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\title{\bf Physics 201/202/207/208 Instructor Lab  Manual}  
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<P>Link to the <A HREF="../index.html"> PHYS 207/208 Homepage </A></P>
<P>This on-line lab manual is still under development and will,
as time permits, continue to be upgraded and restructured. At present
both PHYS 207 and PHYS 208 lab manuals are available in hypertext format.
The 208 HTML lab manual will incorporates interactive JAVA based demonstrations
developed by the
<A HREF="http://webphysics.davidson.edu/Applets/Applets.html" target="newwindow">
The Web Physics Project, Davidson College </A> and other interactive web tools.
<P>
Questions, comments, and/or suggestions are welcome
at 
<A HREF="mailto:winokur@ewald.physics.wisc.edu"> 
E-mail:  M.J. Winokur at winokur@physics.wisc.edu</A>.</P>
<P>Link to the <A HREF="http://badger.physics.wisc.edu"> </A>
  Web-based Laboratory Information Manual}</P>
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%TABLE OF CONTENTS
\noindent {\bf NOTE: M=Mechanics, H=Heat, S=Sound/Waves,
C=Computerized Experiment}
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\vspace*{.2in}
\noindent {\bf NOTE: M=Mechanics, H=Heat, S=Sound/Waves
C=Computerized Experiment}
\newpage
\index{Computer~Based~Learning~Unit!University of Leeds}

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%\section{Introduction}
\noindent\sectionmark{Introduction}
\subsection{\hspace*{-0.3in}Preface}

~~~~~~This is a first pass at a Physics 201/202 and 207/208 Laboratory TA manual.  The goal is to unify and standardize the manner in which our introductory physics laboratories are conducted and administered.  Hopefully it will make teaching of these labs more straightforward than in the recent past. As a first version it is likely that this guide is far from perfect and will require revision.  Comments, suggestions, feedback should be mailed to: mwinokur@wisc.edu. 

Please use the following format in the {\bf subject} lines of your e-mail so that it can be filed appropriately and then considered in an
efficient and effective manner when revisions are made. \\ \\
{\bf Physics Lab:Course:Experiment:Topic} \\ \\
The nature of the topic might be, for example: ``sample data'' or
``typo found''.  All of these will be considered at subsequent revisions.

\subsection{\hspace*{-0.3in}Organization of TA Manual}

All of the experiments are organized according to the following scheme:
%\begin{center}
\subsubsection*{Overview}
%\end{center}
~~~~~The first page contains a brief overview of the experiment followed by an equipment list detailing what will be used for the specific lab.
Also included will be special notes and instructions so that you, as a TA, can make sure than everything will function smoothly. \\

\subsubsection*{1. Things You Need to Tell Them}

~~~~~This and the next two items should be considered well before scheduled meeting time of the laboratory.  If you are not clear on what is it you need to tell them then the laboratory itself is almost certain not to go well.  This will diminish the efficacy and educational merit of the lab for your students as well.

\subsubsection*{2. Misconceptions and Pitfalls}

~~~~~The number ways that things can go wrong far exceeds the space allotted for each individual lab.  Students have a myriad of different skills  and tools at their disposal.  Your minimal goal in getting through the lab will be to make sure each and every student learn the essential facts that are experimentally tested or demonstrated.

\subsubsection*{3. What the student are supposed to learn}

~~~~~This is really a continuation of the first step.  What is written
here represents a working minimum.  It will of course enhance these
laboratories if you take the initiative do more than the minimum.  This all depends on the temperament and style that you project.

\subsubsection*{4. What to expect and sample data}  

~~~~~Although you should be aware of what is supposed to happen, please be sensitive to the fact the experimental physics is often best learned if the students are not told explicitly beforehand what the ``right answer''. 

\subsubsection*{5. Pre-lab/Post-lab: Questions and Answers}
As time permits there will series of web accessible quizzes.

\subsection{\hspace*{-0.3in}Lab Instructor Duties and Responsibilities}

\begin{itemize}
\item Read (don't skim) through the lab manual and TA guide before
you meet with you class.  If this is the first time you have done the
laboratory then you are obliged to run through the experiment {\em} before you get to class.

\item If you have questions about an experiment, direct them to
the course instructor, head TA or laboratory staff before meeting
with your class.

\item Prepare your students properly.  If necessary you can
use a few minutes of the discussion period.

\item Provide a useful introduction for the students.  Emphasizing good technique is part of a useful introduction. Remember not
to tell them exactly what will happen and what the exact outcome will be. If you do then you will deprive the student of the opportunity of finding out answers for themselves.

\item Be friendly and helpful to your students in lab.  If you give them
clear directions and expectations then they will find the lab far more relevant to the course as a whole.

\item Remember that you represent not only yourself but the Department and the University.

\item Grade lab work consistently and fairly.

\end{itemize}

\newpage


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\section{\hspace*{-0.3in}MC-1a Measurement and Error: TA Notes}

\subsection{\hspace*{-0.3in}Overview [Est.~time: 1 hr]}

Students should as a general rule work in groups of three.  Be careful to have a good balance of students in the individual groups.   Most students have some experience with types of errors and their impact on accuracy and precision.  However many will not have developed their critical thinking skill to apply this knowledge in a laboratory setting for assessing results.  First and foremost is the recognition that physics is an {\it experimental} science and so one needs to know what it means to make a measurement and how the process of acquiring data can introduce errors into that particular measurement.

\subsection{\hspace*{-0.3in}Equipment}
Photogate Sensor, Pasco 700 or 750 interface, Computer Workstation

\subsection{\hspace*{-0.3in}Things you need to tell them}

\begin{itemize}

\item Your students are expected to know and recognize the differences between random and systematic sources of error.   

\item They should be able to identify these in simple test situations. For example if a wooden meter stick is mismarked at the end then the measurement will always be systematically too large or too small by a constant offset.  If the humidity is too high and the meter stick swells then their measurements will be proportionately too short for each and every measurement.  

\item In this lab a student should always frame his/her measurement
in this context.   It is essential to understand how one makes a measurement.  Without these metrics the efficacy of demonstrating a physical law is rendered almost useless.

\item Students need to be reminded about writing {\em all} their answers with units, appropriate significant digits and, where necessary, an estimate of uncertainty.

\item They should know and appreciate the difference between the standard deviation and standard deviation of the mean.  Remember that the standard deviation reflects the statistical uncertainty associated with a single measurement.  The standard deviation of the mean is a measure of how close your measured mean is to the actual value {\em assuming}
that systematic errors do not contribute.   
\end{itemize}


\subsection{\hspace*{-0.3in}What Student are Expected to Learn}

\begin{itemize}
\item The difference between random and systematic error and recognize these characteristics if present in simple data sets.

\item Standard deviation and standard deviation of the mean and their meanings.
 
\end{itemize}

\subsection{\hspace*{-0.3in}Misconceptions and Pitfalls}

Students are likely to have an incomplete understanding of the differences between systematic and random errors.  Hence they will often misidentify these two designations.

\subsection{\hspace*{-0.3in}What to expect}
Generally the range of results will be equal to the number of groups you have in lab and not every contingency can be predicted.  In terms of making the simple 2 second time measurement experience suggests that there will be random and systematic sources of error in the data.  At first the timing accuracy will be good and the period will start out close to the stated 2 second period with a scatter representative of the random error.  Only a large number of measurement can reduce this error. In addition it is likely that there will be a systematic drift in the measured period that will increase or decrease with time.

The ``trick" to resolving this systematic error is to reduce the level of random error.  To achieve this the only solution is to make a large number of measurements and look at the average value in terms of the
mean plus or minus the standard deviation of the mean.  If the value of the period agrees with the asked for period within $\overline{\sigma}$ then the measurement is still dominated by random errors (to a 70\% certainty if $1\sigma$ used).  If not then systematic errors are becoming dominant.  This could conceivably due to the computer clock but far more likely at fault is the student.

By splitting up the calculations into to 25 cycle pieces one may be able to see shorted time systematics pertaining to drift.  The major point here is to get your students to recognize that each measurement is not truly independent (i.e. uncorrelated) and that, if necessary, one should look for correlations at shorter time scales.
 
It may be illustrative for each of the groups to compare their with
the class as a whole.  When they are done the should use the screen
graphing tool and print a hard-copy of the DataStudio display.  This
can be taped onto the wall in a common area.  Asking the students to
compare and contrast their results with other groups may prove useful.



\newpage

\section{MC-1b: Density of a Solid: TA Notes } 

\subsection{\hspace*{-0.3in}Overview[Est.~time 1hr]}

Reinforcing the idea of random and systematic errors requires that students see them in different settings.  Measuring the density of a solid is not always as easy as it seems.  In this case we wish to be especially quantitative but, in general, most labs will seem almost qualitative.|

As noted previously your students will necessarily have a multitude of styles and backgrounds.  To help those with limited experience develop their lab notebook skills we will use, on occasion, a worksheet.  This
layout and format should be maintained throughout the rest of the
semester.

A possible answer to the question posed on the 1b worksheet:
The slope and intercept of the plot are examples of systematic error
in terms of offset (from zero) and scaling (a proportional error). \\
Random errors occur during an individual measurement and these are
quantified by the standard deviation calculation. \\

In addition to the lab itself there will be a short post-lab quiz that
further tests their understanding of the differences between systematic
and random errors.

\subsection{\hspace*{-0.3in}Equipment}
Precision micrometer, calibration blocks, digital scale, computer workstation, metal cylinder, worksheet
 
\subsection{\hspace*{-0.3in}Things you need to tell them}
\begin{itemize}
\item Complex measurements (i.e.~density) that have more a single input (i.e., diameter, height, mass) require one to consider multiple factors in assessing a result.  They will not do this routinely as this is an
introductory lab but these issues must be at least consider in a critical measurement. 

\item The exact form of a mathematical expression can influence the
quality of a result.   For example a difference measurement generated
from two precision measurements, e.g., 1.0035$\pm$0.0002 and 1.0029$\pm$0.0002 gives a very limited result.

\item Using a vernier scale is a convenient way of extracting one more
significant digit.  Most digital display devices have this operation internally

\end{itemize}

\subsection{\hspace*{-0.3in}Misconceptions and Pitfalls}  Many students 
cannot use a vernier scale.  Make sure you understand its operation and are able to explain to the class.

\subsection{\hspace*{-0.3in}What Student are Expected to Learn}

\begin{itemize}

\item Calibration of a device before conducting an experiment is
very important.  Most modern electronic devices have an internal calibration
scheme.

\item Using the same device (i.e., the micrometer) for different measurements can produce correlated systematic errors.

\item Record keeping in a notebook requires neat organized tables and
results clearly marked with units and, in most instances, uncertainties.

\end{itemize}

\subsection{\hspace*{-0.3in}What to expect}  

Most student to find this lab exceedingly dull.  We have minimized the number of micrometer readings to just twenty or so.  If the students learn to use the micrometers well then this will actually go quickly.  In the groups of three the should take turns making measurements with the micrometer.  An excel spread sheet can also be made available so that
all data recording and calculations are streamlined.  As if experiment
MC-1A it may be useful for the student to compared there results from the
different groups.
\newpage
\begin{center}
{\Large Experiment 1b Worksheet}
\end{center}

\begin{enumerate}
\item{} 
\begin{tabular}[t]{|rcc|}
\hline 
CALIBRATION TABLE &&\\
Micrometer Serial \# = & \underline{\hspace*{1in}} &\\
MEASUREMENTS  ~~~~ &&\\
Zero gap 1 = &\underline{\hspace*{1in}}& $\pm$ \underline{\hspace*{1in}}\\
         2 = &\underline{\hspace*{1in}}&\\
         3 = &\underline{\hspace*{1in}}&\\
         4 = &\underline{\hspace*{1in}}&\\
         5 = &\underline{\hspace*{1in}}&\\
Mean$\pm  {\sigma}$= &\underline{\hspace*{1in}}&$\pm$ \underline{\hspace*{1in}}\\ 
Gauge block 6 mm  &\underline{\hspace*{1in}}&\\
12 mm &\underline{\hspace*{1in}}&\\
18 mm &\underline{\hspace*{1in}}&\\
24 mm &\underline{\hspace*{1in}}&\\
\hline  
\end{tabular}  

\item
Make a plot of Gauge block thickness (x-axis) versus Micrometer reading.\\ 
Next fit the data to a line; this generates a correction curve 
where \\Corrected value = actual $\times$ slope + intercept\\
slope = \underline{\hspace*{1in}}\\
intercept = \underline{\hspace*{1in}} 

\item Now for the unknown value \\ \\
\begin{tabular}{|r|c|c|c|}
\hline  CYLINDER  & Height ({\underline{$\pm$\hspace*{0.5in}}}) & Width (\underline{$\pm$\hspace*{0.5in}}) & Mass (\underline{$\pm$\hspace*{0.5in}})\\
1= &\underline{\hspace*{1in}}  &\underline{\hspace*{1in}} & \underline{\hspace*{1in}} \\
2= & \underline{\hspace*{1in}}  &\underline{\hspace*{1in}} & \underline{\hspace*{1in}} \\
3= & \underline{\hspace*{1in}}  &\underline{\hspace*{1in}} &\underline{\hspace*{1in}} \\
4= & \underline{\hspace*{1in}}  &\underline{\hspace*{1in}} &\underline{\hspace*{1in}} \\
5= & \underline{\hspace*{1in}}  & \underline{\hspace*{1in}} & \underline{\hspace*{1in}} \\
\hline           Mean$\pm  {\sigma}$ =  &\underline{\hspace*{0.6in}$\pm$\hspace*{0.4in}}
&\underline{\hspace*{0.6in}$\pm$\hspace*{0.4in}}
&\underline{\hspace*{0.6in}$\pm$\hspace*{0.4in}}
\\ 
Corrected  Mean$\pm  {\sigma}$=   
&\underline{\hspace*{0.6in}$\pm$\hspace*{0.4in}}
&\underline{\hspace*{0.6in}$\pm$\hspace*{0.4in}}
&\underline{\hspace*{0.6in}$\pm$\hspace*{0.4in}}
\\ 
Density = &\underline{\hspace*{1in}} &&\\
Max. Density = &\underline{\hspace*{1in}} && \\
Min. Density = &\underline{\hspace*{1in}} && \\
\hline   
\end{tabular} 

\item Final result, density = \underline{\hspace*{0.6in}$\pm$\hspace*{0.4in}}

\item Cut and tape this into you lab notebook.

\item Answer the following question in your notebook. \\
A. Identify  two sources of systematic error and give their magnitude. \\
B. Identify two examples of random error and give their magnitude.
\end{enumerate}

%\newpage 

%\subsection{\hspace*{-0.3in}Overview}
%\subsection{\hspace*{-0.3in}Equipment}
%\subsection{\hspace*{-0.3in}Things you need to tell them}
%\subsection{\hspace*{-0.3in}Misconceptions and Pitfalls}
%\subsection{\hspace*{-0.3in}What Student are Expected to Learn}
%\subsection{\hspace*{-0.3in}What to expect}

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\section{\hspace*{-0.3in}MC-4 Acceleration in Free Fall: TA Notes}

\subsection{\hspace*{-0.3in}Overview [Est.~time: 2 hr]}

Seeing the same thing in different settings reinforces the physical
concepts presented in the course.  In this instance the free-fall of a metal bob is captured by the spark image on the tape.  To expedite the
data analysis the students can use a provided Excel spreadsheet.  In
this case it is simply a matter of making the measurements and entering
the data into the proper column and then using the mouse grab feature.  Make {\em certain} that you know how to use the spreadsheet well enough to take advantage of the automated equation handler.  Thus a single run from start to finish is much less onerous.  The first iteration may take less than one half of an hour; this includes plotting of the data.  

The students are still expected to know how to estimate the uncertainty with a single distance measurement and then qualitatively estimate the limits of error in the difference measurement that gives the average velocity.  Simply adding the magnitude of the two errors (e.g. 2$\times$ 0.2 mm) and dividing by the time step (1/30 sec) is good enough.  If they choose to use the spreadsheet they should still pay close attention to how closely spaced difference measurements will impact one's ability to measure $g$, the acceleration of gravity.  Moreover they are still expected to understand the mathematical steps the spreadsheet employs.

%Using the spreadsheet will make it possible to easily run through option A, the effect of air resistance.  Rather than each group making a $1/m
%\left( $ vs.~$\bra a \ket$ plot it will be more interesting if all the results
%are entered onto a single class plot.

\subsection{\hspace*{-0.3in}Equipment}
Meter stick, computer, spark tape, plastic and metal bobs, spark generator and cushion

\subsection{\hspace*{-0.3in}Things you need to tell them}

\begin{itemize}

\item This is yet another way to measure little $g$ but without
the influence of rolling friction.   

\item Plots of position, velocity and acceleration versus time should appear parabolic, linear and constant respectively.

\item The average acceleration over a small interval will fluctuate
greatly. However the mean acceleration, as ascertained by using the slope of the velocity versus time, over the full range of data
points should work out well relatively well.

\item Students need to be reminded about writing {\em all} their answers with units, approximate limits of error and appropriate significant digits.

\item Students should recognize the effects of taking differences using
small intervals.
     
\end{itemize}


\subsection{\hspace*{-0.3in}What Students are Expected to Learn}

\begin{itemize}
\item In the absence of friction that little $g$ approximates 9.8 m/s$^2$.

\item That errors can propagate so that even reasonably accurate and
precise measurements can lead to large errors.

\item Friction in 
 
\end{itemize}

\subsection{\hspace*{-0.3in}Misconceptions and Pitfalls}

Many students are likely to find estimating the distance between
millimeter marks a challenge at first. 

\subsection{\hspace*{-0.3in}What to expect}



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