Archimedes in the 21st Century by Chris Rorres

Author:Chris Rorres
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Hydrostatic Stability of Floating Objects

In his treatise OFB Archimedes also deals with the stability of bodies floating on the surface of a liquid, especially of homogeneous solids of simple shape. His basic ideas are already shown in Book I, §§8-9, for a segment of a sphere . In Book II, §§ 2 ff. the example of an axisymmetric paraboloid segment as shown in Figure 4 is even more illustrative and will be discussed here.

Figure 4Inclined paraboloid segment (From Nowacki [14])

The stability criterion for hydrostatic equilibrium is based on the experiment of thought to incline the body from its upright condition and to determine whether the resultant gravity and buoyancy forces acting on the body in this condition will tend to restore it to its upright condition. The angle of inclination (heeling angle) is finite but so that the base of the paraboloid segment does not get wetted. For the stability of this body, Archimedes asserts in Proposition II.2:

A homogeneous solid paraboloid segment cut off perpendicularly to its diameter, whose axis is not greater than 1.5 times the paraboloid’s halfparameter, whatever its specific weight , if it floats in a liquid so that its base does not touch the liquid surface, will not remain at rest unless its axis is vertically oriented, but will restore itself to the upright condition.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.