Respuesta :
The equation that describes the stretching of springs is:
[tex]F=k\cdot\Delta x\text{.}[/tex]Where F is the force applied to stretch the spring a length Δx and k is the constant of the spring.
In this case, we have:
[tex]\begin{gathered} F_1=80pd,\text{ }\Delta x_1=8in, \\ F_2=?,\text{ }\Delta x_2=18in\text{.} \end{gathered}[/tex]Replacing the values of F_1 and Δx_1 in the equation above, we have:
[tex]\begin{gathered} F_1=k\cdot\Delta x_1, \\ 80pd=k\cdot8in\text{.} \end{gathered}[/tex]Solving for k, we get:
[tex]k=\frac{80pd}{8in}=10\frac{pd}{in}.[/tex]Replacing the value of k and Δx_2 in the equation, we get the value of F_2:
[tex]F_2=k\cdot\Delta x_2=10\frac{pd}{in}\cdot18in=180pd\text{.}[/tex]Answer
The force required to stretch the spring 18 in is 180 pounds.
