Question

What E is. if E=2 when W=15, find E when W=10

Answer 1

SOLUTION

From the statement, we are told that the elongation E of a spring balance varies directly with the applied weight W of a spring balance. This means

$\begin{gathered} E\propto W \\ \propto is\text{ a sign of proportionality } \end{gathered}$

If we remove the proportionality sign and introduce a constant which is k, the equation becomes

$E=kW$

Now we will use the values E = 2 and W = 15 to find the value of k. This becomes

$\begin{gathered} E=kW \\ 2=15\times k \\ 15k=2 \\ k=\frac{2}{15} \end{gathered}$

So, the relationship between E and K is

$E=\frac{2}{15}W$

From this relationship, if W = 10, then E will be

$\begin{gathered} E=\frac{2}{15}W \\ E=\frac{2}{15}\times10 \\ E=\frac{4}{3} \\ E=1\frac{1}{3} \end{gathered}$

Hence, the answer is

$1\frac{1}{3}$

Or, 1.33