According to Day.M. and Carpi (2002), Archimedes, who is the Greek mathematician, has to determine whether a craftsman had put some gold in the King's crown with silver. After realizing the relationship of volume between the spilled-water and his occupied-body, Archimedes used the concept of density to expose the fraud. (Day.M. and Carpi, 2002)
As Charles points out, density is an essential nature of matter in physics, each element and compound has different densities even they are unique. The formal definition of density is the mass per unit volume. The density is usually expressed in grams per ml. A"per"can be translated as a division mathematically. (Charles, 2003) According to Duncan, the density of a sample of an object of m and V is defined by the equation
Where the mass is m, v is the volume.
In this experiment, the densities of five objects were found as shown in the table.
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sheet of foil
block of wood
Table 1. Five materials and six objects of the experiment
The masses of five substances would be measured by using a simple balance and the principle of moments. The balance is making up of a metre rule, a knife edge and a 50g mass. These are shown in the following diagram.
object of unknown massFigure 1. The construction of measuring the masses of the objects
In the experiment, the metre rule is balanced on the knife edge without any object. After putting the 50g mass and the objects on the metre rule, the positions are adjusted until the rule balance.
According to Fullick, "a uniform beam pivoted at a point can be balanced." The situation is that: W1l1 = W2l2
It can be given in words as: The sum of the clockwise moments equals the sum of the antic lock moments. (Fullick, 2000:37)
From the principle of moments as given above, it can be shown that
m1d1 = m2d2
where m1 =50g, m2 represents the unknown mass, d1 is the perpendicular distance from the fulcrum to the centre of the 50g mass and d2 is the distance from the unknown mass to the pivot.
Croft and Davison illustrates that "the surface area of a sphere of r is given by S= 4Ï€rÂ2 and its volume v can be expressed in V = Ï€r3." Where r is the radius.
The aim of the experiment was to find the densities of several materials by measuring mass and volume, using the formula of moments to measure the mass.
The available apparatus used for measuring density consisted of a metre rule, a knife edge, a 50g mass. A diagram of the apparatus is shown in Figure 2.
object of unknown massFigure 2. Schematic diagram of the apparatus used for measuring mass
A 30 cm ruler was used to measure the length and width of the sheet of aluminum foil. The sheet of foil was folded in half several times and how many layers of folded sheet were recorded. Next, the micrometer screw gauge was used to measure the thickness of the folded sheet. Finally, the thickness of a single sheet of foil was calculated by using data.
The 30 cm ruler and the micrometer screw gauge were used to measure the dimensions of the microscope slide and the block of wood.
The glass marbles were laid down in a straight line and combined as in diagram. Then the length of the six marbles was measured by using the two sets squares and the 30 cm ruler. Lastly, the radius r of a single marble was found. Similarly, the ball bearing was measured by repeating the following steps.
Figure 3. The glass marbles were in a straight line
The metre ruler was arranged to balance on the top of the knife edge. After balancing, the 50g mass was placed on the one side of the metre ruler and the object was put on the other side. The position of the 50g mass and the object was adjusted to balance. Then, the distances d1 and d2 were written down and measured. Similarly, each object was used the same measurement. Finally, the mass of each object was obtained by using the principle of moment.
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Table 1 shows the results of the volume and mass of each object. Column 1 shows the name of five objects. The positions of each object are shown in thee column 2. The third shows the positions of the 50g mass. The forth column illustrates the length, width and thickness or the radium measured in cubic centimetre.
the positions of the object(cm)
the positions of the 50g mass(cm)
length, width and thickness or radium(cm3)
sheet of foil
block of wood
Table 2. Position and volume data from the experiment.
The formula V = Ï€r3 can be used to calculate the volume. The mass can be calculated by using the principle of moment m1d1 = m2d2. Lastly, the densities of five objects were calculated by the principle of density. Table 3 in the following shows the results. The six objects are shown in column 1. The second column shows the masses of each objects. Column 3 shows the volumes. The densities are displayed in column 4.
density (g/ cm3)
sheet of foil
block of wood
Table 3. The results of the experiment.
From table 3, it can be seen that the values of five objects. The table 4 in the following displays the real densities contrast with the densities which were measured in the experiment.
density from result in experiments(g/ cm3)
Table 4. The density of some common substances. (Day and Carpi, 2002)
There are several possible sources of error by using this technique. Errors may have arisen in the measurement of the length, width, thickness or the radium because of eyesight. For instance, the mass and linear dimensions of a block of wood were measured and the results gained, and their associated uncertainties, are shown in table 5.
mass = (144.3Â±0.1) g
length = (8.9Â±0.01)cm
width = (5.9Â±0.01) cm
thickness = (5.5Â±0.01) cm
Table 5. Associated uncertainties of the experiment.
= + + +
= + + +
â-³D= Â±0.0026 g/cm3
Knowing the sources of error cause understanding of how to decrease them. If the length, width and thickness (or radium) were measured by numerical reader, it could be measured much more accurately. The errors of measuring mass can be reduced by using balance equipment.
The masses and volumes were measured to calculate the values of densities.
ÏSheet of foil=2.38, ÏMicroscope slide=2.51, ÏBlock of wood =0.500, Ï Marble=2.55 and ÏBall bearing=9.75 has been obtained. The values of five densities were obtained which agrees with the accepted value. This was mainly caused by human behavior. The results might have been better if reading system had been used to measure the length, width and thickness or the radium.
Charles.E. (2003) [on line] What is DENSITY? Available at
(Access date: 8/12/2009)
Croft.A. and Davison.R. (1997:254)Foundation Maths, 2nd edition. England: Prentice Hall
Day.M.M. and Carpi.A. (2002) [on line] Density
Available at: http://www.visionlearning.com/library/module_viewer.php?mid=37 (Access date: 8/12/2009)
Ducan.T. (2000).Advanced Physics, 5th edition. London: Hodder Murray