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Float Your Boat

BUOYANCY

Buoyancy is an upward force on any object immersed in a fluid. The formula for buoyancy can be defined as:

b u o y a n c y = p r e s s u r e * a r e a

The pressure acting on an object in a fluid is equal to:

p r e s s u r e = d e n s i t y_{f l u i d} * g r a v i t y * d e p t h

Thus,

b u o y a n c y = d e n s i t y_{f l u i d} * g r a v i t y * d e p t h * a r e a

depth * area = volume displaced

b u o y a n c y = d e n s i t y_{f l u i d} * g r a v i t y * v o l u m e d i s p l a c e d

Figure: Free body diagram of a barrel floating in water.

ARCHIMEDES' PRINCIPLE

The buoyant force that is exerted on an object is equal to the weight of the fluid that the object displaces.

Figure: This illustrates Archimedes' Principle of buoyancy. As you can see, the 5kg mass displaces 2kg of water when immersed. The buoyant (upward) force acting on the mass is 2 kg. This reduces the mass's apparent weight by 2 kg - that is, from 5 kg to 3kg as shown.

A diagram illustrating archimedes principle.

SINK OR FLOAT

An object's ability to float depends on its density relative to the density of the fluid.

d e n s i t y = \frac{m a s s}{v o l u m e}

Figure: This series of images compare the buoyancy of three barrels with constant volume but varying mass.

A diagram showing how buoyancy is calculated with a constant volume.

Figure: This series of images compare the buoyancy of three barrels with constant mass but varying volume.

A diagram showing how buoyancy is calculated with constant mass.