Question

A) calculate the extension of wire needed to produce this tensionBCalculate the work done in producing this extension

Answer 1

Given,

The length of the string, L=0.85 m

The diameter of the string, d=6×10⁻⁴ m

The radius of the string, r=3×10⁻⁴ m

The Young's Modulus of the string, Y=190 GPa

The tension, F=66 N

a)

The Young's Modulus is given by,

$Y=\frac{FL}{Al}$

Where A is the area of cross-section of the string and l is the extension produced in the string.

On rearranging the above equation,

$l=\frac{FL}{YA}$

On substituting the known values,

$\begin{gathered} l=\frac{66\times0.85}{190\times10^9\times\pi(3\times10^{-4})^2} \\ =1.04\times10^{-3}\text{ m} \end{gathered}$

Thus the extension of the wire that is needed to be produced is 1.04×10⁻³ m

b)

The work done in producing the extension is given by,

$W=\frac{1}{2}Fl$

On substituting the known values,

$\begin{gathered} W=\frac{1}{2}\times66\times1.04\times10^{-3} \\ =0.034\text{ J} \end{gathered}$

Thus the work done in producing the extension is 0.034 J