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# Buoyancy

Unless otherwise stated, this section comes from College Physics, OpenStax, Rice University, by Paul Peter Urone, California State University, Sacramento, and Roger Hinrichs, State University of New York, College at Oswego, Creative Commons Attribution License v4.0
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### Density and Archimedes’ Principle

Density plays a crucial role in Archimedes’ principle. The average density of an object is what ultimately determines whether it floats.

If its average density is less than that of the surrounding fluid, it will float. This is because 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 is related to that of the fluid. In Figure 11.21, for example, the unloaded ship has a lower density and less of it is submerged compared with the same ship loaded.

We can derive a quantitative expression for the fraction submerged by considering density.

Figure 11.21 An unloaded ship (a) floats higher in the water than a loaded ship (b).

## Buoyancy in movies

Buoyancy of balloons in the movie “Up”

## Sample problems

SEPTEMBER 7, 2014BORIS SAPOZHNIKOV Does the balance beam tip to the right, to the left, or does it remain unchanged?

## Learning Standards

College Board Standards for College Success: Science

Appendix D: AP Physics Enduring Understandings

Enduring Understanding 3C

“At the macroscopic level, forces can be categorized as either long-range (action-at-a-distance) forces or contact forces…. Contact forces (e.g. frictional force, buoyant force) result from the interaction of one object touching another object and are ultimately due to microscopic electric forces…. Buoyant force is caused by the difference in pressure, or force per unit area, exerted on the different surfaces of the object. It is important for students to study each of these forces and to use free-body diagrams to analyze the interactions between objects.”