What is Buoyancy?

To begin our analysis of ships, we discuss the principle of buoyancy. Buoyancy is defined as the net upward force exerted by a fluid on an object. By placing an object into a fluid like the cylinder in Figure 1, it is demonstrated that the weight of the object is balanced by the buoyant force, causing the cylinder to float. However, not all objects float as you are probably aware. Where a rock would sink to the bottom, a plank of wood rests on the surface of the water.

Archimedes principle

    Archimedes discovered  that the volume of fluid displaced by an object is equal to the volume of         the object, which is known as Archimedes Principle. So, if we place an object in a fluid, it is going to experience a net force. Defining up as positive, the equation becomes

  (1)

    Where ${\widevec{F}$is the buoyant force. The buoyant force can then be written as ${m}_{fluid}*g$. From here, we know that the mass of something is         equal to the density (ρ$$) multiplied by the volume, $m=ρ*V$. Equation 1, can now be written as

${\widevec{F}}_{net}=({ρ}_{fluid}*{V}_{fluid})g-({ρ}_{object}*{V}_{obj$ (2)

    Utilizing Archimedes Principle, we can point out that ${V}_{fluid}={V}_{object}$ and thus,

${\widevec{F}}_{net}=({ρ}_{fluid})Vg-({ρ}_{object}$    (3)

From Equation 3, we can see that the net force will be upward (positive), and the object will float, if the density of the fluid is greater than the density of the object. This is the fundamental reason why a boat, whether made of wood or steel, will float in water, because it is hollow and thus is less dense than the water it is in.