Chapter 5, Problem 1RE

If a mass weighing 10 pounds stretches a spring 2.5 feet, a mass weighing 32 pounds will stretch it __________ feet.

To determine

To fill: The blank in the statement “If a mass weighing 10 pounds stretches a spring 2.5 feet, a mass weighing 32 pounds will stretch it ___ feet”.

Answer to Problem 1RE

If a mass weighing 10 pounds stretches a spring 2.5 feet, a mass weighing 32 pounds will stretch it $8$ feet.

Explanation of Solution

Theorem used:

The hook’s low:

If the stiffness of the spring is $K$, mass weight is $w$ and stretch in spring is $S$, then,

$S=\frac{w}{K}$ (1)

Calculation:

Given that a mass weighing 10 pounds stretches a spring 2.5 feet.

Substitute $10\text{lb}$ for $w$ and $2.5\text{feet}$ for $S$ in equation (1).

$\begin{array}{l}2.5\text{feet}=\frac{10\text{lb}}{K}\\ K=4\frac{\text{lb}}{\text{ft}}\end{array}$

Since, the weight is $32\text{lb}$, substitute $32\text{lb}$ for $w$ and $4\frac{\text{lb}}{\text{ft}}$ for $K$ in equation (1).

$\begin{array}{l}S=\frac{\left(32\text{lb}\right)}{\left(4\frac{\text{lb}}{\text{ft}}\right)}\\ S=32\text{lb}\left(\frac{\text{ft}}{\text{4lb}}\right)\\ S=8\text{ft}\end{array}$

Thus, if a mass weighing 10 pounds stretches a spring 2.5 feet, a mass weighing 32 pounds will stretch it $8$ feet.