Buoyancy

Why do some things float and others sink? The first thing that comes to mind for many people is that it depends on how heavy an object is. While an object's weight*, or more properly its mass** does play a role, it is not the only factor. If it were, we could not explain how a giant ocean liner floats while a small pebble sinks. Mass matters, but there is more to it.

The ability of an object to float is described as its buoyancy. The buoyancy of an object is its tendency to float on or rise in a liquid. An object that floats in water is said to be positively buoyant. An object that sinks is negatively buoyant. To determine an object's buoyancy, both its mass and volume* must be taken into consideration. The relationship between object's volume and mass is called its density*. Density is defined as the mass of an object per unit volume. Mathematically, this relationship is described using the following equation

density = mass / volume

The standard metric unit for density is grams per cubic centimeter (g/cm3).

In order to explain how an object's density influences its buoyancy, the behavior of an object placed in water must be understood. When an object is placed in water, even a floating object displaces some of that water. The amount of water displaced is a function of the object's mass. The object sinks into the water until it displaces an amount of water equal to its own mass. A 1 g object will sink until it displaces 1 g of water. This is independent of its size or shape. Since water has a density of 1 g/cm3, a 1 g object will displace 1 cm3 of water.

An object with a mass of 25.2 g can displace up to 25.2 cm3 of water. If the object has a volume greater than 25.2 cm3, it will stop sinking before it is fully immersed in the water. In other words, it will float. If its volume is less than 25.2 cm3, it will not stop before it is fully immersed. It will sink.

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. In the case of water, an object with a density less than 1 g/cm3 will float. The closer its density is to 1 g/cm3, the more of it will sit below the water level. An object with a density of 0.5 g/cm3 will sit half in and half out of the water. Three quarters of an object with an density of 0.75 g/cm3 will be submerged.

Another way to look at the buoyancy of an object is as an interaction of two forces.

  1. The force of gravity (Fg) pulling an object down. This is the weight of the object; its mass time the acceleration due to gravity (9.8 ms-2 on Earth). It is a force and is expressed in Newtons (N).
  2. The buoyant force (Fb) holding the object up. This can be measured as the force of gravity acting on a mass of water equal to the amount of water the object displaces when fully immersed. This is also expressed in Newtons.

Example 1:

An object with an mass of 10 g (0.01 kg)** and a volume of 5 cm3 will have an Fg and Fb of:
Fg = 0.01kg x 9.8 ms-2 = 0.098 kg m s-2 = 0.098 N
Fb = 5 cm3 water = 5 g water = 0.005 kg x 9.8 ms-2 = 0.049 kg m s-2 = 0.049 N
Fg > Fb - the object will sink.

Example 2:

An object with an mass of 10 g (0.01 kg) and a volume of 20 cm3 will have an Fg and Fb of:
Fg = 0.01kg x 9.8 ms-2 = 0.098 kg m s-2 = 0.098 N
Fb = 20 cm3 water = 20 g water = 0.02 kg x 9.8 ms-2 = 1.96 kg m s-2 = 0.196 N
Fg < Fb - the object will float.

The illustration below shows a block placed in water. it explores the relationship between the block’s volume, mass and density, and how this relationship determines the block’s buoyancy. Move the sliders to adjust the mass and volume of the red block.

Demonstration video:

*In common language, weight and mass are used interchangeably. In physics, they have distinct meanings. Mass is the amount of matter, or ‘stuff’ in an object and this property is independent of where the object is located. The standard unit of mass is the kilogram. An object's weight is is a function of the force of gravity acting on its mass. This means that an object's weight will vary depending on where it is found. For example, the force of gravity on the moon is less than it is on the earth so an object with a fixed mass will weigh less on the moon than it will on the earth. Since weight is a force, it is best expressed in the derived unit, the Newton (1 N = 1 kg m / s2).

**Need to converted to kg in order to express the answer in Newtons.


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