Question

A Steel wire 6 m is stretched through 3 mm. The cross sectional area of wire is
2mm². Ifyoung's modulus of steel is 2x10'' N / m². Find elastic energy density
of wire.​

Answer 1

$\huge\underline{\underline{\bf \orange{Question-}}}$

A Steel wire 6 m is stretched through 3 mm. The cross sectional area of wire is

2mm². Ifyoung's modulus of steel is 2x10¹¹ N/m². Find energy Density and elastic potential Energy

$\huge\underline{\underline{\bf \orange{Solution-}}}$

$\large\underline{\underline{\sf Given:}}$

• Lenght ( L ) = 6m
• ∆l = ${\sf 3mm\:\:or\:\:3×10^{-3}m}$
• Area (A) = ${\sf 2mm^2\:\:or\:\:2×10^{-6}m}$
• Young's modulus ( Y ) = 2×10¹¹N/m²

$\large\underline{\underline{\sf To\:Find:}}$

• Energy Density
• Elastic Potential Energy

❏ Energy Density ➝

✪${\boxed{\bf \blue{Energy\: Density=\dfrac{1}{2}×stress×strain} }}$

$\implies{\sf \dfrac{1}{2}×Y×(strain)^2}$

$\implies{\sf \dfrac{1}{2}×2×10^{11}\left(\dfrac{3×10^{-3}}{6}\right)^2}$

$\implies{\sf \dfrac{1}{2}×2×10^{11}×\dfrac{9×10^{-6}}{36} }$

$\implies{\bf \red{Energy\: Density=10^5\:J/m^3} }$

❏ Elastic Potential Energy ➝

✪${\boxed{\bf \blue{Elastic\:PE=Energy\:Density×Volume}}}$

$\implies{\sf 10^5×2×10^{-6}×6 }$

$\implies{\sf 12×10^{-1} }$

$\implies{\bf \red{ 1.2\:J }}$

$\huge\underline{\underline{\bf \orange{Answer-}}}$

Energy Density ${\bf \red{10^5\:J/m^3}}$

Elastic Potential Energy ${\bf \red{1.2\:J}}$