Represent each of the following combinations of units in the correct SI form: (a) GN∙µm, (b) kg/µm, (c) N/ks2, and (d) KN/µs.
Statics of Rigid Bodies 14th Edition by RC Hibbeler, Problem 1-10
Solution:
Part A
\begin{align*}
\text{GN} \cdot \mu \text{m} & = \left( 10^9 \ \text{N} \right)\left( 10^{-6} \ \text{m} \right)\\
& = 10^3 \ \text{N} \cdot \text{m}\\
& = \text{kN} \cdot \text{m}
\end{align*}Part B
\begin{align*}
\text{kg/}\mu\text{m} & = \frac{10^3 \ \text{g}}{10^{-6} \ \text{m}} \\
& = 10^9 \ \frac{\text{g}}{\text{m}} \\
& = \text{Gg/m}
\end{align*}Part C
\begin{align*}
\text{N/ks}^2 & = \frac{\text{N}}{\left( 10^3 \ \text{s} \right)^2}\\
& = \frac{\text{N}}{10^6 \ \text{s}^2} \\
& = 10^{-6} \ \frac{\text{N}}{\text{s}^2} \\
& = \mu \text{N}/\text{s}^2
\end{align*}Part D
\begin{align*}
\text{kN}/ \mu\text{s} & = \frac{10^3 \ \text{N}}{10^{-6} \ \text{s}} \\
& = 10^9 \ \frac{\text{N}}{\text{s}}\\
& = \text{GN/s}
\end{align*}
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