Answer:
50.0543248872 ft
Explanation:
F = Load = 20 ton = [tex]20\times 2000\ lb[/tex]
d = Diameter = 1.25 in
[tex]L_1[/tex] = Initial length = 50 ft
[tex]L_2[/tex] = Final length
A = Area = [tex]\dfrac{\pi}{4}d^2[/tex]
Y = Young's modulus = [tex]30\times 10^6\ psi[/tex]
Young's modulus is given by
[tex]Y=\dfrac{FL}{A\Delta L}\\\Rightarrow Y=\dfrac{FL_1}{\dfrac{\pi}{4}d^2(L_2-L_1)}\\\Rightarrow L_2=\dfrac{4FL_1}{Y\pi d^2}+L_1\\\Rightarrow L_2=\dfrac{4\times 40000\times 50}{30\times 10^6\times \pi\times 1.25^2}+50\\\Rightarrow L_2=50.0543248872\ ft[/tex]
The length during the lift is 50.0543248872 ft