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Hibbeler Statics 14E P1.3 — Representing a combination of units in the correct SI form


Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) Mg/ms, (b) N/mm, and (c) mN/(kgµs).

Statics of Rigid Bodies 14th Edition by RC Hibbeler, Problem 1-3


Solution:

Part A

\begin{align*}
\text{Mg/ms} & = \frac{10^3 \ \text{kg}}{10^{-3} \ \text{s}} \\
& = 10^6 \text{kg/s}\\
& = \text{Gg/s}
\end{align*}

Part B

\begin{align*}
\text{N/mm} & = \frac{1\ \text{N}}{10^{-3} \ \text{m}}\\
& = 10^3 \ \text{N/m}\\
& = \text{kN/m}
\end{align*}

Part C

\begin{align*}
\frac{\text{mN}}{\left( \text{kg} \cdot \mu \text{s} \right)} & = \frac{10^{-3} \ \text{N}}{10^{-6} \ \text{kg} \cdot \text{s}}\\
& =10^3 \ \text{N}/\left( \text{kg} \cdot \text{s} \right)\\
& = \text{kN}/\left( \text{kg} \cdot  \text{s}\right)
\end{align*}

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Expressing units in the correct SI form using an appropriate prefix


Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) kN/μs, (b) Mg/mN, and (c) MN/(kg•ms).

Statics of Rigid Bodies 14th Edition by RC Hibbeler, Problem 1-2


Solution:

Part A

\begin{align*}
\text{KN}/\mu\text{s} & = \frac{\left( 10 \right)^3\ \text{N}}{\left( 10 \right)^{-6}\ \text{s}} \\
& =\left( 10 \right)^9 \ \text{N/s}\\
& = \text{GN/s}
\end{align*}

Part B

\begin{align*}
\text{Mg/mN} & =\frac{\left(10^6\right)\text{g}}{\left(10^{-3}\right)\text{N}}\\
& = 10^9\:\text{g/N}\\
& =\text{Gg/N}
\end{align*}

Part C

\begin{align*}
\text{MN}/\left(\text{kg}\cdot \text{ms}\right) & =\frac{10^6\:\text{N}}{\text{kg}\cdot \left(10^{-3}\right)\text{s}}\\
& =10^9\:\frac{\text{N}}{\text{kg}\cdot \text{s}}\\
& =\text{GN}/\left(\text{kg}\cdot \text{s}\right)
\end{align*}

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