Question

An object with a high density can be floated on an object with a low density in a fluid with a density if the volumes of the objects are right. What is the condition for such a stack having neutral buoyancy, in terms of masses and volumes of the blocks and the density of the water? Express the condition mathematically.

Answer 1

Mass is a physical property which all objects possess, but objects of the same size can have different masses and weights. This difference is characterized by another property, density. Density is defined as the ratio of an object's mass to its volume:

d= m/v Calculation

(1)

Since it is rare to find two different substances with identical densities, density is of value in helping to identify materials.

The specific gravity of a substance is defined as the ratio of the density of the substance to the density of water (1 gram/cm^3). This ratio is a convenient physical property since it has no units and is therefore independent of the system of measure you use to determine it.

Archimedes' principle states that the buoyant force experienced by a submerged object is equal to the weight of the liquid displaced by the object. Experimentally this appears in the fact that the submerged object apparently weighs less by an amount equal to the weight of the liquid displaced. The buoyant force can be expressed as

Calculation

(2)

where d is the density of the liquid, g is the acceleration of gravity and v is the volume of the immersed object (or the immersed part of the body if it floats). In this experiment the pan balances will compare masses in grams rather than weights. Since W=mg, the apparent change in mass when submerged is

(3)