Answer
$ W = 8.33 \ lbf.ft$
$ W = 0.0107 \ BTU$
Work Step by Step
Since $W = \int Fdx $ and the force expression is given by $F = F_{0} + kx$, we have:
$W = \int_{0 \ in}^{1\ in}(F_{0} + kx )dx$
With $F_{0} = 0\ lbf$:
$W = \frac{k}{2}x^{2}|_{0\ in}^{1 \ in}$
With $ k = 200 \frac{lbf}{in}$
$W = 100 \ lbf.in$
With conversions:
$ W = 100 \ lbf.in \times \frac{1\ ft}{12\ in} = 8.33 \ lbf.ft$
$ W = 100 \ lbf.in \times \frac{1\ BTU}{9338.03\ lbf.in} = 0.0107 \ BTU$
