Final answer:
The Titanic sank because of an iceberg collision, which led to water flooding its compartments. This increased the ship's weight and density, causing the buoyant force to become insufficient to keep it afloat, and ultimately, the ship sank because it became denser than the water it displaced.
Step-by-step explanation:
To explain how the Titanic sank using the terms buoyant force, weight, and density, we must first understand Archimedes' Principle. This principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces. An object will float if the buoyant force is greater than its weight and sink if the buoyant force is less.
The Titanic sank because it hit an iceberg that damaged its hull, causing compartments to fill with water. As water entered the ship, its weight increased, and the buoyant force could no longer support it, leading to its sinking. The density of the ship changed as it filled with water, making it denser than the water it displaced, which further contributed to its inability to stay afloat.