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Density and Archimedes' Principle

### 13.10: Density and Archimedes' Principle

When a lump of clay is dropped into water, it sinks. But if the same lump of clay is molded into the shape of a boat, it starts to float. Because of its shape, the clay boat displaces more water than the lump and experiences a greater buoyant force, even though its mass is the same. The same holds true for steel ships. The average density of an object majorly determines if the object will float. If an object's average density is less than that of the surrounding fluid, it will float. The reason is that the fluid, having a higher density, contains more mass and hence more weight in the same volume. The buoyant force, which equals the weight of the fluid displaced, is thus greater than the weight of the object. Likewise, an object denser than the fluid will sink.

The extent to which a floating object is submerged depends on how the object's density compares to the density of the fluid. For example, an unloaded ship has a lower density, and thus a small portion of it is submerged compared with the same ship when it is loaded. The fraction submerged is the ratio of the volume submerged to the object's volume. In other words, the volume submerged equals the volume of fluid displaced. The fraction submerged is also equal to the ratio of the object's density to the density of the fluid. This expression gives insightful information about the type of fluid needed to make an object float or sink. For example, numerous lower-density objects or substances float in higher-density fluids: oil on water, a hot-air balloon in the atmosphere, a bit of cork in wine, an iceberg in saltwater, and hot wax in a "lava lamp," to name a few. A less obvious example is mountain ranges floating on the higher-density crust and mantle beneath them. Even seemingly solid Earth has fluid characteristics.

This text is adapted from Openstax, University Physics Volume 1, Section 14.4: Archimedes' Principle and Buoyancy.

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