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\subsubsection*{PHSX 101L\hfill Experiment 2\hfill Name:\underline{\hspace*{2in}}}
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\noindent
\underline{Title:} Accuracy and Precision: Mass and Speed

\noindent
\underline{Object:} To learn how to improve 
accuracy and precision of measurements by determining the speed of 
sound with simple distance and time measurements, and by measuring 
the mass of some pennies.

\noindent
\underline{Introduction:} \underline{Precision} is indicated by how 
well a group of measurements of the same quantity agree.  The more 
precise the measurements, the more significant figures there will be 
and the closer they will agree.  \underline{Accuracy} is an indication 
of how well a measurement agrees with a ``true'' or accepted value 
(usually a consensus of many measurements by expert scientists).


\underline{Mass of Pennies}:
The mass of objects can be determined with the equal-arm balance, as 
in the previous lab, or with a beam balance.  The beam balances we have 
allow for more precision than the equal-arm balances you used last 
week.  They both work by comparing the object to a standard mass, and 
both would work in regions of different gravitation.  A spring scale, 
on the other hand, would give different readings on the moon than on 
the earth because it measures weight, not mass.  Careful measurement 
of 20 pennies, provided by the instructor, may reveal some interesting 
results.

\underline{Speed of Sound}:
The average speed of an object is the 
distance it travels divided by the time it takes to do so.  The 
average speed 
of an olympic sprinter could be determined by dividing the distance of 
the race, 100 m, by the time it takes, 10 s, giving a speed of 10 
m/s.  If your hair grows 3/4~inch in a month, then the speed of the 
end of your hair is 0.75 inch/month.  If you could measure the amount 
of time needed for light to travel one foot, you would find that it 
would take about 1~ns, so the speed of light is about 1~ft/ns which is 
equivalent to about $3.00 \times 10^{8}$ m/s.


\noindent
By measuring a certain distance and the time it takes sound to travel 
that distance you can determine the speed of sound.  (Because the 
speed of light (cited above) is so much greater than the speed of 
sound, you can ignore the time it takes for the light to travel the 
distance.)  The precision of your measurement can be increased by 
measuring the same quantities a number of times and averaging the 
results.  You should also try to improve the accuracy of your value by 
repeating the experiment for various distances and techniques.

\noindent
\underline{Procedure and Results:} 
\vspace{-.2in}

\underline{Mass of Pennies}:
\vspace{-.2in}

\begin{enumerate}
	\item {\em Zero} the beam balance by adjusting it to read zero with zero 
	load.
	\item Find the mass of each penny to the nearest hundredth of a gram 
	and record it in the table.
	\item Zero the balance again after you are through.
	\item Make a histogram (bar graph) of your measurements by plotting 
	the frequency (number of coins)
	in each mass interval (bin) in your series of measurements.
\end{enumerate}

\begin{tabular}{|c|c|c|}                                       \hline
    \ Penny\          & \ \ Mass  \ \    &   \ \ Year \ \  \\  
     Number           &      (g)         &       Made      \\  \hline
        1             &                  &                 \\  \hline
        2             &                  &                 \\  \hline
        3             &                  &                 \\  \hline
        4             &                  &                 \\  \hline
        5             &                  &                 \\  \hline
        6             &                  &                 \\  \hline
        7             &                  &                 \\  \hline
        8             &                  &                 \\  \hline
        9             &                  &                 \\  \hline
       10             &                  &                 \\  \hline
       11             &                  &                 \\  \hline
       12             &                  &                 \\  \hline
       13             &                  &                 \\  \hline
       14             &                  &                 \\  \hline
       15             &                  &                 \\  \hline
       16             &                  &                 \\  \hline
       17             &                  &                 \\  \hline
       18             &                  &                 \\  \hline
       19             &                  &                 \\  \hline
       20             &                  &                 \\  \hline
\end{tabular} 

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\vspace{.2in}
\underline{Speed of Sound}:
Carefully design your own experiment to measure the speed of sound and 
write the procedure (including a description and diagrams of the 
apparatus you will need).  Include multiple trials that demonstrate 
the principles in the introduction above.  You might want to utilize 
an echo from a flat wall of a building.  Use well-labeled tables and 
graphs where appropriate to record and display your data.  A graph of 
distance (vertical axis) vs.\ time (horizontal axis) should produce a 
straight line whose slope is the speed.  Be sure to compare your value 
for the speed of sound with accepted value given by $v=20.0\sqrt{T}$, 
where $T$ is the air temperature in Kelvin (Celsius plus 273).  Write 
your procedure here:

\newpage

\vspace*{5in}

\newpage

\noindent
\underline{Discussion:} 
\vspace{-.2in}

\underline{Mass of Pennies}:
\vspace{-.2in}
\begin{enumerate}
	\item Did your histogram reveal information about the pennies that 
	was not apparent just by looking at them?
	\vspace{.8in}
	\item How do you account for the two-humped (bi-modal) nature of the 
	histogram?
	\vspace{.8in}
	\item Discuss the validity of measuring all 20 pennies at once and 
	dividing by 20 to get the mass of an average penny.
	\vspace{.8in}
\end{enumerate}


\underline{Speed of Sound}:
\vspace{-.2in}
\begin{enumerate}
	\item How many measurements did you make?  Why this number?  If 
	precision gets better with more measurements, how do you know how 
	many measurements you should make?
	\vspace{.8in}
	\item How could you have done this experiment before the invention of 
	the clock, and how would the precision compare?
	\vspace{.8in}
	\item How much of a role did human reaction time play in your 
	results? (Try to be quantitative here, don't just say ``a lot'' or 
	something.)
	\vspace{.8in}
\end{enumerate}

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\vspace{-.2in}
\underline{Conclusions:}
\vspace{.3in}

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