Question

The elongation E of a spring balance varies directly with the applied weight W. If E =5 when W=25, find E when W=20

Answer 1

This is a question on variation. Our approach is to make equations of the various statements.

$\begin{gathered} \text{The elongation, E varies directly with weight, W can be given as:} \\ E\alpha W \end{gathered}$

Introducing our proportionality constant, we have:

$\begin{gathered} E=kW \\ k=\frac{E}{W} \\ \text{where k is length per weight} \\ k=\frac{5}{25}=\frac{1}{5} \end{gathered}$

Now, we apply this constant to find the value of E given W or W, given E.

Here, we are given W and are asked to find E.

$\begin{gathered} E=kW \\ k=\frac{1}{5} \\ W=20 \\ E=\frac{1}{5}\times20=4 \end{gathered}$

E = 4