Question

The elongation of E of a spring balance varies directly with the applied weight W. If E= 4 when W= 18, find E when w=13

Answer 1

Given:

The elongation (E) varies directly with the applied weight (E).

Steps

We can write this mathematically to be:

`\begin{gathered} E\text{ }\propto\text{ W} \\ E\text{ = k W} \\ \text{where k is the constant of proportionality} \end{gathered}`

If E = 4 when W = 18, we have the equation connecting E and W to be:

`\begin{gathered} 4\text{ = k }*\text{ 18} \\ k\text{ = }(4)/(18) \\ k\text{ = }(2)/(9) \\ E\text{ = }(2)/(9)W \end{gathered}`

When W = 13, the value of E can be found by substitution:

`\begin{gathered} E\text{ = }(2)/(9)W \\ =\text{ }(2)/(9)*13 \\ \approx\text{ 2.889} \end{gathered}`

Hence, the string's elongation when the applied weight is 13 is approximately 2.889 or 26/9