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)
b)
Tag Archives: Statics of Rigid Bodies
![\left(35\:mm\right)^2\left(48\:kg\right)^3=\left[35\left(10^{-3}\right)m\right]^2\left(48\:kg\right)^3=135\:m^2\cdot kg^3](https://s0.wp.com/latex.php?latex=%5Cleft%2835%5C%3Amm%5Cright%29%5E2%5Cleft%2848%5C%3Akg%5Cright%29%5E3%3D%5Cleft%5B35%5Cleft%2810%5E%7B-3%7D%5Cright%29m%5Cright%5D%5E2%5Cleft%2848%5C%3Akg%5Cright%29%5E3%3D135%5C%3Am%5E2%5Ccdot+kg%5E3&bg=ffffff&fg=000000&s=1&c=20201002)
Problem 1-8| General Principles| Engineering Mechanics: Statics| RC Hibbeler
The specific weight (wt./vol.) of brass is 520 lb/ft³. Determine its density (mass/vol.) in SI units. Use an appropriate prefix.
Solution:
First, we will convert 1 Pa to lb/ft².
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 13th Edition by RC Hibbeler, Problem 1-7
Engineering Mechanics: Statics 14th 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
Part B
Part C
Part D
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](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+4.70%5C%3A%5Ctext%7Bslug%2Fft%7D%5E3%5Ctimes+%5Cleft%5B%5Cfrac%7B%5Cleft%281%5C%3A%5Ctext%7Bft%7D%5E3%5Cright%29%5Cleft%2814.59%5C%3A%5Ctext%7Bkg%7D%5Cright%29%7D%7B%5Cleft%280.3048%5C%3A%5Ctext%7Bm%7D%5Cright%29%5E3%5C%3A%5Cleft%281%5C%3A%5Ctext%7Bslug%7D%5Cright%29%7D%5Cright%5D%3D2.42%5C%3A%5Ctext%7BMg%2Fm%7D%5E3&bg=ffffff&fg=000000&s=1&c=20201002)
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