Answer
(a) $S = 0.00055$
$12.018 \space m$
(b) $234.375 \space kg/m^3$
Work Step by Step
(a)
1. Find $S$, if $w = 250$:
$$S = \frac{0.032(250) - 2.5}{10000} = \frac{8 - 2.5}{10000} = \frac{5.5}{10000} = 0.00055$$
2. Calculate the length that disappears due to shrinkage:
$$L_{d} = 12.025 \space m \times 0.00055 \approx 0.006614 \space m$$
3. Find the actual length.
$$L = 12.025 \space m- 0.006614 \space m = 12.018 \space m$$
(b)
1. Find $w$, if $S = 0.00050$
$$0.00050 = \frac{0.032w - 2.5}{ 10000}$$ $$(10000)(0.00050) = 0.032w - 2.5$$ $$5 = 0.032w - 2.5$$ $$5 + 2.5 = 0.032w$$ $$7.5 = 0.032 w$$ $$\frac{7.5}{0.032} = w$$ $$w = 234.375$$
