Answer
$20\; pounds$.
Work Step by Step
Step 1:- Translate the statement to form an equation.
Let the distance that a spring will stretch is $D$
and the force applied to the spring is $F$.
Since $D$ varies directly with $F$, we have:
$\Rightarrow D=kF$ ...... (1)
Step 2:- Substitute the first set of values into the equation (1) to find the value of $k$.
The given values are $F=12\; pounds$ and $D=9\; inches$.
Substitute into the equation (1).
$\Rightarrow 9=k(12)$
Divide both sides by $12$.
$\Rightarrow \frac{9}{12}=\frac{12k}{12}$
Simplify.
$\Rightarrow \frac{3}{4}=k$
Step 3:- Substitute the value of $k$ into the original equation.
Substitute $k=\frac{3}{4}$ into the equation (1).
$\Rightarrow D=\frac{3}{4}F$ ...... (2)
Step 4:- Solve the equation to find the required value.
Substitute $D=15\;inches$ into the equation (2).
$\Rightarrow 15=\frac{3}{4}F$
Multiply both sides by $\frac{4}{3}$ to isolate $F$.
$\Rightarrow \frac{4}{3}\cdot 15=\frac{4}{3}\cdot \frac{3}{4}F$
Simplify.
$\Rightarrow20=F$
Hence, the required force is $20\; pounds$.
