EML 3013C: DYNAMIC SYSTEMS I

Hwk 1: Solutions


1.4 Conversion from whole feet to meters

\begin{displaymath} 24[ft]=24[ft]\times\frac{0.3048[m]}{1[ft]}=7.32m \end{displaymath}

\begin{displaymath} 8[ft]=8[ft]\times\frac{0.3048[m]}{1[ft]}=2.44m \end{displaymath}


1.5 Conversion from whole feet and inches to meters

\begin{displaymath} 209[ft]1[in]=\left( 209+\frac{1}{12}\right) \left[ ft\right]... ...\right) \left[ ft\right] \times\frac{0.3048[m]}{1[ft]}=63.7[m] \end{displaymath}

\begin{displaymath} 199[ft]11[in]=\left( 199+\frac{11}{12}\right) \left[ ft\righ... ...\right) \left[ ft\right] \times\frac{0.3048[m]}{1[ft]}=60.9[m] \end{displaymath}

\begin{displaymath} 60[ft]6[in]=\left( 60+\frac{6}{12}\right) \left[ ft\right] =... ...\right) \left[ ft\right] \times\frac{0.3048[m]}{1[ft]}=18.4[m] \end{displaymath}


1.7 Conversion of units from Horsepower units to Watts

Use Table 1.2 and the definition of the horsepower to derive the conversion between Horsepower and Watts

\begin{displaymath} 1[hp]=550\frac{\left[ ft\right] .\left[ lb\right] }{\left[ s... ...right] \left[ m\right] }{\left[ s\right] }=746\left[ W\right] \end{displaymath}

therefore

(a)

\begin{displaymath} 12[hp]=12[hp]\times\frac{746\left[ W\right] }{1\left[ hp\right] }=8950\left[ W\right] \end{displaymath}

(b)

\begin{displaymath} 10^{5}[hp]=10^{5}[hp]\times\frac{746\left[ W\right] }{1\left[ hp\right] }=7.46\times10^{7}\left[ W\right] \end{displaymath}


1.21: Conversion from SI units to U.S. customary units

(a) In SI base units we have:

\begin{displaymath} D=C_{D}s\left( \frac{1}{2}\rho v^{2}\right) =\left[ m^{2}\ri... ...right] .\left[ m\right] /\left[ s^{2}\right] =\left[ N\right] \end{displaymath}

so D=800N. Express D in U.S. customary base units

\begin{displaymath} D=800\left[ N\right] =800\frac{\left[ kg\right] \left[ m\rig... ...ft[ ft\right] }{\left[ s^{2}\right] }=179.895\left[ lb\right] \end{displaymath}

(b) from part (a), 800N=179.895lb therefore

\begin{displaymath} 1\left[ N\right] =\frac{178.895}{800}\left[ lb\right] =0.2249\left[ lb\right] \end{displaymath}



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