Fluids Investigation #1: Archimedes' Principle Mm weigh less if they are immersed in uid than they do in air. When Objectives Materials Part 1 Question 1.1 an object is immersed in liquid, in addition to the downward pull of gravity an upward force called the buoyant force acts on the object. Archimedes' principle relates the buoyant force to the weight of the uid displaced by the submerged object. You will investigate this relationship in this experiment. Some objects oats While others sink. A solid piece of iron sinks but a huge ship made of iron oats. In this experiment you will also discover the law of oatation. o Investigate the idea behind Archimedes' principle. 0 Explore the idea of oatation. Force probe, masses, string, overow can, two beakers, water, balance, LabQuest Mini interface, computer, pitcher. toIabQuestMini mssbar CHI overflow can beaker - Obtain an electronic balance and measure the mass of a dry beaker. Set the beaker aside. What is the mass of the dry beaker? Force Probe o Setup Attach a force probe to a ring stand and cross bar as shown in the gure above. Plug the force probe into the Chl port of the LabQuest Mini interface. Move the switch on the force probe to the +f-10N setting. Open Log gerPro on your computer. While nothing is hanging from the force probe, zero it by clicking the 'Experiment' menu and selecting 'Zero. . .'. Hang a 1kg brass mass om the force probe. If the force probe is calibrated properly, it should read approximately 9.81N. If it reads smaller than 9.6N or larger than 10.0N, then click the 'Experiment' menu and select 'Calibrate'. Click the 'Calibrate Now' button. When nothing is hanging from the force probe, type '0' in for 'Reading 1' and click 'Keep'. Hang the 1kg mass om the force probe, type '9.81 ' in for 'Reading 2' and click 'Keep', then click 'Done'. After you are done, verify that the force probe reads zero when nothing is hanging om it and reads approximately 9.81N when the 1kg mass is hanging from it. Question 1.2 What is the reading of the force probe when the 1kg brass mass is hanging from it? Equipment 0 Setup Data a Collection Click on the 'Experiment' menu and select 'Data Collection'. Set the 'Duration' to 90 seconds. Suspend a piece of aluminum from the force probe with a string as shown in the diagram above. In addition, setup the rest of the equipment shown in the diagram, however use a different beaker than the one you found the mass for above. Angle the spOut on the overow can slightly downward. Obtain a third beaker and ll it with water. Pour the water into the overow can tmtil it starts overowing. It is critical that you take care in completing this step so that the overow can is completely full. Remove the beaker under the spout of the overow can and replace it with the dry beaker you previously weighed. Take care not to bump the overow can during the rest of the experiment. Begin with the aluminum object suspended above the water in the overow can. Click the 'Collect' button. Wait approximately 30 seconds, then slowly lower the force probe so that the aluminum object is completely submerged in the overow can but does not touch the bottom or sides of the overow can. Make sure that all of the water that ows out of the overow can is collected in the dry beaker. Wait until the data collection is complete. Data o On the resulting graph, click and drag to select a time interval when Analysis the object is suspended in air. Find the average value of the force by clicking the 'Statistics' button on the tool bar. This value is the actual weight. * Similarly nd the average value of the force when the object is submerged in water. This value is the apparent weight. Question 1.3 What is the actual weight of the aluminum obiect? Question 1.4 What is the apparent weight of the aluminum object? . Place the beaker containing the water that owed out of the overow can on an electmnic balance. Question 1.5 What is the mass of the beaker and displaced water? Question 1.6 What is the mass of the displaced water? Show how you determined your answer. Question 1.\"! What is the weight of the displaced water? Show how you determined your answer. Question 1.8 Draw two mm diagrams of the aluminum object, one before and one after it is submerged in water. A m diagram should only contain forces. The forces in your diagrams may include the weight of the object, the tension in the string and the buoyant force. Before Submersion After Submersion Question 1.9 What is the net force on the aluminum object both before and after it is submerged? Hint: in both cases the aluminum object was at rest. Question 1.10 Question 1.1 1 Question 1.12 Question 1.13 Question 1.14 Look at your fteehody. diagram for the aluminum object before it is submerged. How do the weight and tension forces compare? Your answer to the last question should show that before the aluminum object is submerged, the reading of the force probe (i.e., the tension) equals the weight (i.e., the 'actual' weight) of the object. Now look at your freehody diagram after the aluminum object is submerged. Write an expression for the buoyant force in terms of the weight and tension force. Buoyant force = Remember that after the aluminum object is submerged, the reading 011 the force probe (i.e., the tension) is equal to the apparent weight. Hence your answer to the last question should show that the buoyant force can be calculated as: BuOyant force = Actual Weight Apparent Weight Use your results from questions 1.3 and 1.4 to calculate the buoyant force. Show your calculation. Calculate the percent difference between the buoyant force and the weight of the displaced water. Show your calculation. Percent Difference = Comment on how well the buOyant force compares to the weight of the displaced water. Part 2 Question 2.1 Question 2.2 Question 2.3 Question 2.4 Question 2.5 Question 2.6 Question 2."! Question 2.8 Question 2.9 Repeat the experiment you did above for a different metal object. What is the mass of the dry beaker? What is the actual weight of the object? What is the apparent weight of the object? What is the mass of the beaker and displaced water? What is the mass of the displaced water? Show how you determined your answer. What is the weight of the displaced water? Show how you determined your answer. What is the buoyant force on the object? Show your calculation. Calculate the percent difference between the buoyant force and the weight of the displaced water. Show your calculation. Comment on how well the buoyant force compares to the weight of the displaced water. Part 3 For this part you do not need the force probe or the computer. o Find the mass of a block of wood using an electronic balance. Question 3.1 What is the mass of the block of wood? Question 3.2 What is the weight of the block of wood? Show how you determined your answer. . Pour water into the overow can until it is completely ill. . Place a dry beaker (of known mass) under the spout of the overow can. Gently place the block of wood on the water in the overow can (it will oat). Wait till the overow stops completely. Measure the mass of the beaker with the displaced water. Question 3.3 What is the mass of the dry beaker? Question 3.4 What is the mass of the beaker and displaced water? Question 3.5 What is the mass of the displaced water? Show your calculation. Question 3.6 What is the weight of the displaced water? Show your calculatiOn. The Law of Flotation relates the weight of the oating object to the weight of the displaced uid. Question 3.\"! Calculate the percent difference between the weight of the wooden block and the weight of the displaced water. Show your calculation. Question 3.8 Comment on how well the two weights Compare. Question 3.9 Draw a m diagram for the oating block. Your diagram should include the weight and buoyant force. Question 3-10 What is the net force on the oating block? Question 3.11 Are the forces in your Wdiagram equal or is one bigger? Comment According to Archimedes' Law, the weight of the displaced water equals the buoyant force. According to the Law of Floatation, the weight of the displaced water equals the weight of a oating object. Your answers to the last few questions should show why the Law of Floatation is simply a consequence of Archirnedes' Law. Question 3-12 Which of these two laws is true under all conditions? Question 3.13 Under What conditions is the other law true? Part 4 Follow up Question 4.1 The relationship you found between the buoyant force and the weight of the displaced water is called Archimedes' principle. State this principle by writing an equation with words. Question 4.2 The relationship you found between the weight of a floating object and the weight of the displaced water is called the Law of Flotation. As in the last question, state this principle by writing an equation with words. Question 4.3 Two identical containers are placed on two scales as shown in the diagram below. Both are filled with water to the brim. A piece of wood is placed in one of the containers and it floats. The water that overflows does not fall on the scale. Compare the readings on the scales. Explain your reasoning. wood water bucket - scale