Three Methods for Calculating the Buoyant Force Gleue: Physics


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1 Three Methods for Calculating the Buoyant Force Gleue: Physics Name Hr. The Buoyant Force (F b ) is the apparent loss of weight for an object submerged in a fluid. For example if you have an object immersed in water, you have to exert less force to support the object than you would if the object was not in the water. The object itself did not lose mass, so its weight did not really change. When the object is in the water, the displaced water exerts an upward force on the object in a direction which opposes the downward pull of gravity (mg or weight). Pressure = P = F/A Pressure in a liquid = ρ fluid gh Purpose of the activity: In this activity, you will calculate the buoyant force on an object three different ways. You will compare the three different answers you obtained and contrast the three different methods. METHOD A: Using spring scales. 1. Place the hook mass on the spring scale. You will probably need the blue spring scale. Read the spring scale using the Newton scaling (not the grams scaling). This will be the TRUE WEIGHT of the object.. True Weight = mg = N 2. Fill up your cup (or beaker) about ⅔ filled with water. You want enough water in your beaker to allow you to completely submerge the mass. Place a piece of masking tape on the beaker along the water line. See figure A: Figure A: Beaker filled up ⅔ rds full and tape marking water line edge 3. Now holding the mass and hanger with the spring scale, slowly and carefully dunk the mass into the water so it is completely covered. Hold it above the bottom of the beaker. The water level will displace or rise to a higher level (see Figure B). Read the spring scale as closely as possible. This represents the apparent weight or the tension your hand has to provide to support the mass/hanger. Apparent weight = N. Figure B: Mass dunked into the water. Read the new spring scale reading. Figure C: Tape marking the new level of the displaced water. Three Methods for Calculating the Buoyant Force Activity, 01/23/13, p. 1
2 4. With the mass still immersed into the water, place another piece of masking tape level with the new position of the water line (Figure C). Your beaker should now have two pieces of tape showing the water levels before and after the mass was immersed. 5. One method of calculating the buoyant force (F b ) is to subtract the apparent weight of the mass in the water from the true weight (the weight of the mass in air). F b = True weight apparent weight OR F b = line 1 line 3. F b = N (true weight )  N (apparent weight) = N 6. Carefully remove the mass from the water allowing excess water to drip back into the beaker. You can take the hanger and spring scale off of the mass. Please make sure to dry off the mass and spring scale using paper towels METHOD 2 for calculating the buoyant force. Using Archimedes Law 1. A second method for obtaining F b is using Archimedes Law. Archimedes Law states that F b = weight of the water displaced. If we could collect this water and weigh it, then that calculation would be = F b. This is what the two pieces of tape are for on your beaker. 2. Pour the water (from top tape to bottom tape) into an empty cup. 3. Now at this point, we need to weigh this amount of water. Now take this cup to the digital balance and find its mass. Make sure to subtract the mass of a similar cup. a) Mass of displaced water = grams b) Now divide this by 1000 to put this answer in kg: kg 4. We need to determine the weight of this displaced water so take your answer to 3b) and multiply this by 9.8 m/s 2. Weight of the displaced water = N. 6. This weight represents another way to calculate the buoyant force F b (Archimedes Law). So, F b = N (rewrite your answer from #5.) METHOD 3 for calculating the buoyant force. (F b = ρ fluid Vg) 1. In class, we discussed a third method for finding the buoyant force. I showed you that how to derive the following formula: F b = ρ fluid Vg, where ρ fluid is the density of the fluid the object is in, V is the volume of the fluid displaced or the volume of the object, and g is the acceleration due to gravity, 9.8 m/s 2. Three Methods for Calculating the Buoyant Force Activity, 01/23/13, p. 2
3 2. Well, we know what ρ fluid is as we are using water as our fluid. The density of water is 1 g/cm 3 in chemistry units or in physics units = 1000 kg/m We also know what g is (9.8 m/s 2 ). 4. So, the only thing we need to calculate here is V, the volume of the object or fluid displaced. Measure the two dimensions of the cylinder with a ruler. Measure in cm to the nearest hundredth. For example, one of the sides may be 0.95 cm long (this would be the same as 9.5 mm). Height (h) radius (r) cm cm Convert the Height (h) to meters [divide by 100] = meters Convert the radius (r) to meters [divide by 100] = meters 5. Consequently, we can find the volume of the cylinder by using the mathematical equation for the Volume of a cylinder: V = (π r 2 ) h making sure to use the radius and height measurements you found placed in METERS. The Volume of your cylindrical mass = m Now we are ready to find the buoyant force, using the equation given earlier, (F b = ρ fluid V g). Calculate your F b by multiplying the three variables:  the density of the fluid (water) =1000 kg/m 3  the volume just obtained for the cylindrical mass (line 5 of this page) and  g (9.8 m/s 2 ) F b = ρ fluid Vg = N Compare and Contrast: So we have found three ways to calculate the buoyant force (F b ):  Spring Scale method (line 5, page 2 of lab) F b = N  Weight of the displaced water also called Archimedes principle (line 6, page 2 of lab) F b = N  Using F b = ρ fluid Vg (from line 6 directly above) F b = N. We don t know exactly what the F b should be but we could average our results from these three methods: F b (average) = N. Three Methods for Calculating the Buoyant Force Activity, 01/23/13, p. 3
4 To determine if one method was better than another, we could do a percentage error (%) for each method. In this case, percentage error can be found using the following equation: Fb( method1,2, or3) Fb( average) x Fb( average) % error = 100% Find your % errors associated with each method:  % error Spring Scale method: %  % error Weight of the displaced water method: %  % error F b = ρ fluid Vg method % Questions: 1. So which method gave you the best results as referenced to the average F b? 2. Now compare and contrast the methods to find F b. Which method seemed the easiest to do? Explain why 3. What sorts of errors are associated with method 2: weighing the displaced water? 4. Draw a force diagram with the mass held by the string. You should have two forces. Make sure you label them correctly. Three Methods for Calculating the Buoyant Force Activity, 01/23/13, p. 4
5 5. Draw a force diagram with the mass held by the string in the water. You should have three forces. Make sure you label them correctly. 6. How would the buoyant force change if we did the same experiment with ocean water? The density of ocean water is slightly higher at 1025 kg/m 3 than regular water (1000 kg/m 3 ). 7. The buoyant force is the location where the buoyant force vector acts. Compare this to the center of mass. The weight vector would act at this location. Check out these pictures of the centers of buoyancy and mass for a person. Because of the location and action of the lungs, the center of buoyancy is anatomically above the center of mass. People have a hard time floating perfectly horizontally on water. Usually their legs are under the water while the chest area is above the water line. Can you explain why using the positions of the centers of buoyancy and mass? Three Methods for Calculating the Buoyant Force Activity, 01/23/13, p. 5
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