Harmonizing to Day.M. and Carpi ( 2002 ) , Archimedes, who is the Grecian mathematician, has to find whether a craftsman had put some gold in the King ‘s Crown with Ag.
After recognizing the relationship of volume between the spilled-water and his occupied-body, Archimedes used the construct of denseness to expose the fraud. ( Day.M. and Carpi, 2002 )As Charles points out, denseness is an indispensable nature of affair in natural philosophies, each component and compound has different densenesss even they are alone. The formal definition of denseness is the mass per unit volume. The denseness is normally expressed in gms per milliliter. A ” per ” can be translated as a division mathematically.
( Charles, 2003 ) Harmonizing to Duncan, the denseness of a sample of an object of m and V is defined by the equationI?=Where the mass is thousand, v is the volume.In this experiment, the densenesss of five objects were found as shown in the tabular array.
glassmicroscope slideglassmarblealuminiumsheet of foilsteelball bearingwoodblock of woodTable 1.
Five stuffs and six objects of the experimentThe multitudes of five substances would be measured by utilizing a simple balance and the rule of minutes. The balance is doing up of a meter regulation, a knife border and a 50g mass. These are shown in the undermentioned diagram.d1d2object of unknown massFigure 1. The building of mensurating the multitudes of the objectsIn the experiment, the meter regulation is balanced on the knife border without any object. After seting the 50g mass and the objects on the meter regulation, the places are adjusted until the regulation balance.
Harmonizing to Fullick, “ a unvarying beam pivoted at a point can be balanced. ” The state of affairs is that: W1l1 = W2l2It can be given in words as: The amount of the clockwise minutes equals the amount of the fantastic lock minutes. ( Fullick, 2000:37 )From the rule of minutes as given above, it can be shown thatm1d1 = m2d2where 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 country of a domain of R is given by S= 4IˆrA2 and its volume V can be expressed in V = Iˆr3.
” Where R is the radius.The purpose of the experiment was to happen the densenesss of several stuffs by mensurating mass and volume, utilizing the expression of minutes to mensurate the mass.
The available setup used for mensurating denseness consisted of a meter regulation, a knife border, a 50g mass. A diagram of the setup is shown in Figure 2.d1d2object of unknown massFigure 2. Conventional diagram of the setup used for mensurating massA 30 centimeter swayer was used to mensurate the length and breadth of the sheet of aluminium foil.
The sheet of foil was folded in half several times and how many beds of folded sheet were recorded. Following, the micron screw gage was used to mensurate the thickness of the folded sheet. Finally, the thickness of a individual sheet of foil was calculated by utilizing informations.The 30 centimeter swayer and the micron screw gage were used to mensurate the dimensions of the microscope slide and the block of wood.The glass marbles were laid down in a consecutive line and combined as in diagram. Then the length of the six marbles was measured by utilizing the two sets squares and the 30 centimeter swayer. Last, the radius R of a individual marble was found. Similarly, the ball bearing was measured by reiterating the undermentioned stairss.
Figure 3. The glass marbles were in a consecutive lineThe meter swayer was arranged to equilibrate on the top of the knife border. After equilibrating, the 50g mass was placed on the one side of the meter swayer and the object was put on the other side. The place of the 50g mass and the object was adjusted to equilibrate. Then, the distances d1 and d2 were written down and measured. Similarly, each object was used the same measuring. Finally, the mass of each object was obtained by utilizing the rule of minute.
Table 1 shows the consequences of the volume and mass of each object. Column 1 shows the name of five objects. The places of each object are shown in thee column 2.
The 3rd shows the places of the 50g mass. The forth column illustrates the length, breadth and thickness or the Ra measured in three-dimensional centimeter.objectthe places of the object ( centimeter )the places of the 50g mass ( centimeter )length, breadth and thickness or Ra ( cm3 )microscope slide18.104.22.168A-2.52A-0.
578sheet of foil301.629.15A-30A-0.00128ball bearing30.
111.89Diameter=1.606block of wood17.550.58.
9A-5.9A-5.5Table 2. Position and volume informations from the experiment.
The expression V = Iˆr3 can be used to cipher the volume. The mass can be calculated by utilizing the rule of minute m1d1 = m2d2. Last, the densenesss of five objects were calculated by the rule of denseness. Table 3 in the followers shows the consequences. The six objects are shown in column 1. The 2nd column shows the multitudes of each objects.
Column 3 shows the volumes. The densenesss are displayed in column 4.objectmass ( g )volume ( cm3 )denseness ( g/ cm3 )microscope slide5.071.972.57marble51.962.55sheet of foil2.
671.122.38ball bearing19.752.0269.75block of wood144.3288.80.
500Table 3. The consequences of the experiment.From table 3, it can be seen that the values of five objects. The table 4 in the undermentioned displays the existent densenesss contrast with the densenesss which were measured in the experiment.substancedenseness ( g/cm3 )denseness from consequence in experiments ( g/ cm3 )glass2.572.
75wood0.6-0.90.500Table 4. The denseness of some common substances. ( Day and Carpi, 2002 )There are several possible beginnings of mistake by utilizing this technique. Mistakes may hold arisen in the measuring of the length, breadth, thickness or the Ra because of seeing. For case, the mass and additive dimensions of a block of wood were measured and the consequences gained, and their associated uncertainnesss, are shown in table 5.
mass = ( 144.3A±0.1 ) glength = ( 8.9A±0.01 ) centimeterbreadth = ( 5.9A±0.01 ) centimeterthickness = ( 5.
5A±0.01 ) centimeterTable 5. Associated uncertainnesss of the experiment.Density==
= + + +
= + + +
a-?D= A±0.0026 g/cm3Knowing the beginnings of mistake cause apprehension of how to diminish them. If the length, breadth and thickness ( or Ra ) were measured by numerical reader, it could be measured much more accurately. The mistakes of mensurating mass can be reduced by utilizing balance equipment.
The multitudes and volumes were measured to cipher the values of densenesss.I?Sheet of foil=2.38, I?Microscope slide=2.51, I?Block of wood =0.500, I? Marble=2.
55 and I?Ball bearing=9.75 has been obtained. The values of five densenesss were obtained which agrees with the recognized value.
This was chiefly caused by human behaviour. The consequences might hold been better if reading system had been used to mensurate the length, breadth and thickness or the Ra.
( 2003 ) [ on line ] What is DENSITY? Available at: hypertext transfer protocol: //www.elmhurst.edu/~chm/vchembook/120Adensity.html( Access day of the month: 8/12/2009 )Croft.A.
and Davison.R. ( 1997:254 ) Foundation Maths, 2nd edition. England: Prentice HallDay.M.M. and Carpi.
A. ( 2002 ) [ on line ] DensityAvailable at: hypertext transfer protocol: //www.visionlearning.com/library/module_viewer.
php? mid=37 ( Access day of the month: 8/12/2009 )Ducan.T. ( 2000 ) .Advanced Physics, 5th edition. London: Hodder Murray