1. Concept Overview
When an object is placed in a fluid, it experiences an upward push. This upward force is called the buoyant force, and it is responsible for floating, sinking, or partial immersion of objects. Archimedes’ principle explains exactly how this buoyant force works based on the fluid displaced by the object.
This principle forms the basis for understanding floatation, ship design, measuring density, and even how submarines dive and rise.
2. Definition
3. Understanding Buoyant Force
3.1. Why an Upward Force Exists
The pressure in a fluid increases with depth. The bottom surface of an immersed object is deeper than the top surface, so it feels higher pressure from below. This difference in pressure creates an upward force known as the buoyant force.
3.2. Buoyant Force and Fluid Displacement
When an object is lowered into a fluid, it pushes the fluid aside. The fluid pushes back with an equal and opposite force. The magnitude of this upward force is equal to the weight of the displaced fluid.
4. Mathematical Expression
4.1. Buoyant Force Formula
If a volume \(V\) of fluid is displaced and its density is \(\rho\), then the buoyant force is:
\( F_b = \rho V g \)
Where:
- \(F_b\): buoyant force
- \(\rho\): fluid density
- \(V\): volume displaced
- \(g\): acceleration due to gravity
5. Floating, Sinking, and Neutral Equilibrium
5.1. Object Sinks
If the weight of the object is greater than the buoyant force, the object sinks. This happens when the object is denser than the fluid.
5.2. Object Floats
If the buoyant force is equal to or greater than the object’s weight, it floats. Floating objects displace fluid equal to their own weight.
5.3. Neutral Buoyancy
When an object’s weight equals the buoyant force, it stays suspended at a fixed depth. Submarines achieve this by adjusting the water in their ballast tanks.
6. Applications of Archimedes’ Principle
6.1. Ship and Boat Design
Ships float because they displace a large volume of water, even though the material used (like steel) is denser. Large hollow structures ensure enough water is displaced to balance their weight.
6.2. Hydrometer
A hydrometer measures liquid density by floating at different levels in different fluids. It works entirely on buoyant force.
6.3. Submarines
Submarines dive by filling ballast tanks with water, increasing their weight. They rise by pumping water out, decreasing their weight so buoyancy dominates.
6.4. Hot-Air Balloons
Although filled with air, these balloons rise because hot air inside has lower density. The displaced cooler air provides upward buoyant force.
7. Examples to Build Intuition
7.1. Ice Floating on Water
Ice floats because it is less dense than water. It displaces water equal to its own weight, and the buoyant force keeps it afloat.
7.2. Pushing a Ball Under Water
A ball pushed into water quickly pops up when released. The buoyant force is greater than the weight of the ball, pushing it upward strongly.
7.3. Heavy Stones Sinking
A stone sinks because the weight of the stone is greater than the buoyant force produced by the water it displaces.