Engineering Math

\begin{align*} \text{F} & =\text{G}\cdot \frac{\text{m}_1\text{m}_2}{\text{r}^2}\\ & =\left(\frac{\text{m}^3}{\text{kg}\cdot \text{s}^2}\right)\left(\frac{\text{kg}\cdot \text{kg}}{\text{m}^2}\right)\\ & =\frac{\text{kg}\cdot \text{m}}{\text{s}^2}\\ & =\text{N} \end{align*}

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*}

A rocket has a mass of 250(10³) slugs on earth. Specify (a) its mass in SI units and (b) its weight in SI units. If the rocket is on the moon, where the acceleration due to gravity is $g_m=5.30\:ft/s^2$ , determine to three significant figures (c) its weight in SI units and (d) its mass in SI units.

Solution:

a) $250\left(10^3\right)slugs=\left[250\left(10^3\right)\:slugs\right]\left(\frac{14.59\:kg}{1\:slug}\right)=3.6457\left(10^6\right)\:kg=3.65\:Gg$

b) $W_e=mg=\left[3.6475\left(10^6\right)kg\right]\left(9.81\:m/s^2\right)=35.792\left(10^6\right)kg\cdot m/s^2=35.8\:MN$

c) $W_m=mg_m=\left[250\left(10^3\right)slugs\right]\left(5.30\:ft/s^2\right)=\left[1.325\left(10^6\right)lb\right]\left(\frac{4.448\:N}{1\:lb}\right)=5.894\left(10^6\right)N=5.89\:MN$

d) $m_m=m_e=3.65\left(10^6\right)kg=3.65\:Gg$

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Showing How an Equation is Dimensionally Homogeneous

Using the SI system of units, show that Eq. 1–2 is a dimensionally homogeneous equation which gives F in newtons. Determine to three significant figures the gravitational force acting between two spheres that are touching each other. The mass of each sphere is 200 kg and the radius is 300 mm.

Problem 1-17| General Principles| Engineering Mechanics: Statics| RC Hibbeler

If an object has a mass of 40 slugs, determine its mass in kilograms.

Problem 1-16| General Principles| Engineering Mechanics: Statics| RC Hibbeler

What is the weight in newtons of an object that has a mass of: (a) 10 kg, (b) 0.5 g, and (c) 4.50 Mg? Express the result to three significant figures. Use an appropriate prefix.

Problem 1-15| General Principles| Engineering Mechanics: Statics| RC Hibbeler

Determine the mass of an object that has a weight of (a) 20 mN, (b) 150 kN, and (c) 60 MN. Express the answer to three significant figures.

Problem 1-14| General Principles| Engineering Mechanics: Statics| RC Hibbeler

Evaluate each of the following and express with an appropriate prefix: (a) (430 kg) ², (b) (0.002 mg)², and (c) (230 m)³.

Problem 1-13| General Principles| Engineering Mechanics: Statics| RC Hibbeler

Convert each of the following to three significant figures: (a) 20 lb·ft to N·m, (b) 450 lb/ft³ to kN/m³, and (c) 15 ft/h to mm/s.
Continue reading →

Problem 1-12| General Principles| Engineering Mechanics: Statics| RC Hibbeler

Convert each of the following and express the answer using an appropriate prefix: (a) 175 lb/ft³ to kN/m³, (b) 6 ft/h to mm/s, and (c) 835 lb·ft to kN·m. Continue reading →

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.

Problem 1-10| General Principles| Engineering Mechanics: Statics| RC Hibbeler

Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) (0.631 Mm)/(8.60kg)², (b) (35 mm)² (48 kg)³.

Solution:

Problem 1-9| General Principles| Engineering Mechanics: Statics| RC Hibbeler

Solution:

Using the SI system of units, show that Eq. 1–2 is a dimensionally homogeneous equation which gives F in newtons. Determine to three significant figures the gravitational force acting between two spheres that are touching each other. The mass of each sphere is 200 kg and the radius is 300 mm.

If an object has a mass of 40 slugs, determine its mass in kilograms.

What is the weight in newtons of an object that has a mass of: (a) 10 kg, (b) 0.5 g, and (c) 4.50 Mg? Express the result to three significant figures. Use an appropriate prefix.

Determine the mass of an object that has a weight of (a) 20 mN, (b) 150 kN, and (c) 60 MN. Express the answer to three significant figures.

Evaluate each of the following and express with an appropriate prefix: (a) (430 kg) ², (b) (0.002 mg)², and (c) (230 m)³.

Convert each of the following to three significant figures: (a) 20 lb·ft to N·m, (b) 450 lb/ft³ to kN/m³, and (c) 15 ft/h to mm/s. Continue reading →

Convert each of the following and express the answer using an appropriate prefix: (a) 175 lb/ft³ to kN/m³, (b) 6 ft/h to mm/s, and (c) 835 lb·ft to kN·m. Continue reading →

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.

Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) (0.631 Mm)/(8.60kg)², (b) (35 mm)² (48 kg)³.

Solution:

A rocket has a mass of 250(10³) slugs on earth. Specify (a) its mass in SI units and (b) its weight in SI units. If the rocket is on the moon, where the acceleration due to gravity is , determine to three significant figures (c) its weight in SI units and (d) its mass in SI units.

Solution:

Convert each of the following to three significant figures: (a) 20 lb·ft to N·m, (b) 450 lb/ft³ to kN/m³, and (c) 15 ft/h to mm/s.
Continue reading →