Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) (684 µm)/(43 ms), (b) (28 ms)(0.0458 Mm)/(348 mg), (c) (2.68 mm)(426 Mg).
Statics of Rigid Bodies 14th Edition by RC Hibbeler, Problem 1-12
Solution:
Part A
\begin{align*}
\left( 684 \ \mu\text{m} \right)/43 \ \text{ms} & =\frac{684\times 10^{-6} \ \text{m}}{43\times 10^{-3} \ \text{s}}\\
& = \frac{15.9\times 10^{-3}\ \text{m}}{\text{s}}\\
& = 15.9 \ \text{mm/s}
\end{align*}Part B
\begin{align*}
\left( 28 \ \text{ms} \right)\left( 0.0458 \ \text{Mm} \right)/\left( 348 \ \text{mg} \right) & = \frac{\left[ 28\times 10^{-3} \ \text{s} \right]\left[ 45.8\times 10^{-3}\times 10^6 \ \text{m} \right]}{348\times 10^{-3}\times 10^{-3} \ \text{kg}} \\
& = \frac{3.69\times 10^6 \ \text{m}\cdot \text{s}}{\text{kg}}\\
& = 3.69 \ \text{Mm}\cdot \text{s}/\text{kg}\\
\end{align*}Part C
\begin{align*}
\left( 2.68 \ \text{mm} \right)\left( 426 \ \text{Mg} \right) & = \left[ 2.68\times 10^{-3} \ \text{m} \right]\left[ 426\times 10^3 \ \text{kg} \right]\\
& = 1.14\times 10^3 \ \text{m}\cdot \text{kg}\\
& = 1.14 \ \text{km}\cdot \text{kg}\\
\end{align*}
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