The given problem can be exemplified in the following diagram:
To determine the extension force we will use the definition of pressure:
[tex]P=\frac{F}{A}[/tex]Where "F" is the force, and "A" is the area. To determine the area we will use the following equation:
[tex]A=\frac{\pi D^2}{4}[/tex]Where "D" is the diameter. The force acts over the area of the 10 inches diameter alone, therefore we don't need to have into account the area of the rod. Replacing the value of the diameter we get:
[tex]A=\frac{\pi(14in)^2}{4}[/tex]Solving the operation:
[tex]A=153.94in^2[/tex]Replacing in the formula for the pressure we get:
[tex]P=\frac{F}{153.94in^2}[/tex]Since we are required to determine the force, we will multiply both sides by the area:
[tex]153.94in^2P=F[/tex]Replacing the given value of the pressure we get:
[tex](153.94in^2)(700\frac{lbf_{}}{in^2})=F[/tex]Solving the operations we get:
[tex]107756.62lb_f[/tex]Therefore, the extension force is 107756.62 lbf.
