Author Archives: Engineering Math

Expressing units to correct SI form using appropriate prefix

Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) m/ms, (b) μkm, (c) ks/mg, and (d) km·μN.

Statics of Rigid Bodies 14th Edition by RC Hibbeler, Problem 1-9

Solution:

Part A

\displaystyle \text{m/ms}=\left(\frac{\text{m}}{10^{-3}\:\text{s}}\right)=10^3\:\text{m/s}=\:\text{km/s}

Part B

\displaystyle \mu \text{km}=10^{-6}\cdot 10^3\:\text{m}=10^{-3}\:\text{m}=\text{mm}

Part C

\displaystyle \text{ks/mg}=\frac{10^3\:s}{10^{-6}\:\text{kg}}=10^9\:\frac{\text{s}}{\text{kg}}=\text{Gs/kg}

Part D

\displaystyle \text{km} \cdot \mu \text{N}=10^3\:\text{m}\cdot 10^{-6}\:\text{N}\:=10^{-3}\:\text{m}\cdot \text{N}=\text{mm}\cdot \text{N}

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

Rounding off to 3 significant figures

Round off the following numbers to three significant figures: (a) 58 342 m, (b) 68.534 s, (c) 2553 N, and (d) 7555 kg.

Statics of Rigid Bodies 14th Edition by RC Hibbeler, Problem 1-6

Solution:

Part A

\begin{align*}
58 \ 342 \ \text{m} & = 58.342\times 10^{3} \ \text{m}\\
& = 58.342 \ \text{km}\\
& = 58.3 \ \text{km}
\end{align*}

Part B

\begin{align*}
68.534 \ \text{s} & = 68.5 \ \text{s}
\end{align*}

Part C

\begin{align*}
2553 \ \text{N} & = 2.553 \ \text{kN}\\
& = 2.55 \ \text{kN}
\end{align*}

Part D

\begin{align*}
7555 \ \text{kg} & = 7.555\times 10^3 \ \text{kg}\\
& = 7.555 \times 10^3 \times 10^3 \ \text{g}\\
& = 7.555 \times 10^6 \ \text{g} \\
& = 7.555 \ \text{Mg}\\
& = 7.56 \ \text{Mg}
\end{align*}