Experiment 1
Measurement and Density
Objective:
The objective is to measure the mass densities of a few regularshaped solid objects (nonporous with no cavities).
Equipment:
This is the only experiment that requires a fairly sensitive scale (at least good to 1gram precision) and a metric ruler (usually good to 1mm precision). The use of an electronic mass scale and a dial caliper is preferred if you have access to one or both. In experiment 2, you will need a 30.0cm Metric ruler and a protractor. All other experiments will be done online.
Theory:
Measuring instruments have limited precisions that must be considered during use. These limited precisions will result in the transmission and compounding of errors. Observing the use of appropriate number of significant figures is important in obtaining a result that can be trusted to a certain degree. The student should have an understanding of significant figures prior to this experiment. Click on Significant Figures for a review.
Mass density is defined as the mass per unit volume. gm/cm^{3} is, therefore, a unit of mass density. The mass density ρ of an object may be found by dividing its mass M by its volume V.
Formulas used in the calculation of volume (V) are:
Rectangular block or cube: V = length x width x height = lwh.
Sphere: V = (4/3)πR^{3}.
Cylinder: V = πR^{2}l.
Mass densities of a few substances are given in Table 1:
Table 1
Aluminum 2.7 gm/cm^{3}  Ice 0.9 gm/cm^{3}  Brass 8.6 gm/cm^{3} 
Concrete 2.3 gm/cm^{3}  Iron 7.8 gm/cm^{3 }  Lead 11.3 gm/cm^{3} 
Copper 8.9 gm/cm^{3}  Steel 7.8 gm/cm^{3}  Gold 19.3 gm/cm^{3} 
Procedure:
Select a few regularshaped solid objects (a spherical one like a marble or a steel ball from a ball bearing, and a rectangular one like a boxshaped piece of any metal or polished wood) that you may find at home, school, or work. A cylindrical object may be used instead of a spherical one, whichever is available. Make sure that the dimensions of the small items you choose are under 8.0cm and that they are not too heavy for your mass scale. For this experiment only, you need to find a mass scale and have a ruler. If you have access to a dial caliper, it will have a higher precision than a ruler; however, it is not a must. The mass scale should be at least good to 1 gram of precision. The 10.0cm or 30.0cm ruler should be good to 1 mm of precision.
Record the sensitivity and zero reading of each measuring device on the data sheet (See Table 2 under Data). For example, you may use a mass scale that reads 0.6 grams when its pan is empty. If you measure the mass of an object with this scale and read 62.9 grams, for example, the actual mass is 62.3 grams. We say that the Zero of this scale is 0.6 grams.
Read the following carefully:
Obtain the necessary measurements to calculate the volume of each object with the appropriate measuring device. For example, for a rectangular box, you need to measure 3 dimensions: length, width, and height. For a sphere, all you need is its diameter. For a cylinder, you need the radius of its base as well as its length or height. Note: When measuring the diameter of a sphere or a cylinder by a metric ruler, it must be placed in between 2 perfectly rectangular objects as shown in Figure 1. If a caliper or a micrometer is used, this will not be necessary. Also, each measurement should be repeated 3 times (trials). For example, when you are measuring the length of a box, once measure it along one edge, once along the opposite edge, and once at the middle. Make sure that you hold the the ruler parallel to the edge. For the diameter of a sphere, turn the sphere and measure it at 3 different positions. Tables 3 and 4 provide space for 3 recordings of every measurement as well as a space for their mean value. Volume calculations must be on the basis of the mean values in Tables 3 and 4.
Record the readings to the correct number of significant figures (based on the precision of the device used) in Table 2 below. Always estimate between smallest graduations. With estimation, you can give one more significant figure to your reading. For example, suppose that you are measuring the length of a sharp rectangular box made of aluminum with a metric ruler that is usually precise to 1mm. If the mm lines of the ruler are very thin, you will be able to give a higher precision to your measurement than just 1mm. You may be able to estimate your measurement to 0.1 mm of precision.
Determine the masses by weighing them on the mass scale.
Calculate the average values to be used in determining the volume and mass.
Calculate the volume and mass density for each measured object and display these values in a clearly labeled table of results.
If the material of the object you selected matches any of the materials listed above for which mass densities are known, calculate a percent error on the mass density of each object using the following formula. You need to mention the material of each object.
Figure 1
Table 2
Device 
Sensitivity 
Zero 
Ruler or Dial Caliper 

Mass Scale 
I) The rectangular block (Use a Metric ruler)
Table 3
Trial

Length (cm)  Width (cm)  Thickness (cm)  Mass (gram) 
1  
2  
3  
Mean 
II) The cylinder or sphere (Use a dial caliper if available)
Table 4
Trial

Diameter (cm) of Cylinder or Sphere 
Length (cm) for Cylinder Only 
Mass (gram) of Cylinder or Sphere 
1  
2  
3  
Mean 
Comparison of the results:
Use the percent error formula given above to calculate a percent error for each material, if the material used is listed above.
Conclusion:
State your conclusions of the experiment.
Discussion: