Experiment 1
Measurement and
Density
Objectives:
To
measure the mass densities of a few regularshaped 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 30.0cm 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 experiment. For a brief on significant
figures click on the following link: significant
figures.
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) π R^{3} where R
is the radius of the sphere.
Cylinder: V = π R^{2}L 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/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 are not too big to be measured by a
30.0cm
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 30cm long ruler that is good to 1 mm of
precision.

 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.
 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 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.

 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.

 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
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 



Table 2
Calculation(s):
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: