Archimedes Principle Group 6 Physics
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Safford High School**We aren't endorsed by this school
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PHYS 196
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Physics
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Dec 17, 2024
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DEPARTMENT OF PHYSICSCOLLEGE OF NATURAL AND COMPUTATIONAL SCIENCESADDIS ABABA UNIVERSITYGENRAL PHYSICS LAB REPORT EXPERIMENT 6ARCHIMEDES PRINCIPLE Name of Instructor: Dr. Yetagesu Name of Lab Assistant:Lema, Group Members ID 1.Saron TamireUGR/4717/162.Yonathan TsegayeUGR/9602/163.Zekareyas kedirUGR/5392/164.Yordanos BazezewUGR/8540/16Date Of Experiment – Feb 24, 2024Date Of Submission – Mar 5, 2024
PurposeThe purpose of this lab was to investigate the buoyant force acting on brass using 3 differentmethods.Materials Equipment NeededQuantitiesTriple Beam Balance1Graduated Cylinder1Brass Cylinder 1Overflow Container 1Spouted Can1Tap WaterIntroductionBuoyancy, made clear by Archimedes’ Principle, serves as a cornerstone of fluid mechanics, itshows us the behavior of objects submerged in fluids. Archimedes’ Principle states that “thebuoyant force experienced by an object immersed in a fluid, whether partially or completelysubmerged, is equal to the weight of the fluid displaced by the object. This force acts in theupward direction at the center of mass of the displaced fluid”. In other words, the buoyant forceacting on an object is equal to the weight of the fluid displaced. Buoyant Force = Weight of Displaced FluidThe greater the volume of the liquid displaced, the greater the buoyant force.The apparent weight in light of Archimedes’s principle is:-Apparent Weight = Weight - Buoyant Force1
-Buoyant Force = Weight of Displaced Fluid-Apparent Weight = Weight - Weight of Displaced FluidCentral to understanding buoyancy is the concept of fluid pressure. In a static fluid, pressureincreases with depth due to the weight of the fluid above exerting a force downwards.Thisincrease in pressure can be seen in this equation., where is the pressure at depth , is the density of the fluid, and is theacceleration due to gravity. This equation illustrates that pressure is directly proportional to thedensity of the fluid and the depth below the surface.When an object is submerged in a fluid, it experiences pressure from all directions due to thefluid surrounding it. The pressure exerted on the bottom surface of the object is greater than thatexerted on the top surface, resulting in a net upward force known as buoyancy. This force isequal to the weight of the fluid displaced by the object and is given by the equation., where is the buoyant force, is the density of the fluiddisplaced by the object, and is the acceleration due to gravity.There are a multitude of ways to see this in action but in this experiment we will only befocusing on 3 of them namely, the overflow method, the direct method, and the displacementmethod.The overflow method involves measuring the volume of the fluid displaced by a submergedobject as it displaces the liquid. By quantifying the volume overflowed, the volume of thesubmerged object can be determined, which will give us the calculation of the buoyant force.In the direct method, the buoyant force acting on an object is directly measured by suspending itfrom a scale and immersing it in a fluid. By comparing the object’s weight in air to its apparentweight in the fluid, the magnitude of the buoyant force can be obtained.2
The displacement method measures the change in fluid level when an object is submerged in acontainer filled with fluid. The difference in fluid level before and after immersion correspondsto the volume of fluid displaced by the object allowing us to calculate the buoyant force.Furthermore, the influence of material composition on buoyant behavior is explored bycomparing cylindrical objects made from brass, aluminum, and wood. Variations in density andbuoyancy are expected due to differences in material composition and geometry, which willprovide us with valuable insights into the role of material properties in buoyancy.Procedure Method 1 / Overflow Method1.We first measured the mass of the brass and determined its weight using .2.We measured the mass of the overflow container by placing it on a digital balance andreading of its mass as .3.We filled the spouted can fully with water and placed it so that the water pours into theoverflow container.4.We immersed the brass into the water one at a time.5.We measured the mass of the overflow container again, then calculated the differencebetween the final mass of the overflow container and its initial mass to obtainthe mass of the displaced water.6.We calculated the volume of displaced water by dividing the density of water. (1000 kg/m3) by its mass that we got in the last step. 7.We calculated the buoyant force using the formula .8.Finally, we calculated the density of the brass cylinder using the formula .Method 2 / Direct Method1.We took the mass of the brass that we already measured before2.We suspended the brass from a string attached to the triple beam balance.3
3.We partially filled the overflow container with water and immersed the object(whilebeing careful to not touch the container), then we measured the apparent mass of thebrass to determine its weight .4.We determined the buoyant force of the objects by taking the difference between theweight of the object and the apparent weight of the object. .5.Finally, we calculated the density of the brass cylinder using the formula .Method 3 / Displacement Method1.We partially filled the graduated cylinder with water and recorded this value as the initialvolume ().2.We gently immersed the brass to the water and recorded the new water level as .3.We calculated the change in volume which gives us the volume of the displaced water.4.Finally, we calculated the density using .4
Data and data analysisTable 1 - Measurement of Buoyant force/Calculation of density of brass(Overflow Method)TrialMass/weight ofbrass cylinderMass/volume of displaced waterBuoyantForceDensityError(kg)(N)(kg)(kg)(kg)(m3)(N)(kg/m3)%10.00860.0860.01790.01990.0022*10^_61.96*10^_24388-50.620.00870.0870.01780.01910.00121.2*10^_61.176*10^_27398-16.730.008710.08710.01780.01910.00121.2*10^_61.176*10^_27406-16.6Mean0008670.08670.01780.01940.00151.5*10^_61.44*10^_26397-28Table 2 - Measurement of Buoyant force/Calculation of density of brass(Direct Method)TrialMass/weight ofbrass cylinder inair from PART 1Mass/weight of brasscylinder in waterBuoyant forceDensityError(kg)(N)(kg)(N)(N)(kg/m3)%10.00860.0860.007810.07810.00791088622.420.00870. 0870.007810.07810.008991753.230.008710.08710.007810.07810.00996788.86Mean0.008670.08670.007810.07810.00861008113.395
Table 3 - Measurement of Buoyant force/Calculation of density of Object (DisplacementMethod)TrialMass/weight ofbrass cylinder inair from PART 1Volume of water in graduatedcylinderBuoyant forceDensityError(kg)(N)(m3)(m3)(m3)(N)(kg/m3)%10.00860.0860.0000300.00003011*10^_79.8*10^_487755887.120.00870.0870.0000400.00004011*10^_79.8*10^_487755887.130.008710.08710.0000500.00005011*10^_79.8*10^_487755887.1Buoyant force and density had directly relation in our experiment.From the above table we can conclude that direct method is best method because it has low error ascompared to the others.Discussion of the Results:1. The density of brass has been determined in three different ways, each possessing its own merits and demerits. The entire theory behind this experiment is governed by Archimedes' principle, explained through both mathematical and qualitative approaches.2. In the first part of the experiment, the overflow method was employed, utilizing a spouted can collect displaced water. Despite the seeming perfection of the idea, it has its own issues. An error of approximately +2.5% is observed in the data table, potentially deflecting experimental conclusions. This error is attributed to the high surface tension of water, a common property due to water being a polar substance with strong intramolecular interactions. This, in turn, causes the water that should flow into the overflow container to stay in the spouted can, resulting in a decrease in the mass of the displaced fluid. Overcoming this issue can be achieved by conductingthe experiment with a fluid that has low surface interaction, preferably a non-polar liquid.6
3. To optimize the experiment, it was necessary to wait for each water droplet to flow by itselfwithout external vibration or movement. This waiting period is also considered a cause for theexperiment's high percentage error. Additionally, the measurement of mass using triple balancemeters, although within our own ability, contributes to the overall error. Nevertheless, theprimary cause of the error is the tension force existing in water.Conclusion:1. The density of brass has been calculated in three different ways, observing Archimedes' principle causing weightlessness on objects when immersed in water.2. The impact of the tension force is concluded to be higher, deflecting the experimental value bya very high magnitude.3. It is also determined that overflow method was more accurate in our measurement values.ReferenceBuoyant force, Archimedes’ principle,General Physics Module (PHYS 1011)www.Britanica.comAnswers to Post Lab Questions1. Sketch a free-body diagram for an object that is floating in water. How much waterdoes it displace? Does it displace its volume in water? Does it displace its weight inwater?ÌFloating objects don't displace their own volume (only theamount that is submerged underwater); instead, they displace their weight in water forbalance.7
2. Sketch a free-body diagram for an object that is submerged in water. How much waterdoes it displace? Does it displace its volume in water? Does it displace its weight inwater?Submerged objects displace their own volume in water,not their weight. This means it pushes out an amount ofwater equal to the space it occupies, regardless of its own density.3. A nugget of gold and a block of aluminum of the same volume are immersed in water.Which object experiences the greater buoyant force?In this case where both objects are denser than the fluid and have the same volume,density has no effect on the magnitude of the buoyancy force. This is because bothobjects will displace the same amount of the fluid and therefore experience the samebuoyant force.If we take the equationWhere:is the buoyant forceis the density of the fluidis the acceleration due to gravityis the volume of the fluid displaced by the object8
The density of the fluid and the acceleration due to gravity are the same for both objects.The volume of the fluid displaced is also the same, since both objects have the samevolume. Therefore, the buoyant force on both objects will be the same, regardless of theirdensity.4. A ship made of steel (= 7.8×10³ kg/m³) will float in water. Explain, interms of densities, how this is possible.A ship made of steel, despite having a much higher density (7,800 kg/m3) than water(1,000 kg/m3), can float thanks to the concept of average density.According to Archimedes’ principle, any object submerged in a fluid experiences anupward buoyant force equal to the weight of the fluid displaced by the object. If thebuoyant force is greater than the object’s weight, it will float.Unlike a solid block of steel, a ship is not just steel; it’s a complex structure with ahollowinterior. This means the volume of the ship (space it occupies) is much largerthan the volume of the actual steel used in its construction.Density is the mass per unit volume. Even though steel is denser than water, the averagedensityof the entire ship (considering both steel and air) is less than the density of waterbecause of the large air-filled spaces within the ship.Since the average density of the ship is less than water, the weight of the water displacedby the submerged portion of the ship will be greater than the weight of the ship itself.This creates a net upward buoyant force, keeping the ship afloat.In simple terms, even though steel is heavier than water, the large air-filled spaces withinthe ship brings down its average density, making it lighter than the same volume ofwater. This is why buoyant force, which depends on the displayed water’s weight, canovercome the ship’s weight and keep it afloat.9
5. A ship at a sea port is taken out of the water. Does the water at the shore rise, fall, orstay at the same level? Explain, in terms of Archimedes’ principle (density, volume, orweight), why this happensWhen a ship is taken out of the water at a seaport, the water level at the shore will fall.This is explained by Archimedes’ principle, which states that the buoyant force exertedon an object submerged in a fluid is equal to the weight of the fluid displaced by theobject.1.Displacement: When the ship floats in the water, it displaces a certain volume ofwater, creating a “hole” in the water body. This displaced water has a specificweight due to its density.2.Buoyant Force: According to Archimedes’ principle, the water exerts an upwardbuoyant force on the ship equal to the weight of the displaced water. This buoyantforce counteracts the ship’s weight, allowing it to float.3.Removal of the ship: When the ship is removed from the water, the “hole” itcreated fills back up with the surrounding water. This means the displaced volumeof the water is no longer present.4.Loss of weight: Since the volume of displaced water and its corresponding weightare no longer acting on the remaining water, the overall weight of the body at theshore decreases.5.Water level drop: Due to the reduced weight, the water level at the shore fallsproportionally. The fall in level may be small and unnoticeable depending on thesize of the ship and the volume of water at the port.Therefore, the removal of the ship and the loss of the displaced water’s weight cause thewater level at the shore to fall, demonstrating the application of Archimedes’ principle inaction.10