|MadSci Network: Physics|
Chris, We need to understand a couple of concepts to answer your question. First, let’s make sure we understand what is meant by the “density of a body“. Density is the mass of a body divided by the volume occupied by the body (d = m/V). This is an accurate, physically rigorous definition. In a common approximation, sometimes people talk about density as the “weight” of an object divided by its volume. At the surface of the Earth when the force of gravity on an object (a body’s weight) is more or less proportional to its mass, this common approximation is OK too. Second, there are two types of bodies we need to concern ourselves with here. Those are “rigid bodies” and “non-rigid bodies”. Rigid bodies are bodies whose shape stays the same and is unaltered by any forces acting within our question (i.e., air pressure, liquid pressure, force of gravity, etc.). Think of a steel chest or an oil tanker as a more or less rigid body. On the other hand, non-rigid bodies can have their shape altered, compressed, expanded, or distorted by the forces acting within our question. Think of a balloon, or box made of paper or straw as a non- rigid body. If we measure the mass of a RIGID body and measure its volume in air, we can calculate its density in air by dividing the mass by the volume. If we then put that rigid body in a liquid (like water or oil), we will find its mass will not have changed. Because it is a rigid body, its volume will not have changed, either. Therefore, its density will not have changed. The density of a rigid body is the same in air or in the liquid. But, let's do this with a NON-RIGID body. If we measure the mass of a non- rigid body and measure its volume in air, we can calculate its density in air by dividing the mass by the volume. If we then put that non-rigid body in a liquid, we will find its mass will not have changed. However, upon measuring its volume we may find that its volume has changed. If it is compressed (less volume) then its density will have INCREASED. If the body expanded (more volume), its density will have DECREASED. As an example, we can fill a toy balloon (a more or less perfect non- rigid body) with air. If we immerse it in oil by pushing down on it with our hand, it will compress to the point where the pressure exerted by the balloon plus the air inside it equals the pressure exerted by the oil in which it is immersed. The pressure exerted by a body (defined as Force divided by Volume, p = F/V) is directly proportional to its density ( again, d = m/V). Thus, the balloon plus the air will compress until its density EQUALS the density of the oil in which it is immersed. If we then let it go, it will come to the top surface of the oil by expanding. It will “float” on the oil surface because now - in air - its density is less than that of the oil. Hope this helps in answering your question, Dr. Ken Beck
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