\documentclass[11pt]{article}
\usepackage{graphicx}
\newif\iftechexplorer\techexplorerfalse
\setlength{\textheight}{9.5in}
\setlength{\topmargin}{-0.5in}
\setlength{\textwidth}{7in}
\setlength{\oddsidemargin}{-0.25in}
\title{Midterm $\alpha$, Physics 1P23/1P93}
\author{Prof.\ E.~Sternin}
\date{October 25, 2012}
\begin{document}
\pagestyle{headings}
\markright{Physics 1P23/1P93\hrulefill Midterm $\alpha$, October 25, 2012\hrulefill page~}
\maketitle 
\begin{center}
{\Large
\begin{tabular}{|r|c|}
\hline
Name	   & \hspace*{2.5in}	\\ \hline
Student ID &            	\\ \hline
\end{tabular}
}
\end{center}

No examination aids other than those specified on this examination script are permitted 
(FHB 5.1.2.A). Use or possession of unauthorized materials will automatically result
in the award of a zero grade for this examination.

\begin{center}
{\large\bf
	This is a closed--book test, only calculators are allowed \\
	Formulas not on the supplied formula sheet must be derived\\
	~ \\
	Attempt all questions}
\vspace{0.5in}

{\Large
\begin{tabular}{|c|c|c|}
\hline
Question & ~~Mark~~ & ~~Out of~~ \\
\hline \hline
1	& ~a~b~c~d~	& 2 \\ \hline
2	& ~a~b~c~d~	& 2 \\ \hline
3	& ~a~b~c~d~	& 2 \\ \hline
4	& ~a~b~c~d~	& 2 \\ \hline
5	& ~a~b~c~d~	& 2 \\ \hline\hline
6	&	& 10 \\ \hline 
7	&	& 10 \\ \hline 
Total	&	& 30 \\ \hline
\end{tabular}
}	% end \Large
\vspace{0.5in}

This exam contains \pageref{lastpage} pages. Please, verify that your copy is complete.
\end{center}
\newpage
{\it For questions 1--4: circle the correct answer {\bf on the cover page}.}

\begin{itemize}

\item[~(2)~{\bf 1}.]
A flask of water rests on a scale.  If you dip your finger into the water,
without touching the flask, the reading on the scale will
\begin{itemize}
\item[{\bf a.}] decrease.
\item[{\bf b.}] stay the same.
\item[{\bf c.}] increase.
\item[{\bf d.}] increase or decrease depending on the density of your finger.
\end{itemize}
%beta
%A large stone is resting on the bottom of the swimming pool.  The normal force of the bottom
%of the pool on the stone is equal in magnitude to the
%\begin{itemize}
%\item[{\bf a.}] weight of the water displaced by the stone.
%\item[{\bf b.}] weight of the stone.
%\item[{\bf c.}] difference between the weight of the stone and the weight of the displaced water.
%\item[{\bf d.}] sum of the weight of the stone and the weight of the displaced water.
%\end{itemize}

\item[~(2)~{\bf 2}.]
An industrial fabrication process stamps out thin metal pieces, each in the shape
of a square with a circular hole in the middle, from a large thin sheet.  These
pieces are mounted in a large machine.  As these pieces heat up during regular machine
operation, the diameter of the circular hole will
\begin{itemize}
\item[{\bf a.}] increase.
\item[{\bf b.}] stay the same.
\item[{\bf c.}] decrease.
\item[{\bf d.}] behave unpredictably causing the machine to malfunction.
\end{itemize}
%beta: scramble the answers

\item[~(2)~{\bf 3}.]
The Bernoulli effect is responsible for the lift force on an airplane wing.  Wings must
therefore be designed so that
\begin{itemize}
\item[{\bf a.}] air molecules are deflected downward when they hit the wing.
\item[{\bf b.}] air molecules move more rapidly past the upper surface of the wing than past the lower surface.
\item[{\bf c.}]  air molecules move more rapidly past the lower surface of the wing than past the upper surface.
\item[{\bf d.}] wings are thick enough to create a significant pressure difference between the top and bottom surfaces of the wings because of the different heights of the air columns above them.
\end{itemize}
%beta
%You are driving a convertible with its soft ragtop roof up and the windows closed, at the
%100~km/h speed limit.  You observe that the roof
%\begin{itemize}
%\item[{\bf a.}] bows inward.
%\item[{\bf b.}] is not changed from when the car was at rest.
%\item[{\bf c.}] bows outward.
%\item[{\bf d.}] impossible to tell without knowing the atmospheric pressure.
%\end{itemize}

\item[~(2)~{\bf 4}.]
An ideal gas is confined to a container with adjustable volume.  The number of moles
and temperature are constant.  By what factor will the pressure change when volume doubles?
\begin{itemize}
\item[{\bf a.}] $\frac{1}{4}$
\item[{\bf b.}] $\frac{1}{2}$
\item[{\bf c.}] 2
\item[{\bf d.}] 4
\end{itemize}
% beta
%When the translational speed of molecules in an ideal gas triples,
%by what factor does its absolute temperature change?
%\begin{itemize}
%\item[{\bf a.}] $\frac{1}{9}$
%\item[{\bf b.}] $\frac{1}{3}$
%\item[{\bf c.}] 3
%\item[{\bf d.}] 9
%\end{itemize}

\item[~(2)~{\bf 5}.]
Object 1 has four times the specific heat capacity and three times the mass of Object 2.
The two objects are given the same amount of heat.
If the temperature of Object 1 changes by an amount $\Delta T_{1}$, then
the change in temperature of Object 2 is:
\begin{itemize}
\item[{\bf a.}] $\Delta T_{2} = \frac{1}{12} \> \Delta T_{1}$
\item[{\bf b.}] $\Delta T_{2} = \frac{3}{4}  \> \Delta T_{1}$
\item[{\bf c.}] $\Delta T_{2} = \frac{4}{3}  \> \Delta T_{1}$
\item[{\bf d.}] $\Delta T_{2} = 12  \> \Delta T_{1}$
\end{itemize}
% beta: change numbers, scramble answers
%Object 1 has three times the specific heat capacity and twice the mass of Object 2.
%The two objects are given the same amount of heat.
%If the temperature of Object 1 changes by an amount $\Delta T_{1}$, then
%the change in temperature of Object 2 is:
%\begin{itemize}
%\item[{\bf a.}] $\Delta T_{2} = 6  \> \Delta T_{1}$
%\item[{\bf b.}] $\Delta T_{2} = \frac{3}{2}  \> \Delta T_{1}$
%\item[{\bf c.}] $\Delta T_{2} = \frac{2}{3}  \> \Delta T_{1}$
%\item[{\bf d.}] $\Delta T_{2} = \frac{1}{6} \> \Delta T_{1}$
%\end{itemize}

\vfill
\newpage

\item[(10)~{\bf 6}.]
Motor oil, with a viscosity of 0.250~Ns/m$^2$, is flowing through a tube
that has a radius of 3.00~mm and is 1.00~m long.  The difference in pressure
between the two ends of the tube is 300~kPa.
How long does it take to fill a 1-gal (1~gal=3.79~l) container with oil?
%beta
%Suppose an occlusion in an artery reduces its diameter by 15\%, but the volume
%flow rate in the artery remains the same.  By what factor has the pressure drop
%across the length of this artery increased?

\vspace*{3.25in}

\item[(10)~{\bf 7}.]
An aluminum rod is 10.0~cm long and a steel rod is 80.0~cm long when both rods are at a
temperature of $15^\circ$C.  Both rods have the same diameter.  The rods are joined
end-to-end to form a rod 90.0~cm long.  The coefficients of linear expansion of aluminum
and steel are $\alpha_{\rm Al} = 2.4\times 10^{-5}\mbox{ K}^{-1}$ and
$\alpha_{\rm steel}=1.2\times 10^{-5}\mbox{ K}^{-1}$,
respectively.  As the temperature is raised to $90^\circ$C, what is the increase
in the length of the joined rod, in mm? What is the effective coefficient of
linear expansion, $\alpha_{\rm eff}$ of this combination rod?
%beta
%Two metal rods, one silver and the other gold, are attached to each other.
%The free end of the silver rod is connected to a steam chamber, with a temperature
%of $100^\circ$C, and the free end of the gold rod to an ice water bath,
%with a temperature of $0^\circ$C.  The rods are 5.0~cm long, and have a
%square cross-section, 2.0~cm on a side.   What is the temperature at the point
%where the two rods are in contact with one another?  The thermal conductivity
%of silver is $k_{Ag} =417\>$W/(m$\cdot$K), and that of gold is $k_{Au} = 291\>$W/(m$\cdot$K).
%No heat is exchanged between the rods and the surroundings, except at the ends.

\end{itemize}
\label{lastpage}
\end{document}

%save for the final:
%Which of the following temperature-reservoir relationships would yield the highest efficiency for a Carnot engine?
%\begin{itemize}
%\item[{\bf a.}] $T_C=0.15\>T_H$
%\item[{\bf b.}] $T_C=0.25\>T_H$
%\item[{\bf c.}] $T_C=0.50\>T_H$
%\item[{\bf d.}] $T_C=0.90\>T_H$
%\end{itemize}
%beta
%For a cyclic heat engine,
%\begin{itemize}
%\item[{\bf a.}] $\varepsilon > 1$
%\item[{\bf b.}] $Q_H = W_{\mbox{net}}$
%\item[{\bf c.}] $\Delta U = W_{\mbox{net}}$
%\item[{\bf d.}] $Q_H > Q_C$
%\end{itemize}

%A monatomic ideal gas is compressed isothermically to one-third of its initial
%volume.  The resulting pressure will be
%\begin{itemize}
%\item[{\bf a.}] three times as large as its initial value.
%\item[{\bf b.}] equal to its initial value.
%\item[{\bf c.}] one-third as large as its initial value.
%\item[{\bf d.}] impossible to predict on the basis of this data.
%\end{itemize}

