Buoyancy

When asked why do some things float and others sink, the first thing that comes to many people's minds is the weight* of each item. While weight*, or more properly, 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 depends on 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 known. The relationship between an object's volume and mass is called its density*. Density is the mass of an object per unit volume:

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

Observing an object placed in water helps illustrate now an object's density influences its buoyancy. All objects, even those that float, displace some water.

Specifically, when placed in water, an object sinks into the water until it displaces an amount of water equal to its own mass. The more mass an object has, the further it sinks. A 1 g object will sink until it displaces 1 g of water. A 2 g object will sink until it displaces 2 g of water. This behavior is independent of each object's size and shape.

Water has a density of 1 g/cm3. Therefore, the 1 g object will displace 1 cm3 of water. The 2 g object will displace 2 cm3 of water.

An object with a mass of 25.2 g will displace 25.2 cm3 of water. If the object has a volume greater than 25.2 cm3, it will stop sinking before it is completely submerged. In other words, it will float. If its volume is less than 25.2 cm3, it will not stop before its entire volume sinks below the surface.

p>Whether an object will float or sink is dependent on its density, and on 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 a density of 0.75 g/cm3 will be submerged.

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

  1. The force of gravity (Fg) pulling down on an object. This is the weight of the object - its mass time the acceleration due to gravity (9.8 ms-2 on Earth).
  2. The buoyant force (Fb) of the water pushing up on the object. This is equal to the force of gravity acting on a mass of water equal to the amount of water the object displaces when fully immersed.

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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