Physics 101 lab 9v Buoyancy

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Northern Virginia Community College *

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100

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Physics

Date

Oct 30, 2023

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pdf

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7

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Physics 101 Laboratory Exercise (9)V Buoyancy and Archimedes ’ Principle Virtual Lab 2021 Equipment: Several blocks made of different materials: Styrofoam, wood, ice, brick, and aluminum, 100 L container, different fluids: gasoline, oil, water, and honey. Click on the link below and go to Buoyancy Playground to explore the experiment https://phet.colorado.edu/sims/density-and-buoyancy/buoyancy_en.html Introduction: When objects are immersed in water or any other fluid, they push that fluid aside and they appear to weigh less than they do when in the air. Archimedes ’ principle states that the buoyant force on a body in a fluid is equal to the weight of the fluid displaced by the body . We will examine this principle for several objects that either sink or float when immersed in a fluid. The buoyant force of fluid on the object reduces the weight of the object. In this experiment, you will determine and compare the buoyant force on an object and the weight of the fluid displaced by different objects. Objective: In this experiment, you will • Measure the weights of objects in and out of fluid. • Determine the weight of fluid displaced by each object. • Compare buoyant force to weight of fluid displaced for each object. • Use the results of the experiment to explain why objects sink or float. Theory: During the third century B.C. the Greek mathematician Archimedes first studied this relationship between the buoyant force on an object and the weight of the fluid displaced by the object. 𝐹 ? = 𝜌 ? 𝑔𝑉 (1) where 𝜌 ? – is the density of fluid, g – is the acceleration due to gravity, V – is the volume of the fluid. It is the buoyant force that keeps ships afloat in water and hot air balloons floating in air. When we say “fluid displaced” we mean a volume of fluid equal to the submerged volume of the object. The free body diagram of an object submerged in a fluid under the influence of gravity is shown in the figure below. Thus the net force on a totally-submerged object is:
𝐹 𝑛?𝑡 = 𝐹 ? − 𝐹 ? = 𝜌 ? 𝑔𝑉 − 𝜌 𝑂 𝑔𝑉 𝜌 𝑂 − is the density of the object submerged in the fluid Note, that fluids in our experiment are water, gasoline, oil, and honey. Refer to TABLE 10-1 on the last page for liquid and object densities. The acceleration due to gravity g = 9.80 m/s 2 F g In this experiment, the buoyant force will be measured three ways and the results compared. The first method is by the force measurement . This method involves weighing an object first in air, then in fluid, and using the difference in weight as the buoyant force. Though the object's mass does not change, its apparent weight will change when measured while immersed in a fluid that is denser than air. The second method is by the displaced volume method. The volume of fluid displaced by the object is measured and its weight calculated. The weight of the water displaced is equal to the buoyant force exerted on the object, by Archimedes' Principle. The third method is by the buoyant force equation method. By measuring the dimensions of the object and calculating the volume, one can determine the buoyant force using Εq . 1 that would be exerted on the object when it is submerged in a fluid of known density ρ . Please note that for the third method, the volumes of interest are different for objects that float and objects that sink . Experimental procedure : Part I: Force Measurement Method – Weight 1. Measure the weight of objects in air . Place a brick box on the balance and record their weights in the Data Table. Label this weight in air as F A , or Weight in air (N) . Repeat this for Aluminum, Ice, Wood, and Styrofoam boxes accordingly. 2. Collect data in water . Fill the container with enough water to cover the object (use 100 L setting). Lower objects into the container and place them on the underwater balance. Record the weight of the object in the Data Table. Label this weight in water as F W , or Weight in water (N) . The difference between the object’s weight in air and its weight in water is the buoyant force on the object, or 𝐹 ? = 𝐹 ? − 𝐹 𝑊
3. Repeat data collection in water for Aluminum, Ice, Wood, and Styrofoam boxes accordingly 2 for all objects submerged in gasoline , oil , and honey . Record the data in the Data Table 1. 4. NOTE: If the object sinks, you can measure its weight underwater. If the object floats, let it float. Refer to Part III for floating objects measurement Part II: The Displacement Method – Volume 5. Fill the container with water. Record this initial volume as V i or Volume of liquid (L) in the Data Table. If the V i is the same for all liquids, just keep one value for all of them. 6. Gently immerse each box into water. Note the new water level and calculate the change in volume, Volume of water . This is the volume of displaced water. Calculate the weight , of displace water F B using Eq. 1 and the density of water. 7. Repeat the data collection in water for Aluminum, Ice, Wood, and Styrofoam. Also collect the data for different objects in gasoline , oil , and honey respectively. Record their volumes and the weights displaced in Data Table accordingly. Part III: Finding the buoyant force for objects that float 8. Measure the mass and volume of the Wood, Ice and Styrofoam boxes. Fill the container with water. Record their initial volumes V i or Volume of liquid (L) . Immerse the Wood box into the water, note the new volume of water and calculate change Volume of water (L) . This is the Volume of displaced water. 9. Calculate the weight of the displaced water and compare this buoyant force to the wieught of the wood box. Are they the same? 10. Draw the free body diagram for this system. Calculate the density of the wood. 11. Repeat the data collection steps 8 and 9 in gasoline , oil , and honey respectively. Record their volumes and the weights displaced Print out, Fill out, and ATTACH EVERYTHING after this page in your report 1. Go to: Buoyancy Simulation 2. Set the Fluid viscosity to low and click on numbers. 3. Adjust the Object Density and the fluid density and run the simulation to complete data table 1. 4. The section on weight displaced can be completed using equation 1 above.
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Data collection and analyses Data Table 1. Forces and Weights are in (Newtons), Volumes are in (Liters) Object A B C D E Weight in Air (N) 1.96 2.94 7.84 45.08 19.60 Weight in 1g/cm 3 fluid Weight in 0.8 g/cm 3 fluid Weight in 0.9g/cm 3 fluid Weight in 1.4g/cm 3 fluid Weight in 2.5g/cm 3 fluid Buoyant Force 1g/cm 3 fluid Buoyant Force 0.8 g/cm 3 fluid Buoyant Force 0.9 g/cm 3 fluid Buoyant Force 1.4 g/cm 3 fluid Buoyant Force 2.5 g/cm 3 fluid Volume in 1g/cm 3 fluid Volume in 0.8 g/cm 3 fluid Volume in 0.9g/cm 3 fluid Volume in 1.4g/cm 3 fluid) Volume in 2.5g/cm 3 fluid) Buoyant Force in 1g/cm 3 fluid Buoyant Force in 0.8g/cm 3 fluid Buoyant Force in 0.9g/cm 3 fluid Buoyant Force in 1.4g/cm 3 fluid Buoyant Force in 2.5g/cm 3 fluid
Weight displaced (N) 1 g/cm 3 fluid 0.8 g/cm 3 fluid 0.9 g/cm 3 fluid 1.4 g/cm 3 fluid 2.5 g/cm 3 fluid Post lab questions: 1. How does buoyant force compare to the weight of fluid displaced for each object? Note: The answer to this question is known as Archimedes’ Principle . 2. For which objects was buoyant force less than the weight in air? For which objects was buoyant force equal to the weight in air? 3. Explain how buoyant force determines whether an object sinks or floats in water.
Summary and conclusions:
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Express all densities in kg/L Some useful conversion factors: 1 g = 10 -3 kg 1 cm = 10 -2 m 1 m 3 = 10 3 L 1 mL = 1 cm 3 1 L = 10 -3 m 3 1 mL = 10 -6 m 3 Oil 0.92 kg/L Honey 1.42 kg/L Styrofoam 0.15 kg/L Brick 2.00 kg/L Wood 0.40 kg/L

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