\section{MC-14~~Air Track Collisions}

\noindent {OBJECTIVE:}  To study conservation of energy and momentum 
in collision. \\

\noindent {APPARATUS:} \latexonly{\medskip \\} 
\pind{Air track, assorted slotted masses, 
air supply, hose, gliders; photogates \& support 
stands and PASCO interface and computer. \\}

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    <a name="Demo"><h3><u> <font color="ff0000">Pre-lab Quiz</font> </u></h3></a>
     <blockquote>You should be able to complete this brief quiz before proceeding.
     </blockquote>

<ul><ul>
    <li><a
   
    href="../js/q207_m14.htm">Expt.
    M14 Quiz</a>

</ul></ul>
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\tpind{{\bf PRECAUTIONS:} 
{\em The soft aluminum gliders and track surfaces damage easily:
Don't drop!}
With the air pressure on, use a glider to {\em check that the track is 
level and free of high friction areas} (from scratches or plugged air 
holes).  Getting good results can, at times, be surprisingly difficult
in this lab.
All collisions must be free from any glider contact with the rail.  In
general speeds which are too slow are overly influenced by residual friction
and air track leveling errors.  On the other hand, speeds which too high
invariably cause pitch and yaw motions of the gliders which increase the 
likelihood of physical contact with the track.  Good alignment of the needle
assembly is also a necessity.  You should perform a number of preliminary trials
to discern which speeds work best. } \\

\noindent {SUGGESTIONS:}  
\begin{enumerate}
\epind{\item Use the large gliders whenever possible.  Small ones often tilt 
upon impact and hence give excessive friction.
\item Turn on the air supply and experiment with the gliders.  Adjust the
leveling screw so that the nominal cart acceleration is minimized.  Adjust
the air flow so the gliders move freely without rocking side to side.
\item Make sure that the photogates are plugged into the first two phone
jack inputs in the PASCO interface module.  Also set the two photogates
approximately 40 to 50 cm apart and so that they track the 10 cm long
plate atop the glider.
\item Click on the telescope icon below to launch the PASCO data acquisition
software.  It should already be configured to display a two column table which
will display the {\em speed} of the glider as it passes through the infrared
photogate. (It already assumes that the plate is exactly 10 cm long and actually
 measures the time.)  \\  
To start the data acquisition CLICK on the REC icon.  To stop it, CLICK on the
STOP icon (the upper left window is configured like a tape player). 
Each time a glider passes the photogate an entry will appear in the
appropriate table column.  NOTE:  The photogates measure the speed but
do NOT sense the direction of motion.  You are responsible for the latter.
\item The results of this experiment are {\em}very technique sensitive.  Take
 a single glider and practice sending it through both photogates until you
 are able to get reasonably equivalent speed readings from both photogates.
 Check the behavior by launching the glider from both ends and record, in
 your lab book, the speed measured in four or five satisfactory trials. 
 Estimate the precision associated with a pair of velocity measurements
 and show how this will impact your momentum and kinetic energy measurements. } 
\end{enumerate}

\input{toolbar/m14_tb1}

\noindent { EXPERIMENT I:}
\begin{enumerate}
\epind{\item Choose
gliders of equal mass (or make them approximately the same 
by fastening weights on one).  Qualitatively predict the expected outcome of the
next step (i.e., item 2) before attempting the experiment.
\item With glider \#1 at the end of track and glider \#2 at rest near 
the center, give \#1 a push toward glider \#2. \\ To help
prevent confusion, stop 
glider \#2 before it bounces back.\\ As before you should perform multiple
trials until you achieve consistent results and record a few of them.


Check conservation of momentum and energy in the impact.  In 
equation, 
$$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2,$$ 
call velocities to the right positive, those 
to the left negative.
\item Comment on how well these two quantities are conserved and, if your
results seem poorer than expected,
suggest possible sources of error.  

\item Devise a method for determining how elastic is a rubber band collision
and record your results. 
}
\end{enumerate}

\begin{figure}[h] 
\centering 
\includegraphics[width=6.3in]{figs/l104/m14-6a.eps}
\caption{Sketch of the air track configuration for elastic collisions.}
\end{figure}

\noindent Suggested tabulations:  \\ 

\begin{center}
\begin{tabular}{llllll} \hline
Glider: \hspace*{.25in} & \#1  \hspace*{.25in} & \#2 \hspace*{.25in} 
& Velocity Readings: & \#1  \hspace*{.25in} & \#2  \hspace*{.25in} \\ \\ \hline
mass & & & Before impact (u)\\ \\ \hline
length & & & After impact (v)\\ \\ \hline \\ \\
\end{tabular}

\begin{tabular}{rlrlrlrl}
\multicolumn{4}{c}{\underline{Before Impact}} & \multicolumn{4}{c}
{\underline{After Impact}}\\ 
u$_1$ = & \underline{\hspace{.5in}} \hspace{.15in} & u$_2$ = 
& \underline{\hspace{.5in}} \hspace{.15in} & v$_1$ = &
\underline{\hspace{.5in}} \hspace{.15in} & v$_2$ = &
\underline{\hspace{.5in}} \hspace{.15in}\\ \\
m$_1$u$_1$ = &\underline{\hspace{.5in}} \hspace{.25in} & m$_2$u$_2$ = &
\underline{\hspace{.5in}} \hspace{.15in} & m$_1$v$_1$ = &
\underline{\hspace{.5in}} \hspace{.15in} & m$_2$v$_2$ = &
\underline{\hspace{.5in}} \hspace{.15in}\\ \\
$\frac{1}{2}$m$_1$u$_1^2$ = & \underline{\hspace{.5in}} \hspace{.15in} &
$\frac{1}{2}$m$_2$u$_2^2$ = & \underline{\hspace{.5in}} \hspace{.15in} &
$\frac{1}{2}$m$_1$v$_1^2$ = & \underline{\hspace{.5in}} \hspace{.15in} &
$\frac{1}{2}$m$_2$v$_2^2$ = & \underline{\hspace{.5in}} \hspace{.15in}  \\ \\ \\
\end{tabular} 

\begin{tabular}{llllll}
change in momentum & = & \underline{\hspace{.50in}};\hspace{.25in} & \% change in momentum
& = & \underline{\hspace{.75in}}.\\ \\
change in energy & = & \underline{\hspace{.50in}}; & \% change in energy
& = & \underline{\hspace{.75in}}. \\
\end{tabular}
\end{center}


\noindent {EXPERIMENT II:}  \vspace*{.1in} \\ 
\pind{Perform the same procedure as Exp.~I (steps 1, 2 and 3) except start both gliders
from opposite ends of the air track and with considerably different velocities.} \\

\noindent {EXPERIMENT III:}  \vspace*{.1in} \\ 
\pind{Repeat Exp.~II but for inelastic collisions by attaching cylinders 
with needle and wax inserts. Note that the needle must lines up exactly with
the insert or there will be significant sideways motion when the two gliders
strike.} \\

\begin{figure}[h] 
\centering 
\includegraphics[width=6.3in]{figs/l104/m14-7a.eps}
\caption{Sketch of the air track configuration for inelastic collisions.}
\end{figure}

\noindent {EXPERIMENT IV:}  \vspace*{.1in} \\ 
\pind{Increase m$_1$ by adding masses 
and repeat EXP. I.} \\

\noindent {MEASUREMENT OF FRICTION:} \vspace*{.1in} \\ 
\pind{Estimate the frictional force 
between the glider and track by using the velocity data recorded before Exp.~I.
From any net decrease in velocity 
you should be able to obtain the frictional force.  
Does this information help you understand the experimental data? \\}

\noindent {JAVA APPLET:} \vspace*{.1in} \\ 
\pind{If time permits and you are interested the HTML version of the lab has
a link to an applet which animates elastic collisions of two point masses.}



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<img border=2 src="../gif/exclaim.gif" align="left"><font size=+2 color="ff0000"> Interesting resources on the web </font>

       <DL><DD>Mark Sutherland's excellent Java Applet gallery.
Here you will find applets for Projectile Motion, The Damped
Harmonic Oscillator, Elastic Collision, Coupled Oscillations,
Coriolis and Centrifugal Forces, The Kepler Problem,
The Simple Plane Pendulum, Chaos in the Driven Pendulum,
and Motion in an electro-magnetic Field.
<p>
This site also offers lectures in dynamics (mechanics), a
picture gallery and much more.

</DL>

   <table cellpadding=5><tr>
<td valign=top><img border=2 src="../gif/collision.gif"></td>
<td valign=top>
<a href="http://www3.adnc.com/~topquark/fun/JAVA/collision/collision.html"><b>Elastic collisions</b></a><br>
<i>Conservation of energy and momentum</i><p>
This applet animates elastic collisions of two point masses.
The user enters the ratio of the target mass to the projectile mass and the ratio of the projectile's final speed to its initial speed, and the applet animates the collision in the target rest frame and in the center of mass frame. </td> 
</tr></table>

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