# Relationship of density and buoyancy

### Buoyancy - Wikipedia

Buoyancy. Why do some things float and others sink? The first thing that comes to The relationship between object's volume and mass is called its density. Buoyancy force is the weight of displaced fluid. So the buoyant force given by a liquid is directly proportional to the density of that liquid. Buoyant force = density of the liquid * volume of the object inside the liquid * gravitational constant g. Density is defined as the ratio of an object's mass to its volume: apparent masses and compare this to the mass of the water displaced using relationship (3 ).

Chapter 4 - Density and Buoyancy Buoyancy Buoyancy is the upward force caused by a fluid, such as water. This concept helps to explain why some things float while other objects sink. Buoyancy is an important factor in the design of many objects and in a number of water-based activities, such as boating or scuba diving. The mathematician Archimedes discovered much of how buoyancy works almost years ago.

### how dense fluid affect the buoyancy force? - Physics Stack Exchange

In his research, Archimedes discovered that an object is buoyed up by a force equal to the weight of the water displaced by the object.

In other words, a inflatable boat that displaces pounds 45 kilograms of water is buoyed up by that same weight of support. An object that floats in the water is known as being positively buoyant.

- What's the relationship between density and buoyancy?

An object that sinks to the bottom is negatively buoyant, while an object that hovers at the same level in the water is neutrally-buoyant. Similarly, the downward force on the cube is the pressure on the top surface integrated over its area. Therefore, the integral of the pressure over the area of the horizontal top surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the top surface. As this is a cube, the top and bottom surfaces are identical in shape and area, and the pressure difference between the top and bottom of the cube is directly proportional to the depth difference, and the resultant force difference is exactly equal to the weight of the fluid that would occupy the volume of the cube in its absence.

### Buoyancy | Science Primer

This means that the resultant upward force on the cube is equal to the weight of the fluid that would fit into the volume of the cube, and the downward force on the cube is its weight, in the absence of external forces.

This analogy is valid for variations in the size of the cube. If two cubes are placed alongside each other with a face of each in contact, the pressures and resultant forces on the sides or parts thereof in contact are balanced and may be disregarded, as the contact surfaces are equal in shape, size and pressure distribution, therefore the buoyancy of two cubes in contact is the sum of the buoyancies of each cube.

This analogy can be extended to an arbitrary number of cubes. An object of any shape can be approximated as a group of cubes in contact with each other, and as the size of the cube is decreased, the precision of the approximation increases.

The limiting case for infinitely small cubes is the exact equivalence. Angled surfaces do not nullify the analogy as the resultant force can be split into orthogonal components and each dealt with in the same way. Ship stability Illustration of the stability of bottom-heavy left and top-heavy right ships with respect to the positions of their centres of buoyancy CB and gravity CG A floating object is stable if it tends to restore itself to an equilibrium position after a small displacement.

For example, floating objects will generally have vertical stability, as if the object is pushed down slightly, this will create a greater buoyancy force, which, unbalanced by the weight force, will push the object back up. Rotational stability is of great importance to floating vessels. Given a small angular displacement, the vessel may return to its original position stablemove away from its original position unstableor remain where it is neutral. Rotational stability depends on the relative lines of action of forces on an object.

The upward buoyancy force on an object acts through the center of buoyancy, being the centroid of the displaced volume of fluid.

The weight force on the object acts through its center of gravity. A buoyant object will be stable if the center of gravity is beneath the center of buoyancy because any angular displacement will then produce a 'righting moment '. The stability of a buoyant object at the surface is more complex, and it may remain stable even if the centre of gravity is above the centre of buoyancy, provided that when disturbed from the equilibrium position, the centre of buoyancy moves further to the same side that the centre of gravity moves, thus providing a positive righting moment.

If this occurs, the floating object is said to have a positive metacentric height. This is independent of its size or shape.

An object with a mass of If the object has a volume greater than In other words, it will float. If its volume is less than This means whether or not an object will float or sink depends on its own density and the density of the liquid it is placed in. An object with a density of 0. Three quarters of an object with an density of 0.

## What is the relationship between buoyancy and density?

Another way to look at the buoyancy of an object is as an interaction of two forces. The force of gravity Fg pulling an object down. This is the weight of the object; its mass time the acceleration due to gravity 9. It is a force and is expressed in Newtons N.