Young's modulus for a steel wire is 2 10¹¹ ~Pa and its elastic limit is 2.5 10^8 ~Pa . By how much can a steel wire 3 ~m long and 2 ~mm in diameter be stretched before the elastic limit is exceeded?

Step-by-step solution

The cross-sectional area of a wire of radius r=1 ~mm =10⁻³ ~m is A= r^2=3.14 10⁻⁶ ~m ^2 The maximum force that can be applied without exceeding the elastic limit is therefore aligned & F= ( F A )_ (A) & = (2.5 10^8 ~N ~m ⁻² ) (3.14 10⁻⁶ ~m ^2 )=785 ~N aligned When this force is applied, the wire will stretch by aligned & L= L Y F A = (3 ~m )(785 ~N ) (2 10¹¹ ~N / m ^2 ) (3.14 10⁻⁶ ~m ^2 ) & =3.75 10⁻³ ~m =3.75 ~mm aligned