I guess the confusion arises from measuring water by its weight instead of its volume. How much (more) volume of water would you need to fill into cup D to make cup B float in it, if cup D would be wider than cup A?.How much water do you need to fill into a cup C to make cup B float in it, if cup C equals cup A except for a higher rim?.By how much rises the water level, if you put a stone (smaller but as heavy as cup B) into cup A?.Will cup B float again, if you put it back?.You pull the floating cup B out of cup A. Most of the water of cup A spills over the rim except for a tiny amount. You place cup B filled with some water to float in cup A.
This is why only a thin jacket of water around a paper cup is enough to create the pressure to float that cup.Ĭup A is full of water to the rim. A column of water 10m high, and as thin as a pencil, has the same pressure at the bottom as a 10m deep lake (aobut 1 atmosphere). This is all related to the fact that the pressure in a column of fluid under gravity is irrespective of the width of that column and therefore its volume. But buyoancy does not depend on actually pushing out all the fluid out of the object's space it's just that: a visual aid. The "displacement visualization" of buyoancy assumes that the body of water is large enough that the availability of fluid is practically unlimited. This is usually stated as "the volume displaced by the object", but the displacement is an abstraction: there might not be enough fluid available such that when the buoyant object is removed, its entire volume is filled by the fluid that remains. Because of the way the surface integral works out around an object, a short-cut pops out from the mathematics: the buoyant force can be obtained knowing just the gravitational force which acts upon the equivalent volume of the fluid in which the object floats. Each unit of area of the object is acted upon by pressure, and the net difference in pressure between the upper and lower parts of the object creates buyoancy: because the parts of the object's surface which are deeper are subjected to greater pressure than the parts of the object's surface which are immersed less deeply.Īrchimedes' Law is just a corollary which arises from this pressure gradient.
50 grams of water can be displaced in such a way that sufficient depth is created to float a cup of 100 grams.ĭepth, together with density and gravity is what actually creates the pressure that causes buyoancy. The depth of the water is not restricted by the available volume. If the cup requires X centimeters of depth in order to float, and the surface of the water is > X centimeters above the bottom of the larger container (taking into account the displacement caused by the immersion), then the cup will float.
Of course, that body just has to have enough depth to contain the immersion. It is a given that a partially filled cup will float in a body of water.