\input{labpreamble}
\begin{document}
\subsubsection*{PHSX 101L\hfill Experiment 1\hfill Name:\underline{\hspace*{2in}}}

\underline{Title:} Simple Measurements: Density

\underline{Object:} To learn how to make good measurements by 
determining the density of several objects by 
making length and mass measurements.

\underline{Introduction:} The density of an object is defined to be 
its mass divided by its volume: 
\begin{equation}
d={m\over V}
\end{equation}
An object's mass can be measured directly using an equal-arm 
balance.  The volume, however, must be calculated from a combination 
of various length measurements using a meter stick, vernier calipers, 
and a micrometer caliper.

For a rectangular block, the volume is calculated from the product of 
the length, the width, and the height:
\begin{equation}
V = L \times W \times H
\end{equation}
For a disk or a rod the volume is equal to the area of the end ($\pi$ multiplied by the 
square of the radius) multiplied by the thickness or length:
\begin{equation}
V = \pi r^{2}L
\end{equation}


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

\begin{enumerate}

\item 
\underline{Equal-arm balance:}  The object to be measured (weighed or 
``massed'') is placed on the left-hand tray and known masses are placed on 
the right-hand tray until a balance is achieved.  A slider is provided 
for fine adjustments.  Draw a sketch of the equal-arm balance.
\vspace{1.5in}

\item
\underline{Vernier caliper:} The width or thickness of a small object 
can be measured by closing it between the jaws of the caliper.  The 
result is read by noting the position of the zero line of the vernier 
scale.  One additional significant digit can be obtained by observing 
which line of the vernier scale coincides with a line on the main 
scale.  Draw a sketch of the vernier caliper.
\vspace{1.5in}

\item
\underline{Micrometer caliper:} This instrument is a ``C'' shaped 
frame with a screw adjustment.  The object to be measured is placed 
between the anvil and the screw, which is advanced until the object is 
gently but firmly gripped.  Using the micrometer caliper, more 
accurate measurements can be made on smaller objects than with the 
vernier caliper.  Draw a sketch of the micrometer caliper.
\vspace{1.5in}

\end{enumerate}


\underline{Results:} Record the various measurements and calculate the 
density for each of the objects listed below.  Remember to record and 
maintain the proper number of significant figures.

\vspace{-.1in}

\begin{enumerate}
\item
\underline{Wooden block:} Using a meter stick measure and record the 
length, width, and height of the block.  Using the correct formula 
from the theory, compute the density of the wooden block.

\vspace{.1in}

Block \# \underline{\hspace*{.8in}}\hfill Mass = \underline{\hspace*{.8in}}

Length = \underline{\hspace*{.8in}}\hfill 
Width = \underline{\hspace*{.8in}}\hfill Height 
= \underline{\hspace*{.8in}}\hfill Volume = 
\underline{\hspace*{.8in}}

\hfill Experimental Density = \underline{\hspace*{.8in}}

\hfill Accepted Density = \underline{\hspace*{.8in}}

\hfill Percent Difference = \underline{\hspace*{.8in}}

\vspace{.3in}

\item
\underline{Masonite disk:} Using a meter stick and a vernier caliper 
measure the radius and thickness of a masonite disk.  Using the 
correct formula from the theory, compute the density of masonite.

\vspace{.1in}

Disk \# \underline{\hspace*{.8in}} \hfill Mass = \underline{\hspace*{.8in}}

Diameter = \underline{\hspace*{.8in}}\hfill 
Thickness = \underline{\hspace*{.8in}}\hfill Volume = 
\underline{\hspace*{.8in}}

\hfill Experimental Density = \underline{\hspace*{.8in}}

\hfill Accepted Density = \underline{\hspace*{.8in}}

\hfill Percent Difference = \underline{\hspace*{.8in}}

\goodbreak
\vspace{.3in}
\pagebreak
\item
\underline{Aluminum rod:} Using a meter stick and a vernier caliper 
measure the length and diameter of an aluminum rod.  Using the correct 
formula, compute the density of aluminum.

\vspace{.1in}

Rod \# \underline{\hspace*{.8in}} \hfill Mass = \underline{\hspace*{.8in}}

Length = \underline{\hspace*{.8in}}\hfill 
Diameter = \underline{\hspace*{.8in}}\hfill Volume = 
\underline{\hspace*{.8in}}

\hfill Experimental Density = \underline{\hspace*{.8in}}

\hfill Accepted Density = \underline{\hspace*{.8in}}

\hfill Percent Difference = \underline{\hspace*{.8in}}

\vspace{.3in}

\item
\underline{Copper wire:} Measure the length and radius of a copper 
wire using a meter stick and a micrometer caliper.  Compute the 
density of copper.

\vspace{.1in}

\hfill Mass = \underline{\hspace*{.8in}}

Length = \underline{\hspace*{.8in}}\hfill 
Diameter = \underline{\hspace*{.8in}}\hfill Volume = 
\underline{\hspace*{.8in}}

\hfill Experimental Density = \underline{\hspace*{.8in}}

\hfill Accepted Density = \underline{\hspace*{.8in}}

\hfill Percent Difference = \underline{\hspace*{.8in}}

\end{enumerate}

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

\begin{enumerate}

\item If you had a block of copper with the same dimensions as your 
wooden block, what would be its mass?
\vspace{.6in}

\item If you had a disk made of aluminum with the same mass and 
thickness as your masonite disk, what would be its radius?
\vspace{.6in}

\item Given that water has a density of 1.0 g/cm$^{3}$, which of the 
above objects would float on water?  
\begin{enumerate}
\item the wooden block
\item the masonite disk
\item the aluminum rod
\item the copper wire
\end{enumerate}

\item If you were able to measure the mass and volume of a number of 
different-sized samples of the same substance you could plot them on a 
graph of mass (vertical axis) versus volume (horizontal axis).  Each 
data point would represent one of the samples.  You could then draw a 
best-fit straight line with a ruler through (0,0) and your data 
points.  The slope of that straight line would be the density of the 
substance.  For example, some data for water might be like that 
below.  The slope of this straight line could be computed by picking 
two (widely-separated) points {\em on} the line (not data points, 
since they have uncertainty in them) and use $m = {y_{2}-y_{1}\over 
x_{2}-x_{1}}$ to compute the slope of the line.  The slope in the 
following example should be close to 1.0 g/cm$^{3}$, the density of 
water.  
\vspace{.3in}  


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\put(53,58){\circle*{3}} 
\put(78,82){\circle*{3}} 
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\vspace{.2in}
Similar lines for other substances would have different 
slopes; the more dense the substance, the steeper the line.
\vspace{.2in}

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\put(15,15){\line(0,1){125}}
\put(15,15){\line(1,0){180}}
\put(80,0){\makebox(0,0)[b]{volume (cm$^{3}$)}}
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\put(85,130){\makebox(0,0)[b]{Al}}
\put(138,40){\makebox(0,0)[b]{balsa}}
\end{picture}

\item There are also ways to measure the densities of things other 
than solids, such as liquids and gasses.  To find the volume of a 
liquid, you can simply pour it in a graduated cylinder and read the 
volume on the markings on the side (the mass of the liquid can be 
obtained by putting the cylinder on the equal-arm balance when full 
and when empty and subtracting).  In fact, this method of finding 
volume can be modified to work for solids as well: read the volume of 
a liquid in a graduated cylinder, then drop the solid into the liquid; 
the level of the liquid will rise and the difference is the volume of 
the submerged solid.

\item However, if the density of the solid is less than the density 
of the liquid, the object will float instead of sink.  

\end{enumerate}

\vspace{-.1in}
\underline{Conclusions:}

\end{document}
