Question

The length that a hanging spring stretches varies directly with the weight placed at the end of the spring. If a weight of 24 pounds stretched a certain spring 12 inches, how far will the spring stretch of the weight is increased to 43 pounds? Leave the variation constant in fraction form. Round answer to the nearest inch.

Answer 1

It was given that the length of stretch is directly proportional to the weight. Assuming the length is represented by l and the weight by w, we have the following relationship:

`\begin{gathered} l\propto w \\ \therefore \\ l=kw \end{gathered}`

where k is a constant.

The question gives the following parameters:

`\begin{gathered} when\text{ } \\ w=24 \\ l=12 \end{gathered}`

Therefore, we can calculate the constant to be:

`\begin{gathered} 12=k\cdot24 \\ k=(12)/(24) \\ k=(1)/(2) \end{gathered}`

Therefore, the relationship will be:

`l=(1)/(2)w`

If the weight is increased to 43 pounds, the length will be:

`\begin{gathered} l=(1)/(2)\cdot43 \\ l=21.5\approx22\text{ inches} \end{gathered}`

The spring will stretch 22 inches.