Introduction
This experiment is about the experimental measurement of the density of different substances using laboratory measuring equipment. The four measuring equipment used are the following: the digital caliper, the digital micrometer, the traditional platform balance, and the digital scale. The first two instruments are for measuring length; the last two are for measuring mass. These instruments have varying levels of precision and will be used accordingly as needed in the experiment. The dimensions of the substance will be measured using length instruments; after finding the dimensions, the volume of the substance can be computed based on the type of volumetric shape the substance assumes. The density can be computed directly using the measured mass and the calculated volume.
The quantity to be measured in these experiments is density. By definition, density is the measure of the amount of mass per unit volume of a substance. The basic formula is:
Density=ρ=Mass of substanceVolume of substance=mv
In SI, the unit for density is grams per cubic centimetre (gcm3) or kilograms per cubic meter (kgm3). These two sets of units are the related by the equation 1 gcm3=1000kgm3, and can be proven by the following:
gcm3→gcm3×1kg1000g×100cm100cm100cm1m1m1m=1000kgm3
In general, a specific substance has a constant density no matter how much mass or volume it contains. Therefore, having the knowledge of the density of a specific substance, one can determine whether a sample of that substance is pure or not by measuring the sample’s density and comparing it to the pure substance’s known density. The value of the density should not be very far from the known density of the substance. Therefore, the precision of the instruments used in measurement are critical in finding the density of a substance. If the instrument is not precise enough, the measured and calculated value of density might be misleading.
In this experiment, the precision of the instruments used are more than enough in measuring the density in units of grams per cubic centimeter. This is because digital micrometer can measure down to 0.001 mm (can accurately measure centimeter), and the digital scale can measure down to 0.1 grams (can accurately measure grams).
The volume shapes measured in this experiment are cylinder, sphere (ball), cube, and hollow cylinder. For the cylinder, the relevant dimensions measured are length L and the diameter D. From these quantities, the volume is computed using:
V=πD2L4
For the sphere, the relevant dimension measured is the diameter, from which the radius R can be derived. The formula for the volume of sphere is:
V=43πR3
For the cube, the relevant dimensions measured are the length L, the width W, and the height H. The formula for the volume of the cube is:
V=LWH
For the hollow cylinder, the relevant dimensions are the inner diameter Di, the outer diameter Do, and the length L. The formula for the volume of hollow cylinder is:
V=πDo2-Di2L4
Conclusion
This experiment introduced a straightforward method of measuring the density of different substances using laboratory instruments. Also, this experiment effectively teaches how to properly use laboratory instruments in order to acquire accurate results. The knowledge of varying levels of measurement precision must always be noted in order to maintain accuracy with the measured values.
In the experiment, the measured densities for the second (iron ball) and third (aluminum cube) substances were highly accurate because they are almost equal to the standard values. For the first substance (aluminum cylinder), the measured density is slightly off but still fairly accurate considering the consistency of aluminum materials. For the fourth substance (hollow copper cylinder), the measured density value is very far from standard value for the density of copper. The error might be caused by the inappropriate formula for hollow cylinder volume (the hollow inside might not be a perfect cylinder itself), or there might be human errors committed in reading the measuring instruments.
On a side note, it is observed that the multiple length and mass measurements taken from the 1st, 2nd and 3rd substances are precise with respect to one another. However, for the 4th substance (hollow copper cylinder), the multiple measurements of the inner diameter varied greatly (from 1.814 cm up to 2.433 cm). Thus, there really is huge possibility of error in the measured density for this substance.
Reference
"Mass, Density, and Volume." Science of Everyday Things. 2002. Encyclopedia.com. 11 Jan. 2016<http://www.encyclopedia.com>
