Tag Archives: statics

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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Problem 1.2 – Expressing density to SI units

Wood has a density of 4.70 slug/ft3. What is its density expressed in SI units?

Solution:

\displaystyle 4.70\:\text{slug/ft}^3\times \left[\frac{\left(1\:\text{ft}^3\right)\left(14.59\:\text{kg}\right)}{\left(0.3048\:\text{m}\right)^3\:\left(1\:\text{slug}\right)}\right]=2.42\:\text{Mg/m}^3