Given:
The elongation (E) varies directly with the applied weight (E).
Steps
We can write this mathematically to be:
[tex]\begin{gathered} E\text{ }\propto\text{ W} \\ E\text{ = k W} \\ \text{where k is the constant of proportionality} \end{gathered}[/tex]If E = 4 when W = 18, we have the equation connecting E and W to be:
[tex]\begin{gathered} 4\text{ = k }\times\text{ 18} \\ k\text{ = }\frac{4}{18} \\ k\text{ = }\frac{2}{9} \\ E\text{ = }\frac{2}{9}W \end{gathered}[/tex]When W = 13, the value of E can be found by substitution:
[tex]\begin{gathered} E\text{ = }\frac{2}{9}W \\ =\text{ }\frac{2}{9}\times13 \\ \approx\text{ 2.889} \end{gathered}[/tex]Hence, the string's elongation when the applied weight is 13 is approximately 2.889 or 26/9
