Answer
$18.75 inlb$
Work Step by Step
Hooke's Law states that $F=k x$
or, $x=\dfrac{F}{k}=\dfrac{150}{\dfrac{1}{16}}=2400$ m
This implies that $ F=2400 x$
and $F(\dfrac{1}{8})=(2400)(\dfrac{1}{8})=300$
Use formula: $\int x^n=\dfrac{x^{n+1}}{n+1}+C$ and the work done can be found for the limits for $x$ first inch, that is, $0$ to $\dfrac{1}{8}$ as follows:
This implies that
$W=2400 \int_0^{1/8} (x) dx=(2400)[ \dfrac{x^2}{2}]_0^{1/8}$
Thus, $W=1200[ (\dfrac{1}{8})^2-0] =18.75 inlb$
