Question

The distance that a spring will stretch varies directly as the force applied to the spring. Aforce of 9 pounds is needed to stretch a spring 6 inches. What force is required to stretchthe spring 12 inches?The required force to stretch the spring 12 inches is inches. (Simplify youranswer.)

Answer 1

`\begin{gathered} d\text{ }\propto\text{ F} \\ d\text{ = k }*\text{ F (where k is a constant)} \\ d\text{ =kF} \end{gathered}`
`\begin{gathered} d\text{ = 6inches, F= 9pounds} \\ k\text{ =}(d)/(F)=\text{ }(6)/(9)=(2)/(3) \end{gathered}`
`\begin{gathered} d=(2)/(3)F \\ \text{when d = 12 inches} \\ 12\text{ =}(2)/(3)\text{ }* F \\ \\ 2F\text{ = 3}*12 \\ F\text{ = }(36)/(2)\text{ = 18pounds} \end{gathered}`