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\title{\vspace*{-1.5in}\textbf{\S6.6 Part II: Pressure}\\\normalsize (Created by Faan Tone Liu)}
\date{}
\author{}

\begin{document}

\maketitle
%\underline{Math 1300-400: Quiz 1}
\lhead{Math 2300-013: Calculus II}
\chead{Sept. 27, 2017}
\rhead{\S6.6 Part II: Pressure}
\vspace{-.5in}
\noindent
\textbf{Key Points:}
\begin{enumerate}[\qquad$\circ$]
\item $\text{Pressure} = P = \rho \cdot g \cdot d$
\begin{enumerate}[\quad$\bullet$]
\item $\rho = \text{mass density of fluid}$
\item $g = 9.8\frac{\text{m}}{\text{sec}^2}$
\item $d = \text{depth}$
\item Units: 
\end{enumerate}

\item $\text{Force} = \text{Pressure}\times \text{Area}$
\end{enumerate}


\noindent
\textbf{Examples:}\vskip12pt
\begin{enumerate}
\item A $3\text{m}\times 2 \text{m}$ piece of glass sits horizontally $8$m under water. What is the force on each side of the glass?\vskip2in

\item A $3\text{m}\times 2 \text{m}$ piece of glass sits underwater as shown with its top $1$m from the surface of the water. Find the force on each side of the glass.\\[12pt]
\begin{flushright}
\begin{tikzpicture}
\draw[style={decorate, decoration={snake}, draw=blue}] (0,0) -- (4,0);
\draw[|-|] (3.6,-.2) -- (3.6,-.6) node[right]{\small 1m}--(3.6,-1);
\draw (.3,-1.2)--(3.4,-1.2) -- (3.4, -3.2)--(.3,-3.2)--cycle;
\draw[|-|] (3.6,-1.2) -- (3.6,-2.2) node[right]{\small 2m}--(3.6,-3.2);
\draw[|-|] (.3,-3.4) -- (1.85,-3.4) node[below]{\small 3m}--(3.4,-3.4);
\end{tikzpicture}
\end{flushright}
\newpage

\item A round observation window behind the Millenium Hotel looks through a cement wall into boulder creek. What is the force on the window?\\[12pt]
\begin{tikzpicture}
\draw (0,0) -- (4,0)--(4,-3)--(0,-3)--cycle;
\draw[style={decorate, decoration={snake}, draw=blue}] (0,-.5)--(4,-.5);
\draw(2,-1.75) circle (.7);
\draw[|-|] (3,-1.05) -- (3,-1.75) node[right]{\small 1m}--(3,-2.45);
\draw[|-|] (-.2,-.5) -- (-.2,-.775) node[left]{\small 0.5m}--(-.2,-1.05);
\end{tikzpicture}
\vskip2.5in

\item The approximate dimensions of Hoover Dam are shown. Model it as a trapezoid, and calculate the force the water pressure puts on the dam.\\[12pt]
\begin{tikzpicture}
\draw (0,0)--(2,0) node[above]{260m}--(4,0)--(3,-3.5)--(2,-3.5) node[below]{160m}--(1,-3.5)--cycle;
\draw[|-|] (4.2,0) -- (4.2,-1.75) node[right]{\small 200m}--(4.2,-3.5);
\end{tikzpicture}
\end{enumerate}
\end{document}
