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  • Define buoyant force.
  • State Archimedes’ principle.
  • Understand why objects float or sink.
  • Understand the relationship between density and Archimedes’ principle.

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? (See [link] .)

In figures a and b, an anchor and submarine experience buoyancy due to water. In figure c, helium-filled balloons float due to the buoyancy of air.
(a) Even objects that sink, like this anchor, are partly supported by water when submerged. (b) Submarines have adjustable density (ballast tanks) so that they may float or sink as desired. (credit: Allied Navy) (c) Helium-filled balloons tug upward on their strings, demonstrating air’s buoyant effect. (credit: Crystl)

Answers to all these questions, and many others, 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. (See [link] .) 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.

Buoyant force

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

A cylinder of cross-sectional area A experiences an upward force F sub 2 on the bottom of the cylinder and a downward force F sub 1 on its top. Buoyant force is due to the difference between the upward force on the bottom of the cylinder and the downward force on its top.
Pressure due to the weight of a fluid increases with depth since P = hρg size 12{P=hρg} {} . This pressure and associated upward force on the bottom of the cylinder are greater than the downward force on the top of the cylinder. Their difference is the buoyant force F B size 12{F rSub { size 8{B} } } {} . (Horizontal forces cancel.)

Just how great is this buoyant force? To answer this question, think about what happens when a submerged object is removed from a fluid, as in [link] .

An object immersed in a fluid rises if its buoyant force is greater than its weight and sinks if its buoyant force is less than its weight. By Archimedes’ principle the buoyant force equals the weight of the fluid displaced.
(a) An object submerged in a fluid experiences a buoyant force F B size 12{F rSub { size 8{B} } } {} . If F B size 12{F rSub { size 8{B} } } {} is greater than the weight of the object, the object will rise. If F B size 12{F rSub { size 8{B} } } {} is less than the weight of the object, the object will sink. (b) If the object is removed, it is replaced by fluid having weight w fl size 12{w rSub { size 8{"fl"} } } {} . Since this weight is supported by surrounding fluid, the buoyant force must equal the weight of the fluid displaced. That is, F B = w fl size 12{F rSub { size 8{B} } =w rSub { size 8{"fl"} } } {} ,a statement of Archimedes’ principle.

The space it occupied is filled by fluid having a weight w fl size 12{w rSub { size 8{"fl"} } } {} . This weight is supported by the surrounding fluid, and so the buoyant force must equal w fl size 12{w rSub { size 8{"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 B.C.) that he stated this principle long before concepts of force were well established. Stated in words, 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

Practice Key Terms 3

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Source:  OpenStax, Concepts of physics with linear momentum. OpenStax CNX. Aug 11, 2016 Download for free at http://legacy.cnx.org/content/col11960/1.9
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