StabilityFloatingBodies

StabilityFloatingBodies - C lassroom I n this s e c t i o n...

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Classroom In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. "Classroom" is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science. K R Y Simha Usha Srinivasan Department of Mechanical Engineering Indian Institute of Science Bangalore 560 012, India Archimedes : Bathtub Academic par excellence Stability and control of floating bodies is a major aspect of navigation from ancient to modern times. It is indeed remarkable that Archimedean concepts continue to guide watercraft designers even after 2200 years! Extending Euclidean concept to solids, Archimedes solved the problem of a paraboloid floating stably but with its base inclined to the water surface. Here, we revisit Archimedes and present stability maps (A-maps) for paraboloid, solid cone and a prism. For a specific combination of geometry and specific gravity, these A-maps predict whether a solid floats vertically or in a tilted fashion; or, whether it is partially submerged. 1. Introduction Keywords Hydrostatics, stability of float- ing bodies, metacentre, centre of buoyancy, paraboloid, Archimedean map (A-mapl, moment of inertia. Have you ever wondered how pans and pails sink in water as they get filled up? Or, how engineers design boats and ships to stay afloat in the sea? Have you ever noticed how toys and sundry float in a baby bathtub? Would you be able to name the Sicilian genius who transformed his bathtub to one of the most advanced laboratories and whose ideas have survived the test of time like his contemporary Euclid? You would most certainly be able to name the scientist-philosopher who discovered buoyancy 78 RESONANCE I October 2006
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CLASSROOM screaming Eureka! Well, the answer is obviously Archimedes. Schooled in ancient Alexandria, Euclid and Archimedes continue to inspire generations of students and teachers of mathematics, physics and engineering. Archimedes literally immersed himself in a bathtub of ideas and inventions. Hydrostatics and hydrodynamics command a long and respectable history dating back to Archimedes and beyond. Navigation and commerce along rivers and canals and across oceans in the early history of human civilization created huge opportunities for a large number of merchants, poets, pirates, artisans, skilled workers and scientist-philosophers like Archimedes. It is quite interesting to note that analytical excellence demon- strated by Archimedes and Euclid was virtually non-existent before their time in the recorded history of science. It is even more surprising to add that it took another 1900 years for the world to witness the rebirth of mathematical analysis of natural phenomena through calculus invented by Leibniz and Newton. Stability of different shapes of floating bodies in water is a fundamental requirement in the design of boats and ships.
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This note was uploaded on 07/14/2011 for the course MAC 3473 taught by Professor Block during the Spring '08 term at University of Florida.

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StabilityFloatingBodies - C lassroom I n this s e c t i o n...

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