Tag Archives: combinations of SI units

Hibbeler Statics 14E P1.12 — Evaluation of Expression to Three Significant Figures with Appropriate SI Units

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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Hibbeler Statics 14E P1.8 — Representing Combinations of Units in the Correct SI Form using Appropriate Prefix

Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) Mg/mm, (b) mN/μs, (c) μm∙Mg.

Statics of Rigid Bodies 14th Edition by RC Hibbeler, Problem 1-8

Solution:

Part A

\begin{align*}
\text{Mg/mm} & = \frac{10^6 \ \text{g}}{10^{-3} \ \text{m}} \\
& = 10^9 \ \frac{\text{g}}{\text{m}}\\
& = \text{Gg/m}
\end{align*}

Part B

\begin{align*}
\text{mN/} \mu \text{s} & = \frac{10^{-3} \ \text{N}}{10^{-6} \ \text{s}} \\
& = 10^3 \ \frac{\text{N}}{\text{s}} \\
& = \text{kN/s}
\end{align*}

Part C

\begin{align*}
\mu \text{m}\cdot \text{Mg} & = \left( 10^{-6} \ \text{m} \right)\left( 10^6 \ \text{g} \right) \\
& = \text{m}\cdot \text{g}\\
\text{This can also be written as:} \\
& = \text{mm} \cdot \text{kg}
\end{align*}
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Representing combinations of units in correct SI Form

Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) 0.000431 kg, (b) 35.3(10³) N, and (c) 0.00532 km.

Statics of Rigid Bodies 14th Edition by RC Hibbeler, Problem 1-7

Solution:

Part A

\begin{align*}
0.000 \ 431 \ \text{kg} & = 0.431 \times 10^{-3} \ \text{kg}\\
& = 0.431\times 10^{-3} \times 10^3 \ \text{g} \\
& = 0.431 \ \text{g}
\end{align*}

Part B

\begin{align*}
35.3\left( 10^3 \right) \ \text{N} & = 35.3 \ \text{kN}
\end{align*}

Part C

\begin{align*}
0.00532 \ \text{km} & = 0.00532 \times 10^3 \ \text{m} \\
& = 5.32 \times 10^{-3} \times 10^3 \ \text{m} \\
& = 5.32 \ \text{m}
\end{align*}