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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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When you rise from lounging in a warm bath, your arms feel strangely heavy. This is because you no longer have the buoyant support of the water.

Where does this buoyant force come from? Why is it that some things float and others do not? Do objects that sink get any support at all from the fluid? Is your body buoyed by the atmosphere, or are only helium balloons affected?

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Answers are based on the fact that pressure increases with depth in a fluid. This means that the upward force on the bottom of an object in a fluid is greater than the downward force on the top of the object.

There is a net upward, or buoyant force on any object in any fluid.

If the buoyant force is greater than the object’s weight, the object will rise to the surface and float.

If the buoyant force is less than the object’s weight, the object will sink.

If the buoyant force equals the object’s weight, the object will remain suspended at that depth.

The buoyant force is always present whether the object floats, sinks, or is suspended in a fluid.

Pressure due to weight of fluid increases with depth buoyant force

The buoyant force is the net upward force on any object in any fluid.

Just how great is this buoyant force? To answer this question, think about what happens when a submerged object is removed from a fluid:

object submerged in fluid buoyant force

The space it occupied is filled by fluid having a weight w (sub)fl . This weight is supported by the surrounding fluid, and so the buoyant force must equal w(sub)fl , the weight of the fluid displaced by the object.

It is a tribute to the genius of the Greek mathematician and inventor Archimedes (ca. 287–212 BCE) that he stated this principle long before concepts of force were well established.

Archimedes’ principle is as follows: The buoyant force on an object equals the weight of the fluid it displaces.

In equation form, Archimedes’ principle is

F(sub)B=w(sub)fl,

where F(sub)B is the buoyant force and w(sub)fl is the weight of the fluid displaced by the object.

Archimedes’ principle is valid in general, for any object in any fluid, whether partially or totally submerged.

Hmm … High-tech body swimsuits were introduced in 2008 in preparation for the Beijing Olympics. One concern (and international rule) was that these suits should not provide any buoyancy advantage. How do you think that this rule could be verified?

Floating and Sinking

Drop a lump of clay in water. It will sink. Then mold the lump of clay into the shape of a boat, and it will float. Because of its shape, the boat displaces more water than the lump and experiences a greater buoyant force. The same is true of steel ships.

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.

fraction submerged buoyancy

unloaded ship vs loaded buoyant force

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

There are many obvious examples of lower-density objects or substances floating in higher-density fluids:

oil on water, a hot-air balloon, a bit of cork floating in wine, an iceberg, and hot wax in a “lava lamp,” to name a few.

Less obvious examples include lava rising in a volcano,

and mountain ranges floating on the higher-density crust and mantle beneath them.

isostacy_density

Even seemingly solid Earth has fluid characteristics.

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?

Buoyancy Ping pong balls on balance

Online apps & labs

PhET Buoyancy game

Related resources

AP Physics, Fluid Mechanics With Mr. Horwat @ Parkside High

 

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.”

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