Question

Young?? modulus for a steel wire is $2 \times 10^{11}\, Pa$ and its elastic limit is $2.5 \times 10^8\, Pa$. By how much can a steel wire 3 m long and $2 \,mm$ in diameter be stretched before the elastic limit is exceeded?

• A. 3.75 mm
• B. 7.50 mm
• C. 4.75 mm
• D. 4.00 mm

Answer 1

Answer: (A)

3.75 mm

Answer 2

The cross-sectional area of a wire of radius r = 1 mm = 10 m is A = pr = 3.14 ??10 m The maximum force that can be applied without exceeding the elastic limit is therefore $F=\left(\frac{F}{A}\right)_{max} \times\left(A\right)$ = (2.5 ??10 N m) (3.14 ??10-6 m) = 785 N When this force is applied, the wire will stretch by $\Delta L=\frac{L}{Y} \frac{F}{A}=\frac{\left(3m\right)\left(785 N\right)}{\left(2\times10^{11}N/m^{2}\right)\left(3.14\times10^{-6} m^{2}\right)}$ = 3.75 ??10 m = 3.75 mm