# 2504 Mass and Density Measurements

- Page ID
- 440570

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Mass and Density Measurements

1.0 INTRODUCTION

You may be familiar with this riddle. “Which is heavier, a pound of feathers or a pound of lead?” The answer is, they are the same, they are both a pound. Heavy refers to the mass of an object. People are tempted to say “the lead” because there is a physical property that is very different between lead and feathers. The pound of lead would be a very small piece of lead and the pound of feathers would fill several pillows.

Different samples of any substance will have different masses and take up different volumes, but each sample will have the mass to volume ratio, known as density.

Density = mass/volume or D =m/V

The mass of an object can be determined by using a balance. In geometry classes you learned numerous formulas to calculate they volume of a regularly shaped object. For example, a cylinder is

V = πr2h

where π = 3.14, r = radius of the circle, and h = height of the cylinder.

In some cases, the volume of an object is difficult to determine because it has a very irregular shape. By Archimedes principle, you can measure the volume of that object by measuring the volume of water that it displaces.

In this experiment you will be examining the mass, the dimensions, and the volume of several objects and reviewing the relationships among these different properties.

2.0 SAFETY PRECAUTIONS AND WASTE DISPOSAL

3.0 CHEMICALS AND SolutionS

4.0 GLASSWARE AND APPARATUS

5.0 INVESTIGATION

Careful records of your observations are key to answering questions posed by your investigation. A bound laboratory notebook is one way to secure and maintain your records.

- Investigation: Measurement of various physical properties

- Data Collection

Your team will analyze 6 pieces of aluminum and 6 pieces of brass. It is best if the metal pieces are different sizes.

Each piece of metal is called a “slug”.

It is important to collect your data in an organized manner such that the measurement for one “slug” is not entered into the data table for a different “slug”. A data table is provided later in this document (you may use this one or draw your own data table in your notebook).

For each “slug”:

- Record any markings on the “slug” and note whether it is aluminum or brass.

- Measure the mass using an analytical balance. Record all digits for greater accuracy (the more significant figures, the better!)

- Measure the length using a ruler. Obtain as many significant figures as possible by estimating the distance between the 2 smallest marks of the ruler. For example, if your ruler measures millimeters and the length of the “slug” is exactly midway between 33 mm and 34 mm, then record the length as 33.5 mm (If the length is closer to 34 mm, then you might state the length as 33.7 or 33.8 mm. Make your best estimate!)

- Measure the diameter using a ruler or calipers. Again, obtain as many significant figures as possible by estimating the distance between the 2 smallest marks of the ruler.

- Measure the volume of the “slug” by using the water displacement method with a graduated cylinder. This method also works well for irregularly shaped objects (see the image shown below).

- Obtain a graduated cylinder large enough such that the slug will not get stuck.
- Partly fill the graduated cylinder with water. Gently tap the graduated cylinder to displace any air bubbles in the water.
- Measure and record the initial volume. Again, obtain as many significant figures as possible by estimating the distance between the 2 smallest marks of the graduated cylinder.
- Gently slide the “slug” into the graduated cylinder. Don’t let it fall quickly as it may crack the glass graduated cylinder! Gently tap the graduated cylinder to displace any air bubbles in the water.
- Measure and record the final volume. Again, obtain as many significant figures as possible by estimating the distance between the 2 smallest marks.
- The volume of the “slug” is the difference between final and initial volumes. Record this volume.

6.0 DATA RECORDING SHEET

6.1 BRASS DATA TABLE

6.2 ALUMINUM DATA TABLE

7.0 ANALYSIS

- For the 6 aluminum “slugs”, construct a plot of volume determined by the water displacement on the x-axis and mass on the y-axis. Use a graphing program that calculates linear regression or the line of best fit (refer to Expt 2501).
- On the same graph, plot the volume on the x-axis and mass on the y-axis for the 6 brass “slugs”. Also obtain the line of best fit. These 2 lines (one for aluminum and another for brass) should have different slopes.
- Properly label your graph by including a title (“Mass vs. Volume of Metal Slugs”), y-axis label (“Mass in grams”), and x-axis label (“Volume in milliliters”). Also display a legend that clearly identifies which data points are for aluminum and which data points are for brass. Be sure to display both equations for the lines of best fit. Print a copy to include in your lab report.
- Repeat the analysis for a different combination of properties such as 1) volume on the x-axis and length on the y-axis, 2) length on the x-axis and mass on the y-axis, or some other combination of properties of your choosing. Plot this second graph using data for both aluminum and brass slugs, displaying the equations for the lines of best fit for each type of metal. Be sure to properly label your graph as before.

Include in your lab report both of your graphs.

8.0 POST-LAB QUESTIONS

1. Comment on the quality of your data by inspecting how close the data points came to touching the line of best fit. Are there data points that you trust more than others?

2. From the plots of mass versus volume, obtain the slopes of the lines of best fit for aluminum and for brass. Because density is defined as mass divided by volume, the slopes of your lines are your experimentally determined values for the densities of aluminum and brass! Look up the densities for these metals on the internet and discuss how they compare to your slope values. (Because brass is an alloy of copper and zinc, the internet should mention that the density of brass can vary depending on the ratio of copper to zinc.)

3. For your second graph in which you choose to properties to plot, obtain the slopes of the lines of best fit and discuss whether the slopes have any meaning. Also compare the slopes between aluminum and brass: are they similar or different? Hypothesize about the reasons for any similarities or differences.

4. If you had to repeat this lab, would you have chosen different properties to graph? Why or why not?