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Unformatted text preview: 15 Fluids and Elasticity Recommended class days: 3 Background Information Fluids and elasticity are an application of Newtonian mechanics to deformable media. It should come as no surprise that the concepts of density, pressure, and buoyancy present many challenges for students. The major study of student difficulties with this topic is the paper by Loverude et al. (2003) on student understanding of Archimedes’ principle. In one part of this study, students were shown a picture of five blocks of identical size and shape but increasing mass: m 1 < m 2 < m 3 < m 4 < m 5 . They were told that each block would be held halfway down in an aquarium filled with water, then released. The final positions of blocks 2 and 5 were shown, and the students were asked to sketch the final positions of blocks 1, 3, and 4. Only about 40% of students answered correctly after instruction in hydrostatics. The figure shows the most common incorrect response in which the increasing masses form a “descending line.” (The investigators would have accepted as correct block 3 suspended at the point where it was released due to the small probability it might be neutrally buoyant, but such responses were rare.) In explaining their choices, some students demonstrated lingering difficulties with forces, static equilibrium, and Newton’s laws. Others recalled the two equations F B = ρ V disp g and F B = mg (only true for a floating object), but they misapplied the equations or did not recognize which volume was the volume of the displaced fluid. On a deeper level, students’ incorrect explanations were frequently based on one of two incorrect ideas: • A belief that the buoyant force depends on the mass of the block. 10–20% of students stated that a more massive block would cause more fluid displacement, and 10–20% of students believed that the same block would displace more liquid in a less-dense fluid than in a more-dense fluid. These beliefs seem to stem from confusion between the concepts of mass, volume, and density. • A belief that the buoyant force increases linearly with depth. These students confused pressure (which does increase with depth) with the buoyant force, and they showed a poor understanding of the forces acting on a submerged or floating object. 15-1 15-2 Instructor’s Guide In a different question, students were shown two identical cubes floating in liquids of different densities and asked whether the buoyant force on A is greater than, less than, or equal to the buoyant force on B. Since the cubes are in static equilibrium, no knowledge of hydrostatics is needed to recognize that the buoyant forces must be the same. None- theless, 60–80% of students answered incorrectly after instruction. Students hold a strong belief that there must be a larger buoyant force acting on B to cause it to float at a higher level. As one student said, “Since B is higher, it is being pushed up more which means its buoyant force is greater.” Interestingly, this belief is not confined to hydrostatics. When shown two identical blocks Interestingly, this belief is not confined to hydrostatics....
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- Spring '10