Archimedes’ principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the centre of mass of the displaced fluid. Archimedes’ principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes of Syracuse.
The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius, a votive crown for a temple had been made for King Hiero II of Syracuse, who had supplied the pure gold to be used, and Archimedes was asked to determine whether some silver had been substituted by the dishonest goldsmith. Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density. While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. For practical purposes water is incompressible, so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained. This density would be lower than that of gold if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying “Eureka!” (εύρηκα!”, meaning “I have found [it]!”). The test was conducted successfully, proving that silver had indeed been mixed in.
From this principle we can derive that an object will sink when placed into a fluid with a lower mass density than the object.
This database1 of mass densities of various substances contains facts of the form density(Thing, Density) where Density is a value in kg/m3.
Write following predicates:
sink(Thing) which is true if Thing sinks in pure water of 4 degrees Celsius. For simplicity, you may assume that anything with a mass density above 1000 kg/m3 will sink.bathtub_experiment(+List, -Sink, -Float) that takes a list of elements to put in a bath tub containing pure water of 4 degrees Celsius. The result are 2 lists Sink and Float containing the elements that have sunk and stayed afloat. You can use partition/42 for this.