial length + extension

hence L^' = L + l = 1 + 151.65 m = 152.65 m

final length will be 152.65 m

( i have solved the problem by the values as provided by you but please check the values again because it looks like unreal thing that original length is 1 m and the extension is 151.65 m )