Hands-on Activity: Eureka! Or Buoyancy and Archimedes' Principle
Educational Standards :
Pre-Req Knowledge (Return to Contents)
Competancy with basic measurements involving distance, area and volume, units of measure and calculations involving single and multi-step equations.
Learning Objectives (Return to Contents)
After this activity, students should be able to:
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.
Materials List (Return to Contents)
Each group needs:
Introduction/Motivation (Return to Contents)
Most of us know that steel feels heavier than plastic, but why? How do we know what an object is made of? How do large ships made of metal float on water? How are these two questions related? And why do engineers care about the properties of materials? Let's start with the first question.
(Tell the following story of Archimedes and the king's crown.)
A long time ago in ancient Greece, a man named Archimedes was trying to solve a problem. He wanted to know how to tell if a crown was made of real gold. You might know that different materials have different densities (mass per volume). Archimedes reasoned that if he could figure out the density of the crown, he could determine whether it was gold or not. Density = mass / volume, so if you had a regular shape like a cube, it would be easy to measure and calculate the volume. But how could he calculate the volume of the crown? He decided to have a nice bath to think about this. When he got into the bath, the water level rose, and he realized that he could measure the volume of water displaced by the crown, and so discover the volume of the crown, then calculate the density of the crown. Eureka!
Do you know why large ships made of steel can float on water? It is related to what Archimedes noticed when he got in the bath. The displacement of water is what keeps ships afloat and we call it the buoyancy effect. In order for a ship to float on water, it needs to displace its own weight in water. This might be hard to understand right now, but we will do some experiments to prove that this is true.
So, why is this important to engineers? Engineers apply mathematical equations to determine the properties of materials. By predicting how a material will behave in a certain situation, under certain constraints, engineers can determine which material to choose for a given design project. For example, in order to design a boat that will float, engineers must understand buoyancy to determine how objects behave in a fluid (liquid or gas). Differences in densities determine whether an object sinks or floats in a liquid, or how much liquid the object displaces when floating. Engineers must consider material densities and the resulting buoyant forces when designing boats, submarines, underwater pipelines and cables, and aircraft.
Vocabulary/Definitions (Return to Contents)
Procedure (Return to Contents)
Before the Activity
With the Students
More specificss can be found at:
Attachments (Return to Contents)
Assessment (Return to Contents)
Activity Embedded Assessment
Worksheets: Have students complete the two attached worksheets to guide them through the activity. Review their answers to gauge their comprehension.
Meet the Standards: Review students' worksheet answers or administer a separate test to verify that they are able to perform the following NCTM geometry and measurement standards:
Activity Extensions (Return to Contents)
Student Reflection: Ask students to think back on the project and write answers to the following questions:
References (Return to Contents)
Buoyancy. Last revised 26 March 2013. Wikipedia, The Free Encyclopedia. Accessed 28 March 2013. http://en.wikipedia.org/wiki/Buoyancy
Nave, C.R. Buoyancy. Hyperphysics. Department of Physics and Astronomy, Georgia State University. Accessed 28 March, 2013. http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy.html#buoy
Copyright© 2010 by Regents of the University of Colorado; original © 2010 Board of Regents, Washington State University
Supporting Program (Return to Contents)CREAM GK-12 Program, Engineering Education Research Center, College of Engineering and Architecture, Washington State University
Acknowledgements (Return to Contents)
This content was developed by the Culturally Relevant Engineering Application in Mathematics (CREAM) Program in the Engineering Education Research Center, College of Engineering and Architecture at Washington State University under National Science Foundation GK-12 grant no. DGE 0538652. However, these contents do not necessarily represent the policies of the NSF, and you should not assume endorsement by the federal government.