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\fbox{THIS EXAMINATION WILL NOT BE DEPOSITED IN THE LIBRARY RESERVE}

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{\huge Brock University}

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{\large
\begin{tabular}{lcl} 
{\bf Final Examination} &\hspace*{0.3in}& {\bf Number of pages:} \pageref{lastpage}\\
{\bf Course:} Physics 1P23/1P93			& & {\bf Number of Students:} 125 \\
{\bf Date of Examination:} December 12, 2012	& & {\bf Number of hours:} 3 \\
{\bf Time of Examination:} 09:00--12:00 & & {\bf Instructor:} E.~Sternin
\end{tabular}
}

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{\large
\begin{tabular}{|r|c|}
\hline
Name	   & \hspace*{2.5in}	\\ \hline
Student ID &            	\\ \hline
\end{tabular}
}
\end{center}

{\small
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}
{\bf
	This is a closed--book test, only calculators are allowed \\
	Formulas not on the separately supplied formula sheet must be derived\\
	~ \\
	For the multiple-choice questions 1--10 circle one of a--e \underline{on the front page}
}
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{\large
\begin{tabular}{|cc|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
Bonus	& 		&	& 3 \\ \hline
6	& ~a~b~c~d~e~	&	& 2 \\ \hline
7	& ~a~b~c~d~e~	&	& 2 \\ \hline
8	& ~a~b~c~d~e~	&	& 2 \\ \hline
9	& ~a~b~c~d~e~	&	& 2 \\ \hline
10	& ~a~b~c~d~e~	&	& 2 \\ \hline \hline
11	&		&	& 10 \\ \hline
12	&		&	& 10 \\ \hline
13	&		&	& 10 \\ \hline
14	&		&	& 10 \\ \hline
15	&		&	& 10 \\ \hline
16	&		&	& 10 \\ \hline
17	&		&	& 10 \\ \hline
18	&		&	& 10 \\ \hline \hline
Total	&		&	& 103 \\ \hline
\end{tabular}
}	% end \large
\vspace{0.15in}

This exam contains \pageref{lastpage} pages, plus a separate formula sheet. 
Please, verify that your copy is complete.
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\markright{Physics 1P23/1P93\hrulefill Final Exam, December 12, 2012\hrulefill page~}

\begin{itemize}

\item[(2)~{\bf ~1}.]
Which of the following statements is true?
\begin{enumerate}
\addtolength{\itemsep}{-3pt}
\item[{\bf a}.]
Water flows through a pipe with varying width. More water flows per second through the wide section of the pipe than through the narrow one.
\item[{\bf b}.]
If you increase the pressure on the surface of the water, you will increase the buoyant force on objects submerged in that water. 
\item[{\bf c}.]
If a uniform sphere is compressed to half of its original diameter, its mass remains the same but its density becomes eight times as great.
\item[{\bf d}.]
According to Pascal's principle, if you increase the pressure enough so that the force at one end of an oil-filled tube increases by 10~N, 
the force will increase at all points in the tube by 10~N.
\end{enumerate}

\item[(2)~{\bf ~2}.]
A harmonic wave is described by the equation
$
  y(x,t)=(6.00\mbox{ mm}) \times \cos\left[ (3.25\mbox{ m}^{-1})\> x - (7.22\mbox{ s}^{-1})\> t \right] 
$
What is the wavelength of the wave?
\begin{itemize}
\addtolength{\itemsep}{-3pt}
\item[{\bf a}.] 1.93 m
\item[{\bf b}.] 0.870 m
\item[{\bf c}.] 0.380 m
\item[{\bf d}.] 0.139 m
\end{itemize}

\item[(2)~{\bf ~3}.]
Phase equilibrium between the gaseous and liquid states describes the situation when
\begin{itemize}
\item[{\bf a.}] no more molecules leave the liquid and enter the gas.
\item[{\bf b.}] no more molecules leave the gas and enter the liquid.
\item[{\bf c.}] as many molecules go from liquid to gas as from gas to liquid.
\item[{\bf d.}] the liquid is boiling.
\end{itemize}

\item[(2)~{\bf ~4}.]
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}

\item[(2)~{\bf ~5}.]
A submarine rests on the sea bottom.  The normal force exerted
on the sub by the sea-floor is equal to:
\begin{itemize}
\addtolength{\itemsep}{-3pt}
\item[{\bf a.}] the weight of the sub
\item[{\bf b.}] the weight of the displaced water
\item[{\bf c.}] the weight of the sub less the weight of the displaced water
\item[{\bf d.}] the buoyant force
\end{itemize}

\item[(3)~{\bf Bonus}.]
You know that $\sin(2\alpha) = $\underline{\hspace{1.5in}} and 
$\cos(2\alpha) = $\underline{\hspace{2in}}. Given that
$(\alpha+\beta)$ is an expression symmetric with respect to interchanging 
$\alpha$ and $\beta$, write down the expressions for the following trigonometric identities:
\begin{enumerate}
%\addtolength{\itemsep}{-3pt}
\item[{\bf a}.] 
$\sin(\alpha\pm\beta) = $\underline{\hspace{4in}}
\item[{\bf b}.]
$\cos(\alpha\pm\beta) = $\underline{\hspace{4in}}, and then
\item[{\bf c}.] 
simplify
$$\frac{\sin(\alpha+\beta)+\sin(\alpha-\beta)}{\cos(\alpha+\beta)+\cos(\alpha-\beta)} = \mbox{\hspace{5in}}$$
\end{enumerate}
\vfill
\newpage

\item[(2)~{\bf ~6}.]
Bar~1 has a Young's modulus that is bigger than that of Bar~2. This indicates that Bar~1
\begin{itemize}
\addtolength{\itemsep}{-3pt}
\item[{\bf a}.]
is longer than Bar~2.
\item[{\bf b}.]
has a greater cross-sectional area than Bar~2.
\item[{\bf c}.]
has a greater elastic limit than Bar~2.
\item[{\bf d}.]
is made of a material different from that of Bar~2.
\item[{\bf e}.]
will require a greater force to stretch than Bar~2.
\end{itemize}

\item[(2)~{\bf ~7}.]
When you get out of a swimming pool and stand dripping wet in a light breeze,
you feel much colder than you feel after you dry out.  This is primarily
\begin{itemize}
\addtolength{\itemsep}{-3pt}
\item[{\bf a}.]
because the moisture on your skin has good thermal conductivity.
\item[{\bf b}.]
a purely psychological effect resulting from the way the sensory nerves in the
skin are stimulated.
\item[{\bf c}.]
because the water on your skin has a relatively large heat capacity.
\item[{\bf d}.]
because 539 calories of heat are required to evaporate each gram of water from your
skin, and most of this heat flows out of your body.
\item[{\bf e}.]
because the air humidity near the pool is high.
\end{itemize}


\item[(2)~{\bf ~8}.]
Light travels from water (with index of refraction 1.33) 
into air (index of refraction 1.00).
Which of the following statements about this light is true?
\begin{enumerate}
\addtolength{\itemsep}{-3pt}
\item[{\bf a}.]
The light travels faster in the air than in the water.
\item[{\bf b}.]
The light has the same wavelength in the air as it does in the water.
\item[{\bf c}.]
The light has the same speed in the air as in the water.
\item[{\bf d}.]
The wavelength of the light in the water is greater than the wavelength in the air.
\item[{\bf e}.]
For all angles of incidence, some light always enters the air.
\end{enumerate}


\item[(2)~{\bf ~9}.]
The transverse nature of light waves is apparent because
\begin{itemize}
\addtolength{\itemsep}{-3pt}
\item[{\bf a}.]
they are electric in nature.
\item[{\bf b}.]
they are magnetic in nature.
\item[{\bf c}.]
they are electromagnetic in nature.
\item[{\bf d}.]
they can be polarized.
\item[{\bf e}.]
they travel in ether which does not support longitudinal waves.
\end{itemize}

\item[(2)~{\bf 10}.]
In air ($n_{air}=1.00$) a concave mirror has a focal length of 30.0 cm. Under
water ($n_{water}=1.33$) that same mirror would have \underline{\hspace*{1in}} focal length.
\begin{itemize}
\addtolength{\itemsep}{-3pt}
\item[{\bf a}.] a larger
\item[{\bf b}.] the same
\item[{\bf c}.] a smaller
\item[{\bf d}.] infinite
\item[{\bf e}.] negative
\end{itemize}


\vfill
\newpage

\item[(10)~{\bf 11}.]
%%A 200-kg superhero, falling off a building, manages to grab hold of the end of a
%%3.0-m-long flagpole, 5.0~cm in radius, which saves him from falling any further.
%%After the oscillations have died down, the end of the flagpole is sagging 10~cm.
%%What is the shear modulus of the pole? %%% 7.5e6 N/m^2
%K2 8.32
The normal force of the ground on the foot can reach three times a runner's body weight
when the foot strikes the pavement.  By what amount does the 52-cm-long femur
of an 80-kg runner compress at this moment?  The cross-sectional area of the 
femur bone can be taken as $5.2\times 10^{-4}\mbox{m}^2$, and the Young's modulus
for cortical bone is $1.6\times 10^{10}\mbox{N/m}^2$.
\vfill
\newpage

\item[(10)~{\bf 12}.]
Consider a copper belt (a rod)
encircling the Earth (radius 6378~km).  If the temperature of the belt increases by $1.0\>\mbox{C}^\circ$,
how high off the ground would the expanded ring be, assuming uniform clearance all around?
The linear expansion coefficient of Cu is $1.7\times 10^{-5}\>(\mbox{C}^\circ)^{-1}$.
\vfill
\newpage

\item[(10)~{\bf 13}.]
An ideal monatomic gas undergoes a reversible expansion in which its volume changes from
$V_1$ to $V_2=5\times V_1$ while the pressure, varying linearly with volume, changes from $p_1$ 
to $p_2=3\times p_1$.  
\begin{enumerate}
\addtolength{\itemsep}{-3pt}
\item[{\bf a.}]
Sketch, to scale, the $pV$-diagram of the process.
\item[{\bf b.}]
What is the change in internal energy of the gas in this process, in terms of the initial
volume and pressure? %%% 21 p_1 V_1
\item[{\bf c.}]
How much heat is gained by the gas in this process, in terms of the initial
volume and pressure? %%% 29 p_1 V_1
\end{enumerate}
\vfill
\newpage

\item[(10)~{\bf 14}.]
Light in water (refractive index 1.33) has a wavelength of 475.8~nm.  A ray of this light
is incident on the glass (refractive index 1.50) wall of the aquarium
at an angle $26^\circ$ (with respect to the normal).  It exits into the air (refractive index 1.00).
\begin{enumerate}
\addtolength{\itemsep}{-3pt}
\item[{\bf a.}]
Draw a clear diagram indicating what happens at both water-glass and glass-air interfaces.
\item[{\bf b.}]
Calculate the light's  wavelength in the air.
\item[{\bf c.}]
Calculate the angle at which the light enters the air, with respect to the normal to the glass.
\end{enumerate}
\vfill
\newpage

\item[(10)~{\bf 15}.]
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.
\vfill
\newpage

\item[(10)~{\bf 16}.]
A corn syrup is fed through a pipe into a mixing vat at a candy factory.  A different
batch of syrup is found to have a viscosity that is 25\% lower than usual.  To compensate and to
maintain the same rate of syrup flow into the vat, a different pipe of the same length
is substituted.  What is the change in the size (diameter) of the pipe that restores the usual flow rate?
\vfill
\newpage

\item[(10)~{\bf 17}.]
As you stand by the side of the road, a car approaches you at a constant speed, 
sounding its horn, and you hear a frequency of 76~Hz.  After the car goes by,
you hear a frequency of 65~Hz.  What is the speed of the car?

The speed of sound in the air is 343~m/s.
\vfill
\newpage

\item[(10)~{\bf 18}.]
A 4-cm-high object is placed in front of a converging lens of focal length 20~cm.  The image
is formed 60~cm on the other side of the lens.  Draw a diagram approximately to scale.  
Determine the object distance, the image height, and the magnification.
\vfill
\end{itemize}
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%%%%%%%%%%%%%%%%%%%%%%

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\item[(10)~{\bf 16}.]
Which of these statements is true?
\begin{enumerate}
\addtolength{\itemsep}{-3pt}
\item[{\bf a}.]
\item[{\bf b}.]
\item[{\bf c}.]
\item[{\bf d}.]
\item[{\bf e}.]
\end{enumerate}
\vfill
\newpage

