Answer:
[tex]2.23*10^{4}\frac{N}{m^{2} }[/tex]
Explanation:
Modulus of resilience is the maximum amount of strain that an elastic material can support per unit volume, without deformation, and is calculated using the following equation:
μ = σ^2 ÷ 2*E
σ = yield strain= force / cross area
force = 500N; area=π*[tex]r^{2}[/tex]= [tex]{7.8540^{-5}m^{2}[/tex]
σ = [tex]\frac{500N}{7.8540^{-5}m^{2} } =6.3662*10^{6} \frac{N}{m^{2} }[/tex]
E= young modulus: relation between stress and strain, measures stiffness
E=σ/∈, where
∈=(L-Lo)/Lo=7*[tex]10^{-3}[/tex]
where
L=current length = 10 cm * 1.007 = 1.0070*[tex]10^{-1}[/tex] m
Lo=original lenght = 10 cm = 1.0*[tex]10^{-1}[/tex]m
so, E=σ/∈ = [tex]9.0094*10^{8}[/tex]
μ = modulus of resilience = [tex]({6.3662*10^{6}})^{2} / 2*9.094*10^{8} = 2.2283*10^{4} \frac{N}{m^{2} }[/tex]
