Eureka! Or Buoyancy and Archimedes' Principle
Tanker ship Stolt Emerald on the Savannah River in Georgia.Copyright 2008 Ianare' Sevi, Wikimedia Commons {PD} http://commons.wikimedia.org/wiki/File:Tanker_Stolt_Emerald.jpg
Students explore material properties in hands-on and visually evident ways via the Archimedes' principle. First, they design and conduct an experiment to calculate densities of various materials and present their findings to the class. Using this information, they identify an unknown material based on its density. Then, groups explore buoyant forces. They measure displacement needed for various materials to float on water and construct the equation for buoyancy. Using this equation, they calculate the numerical solution for a boat hull using given design parameters.
Engineers apply mathematical equations to determine materials properties. For example, understanding buoyancy is important for determining how objects behave in a fluid (liquid or gas). Differences in densities determine whether objects sink or float in liquids, or how much liquid objects displace when floating. Engineers consider material densities and the resulting buoyant forces when designing boats, submarines, underwater pipelines and cables, and aircraft. Buoyant forces also need to be understood to study and control influence dispersion of pollutants in air or water, or the separation of impurities from molten metals.
After this activity, students should be able to:
- Measure masses and volumes of known and unknown substances.
- Calculate density using given measurements.
- Predict physical behaviors by employing a numerical model.
- Apply predictions to an engineering design challenge.
Goals: This project is designed to connect experimentation with mathematical modeling and demonstrate the power of mathematical models. This project is designed to connect with students across many cultures and different socioeconomic strata. Water and watercraft are used throughout the world. This project provides insights to one aspect of engineering. Students discover how engineers use mathematics to design a boat within desired operating conditions.