Determining the density of an irregular solid - Lab Report Example

? Determining the density of an irregular solid Steve Beckman WGU INT1 December 12, Determining Density of an Irregular Solid 0 Problem ment Challenge to the determination of the density of an irregular solid is poised to its non-conformity to the any three-dimensional object that are used in the functional determination of the volume of natural and synthetic three dimensional objects. An irregular object falls outside the circular, ellipse, triangular, square, and rectangular or sphere basic units used in the mathematical computation of object. From the microscopic point of view, any material usually has a specific arrangement of its atoms. The bonding between the atoms determines the strength of the material. Due to uniformity in the arrangement of particles in any solid, the density of the material is observed to be equal irrespective of the size. It was not until Archimedes invention that the problem of measuring the volume of irregularly shaped object was completely resolved. From Archimedes discovery, the volume of water displaced by a completely submerged object was realized to be similar to the volume of the object, which is submerged in water. Having determined the volume, it is used in the determination of the density of the object after the mass of the object is established through measuring (Franklin Turner Jones, 2007). This paper seeks to give an in-depth analysis of the determination of the density of an irregularly shaped body. 2.0 Relevance of Your Testable Question The research seeks to realize the volume of the irregular object, which is useful in determining the density of the irregular object. Water displaced during the experiment acts as a representative of the irregular object volume, which is difficult to realize through other modern available computation means such as calculus. 3.0 Literature Review 3.1 History of density and Archimedes principle Archimedes principles hail from the era before the global Christendom of the Middle East region. In its ancient form, Archimedes confused volume with density where the water displaced was equated to density rather than the volume. It is interesting to give an account of how this striking discovery was innovated. This Archimedes principle, as the new volume computation methodology was coined, was discovered after Archimedes puzzle over the spilling of water in a bath filled to the brim when he was bathing. Archimedes expected the water to remain at the bath’s brim level even with his body completely immersed in the bath water. He then went on to reason that the volume of the water that spilled over from the bath was equal to the volume of his body submerged under water (Susan Weiner &Blaine Harrison, 2010). However, this literal interpretational use of the Archimedes principle was revised to imply that the buoyancy force experienced by a submerged object is directly proportional to the density of the submerged object. Formula Buoyant force opposes an object’s weight. The pressure exerted on a body while in liquid is proportional to the depth submerged. This thus translates to the fact that the top of an object experiences less pressure than the bottom when fully immersed in water. According to Archimedes principle, the buoyant force on an object is equal to the weight of the fluid it displaces. Thus, for objects of equivalent mass but different volumes, objects with larger volumes have greater buoyancy. Mathematically, Buoyancy = weight of displaced fluid Alternatively, it can be reformulated to Apparent immersed weight = weight – displaced fluid weight By using the weights quotients expanded by the mutual volume, Density/density of fluid = weight/weight of displaced fluid. 3.2 A review from related articles: how to evaluate density of an irregular solid; According to Willis and Shirley (1999), different bodies float differently in fluids of different densities depending on the up thrust force. However, if the density of the given body is higher than that of the relative fluid, the body completely sinks. Normally, water is used in many experiments since it is a universal fluid and has a standard density of unity. Moreover, it is easily available. Density of any given solid is given by; mass of the given solid divided by the volume. For regular bodies, the volume can be easily evaluated using various mathematical formulas. For example, the product of length and height always gives the volume of cuboids while the product of ?, the square of the radius and the height gives the volume of a cylinder. Other regular bodies have defined formulas respectively for instance the prisms and spherical objects. For an irregular body, it is impossible to evaluate the volume using the stipulated formulas. In this case, emersion method or rather the Eureka method is employed. As Archimedes discovered, any body that sinks in a fluid displaces its own volume. Mass is always evaluated by special equipments like the weighing balance. This approach is practically employed for most cases involving the determination of the density of any given solid. Once the mass and the volume are determined accordingly, density is thus calculated by dividing the mass and the volume. 3.3 The origin of eureka Most of the experimental cans used in the experiment of evaluating the density of an irregular solid are referred to as Eureka cans. According to Rorris and Chris (2009), the name is attributed to the Greek scholar, Archimedes, when he discovered that he could displace the volume of his body in a basin of water. Actually, these are regarded as his Eureka moments. Eureka is literally very significant in the field of physical science in that it forms the main bases for the study of the interaction of solids had fluids. 4.0 Experimental Design Procedurally, the experiment was setup in the following steps. 1) Measuring cylinder was filled with 20ml of water 2) Room temperature was taken 3) Different sized rocks were gathered. All rocks were the same type of material 4) The rocks were weighed and the mass/grams were recorded 5) Four rocks were dropped into the cylinder and the difference in water was recorded 6) After all data was collected, I calculated the density of the rocks and recorded the data 7) The data was charted and continued out as a hypothesis 8) The remaining three rocks were recorded and indeed, they matched the projected density on the chart. 5.0. Dependent, Independent, and Controlled Variables The density of the rock represents dependent variable in the research. From the values of the volume of water collected and the mass of the rocks, the density is calculated. Controlled Variables: Temperature - Room Temp 75 degrees Amount of water - 20ml Material - Same type of rock Independent Variable: Different sizes of rocks. 6.0 Research limitations 1. The air column above the water surface also contributes to the water collected on the measuring cylinder. 2. Water viscosity also limits the amount of water that is collected on the measuring cylinder (Pickover, 2009). 7.0 Hypothesis The physical properties of a material depend on its atomic arrangement. In this research, the rocks are of different sizes. Despite this, they have the same atomic configuration. Since density is defined as mass per unit volume, then it is bound to be same for the different sizes of rock with their corresponding volumes since they are made of the same material. 8.0 Research methodology The experiment involved various measurements that are collected as primary data and then used to draw various inferences into the conclusion about means of determining density of an irregular object. 9.0 Results mass (grams) 10.00 12.00 14.00 16.00 18.00 20.00 22.00 Calculated Volume (cm3) 2.07 2.47 2.90 3.31 3.71 4.13 4.54 density (g/cm3) 4.8400 4.8600 4.8350 4.8400 4.8500 4.8460 4.8450 10.0 Data analysis A graph to represent the given data was plotted as shown in the graph (g) shown below; Graph a From the graph shown above,the slope is the density versus volume is observed tobe almost horizontal. This is because the rocks are of the same material and thus has the same density. Despite this, the volume of the fluid is observed to be influenced by the mass of the rocks. This is in line with archimedes principle. 11.0 Discussions and inferences Prior to the discovery of the Archimedes principle, measuring of the density of irregular shaped material was a problem since its volume could not be accurately obtained. According to the Archimedes principle, a solid completely submerged in a liquid will displace the same amount of incompressible liquid equal to its weight. Stated otherwise, an object partly or completely submerged in a liquid experiences the same up thrust force equal to its buoyancy weight on the liquid (Raymond et al, 2009). From the research, the density of the rocks was observed to be the same irrespective of the mass due to uniformity in the atomic configuration of the rock. The calculated densities of the rocks for the different values of masses were 4.8450 plus or minus 0.2 grams per cubic centimeter. The 1gm weight of air column on the stone surface, which is also calculated in the displaced water, introduces the error margin of experiment. References Franklin Turner Jones, R. R. (2007). Laboratory problems in physics: to accompany Crew and Jones's "Elements of physics,". New York: The Macmillan company.Print Jack Ballinger & Gershon Shugar. (2011). Chemical Technicians' Ready Reference Handbook. New York: McGraw-Hill.Print Pickover, C. A. (2009). Archimedes to Hawking: laws of science and the great minds behind them. New York: Oxford University Press. Print Raymond A. Serway, Jerry S. Faughn & Chris Vuille. (2009). College Physics, Volume 1. Belmont: CEGANGE LEARNING .Print Rorris, Chris. The Golden Crown: Galileo's Balance. Drexel University. Retrieved 2009-03-24. Susan A. Weiner & Blaine Harrison. (2010). Introduction to Chemical Principles: A Laboratory Approach. Belmont: CEGANGE LEARNING. Print Willis, Shirley. Tell Me How Ships Float. Illustrated by the author. New York: Franklin Watts, 1999. Read More