Question

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

Answer 1

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* k \\ 15k=2 \\ k=(2)/(15) \end{gathered}`

So, the relationship between E and K is

`E=(2)/(15)W`

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

`\begin{gathered} E=(2)/(15)W \\ E=(2)/(15)*10 \\ E=(4)/(3) \\ E=1(1)/(3) \end{gathered}`

Hence, the answer is

`1(1)/(3)`

Or, 1.33