Answer:
[tex]\triangle I=8.60*10^{-4}m[/tex]
Explanation:
From the question we are told that:
Diameter [tex]d=1.27cm[/tex]
Length [tex]l=5.75m[/tex]
Diameter of aluminum column [tex]d_a=16.14cm[/tex]
Length of aluminum column [tex]l_a=3.25m[/tex]
Load Force [tex]F=8500N[/tex]
Generally the equation for Young modulus is mathematically given by
[tex]\gamma=\frac{FL}{A \triangle L}[/tex]
Given the The load force
[tex]F=\frac{Y_aA_a\triangle I}{L_a}+\frac{YA \triangle I}{L}[/tex]
[tex]\triangle I=\frac{F}{\frac{Y_aA_a}{L_a}}+\frac{YA}{L}[/tex]
[tex]\triangle I=\frac{8500N}{ \frac{7*10^{10} \pi (0.1624^2-0.1614^2)}{4*3.15}+ \frac{20*10^10 \pi (0.0127^2)}{4(5.75)}}[/tex]
[tex]\triangle I=8.60*10^{-4}m[/tex]
