MAPÚA INSTITUTE OF TECHNOLOGYDEPARTMENT OF PHYSICS Muralla St., Intramuros, Manila E206 – Archimedes’ Principle COLLADO, Daniel Joseph B. Abstract Archimedes’ Principle is that weight displaced by an object is equal to the upward force(buoyant force) that is acting on the object. Hence when an object is immersed in liquid which the object is less denser than the liquid the object will float. This principle is applied to determine the specific gravity of coins, solid and liquids. Introduction In a simple vessel with water, any object neither floats nor sink. And that when this object is in contact with water, there is always an observable increase in the water height is observed. This is a simple demonstration of Archimedes principle. Archimedes’ Principle states that the weight of an object in air and it's weight on a liquid is equivalent to the weight of the liquid that is displaced by the body. The body experiences an upward force, which we call the buoyant force, when immersed in a liquid. The amount of this buoyant force equal to the weight of the fluid that is displaced. The experiment studies and applies Archimedes’ principle in determining the density and specific gravity of solids and liquid samples. The method of loss of weight is used to determine the densities and specific gravities of unknown solid and liquid samples. Methods In theory density being the ratio of the mass and volume of an object given mathematically by . And that no same material has the same density. Specific gravity, on the other hand, defined as the weight of a body compared to an equal amount of pure water. Mathematically represented as which is the ratio of the density of the substance to that of the water. Materials particularly Procedure A for the fact that it must be the water to be used.Given that unknown samples are obviously denser than water.84 1.82 Water 1.1) . The experiment is done in a revised order. A supplemental activity is given that uses coins. Part B ( Procedure A) Determining the identity of the unknown solids In order to determine what the identity of the unknown solid sample with a set of is given densities. Results The experiment is divided into four parts. The method of loss COLLADO. being the weight of the object in air and as the weight in water.00% two samples The result for the alcohol that yields with a 2. is the quotient of the ratio of the weight of the object in air and its apparent weight loss in water. The loss of weight method is applicable to objects denser than water. To further help in determining what particular sample we have a table of densities of solids and liquids are given ( Table 1.2.44% 0. The result is as follows for the TABLE 1. it suggests that to determine the Specific Gravity the object must be weighed in air and weigh it while completely immersed in water. it is suggested to use the loss of weight method. specific gravities of the unknown liquids are found and compared to the experimental value of the liquids found on the supplemental table of densities of solid and liquids (Table 1.44 % error can be a result of impurities and/or as a result of the water being tested first with the hydrometer and used when testing the alcohol without having dried completely. this order is followed for flow of this report. ARCHIMEDES’ PRINCIPLE Page 2|4 . succeeding parts of the experiment can be done. this can be mathematically represented . To determine the Specific Gravity. Determination of Specific Gravity of Unknown Liquids Using Hydrometer Sample 1 Sample 2 Specific Gravity 0. PART A ( Procedure C ) Determining the identity of the Unknown liquid Using a hydrometer. And with this important data obtained . DANIEL JOSEPH B. it is essential to determine the specific gravity of these solids in water. one process is important for the other process.00 Percent Error 2.00 Name of Sample Alcohol 0.1 refer to references). two in which has to do with determining the identity of the unknown samples. and lastly another application. Gravity 0.00 g Loss of weight in Liquid.3 Determination of Specific Gravity of Unknown Liquids Sample 1 Weight in air.80 g Specific Gravity. 21. And as discussed the objects are weighed in air and water subsequently keyed into the mathematical formula. Given that the specific gravity of the liquids has to be determined a different ratio is used given as similar to that of the loss of weight method which had a revision in which the numerator where as the weight of the solid sample in air is deduced with the weight of the solid sample in liquid. 17.06 COLLADO. ARCHIMEDES’ PRINCIPLE Page 3|4 .90 g Weight in water.74% 0.89 2.20 g Specific Gravity Name of Sample Percent Error 8. 3. TABLE 1.Determination of Specific Gravity of Unknown Solid Samples Heavier than Water Sample 1 Sample 2 Weight in air.20 g 0. The result is then compared to the nearest value from the data given in Table 1. 19.68% 2.00 TABLE 1.44% 1. 17.65 Copper 8. DANIEL JOSEPH B.4 Determination of Specific Gravity of Solid Lighter than Water Name of Sample: CORK Weight of cork in air.82 Sample 2 17. TABLE 1.3 .of weight is used in this procedure .90 g Weight in water.83 Name of Sample Percent Difference Alcohol 0.1 .60 g Weight in the liquid. 17.05% PART C ( PROCEDURE B) DETERMINATION OF SPECIFIC GRAVITY OF LIQUIDS Since it is known that one liquid sample is water and the other is alcohol from the results of procedure C.70 6. this procedure can be fro counter checking the results of the two procedures.54 Aluminum 2. 1.96 Water 4.90 g 44.60 g 27.40 g Weight of both sinker and cork in water. 1. 19.90 g Specific Gravity.80 g Weight of cork in air and sinker in water. 18.70 g 2. 85 9.61% 8. Thus when a body or an objects floats in water or any liquid for the matter. ARCHIMEDES’ PRINCIPLE Page 4|4 .46 10.htm http://hyperphysics.4 Comparison of Specific Gravity of 3 Philippine Coins ( ₱ 1.00 g 7. Marissa G.33 6.smu.50 g 4.40 9.5% Nickel 24.80 g 5.70 g Ring: Cupro-nickel 8.57 29.70 g 8. Chemistry Teacher.25 7. ₱ 5 . References http://www.70 g 70% Copper 5.edu/hbase/pbuoy.weber.48 Center: Aluminum Bronze 12.74% 10.Table 1.phy-astr.edu/carroll/archimedes/principle.88% Discussion and Conclusion Archimedes’ Principle showed that when a body is immersed in a liquid the volume or weight of the body and the density of the liquid where it is submerged determined the amount of buoyant force ( upward force) that acts on a body.40 g 8.gsu.html http://physics.edu/~scalise/mechmanual/archimedes/lab. DANIEL JOSEPH B.80 g 7.90 g 7.40 g 6.50 g 6.html Acknowledgment Mrs.10 g Nickel 8.5% Zinc 17. & ₱ 10 ) Coin Denomination (₱) Weight in air Weight in water Specific Gravity Weight in Alcohol Specific Gravity (Alcohol) Actual Weight Coin Composition ( Specific Gravity ) Percentage Error ₱ 1 Coin ₱ 5 Coin ₱ 10 Coin 5. the buoyant force is equivalent to the weight of the object due to gravity and only the density that has an effect to the weight of the body.8 7. Our Lady of the Sacred Heart Academy COLLADO.78 4. 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