Answer
$18.75$ in-lb
Work Step by Step
We know that Hooke's Law states that $F=k x$
Then, $x=\dfrac{F}{k}=\dfrac{150}{1/16}=2400$ m
Thus, $F=2400 x \implies F(1/8)=2400 \times (1/8)=300$lb
To calculate the work done, the limits for $x$ will be from $0$ to $1/8$ such that:
$W=\int_0^{1/8} 2400 x=2400[ \dfrac{x^2}{2}]_0^{1/8}$
or, $W=1200[ (1/8)^2-0] =18.75$ in-lb
