006 Sample Laboratory Report: Density of marbles

Introduction

[Written using a past tense prose structure]

Lab group: Mayleen Mori, Jeffrey Joseph, Mary Robert, and Lynnleen Albert

This laboratory explored the relationship between the volume of a marble in cm³ and the mass of a marble in grams. The experiment sought to determine whether the relationship between the volume of a marble and the mass were linearily related. If a linear relationship was found, then the slope of the relationship would be the density of glass. The experimental value for the density of glass would permit comparison to published density values for glass.

Equipment

• Marbles
• Calipers
• Quadruple beam mass balance

Procedure

[Written using a present tense action verb - noun clause structure]

• Measure the diameter of the marble.
• Calculate the volume of the marble.
• Mass the marble.
• Repeat for marbles with different diameters.

Data table

Data chart: xy scattergraph

Analysis

[Findings written in a list format]

1. There is a linear mathematical relationship between the volume and mass.
2. The slope is the experimental density for the glass and has a value of 2.52 grams/cm³.
3. The y-intercept is 0.04 grams.
4. The mathematical relationship for this system is given by the equation:
   mass (grams) = 2.52 × volume (cm³) ‒ 0.04 (grams)
5. Considerations of the theoretic density of glass: According to Keramika (1976) marbles are made of E-glass.¹ E-glass is an alumino-borosilicate glass with a density of 2.57 g/cm³ according to an article in the Wikipedia.² Another source reports a density of 2.55 g/cm³.³ WolframAlpha reports that for 251 different types of glass the median is 2.52 g/cm³.⁴ For window glass WolframAlpha reports a density of 2.58 g/cm³.⁵
   Based on the above data, the Keramika/Wikipedia value of 2.57 g/cm³ appears to be a reasonable theoretic value for the density of the glass used in a glass marble.
6. The error analysis for the difference between the experimentally determined and the theoretically determined density of glass is given by:
   $\Delta \%=\frac{(2.52-2.57)}{2.57}=-1.9\%$

[1] Keramika (1976)
[2] Fiberglass
[3] Azom.com
[4] WolframAlpha
[5] WolframAlpha

Conclusion

[Note that tense is complex. References to the experiment are in the past tense. References to general mathematic or scientific principles are present tense. References to data in this same report are also present tense.]

There is a linear relationship between the volume and the mass, and the slope of that relationship is the density of the material being studied. The experimentally measured density is within 2% of the value of the theoretic density of the type of glass usually used to make marbles. This is a very small percentage error. The small error well supports the possibility that the density of the glass could be 2.57 g/cm³.

While uncertainties in the measurements were small, the volume is particularly sensitive to errors in the diameter measurement. Any error in the measurement of the diameter is cubed in the volume formula. The mass was directly measured, thus the larger contribution to any measurement errors would have been in the measurement of the diameter.

Although there is a possibility that the density of the glass is actually 2.52 g/cm³, the individual marbles are from different sources and may actually be of different densities. Different glasses have different densities. Among the marble measurements, the density calculated for each marble varied from 2.52 g/cm³ to 2.64 g/cm³.