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# Clemson PHYS 201 - Archimedes' Principle

Course: Phys 201-
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Archimedes’ PrincipalAbstract:The purpose of the lab was to determine the densities of irregularly shaped objects. This was done using Archimedes’ Principle. Data was collected for the variously shaped objects both in and out of the fluid. Density was calculated using and density = mass / volume. Percent difference was then calculated. The percent difference between the two density calculations for cylinder 1, cylinder 2, and the cube were 10.03%, 9.93%, and 8.8% in that order.Introduction:The Greek letter  describes density and the equation to find density is  equals mass of the object divided by the volume occupied by the object. Archimedes is a Greek mathematician that discovered the law of hydrostatics, which is now named after him and known as Archimides’ Principle. This equation, , is used in comparison to the more basic equation density = mass / volume.Materials:600 mL beaker, balance on a ring stand, string, a set of objects (1 known cube, and 2 unknown irregular), distilled water, 1 – known cube, 2 – unknown irregular cube.Procedure:Methods:1. The weight was measured and recorded for the objects provided. The beaker was filled one-half to two-thirds full of distilled water. The balance was placed on the ring stand. The string was then tied to a small clip directly under the balance pan. 2. The cube was suspended from the string and the weight was measured on the balance. The cube was placed in the water so that it was totally submerged but not touching the side or bottom of the container. The system was balanced, and the new weight was recorded.3. The density of the cube was determined using the following formula:4. The density of the cube was determined using the definition of mass density.5. Steps 2 and 3 were repeated for the irregular object.Data:Table 1: Recorded DataObject Mair Volume Msub ρexp ρcal % differenceCube 249.5g 29.79 216.6g 7.58 8.38 10.03%Cylinder 1 72.6g 24.54 45.5g 2.68 2.96 9.93%Cylinder 2 201.1g 24,54 174.3g 7.50 8.19 8.80%Calculations:Volume Formulas: V = (r^2)h for the cylinders and V = l^3 for the cubeCylinder Volume = (1.25^2)5 = 24.54Cube Volume = l^3 = 3.1^3 = 29.79ρexp Formula: ρH O (Mair / Mair – Msub)₂ρexp = 1 (249.5 / 249.5 – 216.6)ρcal Formula: Mair / Volumeρcal = 249.5 / 29.79 = 8.38% Difference Formula: ǀ (ρ - ₁ ρ ) / .5(ρ + ρ ) x 100%₂ ₁ ₂ ǀ% Difference = (8.38 – 7.58) / .5(8.38 + 7.58) x 100% = 10.025%ǀ ǀDiagram 1: Forces acting on an object when submerged in water. Conclusion:The calculated percent difference between the two density measurements displays that all three of the objects had relatively low percent differences: 10.03%, 9.93%, and 8.8%. As a result, the low percent difference for Cylinder 1, Cylinder 2, and the Cube communicate that the two density equations agree with each other. While these values were just at or below 10%, there still were sources of error. One of these sources was more than likely from not being placed into the water appropriately as this would have interfered with the Msub measurement. Questions:What is Archimedes principle? How is it related to the concept of hydrostatic pressure? Archimedes principle states that “when a body is completely or partially immersed in a fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body,” (Young & Friedman, 2016). Essentially, objects feel lighter when in fluid. Hydrostatic pressure is“ is the pressure that is exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity. Hydrostatic pressure increases in proportion to depth measured from the surface because of the increasing weight of fluid exerting downward force from above,” (2). They are related because the hydrostatic pressure of the fluid is equal to the force of the object inthe fluid. Identify the composition of the unknown objects based on their densities. If there are several possibilities (due to the percent uncertainty) state which possibly you feel is most likely, and explain why you claim this. - Object 1/Cylinder 1: Aluminum (2.7g/cm^3)- Object 2/ Cylinder 2: Iron (7.87g/cm^3)- Object 3/Cube: It can be inferred that Iron is the most likely composition, as this number is closer to the density number found when using the equation from Archimedes principle.If there was bubble of air trapped in one of your objects, how would it affect the density measurements? Would the density go up, down, or not change at all? Explain. If an air bubble was trapped inside of one of the objects the density measurement would go down. Air is negligible in mass so this would not contribute to the overall mass of the object. If mass decreases and volume remains the same then the density of the object also decreases. Suppose you are finding the weight of a beaker of water, and you have it on the balance andare ready to record the weight. Your partner dips the tip of his or her pen in the water, but does not touch the beaker or the balance. Does the presence of the pen affect the reading onthe balance? If so, how? If not, why not?The presence of the pen affects the reading on the balance. Archimedes principle states that whenan object is placed in a fluid, the fluid exerts an upward for on the object submerged. The pen will exert a downward force on the water so that the pen will increase the reading on the balance.References:1. Young, H. D., & Freedman, R. A. (2016). University Physics with Modern Physics (14th ed.). 2.

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