How do density and buoyancy relate?

Density and buoyancy are closely related concepts in fluid mechanics, and they explain why objects float or sink when placed in a fluid.
1. Density:
• Density is the mass of an object per unit volume. Mathematically, it is given by:
ρ=mV\rho = \frac{m}{V}
where:
o ρ\rho is the density,
o mm is the mass,
o VV is the volume of the object.
• An object will float or sink depending on its density relative to the density of the fluid in which it is placed.
2. Buoyancy:
• Buoyancy is the upward force exerted by a fluid on an object that is immersed in it. This force is responsible for whether an object sinks, floats, or stays suspended in a fluid.
The buoyant force is equal to the weight of the fluid displaced by the object, and it is described by Archimedes' Principle, which states:
Fb=ρfluid⋅Vdisplaced⋅gF_b = \rho_{\text{fluid}} \cdot V_{\text{displaced}} \cdot g
where:
o FbF_b is the buoyant force,
o ρfluid\rho_{\text{fluid}} is the density of the fluid,
o VdisplacedV_{\text{displaced}} is the volume of fluid displaced by the object,
o gg is the acceleration due to gravity.
3. Relationship Between Density and Buoyancy:
• An object will float if the buoyant force is equal to or greater than the gravitational force acting on the object (its weight).
• If the object is less dense than the fluid, it will displace enough fluid to produce a buoyant force that is greater than or equal to its weight, so it will float.
• If the object is denser than the fluid, the buoyant force will be less than the weight of the object, so it will sink.
• If the density of the object is the same as the density of the fluid, the object will remain suspended in the fluid without sinking or rising.
4. Example:
• Wood in Water: Wood has a lower density than water. Therefore, when placed in water, it displaces a volume of water that creates a buoyant force greater than or equal to its weight, causing it to float.
• Iron in Water: Iron is denser than water. When placed in water, the buoyant force is not enough to support its weight, so it sinks.
Conclusion:
• Density determines whether an object will float or sink. An object with lower density than the fluid will float, while an object with higher density will sink. The buoyant force depends on the density of the fluid and the volume of fluid displaced, which explains why objects behave differently in different fluids.