Tag Archives: statics and dynamics free books

The force of gravity acting between two particles

Two particles have a mass of 8 kg and 12 kg, respectively. If they are 800 mm apart, determine the force of gravity acting between them. Compare this result with the weight of each particle.

_{Engineering Mechanics: Statics 13th Edition by RC Hibbeler, Problem 1-20}
_{Engineering Mechanics: Statics 14th Edition by RC Hibbeler, Problem 1-21}

Solution:

The force of gravity acting between them:

\begin{align*} \textbf{F} & =\textbf{G}\cdot \frac{\text{m}_1\text{m}_2}{\text{r}^2}\\ & =66.73\left(10^{-12}\right) \text{m}^3/ \left( \text{kg} \cdot \text{s}^2 \right) \left[\frac{8 \ \text{kg} \left(12\ \text{kg}\right)}{\left(0.8\ \text{m} \right)^2}\right]\\ &=10\left(10^{-9}\right)\ \text{N}\\ & =10.0 \ \text{nN}\\ \end{align*}

The weight of the 8 kg particle

\textbf{W}_1=8\left(9.81\right)=78.5\:\text{N}

Weight of the 12 kg particle

\textbf{W}_2=12\left(9.81\right)=118\:\text{N}

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Expressing the Density of Water in SI Units

Water has a density of 1.94 slug/ft³. What is the density expressed in SI units? Express the answer to three significant figures.

_{Engineering Mechanics: Statics 13^th Edition by RC Hibbeler, Problem 1-19}
_{Engineering Mechanics: Statics 14^th Edition by RC Hibbeler, Problem 1-17}

Solution:

\begin{align*} \rho _w & =\left(\frac{1.94\:\text{slug}}{1\:\text{ft}^3}\right)\left(\frac{14.59\:\text{kg}}{1\:\text{slug}}\right)\left(\frac{1\:\text{ft}^3}{0.3048^3\:\text{m}^3}\right) \\ & =\left(\frac{1.94\:\text{slug}}{1\:\text{ft}^3}\right)\left(\frac{14.59\:\text{kg}}{1\:\text{slug}}\right)\left(\frac{1\:\text{ft}^3}{0.3048^3\:\text{m}^3}\right) \\ & =999.6\:\frac{\text{kg}}{\text{m}^3}\\ & =1.00\:\text{Mg/m}^3\\ \end{align*}

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Evaluation of Expressions to SI Units with Appropriate Prefix

Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) 354 mg (45 km)/(0.0356 kN), (b) (0.00453 Mg)(201 ms), and (c) 435 MN/23.2 mm.

_{Engineering Mechanics: Statics 13^th Edition by RC Hibbeler, Problem 1-11}
_{Engineering Mechanics: Statics 14^th Edition by RC Hibbeler, Problem 1-18}

Solution:

Part A

\begin{align*} \frac{\left(354\:\text{mg}\right)\left(45\:\text{km}\right)}{0.0356\:\text{kN}} & = \frac{\left[354\left(10^{-3}\right)\:\text{g}\right]\left[45\left(10^3\right)\:\text{m}\right]}{0.0356\:\left(10^3\right)\:\text{N}}\\ & = \frac{0.447\:\left(10^3\right)\text{g}\cdot \text{m}}{\text{N}}\\ & = 0.447\:\text{kg}\cdot \text{m/N} \end{align*}

Part B

\begin{align*} \left(0.00453\:\text{Mg}\right)\left(201\:\text{ms}\right) & =\left[4.53\left(10^{-3}\right)\left(10^3\right)\text{kg}\right]\left[201\:\left(10^{-3}\right)\text{s}\right]\\ & =0.911\:\text{kg}\cdot \text{s}\\ \end{align*}

Part C

\begin{align*} 435\:\text{MN}/23.2\:\text{mm} & =\frac{435\:\left(10^6\right)\:\text{N}}{23.2\:\left(10^{-3}\right)\:\text{m}}\\ & = \frac{18.75\left(10^9\right)\:\text{N}}{\text{m}}\\ & =18.8\:\text{GN/m} \end{align*}

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Converting Measurement from Pounds Per Square Inch to Pascal

The pascal (Pa) is actually a very small unit of pressure. To show this, convert 1 Pa = 1N/m² to lb/ft². Atmospheric pressure at sea level is 14.7 lb/in². How many pascals is this?

_{Engineering Mechanics: Statics 13^th Edition by RC Hibbeler, Problem 1-7}
_{Engineering Mechanics: Statics 14^th Edition by RC Hibbeler, Problem 1-16}

Solution:

First, we will convert 1 Pa to lb/ft².

\begin{align*} 1\ \text{Pa} & =\frac{1\:\text{N}}{\text{m}^2}\left(\frac{1\:\text{lb}}{4.4482\:\text{N}}\right)\left(\frac{0.3048^2\:\text{m}^2}{1\:\text{ft}^2}\right)\\ &=20.9\left(10^{-3}\right)\:\text{lb/ft}^2 \end{align*}

Next, we convert 14.7 lb/in² to Pa

\begin{align*} 14.7 \ \text{lb/in}^2 & =\frac{14.7\:\text{lb}}{\text{in}^2}\left(\frac{4.448\:\text{N}}{1\:\text{lb}}\right)\left(\frac{144\:\text{in}^2}{1\:\text{ft}^2}\right)\left(\frac{1\:\text{ft}^2}{0.3048^2\:\text{m}^2}\right)\\ & =101.3\left(10^3\right)\:\text{N/m}^2\\ & =101.3\left(10^3\right) \text{Pa}\\ \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*}

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 14^th 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:

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

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Tag Archives: statics and dynamics free books

The force of gravity acting between two particles

Two particles have a mass of 8 kg and 12 kg, respectively. If they are 800 mm apart, determine the force of gravity acting between them. Compare this result with the weight of each particle.

Expressing the Density of Water in SI Units

Water has a density of 1.94 slug/ft³. What is the density expressed in SI units? Express the answer to three significant figures.

Evaluation of Expressions to SI Units with Appropriate Prefix

Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) 354 mg (45 km)/(0.0356 kN), (b) (0.00453 Mg)(201 ms), and (c) 435 MN/23.2 mm.

Converting Measurement from Pounds Per Square Inch to Pascal

The pascal (Pa) is actually a very small unit of pressure. To show this, convert 1 Pa = 1N/m² to lb/ft². Atmospheric pressure at sea level is 14.7 lb/in². How many pascals is this?

Solution:

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.

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.