Volume and Displacement, re-enacting Archimedes

myminifactory

Introduction This design enables students to learn about volume and displacement by recreating Archimedes' famous bathtub experiment. In this experiment, he discovered a method to measure an object's volume based on the water it displaces. (Reference: Wikipedia) The model features a "bathtub" that can be filled with water and displaced using a displacement object. The size of the tub is carefully set so that the volume inside the tub equals the volume outside the tub at the tub wall level. Application This design can be incorporated into a curriculum to instruct students at various levels, starting from basic concepts like cube volume and displacement to more advanced topics in algebra, solving equations for variables and conditions, density, and 3D printing concepts/error analysis. Volume/Displacement Topics Have students measure the volume of the displacement cube, handle, bathtub, and express it in suitable units. Fill the tub with water, displace it using the displacement cube, note whether the volumes inside and outside the tub are identical. Account for any discrepancies. Fill the tub to its brim and displace the liquid with objects of unknown volume. Remove the object and measure the cavity at the top of the tub to calculate the volume. Algebra Given a known inner-cube size, calculate the required volume for the outer cube. In this example, the outer cube is not a perfect cube - its dimensions are set to match the tub volume at the tub wall level. Derive an equation for this and solve for the length/width dimension given an inner cube size. Remember to account for the wall width! (Solution available in the OpenSCAD code.) Density/Buoyancy Provide displacement objects of various densities/infill percentages. Which object floats? Calculate their density. 3D Printing Applications Using standard 3D printing parameters, calculate the infill percentage from mystery prints. The above experiments make several assumptions based on a perfect mathematical model. When we print an object, it is far from perfect. What are some of the problems with this print? What assumptions cannot be made? How could this model be improved? Cost/Commercial Alternatives The tub uses approximately 60g of PLA, and the displacement cube about 13g, which costs around $1.50. There are no known commercial products available. Improvements/Future Work Passageways for escaping water could be cut into the displacement cube to allow for higher tolerance parts. Graduations could be carved into the side of the objects for easier measurement.