Experiment 1

Measurement and Density

Objectives:

To measure the mass densities of a few regular-shaped solid objects

Equipment:

This is the only experiment that you need to use a fairly sensitive scale (at least to 1 gram precision) and a metric ruler (usually good to 1 mm 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 30.0-cm Metric ruler and a protractor.  All other experiments will be done online.

Theory:

Measurement devices have limited precisions that must be considered during use.  These limited precisions will result in the transmission and compounding of errors if the correct significant figures are not applied to calculations.  The student should have an understanding of significant figures prior to this experimentFor a brief on significant figures click on the following link:  significant figures.

Mass density is defined as the mass per unit volume.  gm/cm3 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) π R3   where R is the radius of the sphere.

Cylinder:  V = π R2L   where R is the radius of its base and L the length of it.

Mass densities of a few substances are given below:

Table 1

 Aluminum     2.7 gm/cm3 Ice        0.9 gm/cm3 Brass      8.6 gm/cm3 Concrete      2.3 gm/cm3 Iron      7.8 gm/cm3 Lead     11.3 gm/cm3 Copper         8.9 gm/cm3 Steel     7.8 gm/cm3 Gold     19.3 gm/cm3

Procedure:

• Select a few regular-shaped solid objects (a spherical one like a marble or a steel ball from a ball bearing, and a rectangular one like a box-shaped 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 are not too big to be measured by a 30.0-cm ruler or the items are not too heavy to be measured by a small mass scale.  As is mentioned under "Equipment", for this experiment only, you need to find an electronic mass scale and a caliper, or at least a mass scale good to 1 gram precision and a regular 30-cm long ruler that is good to 1 mm of precision.
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• Record the sensitivity and zero reading of each measuring device on the data sheet (See the chart 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 on the scale, for example, the actual mass is 62.3 grams.  The Zero of the scale is 0.6 grams.
•  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 and half of it, its radius.  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 1 and 2 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 1 and 2.
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• Record the readings to the correct number of significant figures (based on the precision of the device used) in Tables 1 and 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.
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• Determine the masses by weighing them on the mass scale.
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• Calculate the average values to be used in determining the volume and mass.
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• Calculate the volume and mass density for each measured object and display these values in a clearly labeled table of results.
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• 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

# Data:

 Device Sensitivity Zero Ruler or Dial Caliper Mass Scale

I)  The rectangular block (Use a Metric ruler)

 Trial Length (cm) Width (cm) Thickness (cm) Mass (gram) 1 2 3 Mean

Table 1

II) The cylinder or sphere (Use a dial caliper if available)

 Trial Diameter (cm)of Cylinder or Sphere Length (cm) for Cylinder Only Mass (gram)of Cylinder or Sphere 1 2 3 Mean

### Provide the necessary calculations.

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: